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14 Chemical Kinetics. Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the factors that.

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Presentation on theme: "14 Chemical Kinetics. Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the factors that."— Presentation transcript:

1 14 Chemical Kinetics

2 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the factors that affect the rate of chemical reactions To be able to determine a reaction rate To understand the meaning of a rate law To be able to determine the concentration dependence of the rate of a chemical reaction To be able to predict the individual steps of a simple reaction To begin to understand why chemical reactions occur

3 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.1 Factors That Affect Reaction Rates

4 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.1 Factors That Affect Reaction Rates Chemical kinetics – Study of reaction rates, or the changes in the concentrations of reactants and products with time – By studying kinetics, insights are gained into how to control reaction conditions to achieve a desired outcome Chemical kinetics of a reaction depend on various factors 1. Reactant concentrations 2. Temperature 3. Physical states and surface areas of reactants 4. Solvent and catalyst properties

5 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Concentration Effects Two substances cannot react with each other unless their constituent particles come into contact; if there is no contact, the rate of reaction will be zero. The more reactant particles that collide per unit time, the more often a reaction between them can occur. The rate of reaction usually increases as the concentration of the reactants increases.

6 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Temperature Effects Increasing the temperature of a system increases the average kinetic energy of its constituent particles. As the average kinetic energy increases, the particles move faster, so they collide more frequently per unit time and possess greater energy when they collide, causing increases in the rate of the reaction. Rate of all reactions increases with increasing temperature and decreases with decreasing temperature.

7 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Phase and Surface Area Effects If reactants are uniformly dispersed in a single homogeneous solution, the number of collisions per unit time depends on concentration and temperature. If the reaction is heterogeneous, the reactants are in two different phases, and collisions between the reactants can occur only at interfaces between phases; therefore, the number of collisions between the reactants per unit time is reduced, as is the reaction rate. The rate of a heterogeneous reaction depends on the surface area of the more condensed phase.

8 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Solvent Effects The nature of the solvent can affect the reaction rates of solute particles. Solvent viscosity is also important in determining reaction rates. 1. In highly viscous solvents, dissolved particles diffuse much more slowly than in less viscous solvents and collide less frequently per unit time. 2. Rates of most reactions decrease rapidly with increasing solvent viscosity.

9 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Catalyst Effects Catalyst is a substance that participates in a chemical reaction and increases the rate of the reaction without undergoing a net chemical change itself. Catalysts are highly selective and often determine the product of a reaction by accelerating only one of several possible reactions that could occur.

10 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.2 Reaction Rates and Rate Laws

11 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reaction Rates Reaction rates – Expressed as the concentration of reactant consumed or the concentration of product formed per unit time – Units are moles per liter per unit time (M/s, M/min or M/h) – To measure reaction rates 1. initiate the reaction; 2. measure the concentration of the reactant or product at different times as the reaction progresses; 3. plot the concentration as a function of time on a graph; 4. calculate the change in the concentration per unit time.

12 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reaction Rates – The change in the concentration of either the reactant or the product over a period of time. – For a simple reaction (A  B), rate =  [B] = –  [A]  t  t – Square brackets indicate concentration; and  means “change in.” – Concentration of A decreases with time; and the concentration of B increases with time.

13 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reaction Rates Determining the rate of hydrolysis of aspirin – One can calculate the average reaction rate for a given time interval from the concentrations of either the reactant or one of the products at the beginning of the interval (time = t 0 ) and at the end of the interval (t f ). – Using salicylic acid, one can find the rate of the reaction for the interval between t = 0 and t = 2h; one can also calculate the rate of the reaction from the concentrations of aspirin at the beginning and the end of the same interval.

14 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reaction Rates Calculating the Rate of Fermentation of Sucrose – A reaction in which coefficients are not all the same –The coefficients show that the reaction produces four molecules of ethanol and four molecules of carbon dioxide for every one molecule of sucrose that is consumed –The coefficients in the balanced equation show that the rate at which ethanol is formed is four times faster than the rate at which sucrose is consumed:  [ethanol] = – 4  [sucrose]  t  t This can also be expressed in terms of the reactant or product with the smallest coefficient in the balanced equation rate = –  [sucrose] /  t = ¼(  [ethanol] /  t).

15 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reaction Rates Instantaneous rate of reaction – The rate at any given point in time – As the period of time used to calculate an average rate of a reaction becomes shorter and shorter, the average rate approaches the instantaneous rate – In chemical kinetics, focus is on one particular instantaneous rate, t = 0, which is the initial rate of the reaction; initial rates are determined by measuring the rate of the reaction at various times and then extrapolating a plot of rate versus time to t = 0

16 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Rate Laws Describes the relationships between reactant rates and reactant concentrations May be written from either of two different, but related, perspectives: 1. Differential rate law – Expresses the rate of a reaction in terms of changes in the concentration of one or more reactants,  [R], over a specific time interval,  t – Describes what is occurring on a molecular level during a reaction

17 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Rate Laws 2. Integrated rate law – Describes the rate of a reaction in terms of the initial concentration, [R] 0, and the measured concentration of one or more reactants, [R], after a given amount of time, t – Used for determining the reaction order and the value of the rate constant from experimental measurements Rate law must give the proper units for the rate, M/s Rate law must be determined experimentally

18 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Rate Laws Reaction orders – For a reaction with the general equation aA + bB  cC + dD, the experimentally determined rate law has the form rate = k[A] m [B] n. – The proportionality constant, k, is called the rate constant. 1. Value is characteristic of the reaction and reaction conditions 2. A given reaction has a particular value of the rate constant under a given set of conditions, such as temperature, pressure, and solvent

19 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Rate Laws – Rate of a reaction depends on the rate constant for the given set of reaction conditions and on the concentration of each reactant, raised to the powers m and n – Values of m and n are derived from experimental measurements of the changes in reactant concentrations over time and indicate the reaction order, the degree to which the rate of the reaction depends on the concentration of each reactant – m and n are not related to the stoichiometric coefficients a and b in the balanced chemical equation but must be determined experimentally – Overall reaction order is the sum of all the exponents in the rate law, or m + n

20 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.3 Methods of Determining Reaction Orders

21 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Zeroth-order reaction – Reaction whose rate is independent of concentration – Its differential rate law is rate = k – One can write their rate in a form such that the exponent of the reactant in the rate law is 0 rate = –  [A] = k[reactant] 0 = k(1) = k  t – Since rate is independent of reactant concentration, a graph of the concentration of any reactant as a function of time is a straight line with a slope of –k (concentration decreases with time); a graph of the concentration of any product as a function of time is a straight line with a slope of +k Zeroth-Order Reactions

22 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings – Integrated rate law for a zeroth-order reaction produces a straight line and has the general formula [A] = [A] 0 – kt, where [A] 0 is the initial concentration of reactant A; the rate constant must have the same units as the rate of the reaction, M/s, in a zeroth-order reaction – Equation has the form of the equation for a straight line (y = mx + b); y = [A], mx = – kt, and b = [A] 0 – Occur most often when the reaction rate is determined by available surface area Zeroth-Order Reactions

23 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings First-order reaction – Reaction rate is directly proportional to the concentration of one of the reactants – Have the general form A  products – Differential rate for a first-order reaction is rate = –  [A] = k[A]  t – If the concentration of A is doubled, the rate of the reaction doubles; if the concentration of A is increased by a factor of 10, the rate increases by a factor of 10 – Units of a first-order rate constant are inverse seconds, s –1 – First-order reactions are very common First-Order Reactions

24 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings – Integrated rate law for a first-order reaction can be written in two different ways, one using exponentials and one using logarithms 1. Exponential form, [A] = [A] 0 e –kt, where [A] 0 is the initial concentration of reactant A at t = 0; k is the rate constant, and e is the base of the natural logarithms, which has the value Concentration of A will decrease in a smooth exponential curve over time 2. The logarithmic expression of the relationship between the concentration of A and t is obtained by taking the natural logarithm of each side of the preceding equation and rearranging: ln[A] = ln[A] 0 – kt; the equation has the form of the equation for a straight line; y = ln[A] and b = ln[A] 0 ; and a plot of ln[A] vs. t for a first-order reaction gives a straight line with a slope of –k and an intercept of ln[A] 0 First-Order Reactions

25 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Two kinds of second-order reactions 1. The simplest kind of second-order reaction is one whose rate is proportional to the square of the concentration of the reactant and has the form 2A  products. – Differential rate law is rate = –  [A] = k[A] 2 2  t – Doubling the concentration of A quadruples the rate of the reaction – Units of rate constant is M –1  s –1 or L/mol  s – Concentration of the reactant at a given time is described by the following integrated rate law: 1/ [A] = 1/ [A] 0 + kt, which has the form of an equation of a straight line; y = 1/ [A], b = 1/ [A] 0 ; and a plot of 1/ [A] vs t is a straight line with a slope of k and an intercept of 1/[A] 0 Second-Order Reactions

26 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 2. The second kind has a rate that is proportional to the product of the concentrations of two reactants and has the form A + B  products. – Reaction is first order in A and first order in B – Differential rate law for the reaction is rate = –  [A] = –  [B] = k[A] [B]  t  t – Reaction is first order both in A and in B and has an overall reaction order of 2 Second-Order Reactions

27 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Understanding reaction mechanisms (sets of steps in a reaction) simplifies chemical reactions. The first step in discovering the mechanism of a reaction is to determine the reaction’s rate law, which can be done by designing experiments that measure the concentration(s) of one or more of the reactants or products as a function of time. For the reaction A + B  products, one needs to determine the value of k and the exponents m and n in the equation rate = k[A] m [B] n. Rate data is given in the following table: Determining the Rate Law of a Reaction

28 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings One can determine values of k and exponents m and n in several ways: 1. Keep the initial concentration of B constant while varying the initial concentration of A and calculating the initial rate of the reaction and then deducing the order of the reaction with respect to A 2. Determine the order of reaction with respect to B by studying the reaction rates when the initial concentration of A is kept constant while the concentration of B is varied 3. Determine order of reaction with respect to a given reactant by comparing the different rates obtained when only the concentration of the reactant in question was changed 4. Determine reaction orders by taking the quotient of the rate laws for two different experiments Determining the Rate Law of a Reaction

29 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 5. Obtain the value of m and n directly by finding the ratio of the rate laws for two experiments in which the concentration of one of the reactants is the same such as Experiments 1 and 3 in the table rate 1 = k[A 1 ] m [B 1 ] n rate 3 = k[A 3 ] m [B 3 ] n 6. By selecting two experiments in which the concentration of B is the same, one can solve for the value of m; by selecting two experiments in which the concentration of A is the same, one can solve for n 7. Calculate the rate constant by inserting data from any line from the table into the experimentally determined rate law and solve for k Determinin the Rate Law of a Reaction

30 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders

31 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders For a zeroth-order reaction, a plot of the concentration of any reactant versus time is a straight line with a slope of – k. For a first-order reaction, a plot of the logarithm of the concentration of a reactant versus time is a straight line with a slope of – k. For a second-order reaction, a plot of the inverse of the concentration of a reactant versus time is a straight line with a slope of k. Properties of reactions that obey zeroth-, first-, and second-order rate laws are summarized in the following table.

32 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders

33 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.5 Half-Lives and Radioactive Decay Kinetics

34 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Half-Lives Another approach to describe reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value. The period of time is called the half-life of the reaction, written as t ½. The half-life of a reaction is the time required for the reactant concentration to decrease from [A] 0 to [A] 0 /2. If two reactions have the same order, the faster reaction will have a shorter half-life and the slower reaction will have a longer half-life.

35 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Half-Lives The half-life of a first-order reaction under a given set of reaction conditions is a constant; this is not true for zeroth- or second-order reactions. The half-life of a first-order reaction is independent of the concentration of the reactants. Rearranging the integrated rate law for a first-order reaction produces the equation [A] 0 [A] Substituting [A] 0 /2 for [A] and t ½ for t (to indicate a half-life) into the above equation gives [A] 0 [A] 0 /2 Solving for t ½ : t ½ = 0.693/k For a first-order reaction, each successive half-life is the same length of time and is independent of [A]. = kt ln = ln 2 = kt ½

36 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Radioactive Decay Rates Radioactivity, or radioactive decay, is the emission of a particle or a photon that results from the spontaneous decomposition of the unstable nucleus of an atom. The rate of radioactive decay is an intrinsic property of each radioactive isotope, independent of the chemical and physical form of the radioactive isotope. Rate is also independent of temperature. In a sample of a given radioactive substance, the number of atoms of the radioactive isotope must decrease with time as their nuclei decay to nuclei of a more stable isotope.

37 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Radioactive Decay Rates Using N to represent the number of atoms of the radioactive isotope, the rate of decay of the sample (also called its activity, A) can be defined as the decrease in the number of the radioisotope’s nuclei per unit time A = –  N/  t Activity is measured in disintegrations per second (dps) or disintegrations per minute (dpm) Activity of a sample is directly proportional to the number of atoms of the radioactive isotope in the sample A = kN k is the radioactive decay constant and has units of inverse time (s –1, yr –1 ) and has a characteristic value for each radioactive isotope

38 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Radioactive Decay Rates Combining equations, the relationship between the number of decays per unit time and the number of atoms of the isotope in a sample is obtained –  N/  t = kN The equation is the same as the equation for the rate of a first-order reaction; except that it uses number of atoms instead of concentrations Radioactive decay is a first-order process and can be described in terms of either the differential rate law as above or the integrated rate law N = N 0 e –kt or ln N/N 0 = – kt

39 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Radioactive Decay Rates Because radioactive decay is a first-order process, the time required for half of the nuclei in any sample of a radioactive isotope to decay is a constant, called the half-life of the isotope Half-life tells how radioactive an isotope is (the number of decays per unit time) and is the most commonly cited property of any isotope Isotopes with a short half-life decay more rapidly, undergoing a greater number of radioactive decays per unit time than do isotopes with a long half-life

40 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Radioisotope Dating Techniques Using the half-lives of isotopes, one can estimate the ages of geological and archaeological artifacts. Techniques that have been developed for this application are known as radioisotope dating techniques. The most common method for measuring the age of ancient objects is carbon-14 dating; carbon-14 isotope, created in the upper regions of Earth’s atmosphere, reacts with atmospheric oxygen or ozone to form 14 CO 2. The CO 2 that plants use as a carbon source include a proportion of 14 CO 2 molecules as well as nonradioactive 12 CO 2 and 13 CO 2 ; animals that eat plants ingest these carbon isotopes.

41 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Radioisotope Dating Techniques When the animals or plants die, the carbon-14 nuclei in its tissue decay to nitrogen-14 nuclei by a radioactive process known as beta decay, which releases low-energy electrons (  particles) that can be detected and measured: 14 C  14 N +  – with a half-life of 5700 ± 30 yr. The 14 C/ 12 C ratio in living organisms is 1.3 x 10 –12 with a decay rate of 15 dpm per gram of carbon (dpm/g carbon). Comparing the disintegrations per minute per gram of carbon from an archaeological sample with those from a recently living sample enables scientists to estimate the age of the artifact.

42 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.6 Reaction Rates—A Microscopic View

43 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.6 Reaction Rates—A Microscopic View One of the major reasons for studying chemical kinetics is to use measurements of the macroscopic properties of a system to discover the sequence of events that occur at the molecular level during a reaction. Molecular description is the mechanism of the reaction; it describes how individual atoms, ions, or molecules interact to form particular products. Stepwise changes are called the reaction mechanism, the microscopic path by which reactants are transformed into products by a complex series of reactions that take place in a stepwise fashion.

44 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.6 Reaction Rates—A Microscopic View Each step or individual reaction is called an elementary reaction, and the overall sequence of elementary reactions is the mechanism of the reaction. The sum of the individual steps, or elementary reactions, in the mechanism must give the balanced chemical equation for the overall reaction.

45 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Molecularity and the Rate-Determining Step Species that are formed in one step and consumed in another are intermediates; and they do not appear in the balanced chemical equation for the reaction. Following the two-step mechanism is an example: Step 1 NO 2 + NO 2  NO 3 + NO Elementary reaction Step 2 NO 3 + CO  NO 2 + CO 2 Elementary reaction Sum NO 2 + CO  NO + CO 2 Overall reaction NO 3 is an intermediate in the reaction.

46 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Molecularity and the Rate-Determining Step Using molecularity to describe a rate law – Each elementary step can be described in terms of its molecularity, the number of molecules that collide in that step. – If there is only a single reactant molecule in an elementary reaction, that step is designated as unimolecular. – If there are two reactant molecules, it is bimolecular; if there are three reactant molecules, it is termolecular. – Order of the elementary reaction is the same as its molecularity, but the rate law for the reaction cannot be determined from the balanced equation for the overall reaction.

47 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Molecularity and the Rate-Determining Step – The general rate law for a unimolecular elementary reaction (A  products) is rate = k[A]. – For bimolecular reactions, the reaction rate depends on the number of collisions per unit time, which is proportional to the product of the concentrations of the reactants. – For a bimolecular elementary reaction of the form 2A  products, the general rate law is rate = k[A] 2. – Common types of elementary reactions and their rate laws are summarized in the following table:

48 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Molecularity and the Rate-Determining Step Identifying the rate-determining step – The balanced chemical equation does not necessarily reveal the individual elementary reactions by which the reaction occurs. – One cannot obtain the rate law for a reaction from the overall balanced equation alone. – The rate law for the overall reaction is the same as the rate law for the slowest step in the reaction mechanism, the rate-determining step, because any process that occurs through a sequence of steps can take place no faster than the slowest step in the sequence.

49 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chain Reactions Many reaction mechanisms consist of long series of elementary reactions called chain reactions, in which one or more elementary reactions that contain a highly reactive species repeat again and again during the reaction process. Chain reactions have three stages: 1. initiation, a step that produces one or more reactive intermediates; often these intermediates are radicals, species that have an unpaired valence electron; 2. propagation, reactive intermediates are continuously consumed and regenerated while products are formed; 3. termination, intermediates are also consumed, usually by forming stable products.

50 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.7 The Collision Model of Chemical Kinetics

51 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.7 The Collision Model of Chemical Kinetics A useful tool for understanding the behavior of reacting chemical species The collision model explains the following: – A chemical reaction can occur only when the reactant molecules, atoms, or ions collide with more than a certain amount of kinetic energy and in the proper orientation – Explains why most collisions between molecules do not result in a chemical reaction, because in most collisions, the molecules simply bounce off one another without reacting – Why such chemical reactions occur more rapidly at higher temperatures

52 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Activation Energy A minimum energy (activation energy, E a ) is required for a collision between molecules to result in a chemical reaction. Reacting molecules must have enough energy to overcome electrostatic repulsion and a minimum amount of energy to break chemical bonds so that new ones may be formed. Molecules that collide with less than the activation energy bounce off one another chemically unchanged, with only their direction of travel and their speed altered by the collision. Molecules that are able to overcome the energy barrier react and form an arrangement of atoms called the activation complex or the transition state.

53 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Graphing the Energy Changes during a Reaction One can graph the energy of a reaction by plotting the potential energy of the system as the reaction progresses with time. Plots show an energy barrier that must be overcome for the reaction to occur, which means that the activation energy is always positive. E a provides information about the rate of a reaction and how rapidly the rate changes with temperature. For two similar reactions under comparable conditions, the reaction with the smallest E a will occur more rapidly.

54 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Graphing the Energy Changes during a Reaction Even when the energy of collisions between two reactant species is greater than E a, most collisions do not produce a reaction; the probability of a reaction occurring depends not only on the collision energy, but also on the spatial orientation of the molecules when they collide. The fracture of orientations that result in a reaction is called the steric factor, p, and its value can range from 0 (no orientations of molecules result in reaction) to 1 (all orientations result in reaction).

55 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Arrhenius Equation In the following figure, both the kinetic energy distributions and a potential energy diagram for a reaction are shown

56 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Arrhenius Equation – Shaded areas show that at the lower temperature, only a small fraction of molecules collide with kinetic energy greater than E a ; at the higher temperature, a much larger fraction of molecules collide with kinetic energy greater than E a – The rate of the reaction is much slower at the lower temperature because only a few molecules collide with enough energy to overcome the potential energy barrier

57 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Arrhenius Equation For an A + B elementary reaction, all the factors that affect the reaction rate can be summarized in a single series of relationships: rate = (collision frequency) (steric factor) (fraction of collisions with E > E a ) where rate = k[A] [B] Arrhenius used these relationships to arrive at an equation that relates the magnitude of the rate constant of a reaction to the temperature; the activation energy; and the constant, A, called the frequency factor, which converts concentrations to collisions per second k = Ae –E a /RT (Arrhenius equation)

58 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Arrhenius Equation The Arrhenius equation summarizes the collision model of chemical kinetics, where T is the absolute temperature (in K) and R is the ideal gas constant [8.314 J/(K mol)]. The value of E a indicates the sensitivity of the reaction to changes in temperature. The rate of a reaction with a large E a increases rapidly with increasing temperature, and the rate of a reaction with a smaller E a increases much more slowly with increasing temperature.

59 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Arrhenius Equation If the rate of a reaction at various temperatures is known, the Arrhenius equation can be used to calculate the activation energy by taking the natural logarithm of both sides of the Arrhenius equation. ln k = ln A + (–E a /RT) = ln A + [(–E a /R) (1/T )] The preceding equation is the equation for a straight line, where y = ln k and x = 1/T; a plot of ln k versus 1/T is a straight line with a slope of –E a /R and an intercept of ln A. Knowing the value of E a at one temperature predicts the rate of a reaction at other temperatures.

60 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 14.8 Catalysis

61 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.8 Catalysis Catalysts – Substances that increase the rate of a chemical reaction without being consumed in the process – A catalyst does not appear in the overall stoichiometry of the reaction it catalyzes, but it must appear in at least one of the elementary steps in the mechanism for the catalyzed reaction – Catalyzed pathway has a lower E a, but the net change in energy that results from the reaction (the difference between the energy of the reactants and the energy of the products) is not affected by the presence of a catalyst – Because of its lower E a, the rate of a catalyzed reaction is faster than the rate of the uncatalyzed reaction at the same temperature

62 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.8 Catalysis

63 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 14.8 Catalysis – A catalyst decreases the height of the energy barrier, and its presence increases the rates of both the forward and the reverse reactions by the same amount – There are three major classes of catalysts 1. Heterogeneous catalysts 2. Homogeneous catalysts 3. Enzymes

64 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Heterogeneous Catalysis In heterogeneous catalysis, the catalyst is in a different phase from the reactants. At least one of the reactants interacts with the solid surface (in a physical process called adsorption) in such a way that a chemical bond in the reactant becomes weak and then breaks.

65 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Homogeneous Catalysis In homogeneous catalysis, the catalyst is in the same phase as the reactant(s); the number of collisions between reactants and catalyst is at a maximum because the catalyst is uniformly dispersed throughout the reaction mixture.

66 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Enzymes Enzymes are catalysts that occur naturally in living organisms and are almost all protein molecules with typical molecular masses of 20,000–100,000 amu. Some are homogeneous catalysts that react in aqueous solution within a cellular compartment of an organism. Some are heterogeneous catalysts embedded within the membranes that separate cells and cellular compartments from their surroundings. A reactant in an enzyme-catalyzed reaction is called a substrate. Enzymes can increase reaction rates by enormous factors and tend to be very specific, typically producing only a single product in quantitative yield.

67 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Enzymes Enzymes are expensive, and often cease functioning at temperatures higher than 37ºC, and have limited stability in solution. Enzyme inhibitors cause a decrease in the rate of an enzyme-catalyzed reaction by binding to a specific portion of an enzyme and thus slowing or preventing a reaction from occurring.

68 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 15 Chemical Equilibrium

69 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand what is meant by chemical equilibrium To know the relationship between the equilibrium constant and the rate constants for the forward and reverse reactions To be able to write an equilibrium constant expression for any reaction To be able to solve quantitative problems involving chemical equilibrium To predict the direction of reaction To predict the effects of stresses on a system at equilibrium To understand different ways to control the products of a reaction

70 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 15.1 The Concept of Chemical Equilibrium

71 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 15.1 The Concept of Chemical Equilibrium Chemical equilibrium – A dynamic process – Consists of a forward reaction, in which reactants are converted to products, and a reverse reaction, in which products are converted to reactants – At equilibrium, the forward and reverse reactions proceed at equal rates – Double arrow ( ⇋ ) indicates that both the forward and reverse reactions are occurring simultaneously and is read “is in equilibrium with” – At equilibrium, the composition of the system no longer changes with time – Composition of an equilibrium mixture is independent of the direction from which equilibrium is approached

72 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 15.2 The Equilibrium Constant

73 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 15.2 The Equilibrium Constant Equilibrium state is achieved when the rate of the forward reaction equals the rate of the reverse reaction. Under a given set of conditions, there must be a relationship between the composition of the system at equilibrium and the kinetics of a reaction represented by rate constants. The ratio of the rate constants yields a new constant, the equilibrium constant (K), a unitless quantity and is defined as K = k f /k r. The fundamental relationship between chemical kinetics and chemical equilibrium states that, under a given set of conditions, the composition of the equilibrium mixture is determined by the magnitudes of the rate constants for the forward and reverse reactions.

74 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Developing an Equilibrium Constant Expression In1864, Guldberg and Waage discovered that for any reversible reaction of the general form aA + bB ⇋ cC + dD, where A and B are reactants, C and D are products, and a, b, c, and d are the stoichiometric coefficients in the balanced equation for the reaction, the ratio of the product of the equilibrium concentrations of the products (raised to their coefficients in the balanced equation) to the product of the equilibrium concentrations of the reactants (raised to their coefficients in the balanced equation) is always a constant under a given set of conditions. This equation is called the equilibrium equation. This relationship is known as the law of mass action

75 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Developing an Equilibrium Constant Expression Law of mass action is stated as K = [C] c [D] d [A] a [B] b – K is the equilibrium constant for the reaction – Right side of the equation is called the equilibrium constant expression – Relationship is true for any pair of opposing reactions regardless of the mechanism of the reaction or of the number of steps in the mechanism

76 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Developing an Equilibrium Constant Expression Equilibrium constant (K) – Can vary over a wide range of values and is unitless – Values of K greater than 10 3 indicate a strong tendency for reactants to form products, so equilibrium lies to the right, favoring the formation of products (k f >>k r ) – Values of K less than 10 –3 indicate that the ratio of products to reactants at equilibrium is very small; reactants do not tend to form products readily, and equilibrium lies to the left, favoring the formation of reactants (k f <

77 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Developing an Equilibrium Constant Expression

78 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Variations in the Form of the Equilibrium Constant Expression Equilibrium can be approached from either direction in a chemical reaction, so the equilibrium constant expression and the magnitude of the equilibrium constant depend on the form in which the chemical reaction is written. When a reaction is written in the reverse direction, cC + dD ⇋ aA + bB K and the equilibrium constant expression are inverted: K´= [A] a [B] b [C] c [D] d so K´ = 1/K

79 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Equilibrium Constant Expressions for Systems that Contain Gases For reactions that involve nongaseous substances, the concentrations used in equilibrium calculations are expressed in moles/liter. For gases, the concentrations are expressed in terms of partial pressures where the standard state is 1 atm of pressure. Symbol K p is used to denote equilibrium constants calculated from partial pressures. For the general reaction aA + bB ⇋ cC + dD in which all the components are gases, the equilibrium constant is the ratio of the partial pressures of the products and reactants, each raised to its coefficient in the chemical equation. Kp = (P A ) c (P C ) d (P B ) a (P D ) b

80 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Equilibrium Constant Expressions for Systems that Contain Gases K p is unitless. Partial pressures are expressed in atmospheres or mmHg, so the molar concentration of a gas and its partial pressure do not have the same numerical value but are related by the ideal gas constant R and the temperature K p = K(RT)  n where K is the equilibrium constant expressed in units of concentration and  n is the difference between the number of moles of gaseous products and gaseous reactants; temperature is expressed in kelvins. If  n = 0, K p = K

81 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Homogeneous and Heterogeneous Equilibria Homogeneous equilibrium – When the products and reactants of an equilibrium reaction form a single phase, whether gas or liquid – Concentrations of the reactants and products can vary over a wide range Heterogeneous equilibrium – A system whose reactants, products, or both are in more than one phase – An example is the reaction of a gas with a solid or liquid Molar concentrations of pure liquids and solids do not vary with temperature, so they are treated as constants, this simplifies their equilibrium constant expressions

82 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Equilibrium Constant Expressions for the Sums of Reactions When a reaction can be expressed as the sum of two or more reactions, its equilibrium constant is equal to the product of the equilibrium constants for the individual reactions.  H for the sum of two or more reactions is the sum of the  H values for the individual reactions.

83 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 15.3 Solving Equilibrium Problems

84 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Two fundamental kinds of equilibrium problems 1. Those in which the concentrations of the reactants and products at equilibrium are given and the equilibrium constant for the reaction needs to be calculated 2. Those in which the equilibrium constant and the initial concentrations of reactants are known and the concentration of one or more substances at equilibrium needs to be calculated 15.3 Solving Equilibrium Problems

85 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating an Equilibrium Constant from Equilibrium Concentrations An equilibrium constant can be calculated when equilibrium concentrations, molar concentrations, or partial pressures are substituted into the equilibrium constant expression for the reaction. Sometimes the concentrations of all the substances are not given or the equilibrium concentrations of all the relevant substances for a particular system are not measured. In these cases, the equilibrium concentrations can be obtained from the initial concentrations of the reactants and the balanced equation for the reaction, as long as the equilibrium concentration of one of the substances is known.

86 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Equilibrium Concentrations from the Equilibrium Constant Equilibrium constants can be used to calculate the equilibrium concentrations of reactants and products by using the quantities or concentrations of the reactants, the stoichiometry of the balanced equation for the reaction, and a tabular format to obtain the final concentrations of all species at equilibrium.

87 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 15.4 Nonequilibrium Conditions

88 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 15.4 Nonequilibrium Conditions One must often decide whether a system has reached equilibrium or the composition of the mixture will continue to change with time To make this determination, one needs to know how to analyze the composition of a reaction mixture quantitatively

89 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Reaction Quotient (Q) Reaction quotient (Q) – A quantity used to determine whether a system has reached equilibrium – Expression for the reaction quotient has the same form as the equilibrium constant expression – Q may be derived from a set of values measured at any time during the reaction of any mixture of the reactants and products, regardless of whether the system is at equilibrium – For the general reaction aA + bB ⇋ cC + dD, reaction quotient is defined as Q = [C] c [D] d [A] a [B] b – Q p can be written for any reaction that involves gases by using the partial pressures of the components

90 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Reaction Quotient (Q) Comparing the magnitudes of Q and K allows the determination of whether a reaction mixture is already at equilibrium and, if it is not, how to predict whether its composition will change with time (whether the reaction will proceed to the right or to the left) 1. If Q = K, the system is at equilibrium, no further change in the composition of the system will occur unless the conditions are changed 2. If Q < K, then the ratio of the concentrations of products to the concentration of reactants is less than the ratio at equilibrium; reaction will proceed to the right, forming products at the expense of reactants 3. If Q > K, then the ratio of the concentrations of products to the concentrations of reactants is greater than at equilibrium; reaction will proceed to the left, forming reactants at the expense of products

91 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Reaction Quotient (Q)

92 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Predicting the Direction of Reaction Using a Graph Graphs derived by plotting a few equilibrium concentrations for a system at a given temperature and pressure can be used to predict the direction in which a reaction will proceed Points that do not lie on the line represent nonequilibrium states and the system will adjust to achieve equilibrium

93 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 15.5 Factors That Affect Equilibrium

94 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 15.5 Factors That Affect Equilibrium Strategies are used to increase the yield of the desired products of reactions Reaction conditions are controlled to obtain the maximum amount of the desired product Changes in reaction conditions affect the equilibrium composition of a system

95 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings When a system at equilibrium is perturbed in some way, the effects of the perturbation can be predicted qualitatively using Le Ch âtelier’s principle. This principle states that if a stress is applied to a system at equilibrium, the composition of the system will change to relieve the applied stress. Stress occurs when any change in the system affects the magnitude of Q or K. Le Châtelier’s Principle

96 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Three types of stresses can change the composition of an equilibrium mixture 1. A change in the concentrations (or partial pressures) of the components by the addition or removal of reactants or products 2. A change in the total pressure or volume 3. A change in the temperature of the system Le Châtelier’s Principle

97 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings An equilibrium is disturbed by adding or removing a reactant or product 1. Stress of an added reactant or product is relieved by reaction in the direction that consumes the added substance a. Add reactant—reaction shifts right toward product b. Add product—reaction shifts left toward reactant 2. Stress of removing reactant or product is relieved by reaction in the direction that replenishes the removed substance a. Remove reactant—reaction shifts left b. Remove product—reaction shifts right Changes in Concentration

98 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Changes that occur due to changes in the value of Q c 1. Add reactant—denominator in Q c expression becomes larger A. Q c < K c B. To return to equilibrium, Q c must increase I. Numerator of Q c expression must increase and the denominator must decrease II. Implies net conversion of reactants to products; reaction shifts right Changes in Concentration

99 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 2. Remove reactant—denominator in Q c expression becomes smaller A. Q c > K c B. To return to equilibrium, Q c must decrease I. Numerator of Q c expression must decrease and the denominator must increase II. Implies net conversion of products to reactants; reaction shifts left Changes in Concentration

100 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Changes in Total Pressure or Volume If a balanced reaction contains different numbers of gaseous reactant and product molecules, the equilibrium will be sensitive to changes in volume or pressure; change in pressure (due to changing volume) changes the composition of the equilibrium mixture Increase in pressure (due to decrease in volume) results in a reaction in the direction of a fewer number of moles of gas Decrease in pressure (due to increase in volume) results in a reaction in the direction of a greater number of moles of gas

101 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Changes in Total Pressure or Volume Changes occur due to changes in the value of Q c 1. Decrease volume—molarity increases 2. If reactant side has more moles of gas a. Increase in denominator is greater than increase in numerator and Q c < K c b. To return to equilibrium, Q c must increase; the numerator of the Q c expression must increase and denominator must decrease—it shifts toward fewer moles of gas (reactants to products)

102 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Changes in Total Pressure or Volume 3. If product side has more moles of gas a. Increase in numerator is greater than increase in denominator and Q c > K c b. To return to equilibrium, Q c must decrease; the denominator of the Q c expression must decrease and the numerator must increase—it shifts toward fewer moles of gas (products to reactants) If the reaction involves no change in the number of moles of gas, there is no effect on the composition of the equilibrium mixture Effect of pressure changes on solids and liquids can be ignored

103 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Changes in temperature can change the value of the equilibrium constant without affecting the reaction quotient (Q  K) System is no longer at equilibrium, and the composition of the system will change until Q equals K at the new temperature To predict how an equilibrium system will respond to a change in temperature, one must know the enthalpy change of the reaction,  H rxn 1. Exothermic (heat is released,  H < 0): reactants ⇋ products + heat 2. Endothermic (heat is absorbed,  H > 0): reactants + heat ⇋ products Changes in Temperature

104 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Heat is a product in an exothermic reaction and a reactant in an endothermic reaction; increasing the temperature of a system corresponds to adding heat Le Châtelier’s principle predicts 1. that an exothermic reaction will shift to the left (toward reactants) if the temperature of the system is increased (heat is added); 2. that an endothermic reaction will shift to the right (toward the products) if the temperature of the system is increased; 3. that if  H rxn = 0, then a change in temperature will not affect the equilibrium composition. Changes in Temperature

105 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Value of K c 1. Increasing the temperature increases the magnitude of the equilibrium constant for an endothermic reaction 2. Increasing the temperature decreases the equilibrium constant for an exothermic reaction 3. Increasing the temperature has no effect on the equilibrium constant for a thermally neutral reaction Changes in Temperature

106 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 15.6 Controlling the Products of Reactions

107 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 15.6 Controlling the Products of Reactions One of the primary goals of modern chemistry is to control the identity and quantity of the products of chemical reactions. Two approaches 1. To get a high yield of a desired compound, make the rate of the desired reaction much faster than the rate of any of the other possible reactions that might occur in the system; altering reaction conditions to control reaction rates, thereby obtaining a single product or set of products is called kinetic control. 2. Thermodynamic control—consists of adjusting conditions so that at equilibrium only the desired products are present in significant quantities.

108 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 16 Aqueous Acid-Base Equilibria

109 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the autoionization reaction of liquid water To know the relationship among pH, pOH, and pK w To understand the concept of conjugate acid-base pairs To know the relationship between acid or base strength and the magnitude of K a, K b, pK a, and pK b To understand the leveling effect To be able to predict whether reactants or products are favored in an acid-base equilibrium To understand how molecular structure determines acid and base strengths To be able to use K a and K b values to calculate the percent ionization and pH of a solution of an acid or a base

110 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To be able to calculate the pH at any point in an acid-base titration To understand how the addition of a common ion affects the position of an acid-base equilibrium To understand how a buffer works and how to use the Henderson-Hasselbalch equation to calculate the pH of a buffer

111 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 16.1 The Autoionization of Water

112 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 16.1 The Autoionization of Water Acids and bases can be defined in different ways: 1. Arrhenius definition: An acid is a substance that dissociates in water to produce H + ions (protons), and a base is a substance that dissociates in water to produce OH – ions (hydroxide); an acid-base reaction involves the reaction of a proton with the hydroxide ion to form water 2. Brønsted–Lowry definition: An acid is any substance that can donate a proton, and a base is any substance that can accept a proton; acid-base reactions involve two conjugate acid-base pairs and the transfer of a proton from one substance (the acid) to another (the base) 3. Lewis definition: A Lewis acid is an electron-pair acceptor, and a Lewis base is an electron-pair donor

113 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 16.1 The Autoionization of Water

114 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acid-Base Properties of Water Water is amphiprotic: it can act as an acid by donating a proton to a base to form the hydroxide ion, or as a base by accepting a proton from an acid to form the hydronium ion, H 3 O + Structure of the water molecule 1. Polar O–H bonds and two lone pairs of electrons on the oxygen atom 2. Liquid water has a highly polar structure

115 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Ion-Product Constant of Liquid Water Because water is amphiprotic, one water molecule can react with another to form an OH – ion and an H 3 O + ion in an autoionization process: 2H 2 O (l) ⇋ H 3 O + (aq) + OH – (aq) Equilibrium constant K for this reaction can be written as K = [H 3 O + ] [OH – ] [H 2 O] 2 When pure liquid water is in equilibrium with hydronium and hydroxide ions at 25ºC, the concentrations of hydronium ion and hydroxide ion are equal: [H 3 O + ] = [OH – ] = x 10 –7 M At 25ºC, the density of liquid water is g/mL

116 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Ion-Product Constant of Liquid Water The concentration of liquid water at 25ºC is [H 2 O] = mol/L = (0.997 g/mL) (1 mol/18.02 g) (1000 mL/L) = 55.3 M Because the number of dissociated water molecules is very small, the equilibrium of the autoionization reaction lies far to the left, so the concentration of water is unchanged by the autoionization reaction and can be treated as a constant By treating [H 2 O] as a constant, a new equilibrium constant, the ion-product constant of liquid water (K w ), can be defined: K[H 2 O] 2 = [H 3 O + ] [OH – ] or K w = [H 3 O + ] [OH – ] Substituting the values for [H 3 O + ] and [OH – ] at 25ºC gives K w = (1.003 x 10 –7 ) (1.003 x 10 –7 ) = x 10 –14

117 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Ion-Product Constant of Liquid Water K w varies with temperature, ranging from 1.15 x 10 –15 at 0ºC to 4.99 x 10 –13 at 100ºC In pure water, the concentrations of the hydronium ion and the hydroxide ion are the same, so the solution is neutral If [H 3 O + ] > [OH – ], the solution is acidic If [H 3 O + ] < [OH – ], the solution is basic

118 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship among pH, pOH, and pK w The pH scale is a concise way of describing the H 3 O + concentration and the acidity or basicity of a solution pH and H + concentration are related as follows: pH = –log 10 [H + ] or [H + ] = 10 –pH pH of a neutral solution ([H 3 O + ] = 1.00 x 10 –7 M) is 7.00 pH of an acidic solution is 1.00 x 10 –7 pH of a basic solution is > 7, corresponding to [H 3 O + ] < 1.00 x 10 –7 The pH scale is logarithmic, so a pH difference of 1 between two solutions corresponds to a difference of a factor of 10 in their hydronium ion concentrations

119 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship among pH, pOH, and pK w There is an analogous pOH scale to describe the hydroxide ion concentration of a solution; pOH and [OH – ] are related as follows: pH = –log 10 [OH – ] or [OH – ] = 10 –pOH A neutral solution has [OH – ] = 1.00 x 10 –7, so the pOH of a neutral solution is 7.00 The sum of the pH and the pOH for a neutral solution at 25ºC is = pK w = –log K w = –log([H 3 O + ] [OH – ]) = (–log[H 3 O + ]) + (–log[OH – ]) = pH + pOH At any temperature, pH + pOH = pK w, and at 25ºC, where K w = 1.01 x 10 –14, pH + pOH = 14.00; pH of any neutral solution is just half the value of pK w at that temperature

120 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 16.2 A Qualitative Description of Acid-Base Equilibria

121 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Conjugate Acid-Base Pairs Two species that differ by only a proton constitute a conjugate acid-base pair. 1. Conjugate base has one less proton than its acid; A – is the conjugate base of HA 2. Conjugate acid has one more proton than its base; BH + is the conjugate acid of B In the reaction of HCl with water, HCl, the parent acid, donates a proton to a water molecule, the parent base, forming Cl – ; HCl and Cl – constitute a conjugate acid-base pair. In the reverse reaction, the Cl – ion in solution acts as a base to accept a proton from H 3 O +, forming H 2 O and HCl; H 3 O + and H 2 O constitute a second conjugate acid-base pair.

122 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Conjugate Acid-Base Pairs Any acid-base reaction must contain two conjugate acid-base pairs, which in this example are HCl/Cl – and H 3 O + /H 2 O HCl (aq) + H2O (l)  H3O+ (aq) + Cl– (aq) parent acid parent base conjugate acid conjugate base

123 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acid-Base Equilibrium Constants: K a, K b, pK a, and pK b The magnitude of the equilibrium constant for an ionization reaction can be used to determine the relative strengths of acids and bases The general equation for the ionization of a weak acid in water, where HA is the parent acid and A – is its conjugate base, is HA(aq) + H 2 O(l) ⇋ H 3 O+(aq) + A – (aq) The equilibrium constant for this dissociation is K = [H 3 O + ] [A – ] [H 2 O] [HA] The concentration of water is constant for all reactions in aqueous solution, so [H 2 O] can be incorporated into a new quantity, the acid ionization constant (K a ): K a = K[H 2 O] = [H 3 O + ] [A – ] [HA]

124 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acid-Base Equilibrium Constants: K a, K b, pK a, and pK b Numerical values of K and K a differ by the concentration of water (55.3 M); the larger the value K a, the stronger the acid and the higher the H + concentration at equilibrium Weak bases react with water to produce the hydroxide ion, B(aq) + H 2 O(l) ⇋ BH + (aq) + OH – (aq), where B is the parent base and BH + is its conjugate acid Equilibrium constant for this reaction is the base ionization constant (K b ); concentration of water is constant and does not appear in the equilibrium constant expression but is included in the value of K b The larger the value of K b, the stronger the base and the higher the OH – concentration at equilibrium

125 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acid-Base Equilibrium Constants: K a, K b, pK a, and pK b The sum of the reactions described by K a and K b is the equation for the autoionization of water, and the product of the two equilibrium constants is K w For any conjugate acid-base pair, K a K b = K w pK a = –log 10 K a and pK b = –log 10 K b Smaller values of pK a correspond to larger acid ionization constants and stronger acids Smaller values of pK b correspond to larger base ionization constants and stronger bases At 25ºC, pK a + pK b = 14.00

126 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acid-Base Equilibrium Constants: K a, K b, pK a, and pK b There is an inverse relationship between the strength of the parent acid and the strength of the conjugate base; the conjugate base of a strong acid is a weak base, and the conjugate base of a weak acid is a strong base One can use the relative strengths of acids and bases to predict the direction of an acid-base reaction by following a simple rule: An acid-base equilibrium always favors the side with the weaker acid and base stronger acid + stronger base weaker acid + weaker base In an acid-base reaction, the proton always reacts with the stronger base

127 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Solutions of Strong Acids and Bases: The Leveling Effect No acid stronger than H 3 O + and no base stronger than OH – can exist in aqueous solution, leading to the phenomenon known as the leveling effect. Any species that is a stronger acid than the conjugate acid of water (H 3 O + ) is leveled to the strength of H 3 O + in aqueous solution because H 3 O + is the strongest acid that can exist in equilibrium with water. In aqueous solution, any base stronger than OH – is leveled to the strength of OH – because OH – is the strongest base that can exist in equilibrium with water Any substance whose anion is the conjugate base of a compound that is a weaker acid than water is a strong base that reacts quantitatively with water to form hydroxide ion

128 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Polyprotic Acids and Bases Polyprotic acids contain more than one ionizable proton, and the protons are lost in a stepwise manner. The fully protonated species is always the strongest acid because it is easier to remove a proton from a neutral molecule than from a negatively charged ion; the fully deprotonated species is the strongest base. Acid strength decreases with the loss of subsequent protons, and the pK a increases. The strengths of the conjugate acids and bases are related by pK a + pK b = pK w, and equilibrium favors formation of the weaker acid-base pair.

129 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acid-Base Properties of Solutions of Salts A salt can dissolve in water to produce a neutral, basic, or acidic solution, depending on whether it contains the conjugate base of a weak acid as the anion (A – ) or the conjugate acid of a weak base as the cation (BH + ), or both. Salts that contain small, highly charged metal ions produce acidic solutions in water. The most important parameter for predicting the effect of a metal ion on the acidity of coordinated water molecules is the charge-to-radius ratio of the metal ion. The reaction of a salt with water to produce an acidic or basic solution is called a hydrolysis reaction, which is just an acid-base reaction in which the acid is a cation or the base is an anion.

130 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 16.3 Molecular Structure and Acid-Base Strength

131 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The acid-base strength of a molecule depends strongly on its structure. The stronger the A–H or B–H + bond, the less likely the bond is to break to form H + ions, and thus the less acidic the substance. The larger the atom to which H is bonded, the weaker the bond. Acid strengths of binary hydrides increase as we go down a column of the periodic table. Bond Strengths

132 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The conjugate base (A – or B) contains one more lone pair of electrons than the parent acid (AH or BH + ). Any factor that stabilizes the lone pair on the conjugate base favors dissociation of H + and makes the parent acid a stronger acid. Acid strengths of binary hydrides increase as we go from left to right across a row of the periodic table. Stability of the Conjugate Base

133 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Atoms or groups in a molecule other than those to which H is bonded can induce a change in the distribution of electrons within the molecule, called an inductive effect; this can have a major effect on the acidity or basicity of the molecule. Inductive effect can weaken an O–H bond and allow hydrogen to be more easily lost as H + ions. Inductive Effects

134 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 16.4 Quantitative Aspects of Acid-Base Equilibria

135 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Determining K a and K b The ionization constants K a and K b are equilibrium constants that are calculated from experimentally measured concentrations. What does the concentration of an aqueous solution of a weak acid or base exactly mean? – A 1 M solution is prepared by dissolving 1 mol of acid or base in water and adding enough water to give a final volume of exactly 1 L. – If the actual concentrations of all species present in the solution were listed, it would be determined that none of the values is exactly 1 M because a weak acid or a weak base always reacts with water to some extent.

136 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Determining K a and K b – The extent of the reaction depends on the value of K a or K b, the concentration of the acid or base, and the temperature. – Only the total concentration of both the ionized and unionized species is equal to 1 M. – The analytical concentration (C) is defined as the total concentration of all forms of an acid or base that are present in solution, regardless of their state of protonation. – Thus; a 1 M solution has an analytical concentration of 1 M, which is the sum of the actual concentrations of unionized acid or base and the ionized form.

137 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Determining K a and K b – In addition to the analytical concentration of the acid or base, one must be able to measure the concentration of a least one of the species in the equilibrium constant expression in order to determine the value of K a or K b. – Two common ways to obtain the concentrations 1. By measuring the electrical conductivity of the solution, which is related to the total concentration of ions present 2. By measuring the pH of the solution, which gives [H + ] or [OH – ]

138 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Determining K a and K b Procedure for determining K a for a weak acid and K b for a weak base 1. The analytical concentration of the acid or base is the initial concentration 2. The stoichiometry of the reaction with water determines the change in concentrations 3. The final concentrations of all species are calculated from the initial concentrations and the changes in the concentrations 4. Inserting the final concentration into the equilibrium constant expression enables the value of K a or K b to be calculated

139 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Percent Ionization from K a or K b Need to know the concentrations of all species in solution The reactivity of a weak acid or a weak base is very different from the reactivity of its conjugate base or acid; need to know the percent ionization of a solution of an acid or base in order to understand a chemical reaction Percent ionization is defined as percent ionization of acid = [H + ] C HA percent ionization of base = [OH – ] C B x 100

140 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Percent Ionization from K a or K b To determine the concentrations of species in solutions of weak acids and bases, use a tabular method 1. Make a table that lists the following values for each of the species involved in the reaction a. Initial concentration b. The change in concentration on preceding to equilibrium (–x or +x) c. The final concentration—sum of the initial concentration and the change in concentration d. In constructing the table, define x as the concentration of the acid that dissociates 2. Solve for x by substituting the final concentrations from the table into the equilibrium constant expression

141 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Percent Ionization from K a or K b 3. Calculate the concentrations of the species present in the solution by inserting the value of x into the expressions in the last line of the table (final concentration) 4. Calculate the pH = –log[H 3 O + ] 5. Use the concentrations to calculate the fraction of the original acid that is ionized (the concentration of the acid that is ionized divided by the analytical or initial concentration of the acid times 100%

142 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Percent Ionization from K a or K b Strong acids and bases ionize essentially completely in water; the percent ionization is always approximately 100%, regardless of the concentration The percent ionization in solutions of weak acids and bases is small and depends on the analytical concentration of the weak acid or base; percent ionization of a weak acid or a weak base actually increases as its analytical concentration decreases and percent ionization increases as the magnitude of the ionization constants K a and K b increases

143 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Determining K eq from K a and K b The value of the equilibrium constant for the reaction of a weak acid with a weak base can be calculated from K a (or pK a ), K b (or pK b ), and K w One can quantitatively determine the direction and extent of reaction for a weak acid and a weak base by calculating the value of K for the reaction The equilibrium constant for the reaction of a weak acid with a weak base is the product of the ionization constants of the acid and the base divided by K w

144 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Determining K eq from K a and K b Calculations 1. Write the dissociation reactions for a weak acid and a weak base and then sum them: Acid HA ⇋ H + + A – K a Base B + H 2 O ⇋ HB + + OH – K b Sum HA + B + H 2 O ⇋ H + + A – + HB + + OH – K sum = K a K b 2. Obtain an equation that includes only the acid-base reaction by simply adding the equation for the reverse of the autoionization of water (H + + OH – ⇋ H 2 O), for which K = 1/K w, to the overall reaction and canceling HA + B + H 2 O ⇋ H + + A – + HB + + OH – K sum = K a K b H + + OH – ⇋ H 2 O 1/K w HA + B ⇋ A – + HB + K = (K a K b )/K w

145 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 16.5 Acid-Base Titrations

146 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 16.5 Acid-Base Titrations In acid-base titrations, a buret is used to deliver measured volumes of an acid or base solution of known titration (the titrant) to a flask that contains a solution of a base or an acid, respectively, of unknown concentration (the unknown). If the concentration of the titrant is known, then the concentration of the unknown can be determined. Plotting the pH changes that occur during an acid-base titration against the amount of acid or base added produces a titration curve; the shape of the curve provides important information about what is occurring in solution during the titration.

147 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Strong Acids and Bases Before addition of any strong base, the initial [H 3 O + ] equals the concentration of the strong acid. Addition of strong base before the equivalence point, the point at which the number of moles of base (or acid) added equals the number of moles of acid (or base) originally present in the solution, decreases the [H 3 O + ] because added base neutralizes some of the H 3 O + present. Addition of strong base at the equivalence point neutralizes all the acid initially present and pH = 7.00; the solution contains water and a salt derived from a strong base and a strong acid.

148 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Strong Acids and Bases Addition of a strong base after the equivalence causes an excess of OH – and produces a rapid increase in pH. A pH titration curve shows a sharp increase in pH in the region near the equivalence point and produces an S-shaped curve; the shape depends only on the concentration of the acid and base, not on their identity.

149 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Strong Acids and Bases For the titration of a monoprotic strong acid with a monobasic strong base, the volume of base needed to reach the equivalence point can be calculated from the following relationship: moles of base = moles of acid (volume) b (molarity) b = (volume) a (molarity) a a M a V b M b = V a M a

150 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases The shape of the titration curve for a weak acid or a weak base depends dramatically on the identity of the acid or base and the corresponding value of K a or K b.

151 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases The pH changes much more gradually around the equivalence point in the titration of a weak acid or a weak base. [H + ] of a solution of a weak acid (HA) is not equal to the concentration of the acid but depends on both its pK a and its concentration. Only a fraction of a weak acid dissociates, so [H + ] is less than [HA]; therefore, the pH of a solution of a weak acid is higher than the pH of a solution of a strong acid of the same concentration.

152 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases Comparing the titration curve of a strong acid with a strong base with the titration curve of a weak acid and a strong base 1. Below the equivalence point, the two curves are very different; before any base is added, the pH of the weak acid is higher than the pH of the strong acid 2. pH changes more rapidly during the first part of the titration in a weak acid and strong base titration 3. Due to the higher starting pH, the pH of the weak acid at the equivalence point is greater than 7.00, so solution is basic

153 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases 4. Change in pH for the weak acid/strong base titration around the equivalence point is about half as large as for the strong acid titration; the magnitude of the change at the equivalence point depends on the pK a of the acid being titrated 5. Above the equivalence point, the two curves are identical; once acid has been neutralized, the pH of the solution is controlled only by the amount of excess of OH – present, regardless of whether the acid is weak or strong

154 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases Calculating the pH of a solution of a weak acid or base – If K a or K b and the initial concentration of a weak acid or base are known, one can calculate the pH of a solution of a weak acid or base by setting up a table of initial concentrations, changes in concentrations, and final concentrations – Define x as [H + ] due to the dissociation of the acid – Insert values for final concentrations into the equilibrium equation and solve for x and then pH (pH = –log[H + ])

155 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases Calculating the pH during titration of a weak acid or base – Solved in two steps: a stoichiometric calculation followed by an equilibrium calculation 1. Use stoichiometry of the neutralization reaction to calculate the amounts of acid and conjugate base present in solution after the neutralization reaction has occurred 2. Use the equilibrium equation K = [H 3 O + ] [A – ] / [H 2 O] [HA] to determine [H + ] of the resulting solution

156 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases Identity of the weak acid or base being titrated strongly affects the shape of the titration curve. The shape of titration curves as a function of the pK a or pK b shows that as the acid or base being titrated becomes weaker (its pK a or pK b becomes larger), the pH change around the equivalence point decreases significantly.

157 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Weak Acids and Bases The midpoint of a titration is defined as the point at which exactly enough acid (or base) has been added to neutralize one-half of the acid (or base) originally present and occurs halfway to the equivalence point. At the midpoint of the titration of an acid, [HA] = [A – ]. The pH at the midpoint of the titration of a weak acid is equal to the pK a of the weak acid.

158 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Polyprotic Acids or Bases When a strong base is added to a solution of a polyprotic acid, the neutralization reaction occurs in stages. 1. The most acidic group is titrated first, followed by the next most acidic, and so forth 2. If the pK a values are separated by at least three pK a units, then the overall titration curve shows well-resolved “steps” corresponding to the titration of each proton

159 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Titrations of Polyprotic Acids or Bases

160 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators Most acid-base titrations are not monitored by recording the pH as a function of the amount of the strong acid or base solution used as a titrant Instead, an acid-base indicator is used, and they are compounds that change color at a particular pH and if carefully selected, undergo a dramatic color change at the pH corresponding to the equivalence point of the titration Acid-base indicators are typically weak acids or bases whose changes in color correspond to deprotonation or protonation of the indicator itself

161 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators

162 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators The chemistry of indicators are described by the general equation H  n (aq) ⇋ H + (aq) +  n – (aq), where the protonated form is designated by H  n and the conjugate base by  n – The ionization constant for the deprotonation of indicator H  n is K in = [H + ] [  n – ] / [H  n] The value of pK in determines the pH at which the indicator changes color

163 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators A good indicator must have the following properties: 1. Color change must be easily detected 2. Color change must be rapid 3. Indicator molecule must not react with the substance being titrated 4. The indicator should have a pK in that is within one pH unit of the expected pH at the equivalence point of the titration Synthetic indicators have been developed that meet the above criteria and cover the entire pH range An indicator does not change color abruptly at a particular pH but undergoes a pH titration like any other acid or base

164 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators Choosing the correct indicator for an acid-base titration 1. For titrations of strong acids and strong bases (and vice versa), any indicator with a pK in between 4 and 10 will do 2. For the titration of a weak acid, the pH at the equivalence point is greater than 7, and an indicator such as phenolphthalein or thymol blue, with pK in > 7, should be used 3. For the titration of a weak base, where the pH at the equivalence point is less than 7, an indicator such as methyl red or bromcresol blue, with pK in < 7, should be used

165 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators

166 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Indicators Paper or plastic strips that contain combinations of indicators estimate the pH of a solution by simply dipping a piece of pH paper into it and comparing the resulting color with standards printed on the container

167 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 16.6 Buffers

168 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 16.6 Buffers Buffers are solutions that maintain a relatively constant pH when an acid or a base is added; they protect or “buffer” other molecules in solution from the effects of the added acid or base Buffers contain either a weak acid (HA) and its conjugate base (A – ) or a weak base (B) and its conjugate acid (BH + ) Buffers are critically important for the proper functioning of biological systems; every biological fluid is buffered to maintain its physiological pH

169 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Common Ion Effect The ionization equilibrium of a weak acid (HA) is affected by the addition of either the conjugate base of the acid (A – ) or a strong acid (a source of H + ); LeChâtelier’s principle is used to predict the effect on the equilibrium position of the solution Common-ion effect—the shift in the position of an equilibrium on addition of a substance that provides an ion in common with one of the ions already involved in the equilibrium; equilibrium is shifted in the direction that reduces the concentration of the common ion

170 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Common Ion Effect Buffers are characterized by the following: 1. the pH range over which they can maintain a constant pH— depends strongly on the chemical properties of the weak acid or base used to prepare the buffer (on K) 2. their buffer capacity, the amount of strong acid or base that can be absorbed before the pH changes significantly—depends solely on the concentration of the species in the buffered solution (the more concentrated the buffer solution, the greater its buffer capacity) 3. observed change in the pH of the buffer is inversely proportional to the concentration of the buffer

171 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Common Ion Effect

172 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating the pH of a Buffer The pH of a buffer can be calculated from the concentrations of the weak acid or the weak base used to prepare it, the concentration of the conjugate base or acid, and the pK a or pK b of the weak acid or base An alternative method used to calculate the pH of a buffer solution is based on a rearrangement of the equilibrium equation for the dissociation of a weak acid Ionization reaction is HA ⇋ H + + A – and the equilibrium constant expression is K a = [H + ] [A – ] or [H + ] = K a [HA] [HA] [A – ]

173 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating the pH of a Buffer Taking the logarithm of both sides and multiplying both sides by –1 gives –log[H + ] = –logK a – log([HA]/[A – ]) = – logK a + log([A – ]/[HA]) Replacing the negative logarithms gives pH = pK a + log([A – ]/[HA]) or pH = pk a + log([base]/[acid]) Both forms of the Henderson-Hasselbalch equation Henderson-Hasselbalch equation is valid for solutions whose concentrations are at least a hundred times greater than the value of their K a ’s

174 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating the pH of a Buffer Three special cases where the Henderson-Hasselbalch equation is interpreted without the need for calculations 1. [base] = [acid]. Under these conditions, [base]/[acid] = 1. Because log 1 = 0, pH = pK a, regardless of the actual concentrations of the acid and base (corresponds to the midpoint in the titration of a weak acid or base) 2. [base]/[acid] = 10. Because log 10 = 1, pH = pK a [base]/[acid] = 100. Because log 100 = 2, pH = pK a + 2 Each time the [base]/[acid] ratio is increased by 10, the pH of the solution increases by one unit; if the [base]/[acid] ratio is 0.1, then pH = pK a – 1, so each additional factor-of-10 decrease in the [base]/[acid] ratio causes the pH to decrease by one pH unit

175 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating the pH of a Buffer The Henderson-Hasselbalch equation can also be used to calculate the pH of a buffer solution after the addition of a given amount of strong acid or base A buffer that contains equal amounts of the weak acid (or weak base) and its conjugate base (or acid) in solution is equally effective at neutralizing either added base or added acid

176 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Titrations and Buffers A strong correlation exists between the effectiveness of a buffer solution and the titration curves In a titration of a weak acid with a strong base; – the region around pK a corresponds to the midpoint of the titration, when half the weak acid has been neutralized; this portion of the titration curve corresponds to a buffer because it exhibits the smallest change in pH per increment of added strong base (horizontal nature of the curve in this region); – the flat portion of the curve extends only from a pH value of one unit less than the pK a to a pH value of one unit greater than the pK a ; that is why buffer solutions have a pH that is within ±1 pH units of the pK a of the acid component of the buffer;

177 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Titrations and Buffers – in the region of the titration curve at the lower left, before the midpoint, the acid-base properties of the solution are dominated by the equilibrium for dissociation of the weak acid, corresponding to K a ; – in the region of the titration curve at the upper right, after the midpoint, the acid-base properties of the solution are dominated by the equilibrium for reaction of the conjugate base of the weak acid with water, corresponding to K b.

178 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Blood: A Most Important Buffer Metabolic processes produce large amounts of acids and bases, but organisms are able to maintain a constant internal pH because their fluids contain buffers. pH is not uniform throughout all cells and tissues of a mammal; even within a cell, different compartments can have very different pH values. Because no single buffer system can effectively maintain a constant pH value over the physiological range of 5 to 7.4, biochemical systems use a set of buffers with overlapping ranges; most important of these is the CO 2 /HCO 3 – system, which dominates the buffering action of blood plasma.

179 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17 Solubility and Complexation Equilibria

180 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To be able to calculate the solubility of an ionic compound from its K sp To understand the factors that determine the solubility of ionic compounds To be able to describe complex-ion formation quantitatively To understand why the solubility of many compounds depends on pH To know how to separate metal ions by selective precipitation

181 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 17.1 Determining the Solubility of Ionic Compounds

182 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Solubility Product, K sp When a slightly soluble ionic compound is added to water, some of it dissolves to form a solution, establishing an equilibrium between the pure solid and a solution of its ions. The equilibrium constant for the dissolution of a sparingly soluble salt is the solubility product of the salt, K sp. The concentration of a pure solid is a constant and does not appear in the equilibrium constant expression. Solubility products are determined experimentally by either directly measuring the concentration of one of the component ions or by measuring the solubility of the compound in a given amount of water. K sp is defined in terms of molar concentrations of the component ions.

183 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Ion Product The ion product (Q) of a salt is the product of the concentrations of the ions in solution raised to the same powers as in the solubility product expression. The ion product describes concentrations that are not necessarily equilibrium concentrations, whereas K sp describes equilibrium concentrations. The process of calculating the value of the ion product and comparing it with the magnitude of the solubility product is a way to determine if a solution is unsaturated, saturated, or supersaturated and whether a precipitate will form when solutions of two soluble salts are mixed.

184 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Ion Product Three possible conditions for an aqueous solution of an ionic solid 1. Q < K sp : the solution is unsaturated, and more of the ionic solid will dissolve 2. Q = K sp : the solution is saturated and at equilibrium 3. Q > K sp : the solution is supersaturated, and ionic solid will precipitate

185 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Common Ion Effect and Solubility Solubility product expression – Equilibrium concentrations of cation and anion are inversely related – As the concentration of the anion increases, the maximum concentration of the cation needed for precipitation to occur decreases, and vice versa – K sp is constant

186 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Common Ion Effect and Solubility Common ion effect – The solubility of an ionic compound depends on the concentrations of other salts that contain the same ions. – This dependency is an example of the common ion effect; adding a common cation or anion shifts a solubility equilibrium in the direction predicted by LeChâtelier’s principle. – The solubility of any sparingly soluble salt is almost always decreased by the presence of a soluble salt that contains a common ion.

187 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 17.2 Factors That Affect Solubility

188 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.2 Factors That Affect Solubility The solubility product of an ionic compound describes the concentrations of ions in equilibrium with a solid. There are four reasons that the solubility of a compound may be other than expected: 1. Ion-pair formation 2. Incomplete dissociation of molecular solutes 3. Formation of complex ions 4. Changes in pH

189 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings An ion pair consists of a cation and anion that are in intimate contact in solution, rather than separated by solvent. Ion-Pair Formation

190 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Ions in an ion pair are held together by the same attractive electrostatic forces as for ionic solids. – Ions in an ion pair migrate as a single unit, whose net charge is the sum of the charges on the ions. – The ion pair is a species intermediate between the ionic solid (in which each ion participates in many cation-anion interactions that hold the ions in a rigid array) and the completely dissociated ions in solution (where each is fully surrounded by water molecules and free to migrate independently). Ion-Pair Formation

191 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Ion-Pair Formation Ion pairs – A second equilibrium must be included to describe the solubility of salts that form ion pairs. – An ion pair is represented by the symbols of the individual ions separated by a dot, to indicate that they are associated in solution (Ca 2+ · SO 4 2– ). – The formation of an ion pair is a dynamic process, so a particular ion pair may exist only briefly before dissociating into the free ions, each of which may later associate briefly with other ions. – Ion-pair formation has a major effect on the measured solubility of a salt and is most important for salts that contain M 2+ and M 3+ ions; it is unimportant for salts that contain monocations.

192 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Incomplete Dissociation A molecular solute may be more soluble than predicted by the measured concentrations of ions in solution due to incomplete dissociation. – Common for weak organic acids – Weak acids do not dissociate completely into their constituent ions (H + and A – ) in water – The molecular (undissociated) form of a weak acid (HA) is quite soluble in water – Many carboxylic acids have a limited solubility in water

193 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Incomplete Dissociation

194 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 17.3 Complex-Ion Formation

195 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Metal ions in aqueous solution are hydrated—surrounded by a shell of four to six water molecules. A hydrated ion is one kind of complex ion, a species formed between a central metal ion and one or more surrounding ligands, molecules or ions that contain at least one lone pair of electrons. A complex ion forms from a metal ion and a ligand because of a Lewis acid-base interaction. – The positively charged metal ion acts as a Lewis acid, and the ligand, with one or more lone pairs of electrons, acts as a Lewis base. – Small, highly charged metal ions have the greatest tendency to act as Lewis acids and to form complex ions Complex-Ion Formation

196 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The equilibrium constant for the formation of the complex ion from the hydrated ion is called the formation constant (K f ). Equilibrium constant expression for K f has the same general form as any other equilibrium constant expression. The larger the value of K f, the more stable the product. The Formation Constant

197 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The solubility of a sparingly soluble salt increases if a ligand that forms a stable complex ion is added to the solution. The formation of a complex ion by the addition of a complexing agent increases the solubility of a compound. Complexing agents are molecules or ions that increase the solubility of metal salts by forming soluble metal complexes. The Effect of Complex-Ion Formation on Solubility

198 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 17.4 Solubility and pH

199 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.4 Solubility and pH Solubility of many compounds depend strongly on the pH of the solution – The anion in many sparingly soluble salts is the conjugate base of a weak acid that may become protonated in solution. – The solubility of simple binary compounds such as oxides and sulfides are dependent on pH.

200 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Effect of Acid-Base Equilibria on the Solubility of Salts Examining the effect of pH on the solubility of a representative salt, M + A –, where A – is the conjugate base of the weak acid HA – When the salt dissolves in water, this reaction occurs: M A (s) ⇋ M + (aq) + A – (aq) K sp = [M + ] [A – ] – The anion can also react with water in a hydrolysis reaction: A – (aq) + H 2 O (l) ⇋ OH – (aq) + HA (aq) – If a strong acid is added to the solution, the added H + will react essentially completely with A – to form HA, which decreases [A – ] and which in turn decreases the magnitude of the ion product, Q = [M + ] [A – ] – More MA will dissolve until Q = K sp

201 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Effect of Acid-Base Equilibria on the Solubility of Salts – An acidic pH dramatically increases the solubility of sparingly soluble salts whose anion is the conjugate base of a weak acid; pH has little to no effect on the solubility of salts whose anion is the conjugate base of a strong acid – caves and their associated pinnacles and spires of stone provide one of the most impressive examples of pH-dependent solubility equilibria

202 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acidic, Basic, and Amphoteric Oxides and Hydroxides Oxides and hydroxides can be classified as either basic or acidic. 1. Basic oxides and hydroxides either react with water to produce a basic solution or dissolve readily in aqueous acid. 2. Acidic oxides or hydroxides either react with water to produce an acidic solution or are soluble in aqueous base.

203 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acidic, Basic, and Amphoteric Oxides and Hydroxides There is a clear correlation between the acidic or basic character of an oxide and the position of the element combined with oxygen in the periodic table.

204 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acidic, Basic, and Amphoteric Oxides and Hydroxides – Oxides of metallic elements are generally basic oxides. – Oxides of nonmetallic elements are acidic oxides. – There is a gradual transition from basic metal oxides to acidic nonmetal oxides from the lower left to the upper right of the periodic table; a broad diagonal band of oxides of intermediate character separates the two extremes. – Oxides of the elements in the diagonal region are soluble in both acidic and basic solutions and are called amphoteric oxides; which dissolve in acid to produce water or dissolve in base to produce a soluble complex.

205 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Acidic, Basic, and Amphoteric Oxides and Hydroxides The difference in reactivity is due to the difference in bonding in the two kinds of oxides. – Metals at the far left of the periodic table have low electronegativities; their oxides contain discrete M n+ cations and O 2– anions. – Nonmetal oxides have high electronegativities and form oxides that contain covalent bonds to oxygen. – Because of the high electronegativity of oxygen, the covalent bond between oxygen and the other atom is polarized E  + –O  –. – These oxides act as Lewis acids that react with water to produce an oxoacid. – Oxides of metals in high oxidation states tend to be acidic oxides; they contain covalent bonds to oxygen.

206 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Selective Precipitation Using pH Many dissolved metal ions can be separated by selective precipitation of the cations from solution under specific conditions. pH is used to control the concentration of the anion in solution; this in turn controls which cations precipitate.

207 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 17.5 Qualitative Analysis Using Selective Precipitation

208 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation The composition of relatively complex mixtures of metal ions can be determined using qualitative analysis, a procedure for discovering the identity of metal ions present in the mixture. The technique consists of selectively precipitating only a few kinds of metal ions at a time under given sets of conditions; consecutive precipitation steps become progressively less selective until almost all the metal ions are precipitated.

209 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation

210 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation The traditional scheme of analysis for metal cations involves the separation of cations into five groups by selective precipitation 1. Group 1: Insoluble chlorides – Metal chloride salts are soluble in water; only Ag +, Pb 2+, and Hg 2 2+ form chlorides that precipitate from water – First step in qualitative analysis is to add 6 M HCl, causing AgCl, PbCl 2, and/or Hg 2 Cl 2 to precipitate; precipitate is collected by filtration or centrifugation

211 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation 2. Group 2: Acid-insoluble sulfides – Acidic solution is saturated with H 2 S – Only those metal ions that form very insoluble sulfides precipitate as their sulfide salts under these acidic conditions; all others remain in solution – Precipitates collected by filtration or centrifugation

212 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation 3. Group 3: Base-insoluble sulfides (and hydroxides) – Ammonia or NaOH is added to the solution until it is basic, and then (NH 4 ) 2 S is added – Treatment removes any remaining cations that form insoluble hydroxides or sulfides 4. Group 4: Insoluble carbonates or phosphates – The next metal ions to be removed are those that form insoluble carbonates and phosphates

213 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation 5. Group 5: Alkali metals –All the metal ions that form water-insoluble chlorides, sulfides, carbonates, or phosphates have been removed –Only common ions that remain are the alkali metals and ammonium –Take a second sample from the original solution and add a small amount of NaOH to neutralize the ammonium ion and produce NH 3 ; any ammonia produced can be detected by odor or by litmus paper test, and alkali metal ions, which produce characteristic colors in flame tests, allows them to be identified

214 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 17.5 Qualitative Analysis Using Selective Precipitation Metal ions that precipitate together are separated by various techniques, such as forming complex ions, changing the pH of the solution, or increasing the temperature to redissolve some of the solids

215 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18 Chemical Thermodynamics

216 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the connections among work, heat, and energy To be familiar with the concept of PV work To be able to calculate changes in internal energy To understand the relationship between internal energy and entropy To be able to use a thermodynamic cycle to calculate changes in entropy To understand the relationship between Gibbs free energy and work To know the difference between the information that thermodynamics and kinetics provide about a system To understand the importance of thermodynamics in biochemical systems

217 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemical Thermodynamics Chemical reactions obey two fundamental laws: 1. The law of conservation of mass – States that matter can be neither created nor destroyed – Explains why equations must balance and is the basis for stoichiometry and equilibrium calculations 2. The law of conservation of energy – States that energy can be neither created nor destroyed – Energy takes various forms that can be converted from one to the other

218 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemical Thermodynamics Thermodynamics – The study of the interrelationships among heat, work, and the energy content of a system at equilibrium – Tells whether a particular reaction is energetically possible in the direction in which it is written and the composition of the reaction system at equilibrium – Does not say anything about whether an energetically feasible reaction will actually occur as written – Tells nothing about the rate of the reaction or the pathway by which it will occur – Provides a bridge between the macroscopic properties of a substance and the individual properties of its constituent molecules and atoms

219 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.1 Thermodynamics and Work

220 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.1 Thermodynamics and Work A system is that part of the universe in which we are interested; the surroundings are everything else—the rest of the universe. System + surroundings = universe. A closed system cannot exchange matter with its surroundings; an open system can. State function—the property of a system that depends only on the present state of the system and not on its history. A change in state function depends only on the difference between the initial and final states, not on the pathway used to go from one to the other. Thermodynamics is concerned with state functions and does not deal with how the change between the initial and final state occurs.

221 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Connections among Work, Heat, and Energy The internal energy (E) of a system is the sum of the potential energy and the kinetic energy of all the components; internal energy is a state function. A closed system cannot exchange matter with its surroundings, but it can exchange energy with its surroundings in two ways: 1. By doing work 2. By releasing or absorbing heat, the flow of thermal energy Work and heat are two distinct ways of changing the internal energy of a system.

222 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Connections among Work, Heat, and Energy Work (w) is defined as a force (F) acting through a distance (d): w = Fd. Work occurs only when an object moves against an opposing force; work requires that the system and its surroundings be physically connected. The flow of heat, the transfer of energy due to differences in temperature between two objects, represents a thermal connection between the system and its surroundings. Work causes a physical displacement, and flow of heat causes a temperature change. Units of work and heat must be the same because both processes result in the transfer of energy; units are joules (J).

223 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings PV Work In chemistry, most work is expansion work (PV work) done as the result of a volume change during a reaction when air molecules are pushed aside. Amount of work done by an expanding gas is given by the equation w = – P  V, where P is the pressure against which the system must push and  V is the change in volume of the system. When the pressure or volume of a gas is changed, any mechanical work done is PV work.

224 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings PV Work Work done by the system on the surroundings has a negative value, and work done on the system by the surroundings has a positive value. Work is not a state function; it depends on the path taken.

225 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.2 The First Law of Thermodynamics

226 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.2 The First Law of Thermodynamics The Relationship between the energy change of the system and that of the surroundings is given by the first law of thermodynamics, which states that the energy of the universe is constant. This law can be expressed mathematically as  E univ =  E sys +  E surr = 0  E sys = –  E surr The change in energy of the system is identical in magnitude but opposite in sign to the change in energy of the surroundings. One of the most important factors that determine the outcome of a chemical reaction is the tendency of all systems to move toward the lowest possible energy state.

227 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.2 The First Law of Thermodynamics Heat and work are the only two ways in which energy can be transferred between a system and the surroundings. Any change in the internal energy of the system is the sum of the heat transferred, q, and the work done, w:  E sys = q + w q and w are not state functions on their own; their sum,  E sys, is independent of the path taken and is therefore a state function. Any machine that converts energy to work is designed to want to maximize the amount of work obtained and to minimize the amount of energy released to the environment as heat

228 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Enthalpy To understand the relationship between heat flow, q, and the resulting change in internal energy  E, one must look at two sets of limiting conditions: 1. Reactions that occur at constant volume 2. Reactions that occur at constant pressure Assume that PV work is the only kind of work possible for the system, so  E = q – P  V

229 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Enthalpy Constant volume –If reaction occurs in a closed vessel, the volume of the system is fixed and  V is zero –Heat flow (q v ) must equal  E q v =  E –No PV work can be done, and the change in the internal energy of the system is equal to the amount of heat transferred from the system to the surroundings, or vice versa

230 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Enthalpy Constant pressure –If reaction occurs in an open container at a constant pressure of 1 atm, heat flow is given the symbol q p –Replacing q with q p gives the equation q p =  E + P  V –At constant pressure, the heat flow for any process is equal to the change in the internal energy of the system plus the PV work done –A new state function called enthalpy (H) is defined as H = E + PV –At constant pressure, the change in the enthalpy of a system is  H =  E +  (PV) =  E + P  V –At constant pressure, the change in the enthalpy of a system is equal to the heat flow:  H = q p

231 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between  H and  E If  H for a reaction is known, one can use the change in the enthalpy of the system to calculate its change in internal energy. When a reaction involves only solids, liquids, liquid solutions, or any combination of these, the volume does not change (  V = 0), so  H =  E. If gases are involved,  H and  E can differ significantly; one can calculate  E from the measured value of  H by using the equation  H =  E + P  V and the ideal gas law, PV = nRT.  (PV) =  (nRT), so  H =  E +  (PV) =  E +  (nRT). At constant temperature,  (nRT) = RT  n, where  n is the difference between the final and initial moles of gas, so  E =  H – RT  n.

232 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between  H and  E For reactions that result in a net production of gas,  n > 0 and  E <  H. Endothermic reactions that result in a net consumption of gas have  n  H.

233 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.3 The Second Law of Thermodynamics

234 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings How to predict whether a particular process or reaction would occur spontaneously – Most spontaneous reactions are exothermic, but there are many that are not exothermic. – Reactions can be both spontaneous and highly endothermic. – Enthalpy changes are not the only factors that determine whether a process is spontaneous. – An additional state function called entropy (S) can help explain why some processes proceed spontaneously in only one direction. – Entropy is a thermodynamic property of all substances that is proportional to their degree of disorder The Second Law of Thermodynamics

235 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemical and physical changes in a system are accompanied by either an increase or decrease in the disorder of the system, corresponding to an increase in entropy (  S > 0) or a decrease in entropy (  S < 0), respectively. A change in entropy is defined as the difference between the entropies of the final and initial states:  S = S f – S i. When a gas expands into a vacuum, its entropy increases because the increased volume allows for greater atomic or molecular disorder; the greater the number of atoms or molecules in the gas, the greater the disorder. The magnitude of the entropy of a system depends on the number of microscopic states, or microstates, associated with it; the greater the number of microstates, the greater the entropy. Entropy

236 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings A disordered system has a greater number of possible microstates than does an ordered system, so it has a higher entropy. Liquids that have highly ordered structures due to hydrogen bonding or other intermolecular interactions tend to have significantly higher values of  S vap. The formation of a solution is a process that is accompanied by entropy changes; formation of a liquid solution from a crystalline solid and a liquid solvent results in an increase in the disorder of the system and in its entropy. Entropy

237 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings In a reversible process, every intermediate state between the extremes is an equilibrium state, regardless of the direction of the change. An irreversible process is one in which the intermediate states are not equilibrium states, and change occurs spontaneously in only one direction. A reversible process can change direction at any time, whereas an irreversible process cannot. Work done during the expansion of a gas depends on the opposing external pressure (w = P ext  V), so work done in a reversible process is always equal to or greater than work done in a corresponding irreversible process: w rev  w irrev. Reversible and Irreversible Changes

238 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Whether a process is reversible or irreversible,  E = q + w. E is a state function, so the magnitude of  E does not depend on reversibility and is independent of the path taken:  E = q rev + w rev = q irrev + w irrev.  E for a process is the same whether that process is carried out in a reversible or an irreversible manner. Reversible and Irreversible Changes

239 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The quantity of heat transferred, q rev, is directly proportional to the absolute temperature of an object, T (q rev  T), so the hotter the object, the greater amount of heat transferred. Adding heat to a system increases the kinetic energy of the component atoms and molecules and their disorder (  S  q rev ). For any reversible process  S = q rev /T or q rev = T  S; units of  S are joules/kelvin (J/K). Work done in a reversible process at constant pressure is w rev = –P  V, so  E = q rev + w rev = T  S – P  V; change in the internal energy of the system is related to the change in entropy, the absolute temperature, and the PV work done. The Relationship between Internal Energy and Entropy

240 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Entropy of the universe is unchanged in reversible processes and constitutes part of the second law of thermodynamics: the entropy of the universe remains constant in a reversible process, whereas the entropy of the universe increases in an irreversible (spontaneous) process. The Relationship between Internal Energy and Entropy

241 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.4 Entropy Changes and the Third Law of Thermodynamics

242 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The atoms, molecules, or ions that make up a chemical system can undergo several types of molecular motion: translation, rotation, and vibration. The greater the molecular motion of a system, the greater the number of possible microstates and the higher the entropy. A perfectly ordered system, a perfect crystal at a temperature of absolute zero (0 K) that exhibits no motion, with only a single microstate available would have an entropy of zero Entropy Changes and the Third Law of Thermodynamics

243 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.4 Entropy Changes and the Third Law of Thermodynamics Absolute zero is an ideal temperature that is unobtainable, and a perfect single crystal is an ideal that cannot be achieved, however, the combination of these two ideals constitutes the basis for the third law of thermodynamics: The entropy of any perfectly ordered, crystalline substance at absolute zero is zero. The third law of thermodynamics has two important consequences: 1.It defines as positive the sign of the entropy of any substance at temperatures above absolute zero 2.It provides a fixed reference point that allows the measurement of the absolute entropy of any substance at any temperature

244 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.4 Entropy Changes and the Third Law of Thermodynamics Two different ways to calculate  S for a reaction or physical change 1.Uses tabulated values of absolute entropies of substances, based on the definition of absolute entropy provided by the third law 2.Uses a thermodynamic cycle, based on the fact that entropy is a state function

245 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating  S from Standard Molar Entropy Values One way of calculating  S for a reaction is to use tabulated values of the standard molar entropy (S º ), which is the entropy of 1 mol of a substance at a standard temperature of 298 K Units of S º are J/(mol  K) It is possible to obtain absolute entropy values by measuring the entropy change that occurs between the reference point of 0 K, corresponding to S = 0, and 298 K For substances with the same molar mass and number of atoms, S º values fall in the order S º (gas) > S º (liquid) > S º (solid)

246 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating  S from Standard Molar Entropy Values Substances with similar molecular structures have similar S º values 1.Those with the lowest entropies tend to be rigid crystals composed of small atoms linked by strong, highly directional bonds 2.Those with higher entropies are soft crystalline substances that contain larger atoms and increased molecular motion and disorder

247 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating  S from Standard Molar Entropy Values Absolute entropy of a substance tends to increase with increasing molecular complexity because the number of available microstates increases with molecular complexity Substances with strong hydrogen bonds have lower values of S º, reflecting a more ordered structure To calculate  S º for a chemical reaction from standard molar entropies, the “products minus reactants” rule is used; here the absolute entropy of each reactant and product is multiplied by its stoichiometric coefficient in the balanced chemical equation

248 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating  S from Thermodynamic Cycles A change in entropy can also be calculated using a thermodynamic cycle –The molar heat capacity C p is the amount of heat needed to raise the temperature of 1 mol of a substance by 1ºC at constant pressure –C v is the amount of heat needed to raise the temperature of 1 mol of a substance by 1ºC at constant volume –Increase in entropy with increasing temperature is proportional to the heat capacity of the substance –Entropy change  S is related to heat flow, q rev, by  S = q rev /T

249 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating  S from Thermodynamic Cycles –q rev = nC p  T at constant pressure or nC v  T at constant volume, where n is the number of moles of substance present –The change in entropy for a substance whose temperature changes from T 1 to T 2 is  S =nC p lnT 2 /T 1 (constant pressure) or  S = nC v lnT 2 /T 1 (constant volume) –A combination of heat capacity easurements and experimentally measured values of enthalpies of fusion or vaporization can be used to calculate the entropy change corresponding to a change in the temperature of the sample

250 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating  S from Thermodynamic Cycles

251 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.5 Free Energy

252 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.5 Free Energy One major goal of chemical thermodynamics is to establish criteria for predicting whether a particular reaction or process will occur spontaneously The sign of  S univ is a universally applicable and infallible indicator of the spontaneity of a reaction; if  S univ > 0, the process will occur spontaneously as written; if  S univ < 0, a process cannot occur spontaneously; and if  S univ = 0, the system is at equilibrium Using  S univ requires the calculation of  S for both the system and the surroundings. This is not useful because we are much more interested in the system than in the surroundings; it is also difficult to make quantitative measurements of the surroundings A criterion of spontaneity that is based solely on state functions of the system is more convenient and is provided by a new state function called the Gibbs free energy

253 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Gibbs Free Energy and the Direction of Spontaneous Reactions The Gibbs free energy (G), or free energy, is defined in terms of three other state functions—enthalpy, temperature, and entropy— and is a state function itself: G = H – TS The criterion for predicting spontaneity is based on  G, the change in G at constant temperature and pressure  G =  H – T  S, where all thermodynamic quantities are those of the system At constant pressure,  H = q whether a process is reversible or irreversible, and T  S = q rev, so  G = q – q rev So  G is the difference between the heat released during a process (via a reversible or an irreversible path) and the heat released for the same process occurring in a reversible manner

254 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Gibbs Free Energy and the Direction of Spontaneous Reactions To understand how the sign of  G for the system determines the direction in which change is spontaneous, the equation  S = q rev /T and q =  H is rewritten to give  S surr = –  H sys /T The entropy change of the surroundings is related to the enthalpy change of the system, and since for a spontaneous reaction,  S univ > 0, the equation becomes  S univ =  S sys +  S surr > 0 or  S univ =  S sys –  H sys /T > 0 Multiplying both sides of the inequality by –T reverses its sign and rearranges the equation to  H sys – T  S < 0, which is equal to  G; therefore, for a spontaneous process,  G < 0

255 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Gibbs Free Energy and the Direction of Spontaneous Reactions Relationship between the entropy change of the surroundings and the heat gained or lost by the system provides the key connection between the thermodynamic properties of the system and the change in entropy of the universe This relationship allows one to predict spontaneity by focusing exclusively on the thermodynamic properties and temperature of the system. Highly exothermic processes (  H > 0) would occur spontaneously For a system at constant temperature and pressure, 1. if  G < 0, the process occurs spontaneously 2. if  G = 0, the system is at equilibrium 3. if  G > 0, the process is not spontaneous as written but occurs spontaneously in the reverse direction

256 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Gibbs Free Energy and the Direction of Spontaneous Reactions

257 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between  G and Work Change in free energy,  G, is equal to the maximum amount of work that a system can perform on the surroundings while undergoing a spontaneous change (at constant temperature and pressure):  G = w max

258 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Standard Free-Energy Change Absolute free energies cannot be measured. However, changes in free energy can. The standard free-energy change (  G º ) is the change in free energy when one substance or set of substances in their standard states is converted to one or more other substances also in their standard states The standard free-energy change can be calculated from the definition of free energy if the standard enthalpy and entropy changes are known:  G º =  H º – T  S º If  S º and  H º for a reaction have the same sign, then the sign of  G º depends on the relative magnitudes of the  H º and T  S º terms

259 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Standard Free-Energy Change The standard free energy of formation (  G º f ) of a compound is the change in free energy that occurs when 1 mol of a substance in its standard state is formed from the elements in their standard states Standard free energy of formation of an element in its standard state is zero at K Standard free energy of formation of a compound can be calculated from the standard enthalpy of formation,  H º f, and from the standard entropy of formation,  S º f, using the definition of free energy:  G º f =  H º f – T  S º f

260 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Standard Free-Energy Change Using standard free energies of formation, the standard free energy of a reaction can be calculated by employing the “products minus reactants” rule:  G º rxn =  m  G º f (products) –  n  G º f (reactants), where m and n are the stoichiometric coefficients of each product and reactant in the balanced chemical equation The effect of temperature on the spontaneity of a reaction depends on the sign and magnitude of both  H º and  S º ; the temperature at which a given reaction is at equilibrium can be calculated by setting  G º = 0

261 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.6 Spontaneity and Equilibrium

262 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.6 Spontaneity and Equilibrium Three criteria have been identified for whether a given reaction will occur spontaneously 1.  S univ > 0 2.  G sys < 0 3.The relative magnitude of the reaction quotient Q versus the equilibrium constant K a. Q < K, reaction proceeds spontaneously to the right as written, resulting in the net conversion of reactants to products b. Q > K, reaction proceeds spontaneously to the left as written, resulting in the net conversion of products to reactants c. Q = K, system at equilibrium, no net reaction occurs

263 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Free Energy and the Equilibrium Constant Because  H º and  S º determine the magnitude of  G º and because the equilibrium constant K is a measure of the ratio of the concentrations of products to the concentrations of reactants, K can be expressed in terms of  G º and vice versa For a reversible process that does not involve external work, the change in free energy can be expressed in terms of volume, pressure, entropy, and temperature, eliminating  H from the equation for  G:  G = V  P – S  T and  G = V  P at constant temperature (  T = 0)

264 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Free Energy and the Equilibrium Constant Assuming ideal gas behavior in the equation  G = V  P, V can be replaced by nRT/P (where n is the number of moles of gas and R is the ideal gas constant).  G can be expressed in terms of the initial and final pressures (P 1 and P 2, respectively).  G = (nRT/P)  P = nRT(  P/P) = nRTln(P 2 /P 1 ) If the initial state is the standard state with P 1 = 1 atm, then the change in free energy upon going from the standard state to any other state with a pressure P can be written as G = G º + nRTlnP Using the hypothetical reaction aA + bB ⇋ cC + dD, in which all reactants and products are ideal gases and the lowercase letters correspond to the stoichiometric coefficients for the various species, the expression for  G can be written as  G =  G products –  G reactants

265 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Free Energy and the Equilibrium Constant Substituting G = G º + nRTlnP into the equation:  G = [(cG º C + cRTlnP C ) + (dG º D + dRTlnP D )] – [(aG º A + aRTlnP A ) + (bG º B + bRTlnP B )] Combining terms gives the following relationship between  G and the reaction quotient Q  G =  G º + RTln(P c C P d D /P a A P b B ) =  G º + RTlnQ where  G º indicates that all reactants and products are in their standard states For gases Q = K p at equilibrium, and for a system  G = 0 at equilibrium, so the relationship between  G º and K p for gases can be described as  G º = –RTlnK p

266 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Free Energy and the Equilibrium Constant If the products and reactants are in their standard states and  G º 1 and products are favored over reactants; if  G º > 0, then K p < 1 and reactants are favored over products; if  G º = 0, then K p = 1 and neither reactants nor products are favored and the system is at equilibrium K p is defined in terms of the partial pressures of reactants and products, and the equilibrium constant K is defined in terms of the concentrations of reactants and products; therefore, K p = K(RT)  n, where  n is the number of moles of gaseous product minus the number of moles of gaseous reactant For reactions where  n = 0, K p = K, so  G º = –RT ln K

267 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Free Energy and the Equilibrium Constant The following equation provides insight into how the components of  G º influence the magnitude of the equilibrium constant:  G º =  H º – T  S º = – RT ln K –K becomes larger as  S º becomes more positive, indicating that the magnitude of the equilibrium constant is directly influenced by the tendency of the system to move toward maximum disorder –K increases as  H º decreases, so the magnitude of the equilibrium constant is also directly influenced by the tendency of the system to seek the lowest energy state possible

268 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Temperature Dependence of the Equilibrium Constant The fact that  G º and K are related explains why equilibrium constants are temperature-dependent ln K = –  H º /RT +  S º /R Assuming  H º and  S º are temperature-dependent, for an exothermic reaction (  H º 0), the magnitude of K increases with increasing temperature The magnitude of  H º dictates how rapidly K changes as a function of temperature and the magnitude and sign of  S º affects the magnitude of K, but not its temperature dependence

269 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Temperature Dependence of the Equilibrium Constant If the value of K at a given temperature and the value of  H º for a reaction are known, the value of K can be estimated at any other temperature, even in the absence of information on  S º If K 1 and K 2 are the equilibrium constants for a reaction at temperatures T 1 and T 2, respectively, then ln K 2 – ln K 1 = ln K 2 /K 1 =  H º /R(1/T 1 – 1/T 2 )

270 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.7 Comparing Thermodynamics and Kinetics

271 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.7 Comparing Thermodynamics and Kinetics Thermodynamics –Deals with state functions and can be used to describe the overall properties, behavior, and equilibrium composition of a system –Provides a significant constraint on what can occur during a reaction process Kinetics –Concerned with the particular pathway by which physical or chemical changes occur, so it can address the rate at which a particular process will occur –Describes the detailed steps of what actually occurs on an atomic or molecular level

272 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.7 Comparing Thermodynamics and Kinetics The following table gives the numerical values of the equilibrium constant K that correspond to various values of  G º –If  G º  + 10 kJ/mol or  G º  –10 kJ/mol, an equilibrium is ensured to lie all the way to the left or to the right, respectively –If  G º is quite small (  10 kJ/mol), significant amounts of both products and reactants are present at equilibrium

273 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.7 Comparing Thermodynamics and Kinetics Most reactions have equilibrium constants greater than 1, with the equilibrium strongly favoring either products or reactants In many cases, reactions that are strongly favored by thermodynamics do not occur at a measurable rate, and reactions that are not thermodynamically favored do occur under certain nonstandard conditions A reaction that is not thermodynamically spontaneous under standard conditions can be made to occur spontaneously by varying reaction conditions, by using a different reaction to obtain the same product, by supplying external energy, or by coupling the unfavorable reaction to another reaction for which  G º << 0

274 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 18.8 Thermodynamics and Life

275 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 18.8 Thermodynamics and Life A living cell can be viewed as a low-entropy system that is not in equilibrium with its surroundings and is capable of replicating itself A constant input of energy is needed to maintain the cell’s highly organized structure and its intricate system of chemical reactions A cell needs energy to synthesize complex molecules from simple precursors, to create and maintain differences in the concentrations of various substances inside and outside of the cell, and to do mechanical work

276 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Energy Flow between the Cell and Its Surroundings A cell is an open system that can exchange matter with its surroundings as well as absorb energy from its environment in the form of heat or light Cells utilize the energy obtained to maintain the nonequilibrium state that is essential for life Nonequilibrium thermodynamics have been developed to quantitatively describe open systems such as living cells The only way a cell can maintain a low-entropy, nonequilibrium state characterized by a high degree of structural organization is to increase the entropy of the surroundings; a cell releases some of the energy it obtains from its environment as heat that is transferred to its surroundings, resulting in an increase in S surr

277 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Extracting Energy from the Environment Organisms can be divided into two categories 1.Phototrophs, whose energy source is light 2.Chemotrophs, whose energy source is chemical compounds, obtained by consuming or breaking down other organisms All organisms utilize oxidation-reduction, or redox, reactions to drive the synthesis of complex biomolecules –Organisms that can use only O 2 as the oxidant are aerobic organisms that can’t survive in the absence of O 2 –Many organisms that use other oxidants or oxidized organic compounds can live only in the absence of O 2 and are called anaerobic organisms

278 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Extracting Energy from the Environment Fundamental reaction by which all green plants and algae (phototrophs) obtain energy from sunlight is photosynthesis, the photochemical reduction of CO 2 to a reduced carbon compound One of the main processes chemotrophs use to obtain energy is respiration, which is the reverse of photosynthesis Some chemotrophs obtain energy by fermentation, in which both the oxidant and reductant are organic compounds

279 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Role of NADH and ATP in Metabolism Regardless of the identity of the substances from which an organism obtains energy, the energy must be released in very small increments if it is to be useful to the cell Cells store part of the energy that is released as ATP (adenosine triphosphate) Most organisms use a number of intermediate species to shuttle electrons between the terminal reductant and the terminal oxidant; intermediate species oxidizes the energy-rich reduced compound, and the now-reduced intermediate migrates to another site, where it is oxidized

280 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The most important of these electron-carrying intermediates is NAD +, whose reduced form is NADH The Role of NADH and ATP in Metabolism

281 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Energy from the oxidation of nutrients is made available to cells through the synthesis of ATP; its energy is used by the cell to synthesize substances through coupled reactions and to perform work For biochemical reactions, a new standard state has been defined in which the H + concentration is 1 x 10 –7 M (pH 7) and all other reactants and products are present in standard-state conditions (1 M or 1 atm) The free-energy change and equilibrium constant for a reaction under these new standard conditions are denoted by the addition of a prime sign (´) to the conventional symbol The Role of NADH and ATP in Metabolism

282 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Energy Storage in Cells All organisms use ATP as the immediate free-energy source in biochemical reactions, but ATP is not an efficient form in which to store energy on a long-term basis The body stores energy as sugars, proteins, and fats before using it to produce ATP

283 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19 Electrochemistry

284 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To distinguish between galvanic and electrolytic cells To predict spontaneous reactions using redox potentials To balance redox reactions using half-reactions To understand the relationship between cell potential and the equilibrium constant To be able to measure solution concentrations using cell potentials To describe how commercial galvanic cells operate To describe the process of corrosion To understand electrolysis and to be able to describe it quantitatively

285 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrochemistry In oxidation-reduction (redox) reactions, electrons are transferred from one species (the reductant) to another (the oxidant). Transfer of electrons provides a means for converting chemical energy to electrical energy, or vice versa. The study of the relationship between electricity and chemical reactions is called electrochemistry.

286 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.1 Describing Electrochemical Cells

287 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.1 Describing Electrochemical Cells Electrochemical process—electrons flow from one chemical substance to another, driven by an oxidation-reduction (redox) reaction Redox reaction – Occurs when electrons are transferred from a substance that is oxidized to one that is being reduced – Reductant is the substance that loses electrons and is oxidized in the process – Oxidant is the species that gains electrons and is reduced in the process

288 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.1 Describing Electrochemical Cells – Described as two half-reactions, one representing the oxidation process and one the reduction process Reductive half-reaction: Br 2 (aq) + 2e –  2Br – (aq) Oxidative half-reaction: Zn (s)  Zn 2+ (aq) + 2e – – Adding the two half-reactions gives the overall chemical reaction Zn (s) + Br 2 (aq)  ZnBr 2 (aq) – A redox reaction is balanced when the number of electrons lost by the reductant is equal to the number of electrons gained by the oxidant; overall process is electrically neutral – An electric current is produced from the flow of electrons from reductant to oxidant

289 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.1 Describing Electrochemical Cells Electrochemical cell – An apparatus that is used to generate electricity from a spontaneous redox or that uses electricity to drive a nonspontaneous redox reaction – There are two types of electrochemical cells 1. Galvanic cell (voltaic cell) — uses the energy released during a spontaneous redox reaction (  G < 0) to generate electricity 2. Electrolytic cell — consumes electrical energy from an external source, using it to cause a nonspontaneous redox reaction to occur (  G > 0)

290 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.1 Describing Electrochemical Cells

291 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.1 Describing Electrochemical Cells – Both types of cells contain two electrodes, which are solid metals connected to an external circuit that provides an electrical connection between systems – Oxidation half-reaction occurs at one electrode, the anode, and the reduction half-reaction occurs at the other, the cathode – When circuit is closed, electrons flow from the anode to the cathode; electrodes are connected by an electrolyte, which is an ionic substance or solution that allows ions to transfer between the electrodes, thereby maintaining the system’s electrical neutrality

292 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Galvanic (Voltaic) Cells To illustrate the basic principles of a galvanic cell –look at the reaction of metallic zinc with cupric ion (Cu 2+ ) to give copper metal and Zn 2+ ion Zn (s) + Cu 2+ (aq)  Zn 2+ (aq) + Cu (s) –a copper strip is inserted into a beaker that contains a 1 M solution of Cu 2+ ions, and a zinc strip is inserted into a different beaker that contains a 1 M solution of Zn 2+ ions –two metal strips serve as electrodes and are connected by a wire that allows electricity to flow; the compartments are connected by a salt bridge, a U-shaped tube inserted into both solutions and contains a concentrated liquid or gelled electrolyte to maintain electrical neutrality

293 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Galvanic (Voltaic) Cells –when the circuit is closed, a spontaneous reaction occurs: zinc metal is oxidized to Zn2+ ions at the zinc electrode (the anode), and Cu2+ ions are reduced to Cu metal at the copper electrode (the cathode) –as reaction progresses, the zinc strip dissolves and the concentration of Zn 2+ ions in the Zn 2+ solution increases; the copper strip gains mass and the concentration of Cu 2+ ions in the Cu 2+ solution decreases –electrons that are released at the anode flow through the wire, producing an electric current; galvanic cells transform chemical energy into electrical energy that can be used to do work –the electrolyte in the salt bridge serves two purposes: to complete the circuit by carrying electrical charge and to maintain electrical neutrality in both solutions by allowing ions to migrate between the two solutions

294 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Galvanic (Voltaic) Cells

295 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Galvanic (Voltaic) Cells –a voltmeter is used to measure the difference in electrical potential between the two compartments –the potential of the cell, measured in volts, is the difference in electrical potential between the two half-reactions; electrical potential is related to the energy needed to move a charged particle in an electric field –electrons from the oxidative half-reaction are released at the anode, so the anode in a galvanic cell is negatively charged; the cathode, which attracts electrons, is positively charged

296 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Constructing a Cell Diagram Because galvanic cells are cumbersome to describe in words, a line notation called a cell diagram has been developed In a cell diagram –the identity of the electrodes and the chemical contents of the compartments are indicated by their chemical formulas, with the anode written on the far left and the cathode on the far right; –phase boundaries are shown by single vertical lines; –the salt bridge, which has two phase boundaries, is shown by a double vertical line; Here’s a cell diagram for Zn/Cu cell: Zn(s)| Zn 2+ (aq, 1M) || Cu 2+ (aq, 1 M) | Cu(s) Anode Salt Bridge Cathode

297 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Constructing a Cell Diagram In a single-compartment galvanic cell, the voltage produced by a redox reaction can be measured more accurately using two electrodes immersed in a single beaker containing an electrolyte that completes the circuit; arrangement reduces errors caused by resistance to the flow of charge at a boundary, called the junction potential –Cell diagram does not include a double vertical line for the salt bridge (no salt bridge) and does not include solution concentrations Pt(s) | H 2 (g) | HCl(aq) | AgCl(s) | Ag(s)

298 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.2 Standard Potentials

299 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.2 Standard Potentials In a galvanic cell, current is produced when electrons flow externally through the circuit from the anode to the cathode because of a difference in potential energy between two electrodes in the electrochemical cell The flow of electrons in an electrochemical cell depends on the identity of the reacting substances, the difference in the potential energy of their valence electrons, the concentrations of the reacting species, and the temperature of the system

300 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.2 Standard Potentials The potential of the cell under standard conditions (1 M for solutions and 1 atm for gases, pure solids, or liquids for other substances) and at a fixed temperature (25ºC) is called the standard cell potential, E º cell –Used in order to develop a scale of relative potentials that will allow the prediction of the direction of an electrochemical reaction and the magnitude of the driving force for the reaction –Used to measure the potentials for oxidations and reductions of different substances under comparable conditions

301 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Measuring Standard Electrode Potentials Impossible to measure the potential of a single electrode; only the difference between the potentials of two electrodes can be measured Can compare the standard cell potentials for two different galvanic cells that have one kind of electrode in common—allows the measurement of the potential difference between two dissimilar electrodes All tabulated values of standard electrode potentials by convention are listed as standard reduction potentials in order to compare standard potentials for different substances

302 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Measuring Standard Electrode Potentials The standard cell potential is the reduction potential of the reductive half-reaction minus the reduction potential of the oxidative half-reaction (E º cell = E º cathode – E º anode ). The potential of the standard hydrogen electrode (SHE) is defined as 0 V under standard conditions. The potential of a half-reaction measured against the SHE under standard conditions is called the standard electrode potential for that half-reaction. The standard cell potential is a measure of the driving force for a given redox reaction. All E º values are independent of the stoichiometric coefficients for the half-reactions.

303 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Balancing Redox Reactions Using the Half-Reaction Method Redox reactions can be balanced using the half-reaction method, where the overall redox reaction is divided into an oxidation half-reaction and a reduction half-reaction, each one balanced for mass and charge The half-reactions selected from tabulated lists must exactly reflect reaction conditions

304 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Balancing Redox Reactions Using the Half-Reaction Method In an alternative method, the atoms in each half-reaction are balanced, and then the charges are balanced; one does not need to use the tabulated half-reactions; instead, focus on the atoms whose oxidation states change by using the following steps: 1.Write the reduction half-reaction and the oxidation half-reaction 2.Balance the atoms by balancing elements other than O and H; then balance O atoms by adding H 2 O, and balance H atoms by adding H + 3.Balance the charges in each half-reaction by adding electrons

305 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Balancing Redox Reactions Using the Half-Reaction Method 4.Multiply the reductive and oxidative half-reactions by appropriate integers to obtain the same number of electrons in both half-reactions 5.Add the two half-reactions and cancel substances that appear on both sides of the equation 6.Check to make sure that all atoms and charges are balanced

306 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Standard Cell Potentials The standard cell potential for a redox reaction, E º cell, is a measure of the tendency of the reactants in their standard states to form the products in their standard states—it is a measure of the driving force for the reaction (voltage) Calculations for the standard potential for the Zn/Cu cell represented by the cell diagram: Zn(s) | Zn 2+ (aq, 1 M || Cu 2+ (aq, 1M) | Cu(s) Cathode: Cu 2+ (aq) + 2e –  Cu(s) E º cathode = 0.34 V Anode: Zn(s)  Zn 2+ (aq, 1M) + 2e – E º anode = –0.76 V Overall: Zn(s) + Cu 2+ (aq)  Zn 2+ (aq) + Cu(s) E º cell = E º cathode – E º anode = 1.10 V

307 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Calculating Standard Cell Potentials If the value of E º cell (the standard cell potential) is positive, the reaction will occur spontaneously as written If the value of E º cell is negative, then the reaction is not spontaneous and it will not occur as written under standard conditions; it will proceed spontaneously in the opposite direction

308 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reference Electrodes and Measuring Concentrations When using a galvanic cell to measure the concentration of a substance, we are interested in the potential of only one of the electrodes of the cell, the indicator electrode, whose potential is related to the concentration of the substance being measured To ensure that any change in the measured potential of the cell is due to only the substance being analyzed, the potential of the other electrode, the reference electrode, must be constant Whether oxidation or reduction occurs depends on the potential of the sample versus the potential of the reference electrode

309 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reference Electrodes and Measuring Concentrations Types of reference electrodes 1. Standard hydrogen electrode (SHE)—consists of a strip of platinum wire in contact with an aqueous solution containing 1 M H +, which is in equilibrium with H 2 gas at a pressure of 1 atm at the Pt-solution interface 2. Silver-silver chloride electrode—consists of a silver wire coated with a thin layer of AgCl that is dipped into a chloride ion solution with a fixed concentration 3. Saturated calomel electrode (SCE)—consists of a platinum wire inserted into a moist paste of liquid mercury, Hg 2 Cl 2, and KCl

310 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reference Electrodes and Measuring Concentrations One of the most common uses of electrochemistry is to measure the H + ion concentration of a solution –A glass electrode is used for this purpose, in which an internal Ag/AgCl electrode is immersed in a 0.10 M HCl solution that is separated from the solution by a very thin glass membrane that absorbs protons –The extent of the adsorption on the inner side is fixed but the adsorption of protons on the outer surface depends on the pH of the solution

311 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Reference Electrodes and Measuring Concentrations Ion-selective electrodes –Used to measure the concentration of a particular species in solution; designed so that their potential depends on only the concentration of the desired species –Contains an internal reference electrode that is connected by a solution of an electrolyte to a crystalline inorganic material or membrane, which acts as the sensor

312 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.3 Comparing Strengths of Oxidants and Reductants

313 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The following table lists the standard potentials for a wide variety of chemical substances that allow us to compare the oxidative and reductive strengths of a variety of substances The half-reaction for the standard hydrogen electrode lies halfway down on the table –All species that lie above it in the table are stronger oxidants than H +, and all those that lie below it are weaker –All species that lie below H 2 are stronger reductants than H 2, and those that lie above H 2 are weaker 19.3 Comparing Strengths of Oxidants and Reductants

314 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Because the half-reactions in the table are arranged in order of their E º values, the table can be used to predict the relative strengths of various oxidants and reductants –Any species on the left side of a half-reaction will spontaneously oxidize any species on the right side of another half-reaction that lies below it in the table –Any species on the right side of one half-reaction will spontaneously reduce any species on the left side of another half-reaction that lies above it in the table 19.3 Comparing Strengths of Oxidants and Reductants

315 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.4 Electrochemical Cells and Thermodynamics

316 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Cell Potential and Free Energy Electrochemical cells convert chemical to electrical energy, and vice versa Total amount of energy produced by an electrochemical cell and the amount of energy available to do electrical work depends on both the cell potential and the total number of electrons that are transferred from the reductant to the oxidant during the course of the reaction Resulting electric current measured in coulombs (C), an S  unit that measures the number of electrons passing a given point in 1 s; coulomb defined as 6.25 x e – /s and relates electrical potential (in volts) to energy (in joules) 1J/1V = 1 coulomb = 6.25 x e – /s

317 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Cell Potential and Free Energy Electric current is measured in amperes (A); 1 ampere is defined as the flow of 1 coulomb per second past a given point (1C = 1A/s) In chemical reactions one must relate the coulomb to the charge on a mole of electrons; multiplying the charge on the electron by Avogadro’s number gives the charge on 1 mol of electrons, the faraday (F) F = ( x 10 –19 C) ( x /1 mol e – ) = x 10 4 C/mol e – = 96,485.5 J(V · mol e – ) Total charge transferred from the reductant to the oxidant is nF, where n is the number of moles of electrons

318 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Cell Potential and Free Energy The maximum amount of work that can be produced by an electrochemical cell, w max, is equal to the product of the cell potential, E cell, and the total charge transferred during the reaction, nF: w max = –nFE cell Work is expressed as a negative number because work is being done by the system on the surroundings  G is also a measure of the maximum amount of work that can be performed during a chemical reaction (  G = w max ; there must be a relationship between the potential of an electrochemical cell and the change in free energy,  G  G = –nFE cell A spontaneous redox reaction is characterized by a negative value of  G and a positive value of E cell

319 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Potentials for the Sums of Half-Reactions When the standard potential for a half-reaction is not available, the relationships between standard potentials and free energy can be used to obtain the potential of any other half-reaction that can be written as the sum of two or more half-reactions whose standard potentials are available Values of E º for half-reactions cannot be added to give E º for the sum of the half-reactions because E º is not a state function Because  G º is a state function, the sum of the  G values for the individual reactions gives  G º for the overall reaction, which is proportional to both the potential and the number of electrons (n) transferred

320 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Potentials for the Sums of Half-Reactions To obtain the value of E º for the overall half-reaction, the values of  G º (= –nFE º ) must be added for each half-reaction to obtain  G º for the overall half-reaction Substitute values into equation  G º = nFE º cell and solve for E º

321 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Cell Potential and the Equilibrium Constant Can use the relationship between  G º and the equilibrium constant K to obtain a relationship between E º cell and K For a general reaction of the type aA + bB  cC + dD, the standard free-energy change and the equilibrium constant are related by the equation  G º = –RTlnK Given the relationship between the standard free-energy change and the standard cell potential, the following equation can be written: –nFE º cell = –RTlnK

322 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Cell Potential and the Equilibrium Constant Rearranging the equation gives E º cell = (RT/nF)lnK For T = 298 K, the equation is simplified to E º cell = (RT/nF)lnK = [8.314 J/(mol·K)] (298 K) log K n[96,486 J/(V · mol)] = ( V/n)log K The standard cell potential, E º cell, is directly proportional to the logarithm of the equilibrium constant

323 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Relationship between Cell Potential and the Equilibrium Constant The following figure summarizes the relationships developed based on properties of the system (based on the equilibrium constant, standard free-energy change, and standard cell potential) and the criteria for spontaneity (  G º < 0)

324 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Effect of Concentration on Cell Potential: The Nernst Equation The actual free-energy change for a reaction under non- standard conditions,  G, is given by  G =  G º + RTln Q We also know that  G = –nFE cell and  G º = –nFE º cell, so substituting these expressions in the preceding equation gives –nFE cell = –nFE º cell + RT lnQ Dividing both sides of this equation by –nF gives the Nernst equation: E cell = E º cell – (RT/nF)lnQ The Nernst equation determines the spontaneous direction of any redox reaction under any reaction conditions from values of the relevant standard reduction potentials

325 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Effect of Concentration on Cell Potential: The Nernst Equation When a redox reaction is at equilibrium (  G = 0), the Nernst equation reduces to E º cell = (RT/nF)ln K because Q = K and there is no net transfer of electrons (E cell = 0) Substituting the values of the constants into the Nernst equation with T = 298 K and converting to base-10 logarithms gives the relationship of the actual cell potential (E cell ), the standard cell potential (E º cell ), and the reactant and product concentrations at room temperature (contained in Q): E cell = E º cell – ( V/n)logQ

326 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Effect of Concentration on Cell Potential: The Nernst Equation

327 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Concentration Cells A voltage can be generated by constructing an electrochemical cell in which each compartment contains the same redox active solution but at different concentrations; voltage is produced as the concentrations equilibrate An electrochemical cell in which the anode and cathode compartments are identical except for the concentration of a reactant is called a concentration cell Because  G = 0 at equilibrium, the measured potential of a concentration cell is zero at equilibrium

328 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Using Cell Potentials to Measure Solubility Products A galvanic cell can be used to measure the solubility product of a sparingly soluble substance Measure the solubility product of AgCl, K sp = [ Ag + ][Cl – ] –One compartment contains a silver wire inserted into a 1.0 M solution of Ag + –The other compartment contains a silver wire inserted into a 1.0 M Cl – solution saturated with AgCl –The potential due to the difference in [Ag + ] between the two cells can be used to determine K sp

329 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Using Cell Potentials to Measure Concentrations A galvanic cell can be used to calculate the concentration of a species given a measured potential and the concentrations of all the other species by using the Nernst equation

330 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.5 Commercial Galvanic Cells

331 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.5 Commercial Galvanic Cells Galvanic cells can be self-contained and portable and can be used as batteries and fuel cells 1.A battery (storage cell) is a galvanic cell (or a series of galvanic cells) that contains all the reactants needed to produce electricity. 2.A fuel cell is a galvanic cell that requires a constant external supply of one or more reactants in order to generate electricity.

332 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries Two basic kinds of batteries 1. Disposable, or primary, batteries in which the electrode reactions are effectively irreversible and which cannot be recharged 2. Rechargeable, or secondary, batteries, which form an insoluble product that adheres to the electrodes; can be recharged by applying an electrical potential in the reverse direction, which temporarily converts a rechargeable battery from a galvanic cell to an electrolytic cell Major difference between batteries and galvanic cells is that commercial batteries use solids or pastes rather than solutions as reactants to maximize the electrical output per unit mass

333 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries When a battery consists of more than one galvanic cell, the cells are connected in series—that is, with the positive (+) terminal of one cell connected to the negative (–) terminal of the next, and so on The overall voltage of the battery is the sum of the voltages of the individual cells

334 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries Leclanché dry cell –A “wet cell” in which the electrolyte is an acidic water-based paste containing MnO 2, NH 4 Cl, ZnCl 2, graphite, and starch –Used in flashlights, Walkmen, and GameBoys and is disposable –Cell not very efficient in producing electrical energy and has a limited shelf life –The alkaline battery is a Leclanché cell adapted to operate under alkaline, or basic, conditions; has a longer shelf life and more constant output voltage than the Leclanché dry cell

335 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries “Button” batteries –The anode is a zinc-mercury amalgam, and the cathode can be either HgO or Ag 2 O as the oxidant –Are reliable and have a high output-to-mass ratio, which allows them to be used in calculators, cameras, hearing aids, and watches, where their small size is crucial –Disposable

336 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries Lithium-iodine battery –Water-free battery –Consists of two cells separated by a metallic nickel mesh that collects charge from the anodes –The anode is lithium metal, and the cathode is a solid complex of  2 –Electrolyte is a layer of solid Li  that allows Li + ions to diffuse from the cathode to the anode –Highly reliable and long-lived –Used in cardiac pacemakers, medical implants, smoke alarms, and in computers –Disposable

337 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries

338 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries Nickel-cadmium (nicad) battery –Used in small electrical appliances and in devices like drills and portable vacuum cleaners –A water-based cell with a cadmium anode and a highly oxidized nickel cathode –This design maximizes the surface area of the electrodes and minimizes the distance between them, which gives the battery both a high discharge current and a high capacity –Lightweight, rechargeable, and high capacity but tend to lose capacity quickly and do not store well; also presents disposal problems because of the toxicity of cadmium

339 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries

340 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries Lead-acid (lead storage) battery –Provides the starting power in automobiles and boats; can be discharged and recharged many times –The anodes in each cell of this rechargeable battery are plates or grids of lead containing spongy lead metal, while the cathodes are similar grids containing powdered lead dioxide, PbO 2 –The electrolyte is an aqueous solution of sulfuric acid –The value of E º for such a cell is 2 V; connecting three cells in series produces a 6-V battery, and a typical 12-V car battery contains six of these cells connected in series

341 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Batteries

342 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Fuel Cells A galvanic cell that requires an external supply of reactants because the products of the reaction are continuously removed Does not store electrical energy but allows electrical energy to be extracted directly from a chemical reaction Have reliability problems and are costly Used in space vehicles

343 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.6 Corrosion

344 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.6 Corrosion Corrosion is a galvanic process by which metals deteriorate through oxidation, usually but not always to their oxides One of the most common techniques used to prevent corrosion is to apply a protective coating of another metal that is more difficult to oxidize Alternatively, a more easily oxidized metal can be applied to a metal surface, thus providing cathodic protection of the surface; galvanized steel is protected by a thin layer of zinc Sacrificial electrodes can also be attached to an object to protect it

345 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 19.7 Electrolysis

346 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 19.7 Electrolysis Galvanic cells — a spontaneous chemical reaction is used to generate electrical energy In an electrolytic cell, the opposite process, called electrolysis, occurs: an external voltage is applied to drive a nonspontaneous reaction

347 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrolytic Cells An electrochemical cell in which one electrode is copper metal immersed in a 1 M Cu 2+ solution and the other electrode is cadmium metal immersed in a 1 M Cd 2+ solution is set up, and then the circuit is closed –Cadmium electrode begins to dissolve (Cd is oxidized to Cd 2+ ) and thus is the anode, while metallic copper will be deposited on the copper electrode (Cu 2+ is reduced to Cu), which is the cathode –Overall reaction is thermodynamically spontaneous as written (  G º < 0); in this direction, the system is acting as a galvanic cell –The reverse reaction, the reduction of Cd 2+ by Cu, is thermodynamically nonspontaneous and will only occur with an input of an applied voltage

348 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrolytic Cells –Can force the reaction to proceed in the reverse direction by applying an electrical potential from an external power supply; applied voltage forces electrons through the circuit in the reverse direction, converting a galvanic cell to an electrolytic cell –The copper electrode is now the anode (Cu is oxidized) and the cadmium electrode is now the cathode (Cd 2+ is reduced) –Signs of the electrodes have changed to reflect the flow of electrons in the circuit

349 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrolytic Cells

350 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrolytic Cells Differences between galvanic and electrolytic cells

351 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrolytic Reactions At sufficiently high temperatures, ionic solids melt to form liquids that conduct electricity extremely well due to the high concentrations of ions Sodium metal is produced commercially by electrolysis of molten mixture of NaCl and CaCl 2 in a Downs cell The Hall-Heroult process is used to produce aluminum commercially by electrolysis of a molten mixture of aluminum oxide and cryolite Electrolysis can also be used to drive the thermodynamically nonspontaneous decomposition of water into its constituent elements, H 2 and O 2, by adding a small amount of an ionic solute to the water to make it electrically conductive

352 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electrolytic Reactions Overvoltages are needed in all electrolytic processes An overvoltage is an added voltage and represents the additional driving force required to overcome barriers such as a large activation energy and a junction potential

353 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Electroplating In a process called electroplating, a layer of a second metal is deposited on the metal electrode that acts as the cathode during electrolysis Electroplating is used to enhance the appearance of metal objects and protect them from corrosion

354 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Quantitative Considerations The amount of material consumed or produced in a reaction can be calculated from the stoichiometry of an electrolysis reaction, the amount of current passed, and the duration of the electrolytic reaction Charge (C) = current (A) X times(s) moles e – = charge (C) 96,486 C/mol (1 faraday) The stoichiometry can be used to determine the combination of current and time needed to produce a given amount of material

355 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 20 Nuclear Chemistry

356 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the factors that affect nuclear stability To know the different kinds of radioactive decay To be able to balance a nuclear reaction To be able to interpret a radioactive decay series To know the differences between ionizing and nonionizing radiation and their effects on matter To be able to identify natural and artificial sources of radiation To be able to calculate a mass-energy balance and a nuclear binding energy To understand the differences between nuclear fission and fusion To understand how nuclear reactors operate To understand how nuclear transmutation reactions led to the formation of the elements in the stars and how they can be used to synthesize transuranium elements

357 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Nuclear Reactions Differences between nuclear reactions and chemical processes 1.In a nuclear reaction, the identities of the elements change 2.Nuclear reactions are accompanied by the release of enormous amounts of energy 3.The yields and rates of a nuclear reaction are unaffected by changes in temperature, pressure, or the presence of catalysts

358 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 20.1 The Components of the Nucleus

359 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 20.1 The Components of the Nucleus Most of the known elements have at least one isotope whose atomic nucleus is stable indefinitely A great majority of elements also have isotopes that are unstable and disintegrate, or decay, at measurable rates by emitting radiation Some elements have no stable isotopes and eventually decay to other elements The process of nuclear decay is a nuclear reaction that results in changes inside the atomic nucleus

360 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Atomic Nucleus Each element can be represented by the notation Z X –A is the mass number, the sum of the numbers of protons and neutrons –Z is the atomic number, the number of protons –The protons and neutrons that make up the nucleus of an atom are called nucleons –An atom with a particular number of protons and neutrons is called a nuclide –Nuclides that have the same number of protons but different numbers of neutrons are called isotopes –The number of neutrons is equal to A – Z A

361 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Atomic Nucleus Isotopes of oxygen can be represented in any of these ways: A X: 16 O 17 O 18 O Z A X: 16 O 17 O 18 O Element-A: Oxygen-16 Oxygen-17 Oxygen-18 Isotopes of naturally occurring elements on Earth are present in nearly fixed proportions with each proportion constituting an isotope’s natural abundance

362 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The Atomic Nucleus Any nucleus that is unstable and decays spontaneously is said to be radioactive, emitting subatomic particles and electromagnetic radiation The emissions are collectively called radioactivity and can be measured Isotopes that emit radiation are called radioisotopes The rate at which radioactive decay occurs is characteristic of the isotope and is reported as a half-life (t ½ ), the amount of time required for half the initial number of nuclei present to decay in a first-order reaction

363 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Nuclear Stability The nucleus of an atom occupies a tiny fraction of the volume of the atom and contains the number of protons and neutrons that is characteristic of a given isotope Electrostatic repulsions would cause the positively charged protons to repel each other, but the nucleus does not fly apart because of the strong nuclear force, an extremely powerful but very short- range attractive force between nucleons All stable nuclei except the hydrogen-1 nucleus contain at least one neutron to overcome the electrostatic repulsion between protons

364 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Nuclear Stability As the number of protons in the nucleus increases, the number of neutrons needed for a stable nucleus increases even more rapidly; too many protons (or too few neutrons) in the nucleus result in an imbalance between forces, which leads to nuclear instability Relationship between the numbers of protons and neutrons in stable nuclei is shown in the following figure –The stable isotopes form a “peninsula of stability” in a “sea of instability” –Only three stable isotopes, 1 H, 3 He, and 4 He, have a neutron-to-proton ratio less than or equal to 1; all other stable nuclei have a higher neutron-to-proton ratio, which increases steadily to about 1.5 for the heaviest nuclei –All elements with Z > 83 are unstable and radioactive

365 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Nuclear Stability More than half of the stable nuclei have even numbers of both neutrons and protons; only 6 of the 279 stable nuclei do not have odd numbers of both Certain numbers of neutrons or protons result in especially stable nuclei; these are the so-called magic numbers 2, 8, 20, 50, 82, and 126 Nuclei with magic numbers of both protons and neutrons are said to be “doubly magic” and are even more stable

366 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Superheavy Elements In addition to the “peninsula of stability,” the preceding figure shows a small “island of stability” that exists in the upper right corner The island corresponds to the superheavy elements, with atomic numbers near the magic number of 126, and may be stable enough to exist in nature

367 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 20.2 Nuclear Reactions

368 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 20.2 Nuclear Reactions Two general kinds of nuclear reactions 1. Nuclear decay reaction (or radioactive decay) –An unstable nucleus emits radiation and is transformed into the nucleus of one or more other elements –Resulting daughter nuclei have a lower mass and are lower in energy (more stable) than the parent nucleus that decayed –Occur spontaneously under all conditions 2. Nuclear transmutation reaction –A nucleus reacts with a subatomic particle or another nucleus to form a product nucleus that is more massive than the starting material –Occur spontaneously only under special conditions

369 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Each of the three general classes of radioactive nuclei is characterized by a different decay process or set of processes 1.Neutron-rich nuclei –Have too many neutrons and have a neutron-to-proton ratio that is too high to give a stable nucleus –These nuclei decay by a process that converts a neutron to a proton, thereby decreasing the neutron-to-proton ratio 2.Neutron-poor nuclei –Have too few neutrons and have a neutron-to-proton ratio that is too low to give a stable nucleus –These nuclei decay by processes that convert a proton to a neutron, thereby increasing the neutron-to-proton ratio Classes of Radioactive Nuclei

370 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 3. Heavy nuclei –Heavy nuclei (with A  200) are intrinsically unstable, regardless of the neutron-to-proton ratio –All nuclei with Z > 83 are unstable –Decay by emitting an  particle, which decreases the number of protons and neutrons in the original nucleus by 2 –Since the neutron-to-proton ratio in an  particle is 1, the net result of alpha emission is an increase in the neutron-to-proton ratio Classes of Radioactive Nuclei

371 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Can use the number and type of nucleons present to write a balanced equation for a nuclear decay reaction –Procedure allows us to predict the identity of either the parent or daughter nucleus if the identity of only one is known –Regardless of the mode of decay, the total number of nucleons is conserved in all nuclear reactions, as is the total positive charge To describe nuclear decay reactions, the A X notation for nuclides has been extended to include radioactive emissions Nuclear Decay Reactions

372 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings The following table lists the name and symbol for each type of emitted radiation 1.The left superscript in the symbol for a particle gives the mass number, which is the total number of protons and neutrons –For a proton or a neutron, A = 1 –Because neither an electron nor a positron contains protons or neutrons, its mass number is 0 2.The left subscript gives the charge of the particle –Protons carry a positive charge, so Z = +1 for a proton –A neutron contains no protons and is electrically neutral, so Z = 0 –For an electron, Z = –1, and for a positron, Z = +1 –Because  rays are high-energy photons, both A and Z are 0 Nuclear Decay Reactions

373 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 3.In some cases, two different symbols are used for particles that are identical but produced in different ways –Symbol 0 e, simplified to e – represents a free electron or an electron associated with an atom –Symbol 0 , simplified to  – denotes an electron that originates from within the nucleus, which is a  particle – 4 He refers to the nucleus of a helium atom, and 4  is an identical particle ejected from a heavier nucleus Nuclear Decay Reactions 2 2

374 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings There are six fundamentally different kinds of nuclear decay reactions, each of which releases a different kind of particle or energy (see table) Nuclear Decay Reactions

375 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 1.Alpha decay –Nuclei with mass numbers greater than 200 undergo alpha decay, which results in the emission of a helium-4 nucleus as an  particle, 4  –The daughter nuclide contains two fewer protons and two fewer neutrons than the parent, thus  -particle emission produces a daughter nucleus with a mass number A that is lower by 4 and a nuclear charge Z that is lower by 2 than the parent nucleus A X A-4 X′ + 4  parent daughter αparticle Nuclear Decay Reactions 2 ZZ-2 → 2

376 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 2.Beta decay –Nuclei that contain too many neutrons undergo beta decay, in which a neutron is converted to a proton and a high- energy electron that is ejected from the nucleus as a  particle n p + 0 β unstable neutron proton retained beta particle emitted in nucleus by nucleus by nucleus –Beta decay does not change the mass number of the nucleus but results in an increase of +1 in the atomic number due to the addition of a proton in the daughter nucleus; beta decay decreases the neutron-to-proton ratio, moving the nucleus toward the band of stable nuclei A X A X′ + 0 β parent daughter  particle Nuclear Decay Reactions → → Z+1 1 Z 0 1 1

377 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 3.Positron emission –A positron has the same mass as an electron but opposite charge –Positron emission is the opposite of beta decay and is characteristic of neutron-poor nuclei which decay by the transformation of a proton to a neutron and a high-energy positron that is emitted 1 p  1 n + 0  –Positron emission does not change the mass number of the nucleus, however the atomic number of the daughter nucleus is lower by 1 than that of the parent. The neutron-to-proton ratio increases, moving nucleus closer to the band of stable nuclei A X  A X′ + 0  parent daughter positron Nuclear Decay Reactions Z-1 +1 Z

378 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 4.Electron capture –A neutron-poor nucleus can decay by either positron emission or electron capture (EC), in which an electron in an inner shell reacts with a proton to produce a neutron 1 p + 0 e  1 n –When a second electron moves from an outer shell to take the place of the lower-energy electron that was absorbed by the nucleus, an X-ray is emitted. The overall reaction for electron capture is A X + 0 e  A X’ + X-ray parent electron daughter –The mass number does not change, but the atomic number of the daughter nucleus is lower by 1 than that of the parent; neutron-to-proton ratio increases, moving the nucleus toward the band of stable nuclei Nuclear Decay Reactions 1 0 Z -1 Z

379 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 5.Gamma emission –Many nuclear decay reactions produce daughter nuclei that are in a nuclear excited state –A nucleus in an excited state releases energy in the form of a photon when it returns to the ground state –These high-energy photons are  rays –Gamma emission can occur instantaneously or after a significant delay –General formula A X*  A X + 0  –Because  rays are energy, their emission does not affect either the mass number or the atomic number of the daughter nuclide; gamma-ray emission is the only kind of radiation that does not involve the conversion of one element to another but is observed in conjunction with some other nuclear decay reaction Nuclear Decay Reactions Z 0 Z

380 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 6.Spontaneous fission –Only very massive nuclei with high neutron-to-proton ratios can undergo spontaneous fission, in which the nucleus breaks into two pieces that have different atomic numbers and atomic masses –Process most important for trans-actinide elements with Z  104 –Spontaneous fission is accompanied by the release of large amounts of energy and is accompanied by the emission of several neutrons –The number of nucleons is conserved; the sum of the mass numbers of the products equals the mass number of the reactant; the sum of the atomic numbers of the products is the same as the atomic number of the parent nuclide Nuclear Decay Reactions

381 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Impossible for any nuclide with Z > 85 to decay to a stable daughter nuclide in a single step, except via nuclear fission Radioactive isotopes with Z > 85 usually decay to a daughter nucleus that is radioactive, which in turn decays to a second radioactive daughter nucleus, and so forth, until a stable nucleus finally results This series of sequential alpha- and beta-decay reactions is called a radioactive decay series Radioactive Decay Series

382 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Some nuclei spontaneously transform into nuclei with a different number of protons, producing a different element These naturally occurring radioactive isotopes decay by emitting subatomic particles Should be possible to carry out the reverse reaction, converting a stable nucleus to another more massive nucleus by bombarding it with subatomic particles in a nuclear transmutation reaction Induced Nuclear Reactions

383 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Uranium (Z = 92) is the heaviest naturally occurring element; all the elements with Z > 92, the transuranium elements, are artificial and have been prepared by bombardment of suitable target nuclei with smaller particles Bombarding the target with more massive nuclei creates elements that have atomic numbers greater than that of the target nucleus Accelerating positively charged particles to the speeds needed to overcome the electrostatic repulsions between them and the target nuclei requires a device called a particle accelerator, which uses electrical and magnetic fields to accelerate the particles Synthesis of Transuranium Elements

384 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Types of particle accelerators 1.The linear accelerator is the simplest particle accelerator in which a beam of particles is injected at one end of a long evacuated tube; rapid alternation of the polarity of the electrodes along the tube causes the particles to be alternately accelerated toward a region of opposite charge and repelled by a region with the same charge, resulting in a tremendous acceleration as the particle travels down the tube. 2.A cyclotron achieves the same outcome in less space and forces the charged particles to travel in a circular path; particles are injected into the center of a ring and accelerated by rapidly alternating the polarity of two large D-shaped electrodes above and below the ring, which accelerates the particles outward along a spiral path toward the target. Synthesis of Transuranium Elements

385 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 3.The synchrotron is a hybrid of the previous two designs and contains an evacuated tube similar to that of the linear accelerator, but the tube is circular and can be more than a mile in diameter; charged particles are accelerated around the circle by a series of magnets whose polarities rapidly alternate. Synthesis of Transuranium Elements

386 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Chemistry: Principles, Patterns, and Applications, 1e 20.3 The Interaction of Nuclear Radiation with Matter

387 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings Nuclear reactions do not cause chemical reactions directly. The particles and photons emitted during nuclear decay are very energetic, and they can indirectly produce chemical changes in the matter surrounding the nucleus that has decayed The Interaction of Nuclear Radiation with Matter