2 CHAPTER OBJECTIVESTo understand the factors that affect the rate of chemical reactionsTo be able to determine a reaction rateTo understand the meaning of a rate lawTo be able to determine the concentration dependence of the rate of a chemical reactionTo be able to predict the individual steps of a simple reactionTo begin to understand why chemical reactions occur
3 Chemistry: Principles, Patterns, and Applications, 1e 14.1 Factors That Affect Reaction Rates
4 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 factors1. Reactant concentrations2. Temperature3. Physical states and surface areas of reactants4. Solvent and catalyst properties
5 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 Temperature EffectsIncreasing 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 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 Solvent EffectsThe 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 Catalyst EffectsCatalyst 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 Chemistry: Principles, Patterns, and Applications, 1e 14.2 Reaction Rates and Rate Laws
11 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 rates1. 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 Reaction Rates • 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 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 = t0) and at the end of the interval (tf).– 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 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 tThis can also be expressed in terms of the reactant or product with the smallest coefficient in the balanced equationrate = – [sucrose] / t = ¼([ethanol] /t).
15 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 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 Rate Laws • Rate law must give the proper units for the rate, M/s 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 Rate Laws • Reaction orders – For a reaction with the general equation aA + bB cC + dD,the experimentally determined rate law has the formrate = k[A]m [B]n.– The proportionality constant, k, is called the rate constant.1. Value is characteristic of the reaction and reaction conditions2. A given reaction has a particular value of the rate constant under a given set of conditions, such as temperature, pressure, and solvent
19 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 Chemistry: Principles, Patterns, and Applications, 1e 14.3 Methods of Determining Reaction Orders
21 Zeroth-Order Reactions – 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 0rate = – [A] = k[reactant]0 = k(1) = kt– 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
22 Zeroth-Order Reactions – 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
23 First-Order Reactions – 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 israte = – [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
24 First-Order Reactions – Integrated rate law for a first-order reaction can be written in two different ways, one using exponentials and one using logarithms1. Exponential form, [A] = [A]0e–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 time2. 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
25 Second-Order Reactions • Two kinds of second-order reactions1. 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]22t– Doubling the concentration of A quadruples the rate of the reaction– Units of rate constant is M–1s–1 or L/mols– 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
26 Second-Order Reactions 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 israte = – [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
27 Determining the Rate Law of a Reaction • 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 equationrate = k[A]m [B]n.• Rate data is given in the following table:
28 Determining the Rate Law of a Reaction • 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 A2. 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 varied3. 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 changed4. Determine reaction orders by taking the quotient of the rate laws for two different experiments
29 Determinin the Rate Law of a Reaction 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 14.4.rate1 = k[A1]m [B1]nrate3 = k[A3]m [B3]n6. 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 n7. Calculate the rate constant by inserting data from any line from the table into the experimentally determined rate law and solve for k
30 Chemistry: Principles, Patterns, and Applications, 1e 14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders
31 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 14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders
33 Chemistry: Principles, Patterns, and Applications, 1e 14.5 Half-Lives and Radioactive Decay Kinetics
34 Half-LivesAnother 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 t½ .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 Half-LivesThe 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 t½ for t (to indicate a half-life) into the above equation gives [A]0[A]0 /2• Solving for t½: t½ = 0.693/k• For a first-order reaction, each successive half-life is the same length of time and is independent of [A].ln= ktln= ln 2 = kt½
36 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 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/tActivity 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 = kNk 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 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 lawN = N0e–kt or ln N/N0 = – kt
39 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 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 14CO2.• The CO2 that plants use as a carbon source include a proportion of 14CO2 molecules as well as nonradioactive 12CO2 and 13CO2; animals that eat plants ingest these carbon isotopes.
41 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: 14C 14N + – with a half-life of 5700 ± 30 yr.• The 14C/ 12C 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 Chemistry: Principles, Patterns, and Applications, 1e 14.6 Reaction Rates—A Microscopic View
43 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 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 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 NO2 + NO2 NO3 + NO Elementary reactionStep 2 NO3 + CO NO2 + CO Elementary reactionSum NO2 + CO NO + CO Overall reaction• NO3 is an intermediate in the reaction.
46 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 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 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 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 Chemistry: Principles, Patterns, and Applications, 1e 14.7 The Collision Model of Chemical Kinetics
51 14.7 The Collision Model of Chemical Kinetics A useful tool for understanding the behavior of reacting chemical speciesThe 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 Activation EnergyA minimum energy (activation energy, Ea) 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 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.Ea 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 Ea will occur more rapidly.
54 Graphing the Energy Changes during a Reaction Even when the energy of collisions between two reactant species is greater than Ea, 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 The Arrhenius Equation In the following figure, both the kinetic energy distributions and a potential energy diagram for a reaction are shown
56 The Arrhenius Equation – Shaded areas show that at the lower temperature, only a small fraction of molecules collide with kinetic energy greater than Ea; at the higher temperature, a much larger fraction of molecules collide with kinetic energy greater than Ea– 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 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 > Ea) 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 secondk = Ae–Ea /RT (Arrhenius equation)
58 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 Ea indicates the sensitivity of the reaction to changes in temperature.The rate of a reaction with a large Ea increases rapidly with increasing temperature, and the rate of a reaction with a smaller Ea increases much more slowly with increasing temperature.
59 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 + (–Ea /RT) = ln A + [(–Ea /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 –Ea /R and an intercept of ln A.• Knowing the value of Ea at one temperature predicts the rate of a reaction at other temperatures.
60 Chemistry: Principles, Patterns, and Applications, 1e 14.8 Catalysis
61 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 Ea, 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 Ea, the rate of a catalyzed reaction is faster than the rate of the uncatalyzed reaction at the same temperature
63 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 catalysts1. Heterogeneous catalysts2. Homogeneous catalysts3. Enzymes
64 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 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 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 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.
69 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 reactionsTo be able to write an equilibrium constant expression for any reactionTo be able to solve quantitative problems involving chemical equilibriumTo predict the direction of reactionTo predict the effects of stresses on a system at equilibriumTo understand different ways to control the products of a reaction
70 Chemistry: Principles, Patterns, and Applications, 1e 15.1 The Concept of Chemical Equilibrium
71 15.1 The Concept of 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 Chemistry: Principles, Patterns, and Applications, 1e 15.2 The Equilibrium Constant
73 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 = kf /kr.• 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 Developing an Equilibrium Constant Expression • In1864, Guldberg and Waage discovered that for any reversible reaction of the general formaA + 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 Developing an Equilibrium Constant Expression • Law of mass action is stated asK = [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 Developing an Equilibrium Constant Expression • Equilibrium constant (K)– Can vary over a wide range of values and is unitless– Values of K greater than 103 indicate a strong tendency for reactants to form products, so equilibrium lies to the right, favoring the formation of products (kf >>kr)– 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 (kf<<kr)– Values of K between 103 and 10–3 are not very large or small, so there is no strong tendency to form either products or reactants; at equilibrium, there are significant amounts of both products and reactants (kf kr)
78 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 + bBK and the equilibrium constant expression are inverted:K´= [A]a [B]b[C]c [D]dso K´ = 1/K
79 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 Kp 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.(PA)c (PC)d(PB)a (PD)bKp =
80 Equilibrium Constant Expressions for Systems that Contain Gases • Kp 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 temperatureKp = K(RT)nwhere 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, Kp = K
81 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 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 Chemistry: Principles, Patterns, and Applications, 1e 15.3 Solving Equilibrium Problems
84 15.3 Solving Equilibrium Problems Two fundamental kinds of equilibrium problems1. Those in which the concentrations of the reactants and products at equilibrium are given and the equilibrium constant for the reaction needs to be calculated2. 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
85 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 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 Chemistry: Principles, Patterns, and Applications, 1e 15.4 Nonequilibrium Conditions
88 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 timeTo make this determination, one needs to know how to analyze the composition of a reaction mixture quantitatively
89 The 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– Qp can be written for any reaction that involves gases by using the partial pressures of the components
90 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 changed2. 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 reactants3. 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
92 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 Chemistry: Principles, Patterns, and Applications, 1e 15.5 Factors That Affect Equilibrium
94 15.5 Factors That Affect Equilibrium Strategies are used to increase the yield of the desired products of reactionsReaction conditions are controlled to obtain the maximum amount of the desired productChanges in reaction conditions affect the equilibrium composition of a system
95 Le Châtelier’s Principle • When a system at equilibrium is perturbed in some way, the effects of the perturbation can be predicted qualitatively using Le Châtelier’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.
96 Le Châtelier’s Principle • Three types of stresses can change the composition of an equilibrium mixture1. A change in the concentrations (or partial pressures) of the components by the addition or removal of reactants or products2. A change in the total pressure or volume3. A change in the temperature of the system
97 Changes in Concentration • An equilibrium is disturbed by adding or removing a reactant or product1. Stress of an added reactant or product is relieved by reaction in the direction that consumes the added substancea. Add reactant—reaction shifts right toward productb. Add product—reaction shifts left toward reactant2. Stress of removing reactant or product is relieved by reaction in the direction that replenishes the removed substancea. Remove reactant—reaction shifts leftb. Remove product—reaction shifts right
98 Changes in Concentration • Changes that occur due to changes in the value of Qc1. Add reactant—denominator in Qc expression becomes largerA. Qc < KcB. To return to equilibrium, Qc must increaseI. Numerator of Qc expression must increase andthe denominator must decreaseII. Implies net conversion of reactants toproducts; reaction shifts right
99 Changes in Concentration 2. Remove reactant—denominator in Qc expression becomes smallerA. Qc > KcB. To return to equilibrium, Qc must decreaseI. Numerator of Qc expression must decrease andthe denominator must increaseII. Implies net conversion of products to reactants;reaction shifts left
100 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 Changes in Total Pressure or Volume • Changes occur due to changes in the value of Qc1. Decrease volume—molarity increases2. If reactant side has more moles of gasa. Increase in denominator is greater than increase in numerator and Qc < Kcb. To return to equilibrium, Qc must increase; the numerator of the Qc expression must increase and denominator must decrease—it shifts toward fewer moles of gas (reactants to products)
102 Changes in Total Pressure or Volume 3. If product side has more moles of gasa. Increase in numerator is greater than increase in denominator and Qc > Kcb. To return to equilibrium, Qc must decrease; the denominator of the Qc 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 Changes in Temperature • 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, Hrxn1. Exothermic (heat is released, H < 0): reactants ⇋ products + heat2. Endothermic (heat is absorbed, H > 0): reactants + heat ⇋ products
104 Changes in Temperature • 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 predicts1. 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 Hrxn = 0, then a change in temperature will not affect the equilibrium composition.
105 • Value of Kc Changes in Temperature 1. Increasing the temperature increases the magnitude of the equilibrium constant for an endothermic reaction2. Increasing the temperature decreases the equilibrium constant for an exothermic reaction3. Increasing the temperature has no effect on the equilibrium constant for a thermally neutral reaction
106 Chemistry: Principles, Patterns, and Applications, 1e 15.6 Controlling the Products of Reactions
107 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 approaches1. 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.
109 CHAPTER OBJECTIVESTo understand the autoionization reaction of liquid waterTo know the relationship among pH, pOH, and pKwTo understand the concept of conjugate acid-base pairsTo know the relationship between acid or base strength and the magnitude of Ka, Kb, pKa, and pKbTo understand the leveling effectTo be able to predict whether reactants or products are favored in an acid-base equilibriumTo understand how molecular structure determines acid and base strengthsTo be able to use Ka and Kb values to calculate the percent ionization and pH of a solution of an acid or a base
110 CHAPTER OBJECTIVESTo be able to calculate the pH at any point in an acid-base titrationTo understand how the addition of a common ion affects the position of an acid-base equilibriumTo understand how a buffer works and how to use the Henderson-Hasselbalch equation to calculate the pH of a buffer
111 Chemistry: Principles, Patterns, and Applications, 1e 16.1 The Autoionization of Water
112 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 water2. 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
114 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, H3O+Structure of the water molecule1. Polar O–H bonds and two lone pairs of electrons on the oxygen atom2. Liquid water has a highly polar structure
115 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 H3O+ ion in an autoionization process:2H2O(l)⇋H3O+ (aq) + OH– (aq)• Equilibrium constant K for this reaction can be written asK = [H3O+] [OH–][H2O]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: [H3O+] = [OH–] = x 10–7 M• At 25ºC, the density of liquid water is g/mL
116 The Ion-Product Constant of Liquid Water The concentration of liquid water at 25ºC is[H2O] = 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 [H2O] as a constant, a new equilibrium constant, the ion-product constant of liquid water (Kw), can be defined:K[H2O]2 = [H3O+] [OH–] or Kw = [H3O+] [OH–]• Substituting the values for [H3O+] and [OH–] at 25ºC gives Kw = (1.003 x 10–7) (1.003 x 10–7) = x 10–14
117 The Ion-Product Constant of Liquid Water • Kw 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 [H3O+] > [OH–], the solution is acidic• If [H3O+] < [OH–], the solution is basic
118 The Relationship among pH, pOH, and pKw • The pH scale is a concise way of describing the H3O+ concentration and the acidity or basicity of a solution• pH and H+ concentration are related as follows:pH = –log10[H+] or [H+] = 10–pH• pH of a neutral solution ([H3O+] = 1.00 x 10–7 M) is 7.00• pH of an acidic solution is < 7, corresponding to [H3O+] > 1.00 x 10–7• pH of a basic solution is > 7, corresponding to [H3O+] < 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 The Relationship among pH, pOH, and pKw • There is an analogous pOH scale to describe the hydroxide ion concentration of a solution; pOH and [OH–] are related as follows:pH = –log10[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 = 14.00pKw = –log Kw = –log([H3O+] [OH–]) =(–log[H3O+]) + (–log[OH–]) = pH + pOH• At any temperature, pH + pOH = pKw, and at 25ºC, where Kw = 1.01 x 10–14, pH + pOH = 14.00; pH of any neutral solution is just half the value of pKw at that temperature
120 Chemistry: Principles, Patterns, and Applications, 1e 16.2 A Qualitative Description of Acid-Base Equilibria
121 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 HA2. 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 H3O+, forming H2O and HCl; H3O+ and H2O constitute a second conjugate acid-base pair.
122 Conjugate Acid-Base Pairs • Any acid-base reaction must contain two conjugate acid-base pairs, which in this example are HCl/Cl– and H3O+/H2O• HCl (aq) H2O (l) H3O+ (aq) + Cl– (aq)parent acid parent base conjugate acid conjugate base
123 Acid-Base Equilibrium Constants: Ka, Kb, pKa, and pKb • 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) + H2O(l) ⇋ H3O+(aq) + A–(aq)• The equilibrium constant for this dissociation isK = [H3O+] [A–][H2O] [HA]• The concentration of water is constant for all reactions in aqueous solution, so [H2O] can be incorporated into a new quantity, the acid ionization constant (Ka):Ka = K[H2O] = [H3O+] [A–][HA]
124 Acid-Base Equilibrium Constants: Ka, Kb, pKa, and pKb • Numerical values of K and Ka differ by the concentration of water (55.3 M); the larger the value Ka, the stronger the acid and the higher the H+ concentration at equilibrium• Weak bases react with water to produce the hydroxide ion, B(aq) + H2O(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 (Kb); concentration of water is constant and does not appear in the equilibrium constant expression but is included in the value of Kb• The larger the value of Kb, the stronger the base and the higher the OH– concentration at equilibrium
125 Acid-Base Equilibrium Constants: Ka, Kb, pKa, and pKb • The sum of the reactions described by Ka and Kb is the equation for the autoionization of water, and the product of the two equilibrium constants is Kw• For any conjugate acid-base pair, KaKb = Kw• pKa = –log10Ka and pKb = –log10Kb• Smaller values of pKa correspond to larger acid ionization constants and stronger acids• Smaller values of pKb correspond to larger base ionization constants and stronger bases• At 25ºC, pKa + pKb = 14.00
126 Acid-Base Equilibrium Constants: Ka, Kb, pKa, and pKb • 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 basestronger acid + stronger base weaker acid + weaker base• In an acid-base reaction, the proton always reacts with the stronger base
127 Solutions of Strong Acids and Bases: The Leveling Effect • No acid stronger than H3O+ 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 (H3O+) is leveled to the strength of H3O+ in aqueous solution because H3O+ 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 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 pKa increases.• The strengths of the conjugate acids and bases are related by pKa + pKb = pKw, and equilibrium favors formation of the weaker acid-base pair.
129 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 Chemistry: Principles, Patterns, and Applications, 1e 16.3 Molecular Structure and Acid-Base Strength
131 Bond StrengthsThe 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.
132 Stability of the Conjugate Base 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.
133 Inductive EffectsAtoms 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.
134 Chemistry: Principles, Patterns, and Applications, 1e 16.4 Quantitative Aspects of Acid-Base Equilibria
135 Determining Ka and KbThe ionization constants Ka and Kb 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 Determining Ka and Kb– The extent of the reaction depends on the value of Ka or Kb, 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 Determining Ka and Kb– 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 Ka or Kb.– Two common ways to obtain the concentrations1. By measuring the electrical conductivity of the solution, which is related to the total concentration of ions present2. By measuring the pH of the solution, which gives [H+] or [OH–]
138 Determining Ka and Kb• Procedure for determining Ka for a weak acid and Kb for a weak base1. The analytical concentration of the acid or base is the initial concentration2. The stoichiometry of the reaction with water determines the change in concentrations3. The final concentrations of all species are calculated from the initial concentrations and the changes in the concentrations4. Inserting the final concentration into the equilibrium constant expression enables the value of Ka or Kb to be calculated
139 Calculating Percent Ionization from Ka or Kb • 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 aspercent ionization of acid = [H+]CHApercent ionization of base = [OH–] CBx 100x 100
140 Calculating Percent Ionization from Ka or Kb • To determine the concentrations of species in solutions of weak acids and bases, use a tabular method1. Make a table that lists the following values for each of the species involved in the reactiona. Initial concentrationb. The change in concentration on preceding to equilibrium(–x or +x)c. The final concentration—sum of the initial concentration and the change in concentrationd. In constructing the table, define x as the concentration of the acid that dissociates2. Solve for x by substituting the final concentrations from the table into the equilibrium constant expression
141 Calculating Percent Ionization from Ka or Kb 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[H3O+]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 Calculating Percent Ionization from Ka or Kb • 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 Ka and Kb increases
143 Determining Keq from Ka and Kb • The value of the equilibrium constant for the reaction of a weak acid with a weak base can be calculated from Ka (or pKa), Kb (or pKb), and Kw• 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 Kw
144 Determining Keq from Ka and Kb • Calculations1. Write the dissociation reactions for a weak acid and a weak base and then sum them:Acid HA ⇋ H+ + A– KaBase B + H2O ⇋ HB+ + OH– KbSum HA + B + H2O ⇋ H+ + A– + HB+ + OH– Ksum = KaKb2. 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– ⇋ H2O), for which K = 1/Kw, to the overall reaction and cancelingHA + B + H2O ⇋ H+ + A– + HB+ + OH– Ksum = KaKbH+ + OH– ⇋ H2O /KwHA + B ⇋ A– + HB K = (KaKb)/Kw
145 Chemistry: Principles, Patterns, and Applications, 1e 16.5 Acid-Base Titrations
146 16.5 Acid-Base TitrationsIn 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 Titrations of Strong Acids and Bases Before addition of any strong base, the initial [H3O+] 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 [H3O+] because added base neutralizes some of the H3O+ 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 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 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)aVbMb = VaMa
150 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 Ka or Kb.
151 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 pKa 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 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 base1. 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 acid2. pH changes more rapidly during the first part of the titration in a weak acid and strong base titration3. 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 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 pKa of the acid being titrated5. 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 ofwhether the acid is weak or strong
154 Titrations of Weak Acids and Bases Calculating the pH of a solution of aweak acid or base– If Ka or Kb 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 Titrations of Weak Acids and Bases Calculating the pH during titration of aweak acid or base– Solved in two steps: a stoichiometric calculation followed by an equilibrium calculation1. Use stoichiometry of the neutralization reaction to calculate the amounts of acid and conjugate base present in solution after the neutralization reaction has occurred2. Use the equilibrium equation K = [H3O+] [A–] / [H2O] [HA] to determine [H+] of the resulting solution
156 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 pKa or pKb shows that as the acid or base being titrated becomes weaker (its pKa or pKb becomes larger), the pH change around the equivalence point decreases significantly.
157 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 pKa of the weak acid.
158 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 forth2. If the pKa values are separated by at least three pKa units, then the overall titration curve shows well-resolved “steps” corresponding to the titration of each proton
160 IndicatorsMost 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 titrantInstead, 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 titrationAcid-base indicators are typically weak acids or bases whose changes in color correspond to deprotonation or protonation of the indicator itself
162 IndicatorsThe chemistry of indicators are described by the general equation Hn(aq) ⇋ H+ (aq) + n–(aq), where the protonated form is designated by Hn and the conjugate base by n–The ionization constant for the deprotonation of indicator Hn is Kin = [H+] [n–] / [Hn]The value of pKin determines the pH at which the indicator changes color
163 Indicators • A good indicator must have the following properties: 1. Color change must be easily detected2. Color change must be rapid3. Indicator molecule must not react with the substance being titrated4. The indicator should have a pKin 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 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 pKin between 4 and 10 will do2. 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 pKin > 7, should be used3. 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 pKin < 7, should be used
166 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 Chemistry: Principles, Patterns, and Applications, 1e 16.6 Buffers
168 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 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 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
172 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 pKa or pKb 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 isKa = [H+] [A–] or [H+] = Ka[HA][HA] [A–]
173 Calculating the pH of a Buffer • Taking the logarithm of both sides and multiplying both sides by –1 gives–log[H+] = –logKa – log([HA]/[A–]) = – logKa + log([A–]/[HA])• Replacing the negative logarithms givespH = pKa + log([A–]/[HA]) or pH = pka + 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 Ka’s
174 Calculating the pH of a Buffer • Three special cases where the Henderson-Hasselbalch equation is interpreted without the need for calculations1. [base] = [acid]. Under these conditions, [base]/[acid] = 1. Because log 1 = 0, pH = pKa, 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 = pKa + 13. [base]/[acid] = 100. Because log 100 = 2, pH = pKa+ 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 = pKa – 1, so each additional factor-of-10 decrease in the [base]/[acid] ratio causes the pH to decrease by one pH unit
175 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 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 pKa 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 pKa to a pH value of one unit greater than the pKa ; that is why buffer solutions have a pH that is within ±1 pH units of the pKa of the acid component of the buffer;
177 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 Ka;– 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 Kb.
178 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 CO2/HCO3– system, which dominates the buffering action of blood plasma.
180 CHAPTER OBJECTIVESTo be able to calculate the solubility of an ionic compound from its KspTo understand the factors that determine the solubility of ionic compoundsTo be able to describe complex-ion formation quantitativelyTo understand why the solubility of many compounds depends on pHTo know how to separate metal ions by selective precipitation
181 Chemistry: Principles, Patterns, and Applications, 1e 17.1 Determining the Solubility of Ionic Compounds
182 The Solubility Product, Ksp 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, Ksp.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.Ksp is defined in terms of molar concentrations of the component ions.
183 The Ion ProductThe 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 Ksp 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 The Ion ProductThree possible conditions for an aqueous solution of an ionic solid1. Q < Ksp: the solution is unsaturated, and more of the ionic solid will dissolve2. Q = Ksp: the solution is saturated and at equilibrium3. Q > Ksp: the solution is supersaturated, and ionic solid will precipitate
185 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– Ksp is constant
186 The Common Ion Effect and Solubility – 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 Chemistry: Principles, Patterns, and Applications, 1e 17.2 Factors That Affect Solubility
188 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 formation2. Incomplete dissociation of molecular solutes3. Formation of complex ions4. Changes in pH
189 Ion-Pair Formation• An ion pair consists of a cation and anion that are in intimate contact in solution, rather than separated by solvent.
190 Ion-Pair Formation• 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).
191 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 (Ca2+ ·SO42–).– 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 M2+ and M3+ ions; it is unimportant for salts that contain monocations.
192 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
194 Chemistry: Principles, Patterns, and Applications, 1e 17.3 Complex-Ion Formation
195 17.3 Complex-Ion Formation 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.
196 The Formation Constant The equilibrium constant for the formation of the complex ion from the hydrated ion is called the formation constant (Kf).Equilibrium constant expression for Kf has the same general form as any other equilibrium constant expression.The larger the value of Kf, the more stable the product.
197 The Effect of Complex-Ion Formation on Solubility 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.
198 Chemistry: Principles, Patterns, and Applications, 1e 17.4 Solubility and pH
199 17.4 Solubility and pHSolubility 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 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) Ksp = [M+] [A–]– The anion can also react with water in a hydrolysis reaction:A–(aq) + H2O(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 = Ksp
201 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 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 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 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 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 Mn+ cations and O2– 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 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 Chemistry: Principles, Patterns, and Applications, 1e 17.5 Qualitative Analysis Using Selective Precipitation
208 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 17.5 Qualitative Analysis Using Selective Precipitation
210 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 precipitation1. Group 1: Insoluble chlorides– Metal chloride salts are soluble in water; only Ag+, Pb2+, and Hg22+ form chlorides that precipitate from water– First step in qualitative analysis is to add 6 M HCl, causing AgCl, PbCl2, and/or Hg2Cl2 to precipitate; precipitate is collected by filtration or centrifugation
211 17.5 Qualitative Analysis Using Selective Precipitation 2. Group 2: Acid-insoluble sulfides– Acidic solution is saturated with H2S– 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 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 (NH4)2 S is added– Treatment removes any remaining cations that form insoluble hydroxides or sulfides4. Group 4: Insoluble carbonates or phosphates– The next metal ions to be removed are those that form insoluble carbonates and phosphates
213 17.5 Qualitative Analysis Using Selective Precipitation 5. Group 5: Alkali metalsAll the metal ions that form water-insoluble chlorides, sulfides, carbonates, or phosphates have been removedOnly common ions that remain are the alkali metals and ammoniumTake a second sample from the original solution and add a small amount of NaOH to neutralize the ammonium ion and produce NH3; 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 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
216 CHAPTER OBJECTIVESTo understand the connections among work, heat, and energyTo be familiar with the concept of PV workTo be able to calculate changes in internal energyTo understand the relationship between internal energy and entropyTo be able to use a thermodynamic cycle to calculate changes in entropyTo understand the relationship between Gibbs free energy and workTo know the difference between the information that thermodynamics and kinetics provide about a systemTo understand the importance of thermodynamics in biochemical systems
217 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 calculations2. 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 Chemical 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 Chemistry: Principles, Patterns, and Applications, 1e 18.1 Thermodynamics and Work
220 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 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 work2. 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 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 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 = – PV, 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 PV WorkWork 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 Chemistry: Principles, Patterns, and Applications, 1e 18.2 The First Law of Thermodynamics
226 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 asEuniv = Esys + Esurr = 0Esys = – EsurrThe 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 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:Esys = q + w• q and w are not state functions on their own; their sum, Esys, 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 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 volume2. Reactions that occur at constant pressure• Assume that PV work is the only kind of work possible for the system, so E = q – PV
229 Enthalpy • Constant volume If reaction occurs in a closed vessel, the volume of the system is fixed and V is zeroHeat flow (qv) must equal Eqv = ENo 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 Enthalpy • Constant pressure If reaction occurs in an open container at a constant pressure of 1 atm, heat flow is given the symbol qpReplacing q with qp gives the equation qp = E + PVAt constant pressure, the heat flow for any process is equal to the change in the internal energy of the system plus the PV work doneA new state function called enthalpy (H) is defined as H = E + PVAt constant pressure, the change in the enthalpy of a system is H = E + (PV) = E + PVAt constant pressure, the change in the enthalpy of a system is equal to the heat flow: H = qp
231 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 + PV and the ideal gas law, PV = nRT.• (PV) = (nRT), so H = E + (PV) = E + (nRT).• At constant temperature, (nRT) = RTn, where n is the difference between the final and initial moles of gas, so E = H – RTn.
232 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 < 0 and E > H.
233 Chemistry: Principles, Patterns, and Applications, 1e 18.3 The Second Law of Thermodynamics
234 18.3 The Second Law of Thermodynamics 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.
235 EntropyChemical 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 = Sf – Si.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.
236 EntropyA 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 Svap.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.
237 Reversible and Irreversible Changes • 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 = PextV), so work done in a reversible process is always equal to or greater than work done in a corresponding irreversible process: wrev wirrev.
238 Reversible and Irreversible Changes • 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 = qrev + wrev = qirrev + wirrev.• E for a process is the same whether that process is carried out in a reversible or an irreversible manner.
239 The Relationship between Internal Energy and Entropy • The quantity of heat transferred, qrev, is directly proportional to the absolute temperature of an object, T (qrev 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 qrev).• For any reversible process S = qrev/T or qrev = TS; units of S are joules/kelvin (J/K).• Work done in a reversible process at constant pressure is wrev = –PV, so E = qrev + wrev = TS – PV; change in the internal energy of the system is related to the change in entropy, the absolute temperature, and the PV work done.
240 The Relationship between Internal Energy and Entropy • 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.
241 Chemistry: Principles, Patterns, and Applications, 1e 18.4 Entropy Changes and the Third Law of Thermodynamics
242 18.4 Entropy Changes and the Third Law of Thermodynamics 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.
243 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:It defines as positive the sign of the entropy of any substance at temperatures above absolute zeroIt provides a fixed reference point that allows the measurement of the absolute entropy of any substance at any temperature
244 18.4 Entropy Changes and the Third Law of Thermodynamics • Two different ways to calculate S for a reaction or physical changeUses tabulated values of absolute entropies of substances, based on the definition of absolute entropy provided by the third lawUses a thermodynamic cycle, based on the fact that entropy is a state function
245 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 (Sº), which is the entropy of 1 mol of a substance at a standard temperature of 298 K• Units of Sº are J/(molK)• 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, Sº values fall in the order Sº(gas) > Sº(liquid) > Sº(solid)
246 Calculating S from Standard Molar Entropy Values • Substances with similar molecular structures have similar Sº valuesThose with the lowest entropies tend to be rigid crystals composed of small atoms linked by strong, highly directional bondsThose with higher entropies are soft crystalline substances that contain larger atoms and increased molecular motion and disorder
247 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 Sº, reflecting a more ordered structure• To calculate Sº 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 Calculating S from Thermodynamic Cycles • A change in entropy can also be calculated using a thermodynamic cycleThe molar heat capacity Cp is the amount of heat needed to raise the temperature of 1 mol of a substance by 1ºC at constant pressureCv is the amount of heat needed to raise the temperature of 1 mol of a substance by 1ºC at constant volumeIncrease in entropy with increasing temperature is proportional to the heat capacity of the substanceEntropy change S is related to heat flow, qrev, by S = qrev/T
249 Calculating S from Thermodynamic Cycles qrev = nCpT at constant pressure or nCvT at constant volume, where n is the number of moles of substance presentThe change in entropy for a substance whose temperature changes from T1 to T2 is S =nCplnT2/T1 (constant pressure) or S = nCvlnT2/T1 (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
251 Chemistry: Principles, Patterns, and Applications, 1e 18.5 Free Energy
252 18.5 Free EnergyOne major goal of chemical thermodynamics is to establish criteria for predicting whether a particular reaction or process will occur spontaneouslyThe sign of Suniv is a universally applicable and infallible indicator of the spontaneity of a reaction; if Suniv > 0, the process will occur spontaneously as written; if Suniv < 0, a process cannot occur spontaneously; and if Suniv = 0, the system is at equilibriumUsing Suniv 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 surroundingsA 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 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 – TSThe criterion for predicting spontaneity is based on G, the change in G at constant temperature and pressureG = H – TS,where all thermodynamic quantities are those of the systemAt constant pressure, H = q whether a process is reversible or irreversible, and TS = qrev, so G = q – qrevSo 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 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 = qrev/T and q = H is rewritten to give Ssurr = – Hsys/TThe entropy change of the surroundings is related to the enthalpy change of the system, and since for a spontaneous reaction, Suniv > 0, the equation becomesSuniv = Ssys + Ssurr > 0 or Suniv = Ssys – Hsys/T > 0• Multiplying both sides of the inequality by –T reverses its sign and rearranges the equation to Hsys– TS < 0, which is equal to G; therefore, for a spontaneous process, G < 0
255 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 universeThis relationship allows one to predict spontaneity by focusing exclusively on the thermodynamic properties and temperature of the system. Highly exothermic processes (H << 0) that increase the disorder of the system (Ssys >> 0) would occur spontaneouslyFor a system at constant temperature and pressure,1. if G < 0, the process occurs spontaneously2. if G = 0, the system is at equilibrium3. if G > 0, the process is not spontaneous as written but occurs spontaneously in the reverse direction
256 Gibbs Free Energy and the Direction of Spontaneous Reactions
257 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 = wmax
258 Standard Free-Energy Change Absolute free energies cannot be measured. However, changes in free energy can.The standard free-energy change (Gº) 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 statesThe standard free-energy change can be calculated from the definition of free energy if the standard enthalpy and entropy changes are known: Gº = Hº – TSºIf Sº and Hº for a reaction have the same sign, then the sign of Gº depends on the relative magnitudes of the Hº and TSº terms
259 Standard Free-Energy Change The standard free energy of formation (Gºf) 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 statesStandard free energy of formation of an element in its standard state is zero at KStandard free energy of formation of a compound can be calculated from the standard enthalpy of formation, Hºf, and from the standard entropy of formation, Sºf, using the definition of free energy: Gºf = Hºf – TSºf
260 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:Gºrxn = mGºf (products) – nGºf (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 Hº and Sº; the temperature at which a given reaction is at equilibrium can be calculated by setting Gº = 0
261 Chemistry: Principles, Patterns, and Applications, 1e 18.6 Spontaneity and Equilibrium
262 18.6 Spontaneity and Equilibrium Three criteria have been identified for whether a given reaction will occur spontaneouslySuniv > 0Gsys < 0The relative magnitude of the reaction quotient Q versus the equilibrium constant Ka. Q < K, reaction proceeds spontaneously to the right as written, resulting in the net conversion of reactants to productsb. Q > K, reaction proceeds spontaneously to the left as written, resulting in the net conversion of products to reactantsc. Q = K, system at equilibrium, no net reaction occurs
263 Free Energy and the Equilibrium Constant • Because H º and S º determine the magnitude of Gº 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 Gº 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 = VP – ST and G = VP at constant temperature (T = 0)
264 Free Energy and the Equilibrium Constant • Assuming ideal gas behavior in the equation G = VP, 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 (P1 and P2, respectively).G = (nRT/P)P = nRT(P/P) = nRTln(P2 /P1)• If the initial state is the standard state with P1 = 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 = Gº + 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 = Gproducts – Greactants
265 Free Energy and the Equilibrium Constant • Substituting G = Gº + nRTlnP into the equation:G = [(cGºC + cRTlnPC) + (dGºD + dRTlnPD)] – [(aGºA + aRTlnPA) + (bGºB + bRTlnPB)]• Combining terms gives the following relationship between G and the reaction quotient QG = Gº + RTln(PcCPdD/PaAPbB) = Gº + RTlnQwhere Gº indicates that all reactants and products are in their standard states• For gases Q = Kp at equilibrium, and for a system G = 0 at equilibrium, so the relationship between Gº and Kp for gases can be described as Gº = –RTlnKp
266 Free Energy and the Equilibrium Constant • If the products and reactants are in their standard states and Gº < 0, then Kp > 1 and products are favored over reactants; if Gº > 0, then Kp < 1 and reactants are favored over products; if Gº = 0, then Kp = 1 and neither reactants nor products are favored and the system is at equilibrium• Kp 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, Kp = 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, Kp = K, so Gº = –RT ln K
267 Free Energy and the Equilibrium Constant • The following equation provides insight into how the components of Gº influence the magnitude of the equilibrium constant: Gº = Hº – TSº = –RT ln KK becomes larger as Sº becomes more positive, indicating that the magnitude of the equilibrium constant is directly influenced by the tendency of the system to move toward maximum disorderK increases as Hº 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 Temperature Dependence of the Equilibrium Constant • The fact that Gº and K are related explains why equilibrium constants are temperature-dependentln K = – Hº/RT + Sº/R• Assuming Hº and Sº are temperature-dependent, for an exothermic reaction (Hº < 0), the magnitude of K decreases with increasing temperature and for an endothermic reaction (Hº > 0), the magnitude of K increases with increasing temperature• The magnitude of Hº dictates how rapidly K changes as a function of temperature and the magnitude and sign of Sº affects the magnitude of K, but not its temperature dependence
269 Temperature Dependence of the Equilibrium Constant • If the value of K at a given temperature and the value of Hº for a reaction are known, the value of K can be estimated at any other temperature, even in the absence of information on Sº• If K1 and K2 are the equilibrium constants for a reaction at temperatures T1 and T2, respectively, thenln K2 – ln K1 = ln K2/K1 = Hº/R(1/T1 – 1/T2)
270 Chemistry: Principles, Patterns, and Applications, 1e 18.7 Comparing Thermodynamics and Kinetics
271 18.7 Comparing Thermodynamics and Kinetics Deals with state functions and can be used to describe the overall properties, behavior, and equilibrium composition of a systemProvides a significant constraint on what can occur during a reaction process• KineticsConcerned with the particular pathway by which physical or chemical changes occur, so it can address the rate at which a particular process will occurDescribes the detailed steps of what actually occurs on an atomic or molecular level
272 18.7 Comparing Thermodynamics and Kinetics The following table gives the numerical values of the equilibrium constant K that correspond to various values of GºIf Gº + 10 kJ/mol or Gº –10 kJ/mol, an equilibrium is ensured to lie all the way to the left or to the right, respectivelyIf Gº is quite small (10 kJ/mol), significant amounts of both products and reactants are present at equilibrium
273 18.7 Comparing Thermodynamics and Kinetics Most reactions have equilibrium constants greater than 1, with the equilibrium strongly favoring either products or reactantsIn 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 conditionsA 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 whichGº<< 0
274 Chemistry: Principles, Patterns, and Applications, 1e 18.8 Thermodynamics and Life
275 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 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 lightCells utilize the energy obtained to maintain the nonequilibrium state that is essential for lifeNonequilibrium thermodynamics have been developed to quantitatively describe open systems such as living cellsThe 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 Ssurr
277 Extracting Energy from the Environment • Organisms can be divided into two categoriesPhototrophs, whose energy source is lightChemotrophs, 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 biomoleculesOrganisms that can use only O2 as the oxidant are aerobic organisms that can’t survive in the absence of O2Many organisms that use other oxidants or oxidized organic compounds can live only in the absence of O2 and are called anaerobic organisms
278 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 CO2 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 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 The Role of NADH and ATP in Metabolism • The most important of these electron-carrying intermediates is NAD+, whose reduced form is NADH
281 The Role of NADH and ATP in Metabolism • 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
282 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
284 CHAPTER OBJECTIVESTo distinguish between galvanic and electrolytic cellsTo predict spontaneous reactions using redox potentialsTo balance redox reactions using half-reactionsTo understand the relationship between cell potential and the equilibrium constantTo be able to measure solution concentrations using cell potentialsTo describe how commercial galvanic cells operateTo describe the process of corrosionTo understand electrolysis and to be able to describe it quantitatively
285 ElectrochemistryIn 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 Chemistry: Principles, Patterns, and Applications, 1e 19.1 Describing Electrochemical Cells
287 19.1 Describing Electrochemical Cells Electrochemical process—electrons flow from one chemical substance to another, driven by an oxidation-reduction (redox) reactionRedox 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 19.1 Describing Electrochemical Cells – Described as two half-reactions, one representing the oxidation process and one the reduction processReductive half-reaction: Br2 (aq) + 2e– 2Br –(aq)Oxidative half-reaction: Zn (s) Zn2+(aq) + 2e–– Adding the two half-reactions gives the overall chemical reaction Zn (s) + Br2 (aq) ZnBr2 (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 19.1 Describing Electrochemical Cells – 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 cells1. Galvanic cell (voltaic cell)—uses the energy released during a spontaneous redox reaction (G < 0) to generate electricity2. Electrolytic cell—consumes electrical energy from an external source, using it to cause a nonspontaneous redox reaction to occur (G > 0)
291 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 Galvanic (Voltaic) Cells To illustrate the basic principles of a galvanic celllook at the reaction of metallic zinc with cupric ion (Cu2+) to give copper metal and Zn2+ ionZn(s) + Cu2+(aq) Zn2+(aq) + Cu(s)a copper strip is inserted into a beaker that contains a 1 M solution of Cu2+ ions, and a zinc strip is inserted into a different beaker that contains a 1 M solution of Zn2+ ionstwo 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 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 Zn2+ ions in the Zn2+ solution increases; the copper strip gains mass and the concentration of Cu2+ ions in the Cu2+ solution decreaseselectrons 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 workthe 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
295 Galvanic (Voltaic) Cells a voltmeter is used to measure the difference in electrical potential between the two compartmentsthe 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 fieldelectrons 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 Constructing a Cell Diagram Because galvanic cells are cumbersome to describe in words, a line notation called a cell diagram has been developedIn a cell diagramthe 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)| Zn2+(aq, 1M) || Cu2+(aq, 1 M) | Cu(s)Anode Salt Bridge Cathode
297 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 potentialCell diagram does not include a double vertical line for the salt bridge (no salt bridge) and does not include solution concentrationsPt(s) | H2(g) | HCl(aq) | AgCl(s) | Ag(s)
298 Chemistry: Principles, Patterns, and Applications, 1e 19.2 Standard Potentials
299 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 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, EºcellUsed 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 reactionUsed to measure the potentials for oxidations and reductions of different substances under comparable conditions
301 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 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 (Eºcell = Eºcathode – Eºanode).• 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 Eº values are independent of the stoichiometric coefficients for the half-reactions.
303 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 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:Write the reduction half-reaction and the oxidation half-reactionBalance the atoms by balancing elements other than O and H; then balance O atoms by adding H2O, and balance H atoms by adding H+Balance the charges in each half-reaction by adding electrons
305 Balancing Redox Reactions Using the Half-Reaction Method Multiply the reductive and oxidative half-reactions by appropriate integers to obtain the same number of electrons in both half-reactionsAdd the two half-reactions and cancel substances that appear on both sides of the equationCheck to make sure that all atoms and charges are balanced
306 Calculating Standard Cell Potentials • The standard cell potential for a redox reaction, Eºcell, 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) | Zn2+(aq, 1 M || Cu2+(aq, 1M) | Cu(s)Cathode: Cu2+(aq) + 2e– Cu(s) Eºcathode = 0.34 VAnode: Zn(s) Zn2+(aq, 1M) + 2e– Eºanode = –0.76 VOverall: Zn(s) + Cu2+(aq) Zn2+(aq) + Cu(s)Eºcell = Eºcathode – Eºanode = 1.10 V
307 Calculating Standard Cell Potentials • If the value of Eºcell (the standard cell potential) is positive, the reaction will occur spontaneously as written• If the value of Eºcell 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 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 Reference Electrodes and Measuring Concentrations • Types of reference electrodes1. 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 H2 gas at a pressure of 1 atm at the Pt-solution interface2. 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 concentration3. Saturated calomel electrode (SCE)—consists of a platinum wire inserted into a moist paste of liquid mercury, Hg2Cl2, and KCl
310 Reference Electrodes and Measuring Concentrations • One of the most common uses of electrochemistry is to measure the H+ ion concentration of a solutionA 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 protonsThe 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 Reference Electrodes and Measuring Concentrations • Ion-selective electrodesUsed to measure the concentration of a particular species in solution; designed so that their potential depends on only the concentration of the desired speciesContains 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 Chemistry: Principles, Patterns, and Applications, 1e 19.3 Comparing Strengths of Oxidants and Reductants
313 19.3 Comparing Strengths of Oxidants and Reductants 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 substancesThe half-reaction for the standard hydrogen electrode lies halfway down on the tableAll species that lie above it in the table are stronger oxidants than H+, and all those that lie below it are weakerAll species that lie below H2 are stronger reductants than H2, and those that lie above H2 are weaker
314 19.3 Comparing Strengths of Oxidants and Reductants Because the half-reactions in the table are arranged in order of their Eº values, the table can be used to predict the relative strengths of various oxidants and reductantsAny 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 tableAny 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
315 Chemistry: Principles, Patterns, and Applications, 1e 19.4 Electrochemical Cells and Thermodynamics
316 The Relationship between Cell Potential and Free Energy Electrochemical cells convert chemical to electrical energy, and vice versaTotal 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 reactionResulting 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 1018 e–/s and relates electrical potential (in volts) to energy (in joules)1J/1V = 1 coulomb = 6.25 x 1018 e–/s
317 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 10–19C) ( x 1023/1 mol e–) =x 104C/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 The Relationship between Cell Potential and Free Energy The maximum amount of work that can be produced by an electrochemical cell, wmax, is equal to the product of the cell potential, Ecell, and the total charge transferred during the reaction, nF: wmax = –nFEcellWork is expressed as a negative number because work is being done by the system on the surroundingsG is also a measure of the maximum amount of work that can be performed during a chemical reaction (G = wmax; there must be a relationship between the potential of an electrochemical cell and the change in free energy, GG = –nFEcell• A spontaneous redox reaction is characterized by a negative value of G and a positive value of Ecell
319 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 availableValues of Eº for half-reactions cannot be added to give Eº for the sum of the half-reactions because Eº is not a state functionBecause Gº is a state function, the sum of the G values for the individual reactions gives Gº for the overall reaction, which is proportional to both the potential and the number of electrons (n) transferred
320 Potentials for the Sums of Half-Reactions To obtain the value of Eº for the overall half-reaction, the values of Gº (= –nFEº) must be added for each half-reaction to obtain Gº for the overall half-reactionSubstitute values into equation Gº = nFEºcell and solve for Eº
321 The Relationship between Cell Potential and the Equilibrium Constant Can use the relationship between Gº and the equilibrium constant K to obtain a relationship between Eºcell and KFor a general reaction of the type aA + bB cC + dD, the standard free-energy change and the equilibrium constant are related by the equation Gº = –RTlnKGiven the relationship between the standard free-energy change and the standard cell potential, the following equation can be written: –nFEºcell = –RTlnK
322 The Relationship between Cell Potential and the Equilibrium Constant Rearranging the equation givesEºcell = (RT/nF)lnK• For T = 298 K, the equation is simplified toEºcell = (RT/nF)lnK = [8.314 J/(mol·K)] (298 K) log Kn[96,486 J/(V·mol)]= ( V/n)log K• The standard cell potential, Eºcell, is directly proportional to the logarithm of the equilibrium constant
323 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 (Gº < 0)
324 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 byG = Gº + RTln QWe also know that G = –nFEcell and Gº = –nFEºcell, sosubstituting these expressions in the preceding equation gives –nFEcell = –nFEºcell + RT lnQ• Dividing both sides of this equation by –nF gives the Nernst equation: Ecell = Eºcell – (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 The Effect of Concentration on Cell Potential: The Nernst Equation • When a redox reaction is at equilibrium (G = 0), the Nernst equation reduces toEºcell = (RT/nF)ln K because Q = K and there is no net transfer of electrons (Ecell = 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 (Ecell), the standard cell potential (Eºcell), and the reactant and product concentrations at room temperature (contained in Q):Ecell = Eºcell – ( V/n)logQ
326 The Effect of Concentration on Cell Potential: The Nernst Equation
327 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 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, Ksp = [ 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 AgClThe potential due to the difference in [Ag+] between the two cells can be used to determine Ksp
329 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 Chemistry: Principles, Patterns, and Applications, 1e 19.5 Commercial GalvanicCells
331 19.5 Commercial Galvanic Cells • Galvanic cells can be self-contained and portable and can be used as batteries and fuel cellsA battery (storage cell) is a galvanic cell (or a series of galvanic cells) that contains all the reactants needed to produce electricity.A fuel cell is a galvanic cell that requires a constant external supply of one or more reactants in order to generate electricity.
332 Batteries • Two basic kinds of batteries 1. Disposable, or primary, batteries in which the electrode reactions are effectively irreversible and which cannot be recharged2. 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 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 Batteries • Leclanché dry cell A “wet cell” in which the electrolyte is an acidic water-based paste containing MnO2, NH4Cl, ZnCl2, graphite, and starchUsed in flashlights, Walkmen, and GameBoys and is disposableCell not very efficient in producing electrical energy and has a limited shelf lifeThe 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 Batteries • “Button” batteries The anode is a zinc-mercury amalgam, and the cathode can be either HgO or Ag2O as the oxidantAre 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 crucialDisposable
336 • Lithium-iodine battery Batteries• Lithium-iodine batteryWater-free batteryConsists of two cells separated by a metallic nickel mesh that collects charge from the anodesThe anode is lithium metal, and the cathode is a solid complex of 2Electrolyte is a layer of solid Li that allows Li+ ions to diffuse from the cathode to the anodeHighly reliable and long-livedUsed in cardiac pacemakers, medical implants, smoke alarms, and in computersDisposable
338 Batteries • Nickel-cadmium (nicad) battery Used in small electrical appliances and in devices like drills and portable vacuum cleanersA water-based cell with a cadmium anode and a highly oxidized nickel cathodeThis 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 capacityLightweight, 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
340 Batteries • Lead-acid (lead storage) battery Provides the starting power in automobiles and boats; can be discharged and recharged many timesThe 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, PbO2The electrolyte is an aqueous solution of sulfuric acidThe value of Eº 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
342 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 Chemistry: Principles, Patterns, and Applications, 1e 19.6 Corrosion
344 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 Chemistry: Principles, Patterns, and Applications, 1e 19.7 Electrolysis
346 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 Electrolytic Cells• An electrochemical cell in which one electrode is copper metal immersed in a 1 M Cu2+ solution and the other electrode is cadmium metal immersed in a 1 M Cd2+ solution is set up, and then the circuit is closedCadmium electrode begins to dissolve (Cd is oxidized to Cd2+) and thus is the anode, while metallic copper will be deposited on the copper electrode (Cu2+ is reduced to Cu), which is the cathodeOverall reaction is thermodynamically spontaneous as written (Gº < 0); in this direction, the system is acting as a galvanic cellThe reverse reaction, the reduction of Cd2+ by Cu, is thermodynamically nonspontaneous and will only occur with an input of an applied voltage
348 Electrolytic CellsCan 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 cellThe copper electrode is now the anode (Cu is oxidized) and the cadmium electrode is now the cathode (Cd2+ is reduced)Signs of the electrodes have changed to reflect the flow of electrons in the circuit
350 Electrolytic Cells• Differences between galvanic and electrolytic cells
351 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 CaCl2 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, H2 and O2, by adding a small amount of an ionic solute to the water to make it electrically conductive
352 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 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 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 reactionCharge (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
356 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 Nuclear ReactionsDifferences between nuclear reactions and chemical processesIn a nuclear reaction, the identities of the elements changeNuclear reactions are accompanied by the release of enormous amounts of energyThe yields and rates of a nuclear reaction are unaffected by changes in temperature, pressure, or the presence of catalysts
358 Chemistry: Principles, Patterns, and Applications, 1e 20.1 The Components of the Nucleus
359 20.1 The Components of the Nucleus Most of the known elements have at least one isotope whose atomic nucleus is stable indefinitelyA great majority of elements also have isotopes that are unstable and disintegrate, or decay, at measurable rates by emitting radiationSome elements have no stable isotopes and eventually decay to other elementsThe process of nuclear decay is a nuclear reaction that results in changes inside the atomic nucleus
360 The Atomic Nucleus• Each element can be represented by the notation Z XA is the mass number, the sum of the numbers of protons and neutronsZ is the atomic number, the number of protonsThe protons and neutrons that make up the nucleus of an atom are called nucleonsAn atom with a particular number of protons and neutrons is called a nuclideNuclides that have the same number of protons but different numbers of neutrons are called isotopesThe number of neutrons is equal to A – ZA
361 The Atomic Nucleus• Isotopes of oxygen can be represented in any of these ways:A X: O O OZAX: O O OElement-A: Oxygen Oxygen 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 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 (t½), the amount of time required for half the initial number of nuclei present to decay in a first-order reaction
363 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 Nuclear StabilityAs 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 instabilityRelationship between the numbers of protons and neutrons in stable nuclei is shown in the following figureThe stable isotopes form a “peninsula of stability” in a “sea of instability”Only three stable isotopes, 1H, 3He, and 4He, 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 nucleiAll elements with Z > 83 are unstable and radioactive
365 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 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 Chemistry: Principles, Patterns, and Applications, 1e 20.2 Nuclear Reactions
368 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 elementsResulting daughter nuclei have a lower mass and are lower in energy (more stable) than the parent nucleus that decayedOccur spontaneously under all conditions2. Nuclear transmutation reactionA nucleus reacts with a subatomic particle or another nucleus to form a product nucleus that is more massive than the starting materialOccur spontaneously only under special conditions
369 Classes of Radioactive Nuclei Each of the three general classes of radioactive nuclei is characterized by a different decay process or set of processesNeutron-rich nucleiHave too many neutrons and have a neutron-to-proton ratio that is too high to give a stable nucleusThese nuclei decay by a process that converts a neutron to a proton, thereby decreasing the neutron-to-proton ratioNeutron-poor nucleiHave too few neutrons and have a neutron-to-proton ratio that is too low to give a stable nucleusThese nuclei decay by processes that convert a proton to a neutron, thereby increasing the neutron-to-proton ratio
370 Classes of Radioactive Nuclei 3. Heavy nucleiHeavy nuclei (with A 200) are intrinsically unstable, regardless of the neutron-to-proton ratioAll nuclei with Z > 83 are unstableDecay by emitting an particle, which decreases the number of protons and neutrons in the original nucleus by 2Since 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
371 Nuclear Decay Reactions • Can use the number and type of nucleons present to write a balanced equation for a nuclear decay reactionProcedure allows us to predict the identity of either the parent or daughter nucleus if the identity of only one is knownRegardless 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 AX notation fornuclides has been extended to include radioactive emissions
372 Nuclear Decay Reactions • The following table lists the name and symbol for each type of emitted radiationThe left superscript in the symbol for a particle gives the mass number, which is the total number of protons and neutronsFor a proton or a neutron, A = 1Because neither an electron nor a positron contains protons or neutrons, its mass number is 0The left subscript gives the charge of the particleProtons carry a positive charge, so Z = +1 for a protonA neutron contains no protons and is electrically neutral, so Z = 0For an electron, Z = –1, and for a positron, Z = +1Because rays are high-energy photons, both A and Z are 0
373 Nuclear Decay Reactions In some cases, two different symbols are used for particles that are identical but produced in different waysSymbol 0e, simplified to e– represents a free electron or an electron associated with an atomSymbol 0, simplified to – denotes an electron that originates from within the nucleus, which is a particle4He refers to the nucleus of a helium atom, and 4 is an identical particle ejected from a heavier nucleus-1-122
374 Nuclear Decay Reactions • There are six fundamentally different kinds of nuclear decay reactions, each of which releases a different kind of particle or energy (see table)
375 Nuclear Decay Reactions Alpha decayNuclei with mass numbers greater than 200 undergo alpha decay, which results in the emission of a helium-4 nucleus as an particle, 4The 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 nucleusAX A-4X′ + 4parent daughter αparticle2→ZZ-22
376 Nuclear Decay Reactions Beta decayNuclei 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 particlen p βunstable neutron proton retained beta particle emittedin nucleus by nucleus by nucleusBeta 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 nucleiAX A X′ βparent daughter particle→111-1→Z+1Z-1
377 Nuclear Decay Reactions Positron emissionA positron has the same mass as an electron but opposite chargePositron 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 emitted1p 1n 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 nucleiAX A X′ parent daughter positron1+1ZZ-1+1
378 Nuclear Decay Reactions Electron captureA 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 p e 1 nWhen 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 isAX + 0e A X’ X-rayparent electron daughterThe 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 nuclei1-1Z-1Z-1
379 Nuclear Decay Reactions Gamma emissionMany nuclear decay reactions produce daughter nuclei that are in a nuclear excited stateA nucleus in an excited state releases energy in the form of a photon when it returns to the ground stateThese high-energy photons are raysGamma emission can occur instantaneously or after a significant delayGeneral formula AX* AX 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 reactionZZ
380 Nuclear Decay Reactions Spontaneous fissionOnly 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 massesProcess most important for trans-actinide elements with Z 104Spontaneous fission is accompanied by the release of large amounts of energy and is accompanied by the emission of several neutronsThe 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
381 Radioactive Decay Series • 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
382 Induced Nuclear Reactions Some nuclei spontaneously transform into nuclei with a different number of protons, producing a different elementThese naturally occurring radioactive isotopes decay by emitting subatomic particlesShould 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
383 Synthesis of Transuranium Elements • 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
384 Synthesis of Transuranium Elements • Types of particle acceleratorsThe 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.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.
385 Synthesis of Transuranium Elements 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.
386 Chemistry: Principles, Patterns, and Applications, 1e 20.3 The Interaction of Nuclear Radiation with Matter
387 20.3 The Interaction of Nuclear Radiation with Matter 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.
388 Ionizing versus Nonionizing Radiation • Effects of radiation on matter are determined by the energy of the radiation, which depends on the nuclear decay reaction that produced it.Nonionizing radiationLow in energy; when it collides with an atom in a molecule or ion, most of its energy can be absorbed without causing a structural or chemical changeThe kinetic energy of the radiation is transferred to the atom or molecule with which it collides, causing it to rotate, vibrate, or move more rapidlyThis energy can be transferred to adjacent molecules or ions in the form of heat, so many radioactive substances are warm to the touch
389 Ionizing versus Nonionizing Radiation Higher in energy and some of its energy can be transferred to one or more atoms with which it collides as it passes through matterIf enough energy is transferred, electrons can be excited to very high energy levels, resulting in the formation of positively charged ionsMolecules ionized in this way are highly reactive and can decompose or undergo other chemical changes that create a cascade of reactive molecules that can damage biological tissues and other materials
390 The Effects of Ionizing Radiation on Matter • The effects of ionizing radiation depend on four factorsThe type of radiation, which dictates how far it can penetrate into matterThe energy of the individual particles or photonsThe number of particles or photons that strike a given area per unit timeThe chemical nature of the substance exposed to the radiation
391 The Effects of Ionizing Radiation on Matter • The relative abilities of the various forms of ionizing radiation to penetrate tissues are:1. radiationReacts strongly with matter because of its high charge and massDoes not penetrate deeply into an object and can be stopped by clothing or skinAlpha particles most damaging if their source is inside the body because their energy is absorbed by internal tissues
392 The Effects of Ionizing Radiation on Matter rays, with no charge and no mass, do not interact strongly with matter and penetrate deeply into most objects, including the human bodyLead or concrete needed to completely stop raysThe most dangerous type when they come from a source outside the body radiationIntermediate in mass and charge between particles and rays, so interaction with matter is intermediateBeta particles penetrate paper or skin but can be stopped by wood or a thin sheet of metal
393 The Effects of Ionizing Radiation on Matter There are many ways to measure radiation exposure, or the doseThe roentgen (R) is used to measure the amount of energy absorbed by dry air and is used to describe exposure quantitativelyDamage to biological tissues is proportional to the amount of energy absorbed by tissues, not airThe most common unit to measure the effects of radiation on biological tissue is the rad (radiation absorbed dose); S unit is the gray (Gy)
394 The Effects of Ionizing Radiation on Matter Rad is defined as the amount of radiation that causes 0.01 J of energy to be absorbed by 1 kg of matter, and the gray is defined as the amount of radiation that causes 1 J of energy to be absorbed per kilogram1 rad = J/kg Gy = 1J/kgThe amount of tissue damage caused by 1 rad of particles is much greater than the damage caused by 1 rad of particles or rays because particles have higher masses and charge
395 The Effects of Ionizing Radiation on Matter A unit called the rem (roentgen equivalent in man) describes the actual amount of tissue damage caused by a given amount of radiationThe number of rems of radiation is equal to the number of rads multiplied by the RBE (relative biological effectiveness) factor, which is 1 for particles, rays, and X-rays, and 20 for particlesMost measurements are reported in millirems
396 Natural Sources of Radiation We are continuously exposed to measurable background radiation from a variety of natural sources, which is equal to about 150–600 mrem/yrCosmic rays, high-energy particles, and rays emitted by the sun and other stars that bombard Earth continuouslyCosmogenic radiation, produced by the interaction of cosmic rays with gases in the upper atmosphereTerrestrial radiation, due to the remnants of radioactive elements that were present on the primordial Earth and their decay products
397 Natural Sources of Radiation Tissues also absorb radiation (40 mrem/yr) from naturally occurring radioactive elements present in our bodiesRadon is the most important source of background radiationThe heaviest of the noble gases and tends to accumulate in enclosed spacesRadon exposure can cause lung damage or cancer
398 Artificial Sources of Radiation • In addition to naturally occurring background radiation, humans are exposed to small amounts of radiation from a variety of artificial sourcesX-rays used for diagnostic purposes in medicine and dentistry; X-rays are photons with much lower energy than raysTelevision screens and computer monitors with cathode-ray tubes that produce X-raysLuminescent dialsResidual fallout from atmospheric nuclear-weapons testingNuclear power industry
399 Assessing the Impact of Radiation Exposure • The radiation exposure from artificial sources, when combined with the exposure from natural sources, poses a significant risk to human health• The effects of single radiation doses of different magnitudes on humans are listed in the following table
400 Assessing the Impact of Radiation Exposure • A large dose of radiation spread over time is less harmful than the same total amount of radiation administered over a short time• Tissues most affected by large, whole-body exposures are bone marrow, intestinal tissue, hair follicles, and reproductive organs
401 Chemistry: Principles, Patterns, and Applications, 1e 20.4 Thermodynamic Stability of the Atomic Nucleus
402 20.4 Thermodynamic Stability of the Atomic Nucleus Nuclear reactions are accompanied by changes in energyEnergy changes in nuclear reactions are enormous compared with those of even the most energetic chemical reactionsEnergy changes in a typical nuclear reaction are so large that they result in a measurable change of mass
403 Mass-Energy BalanceNuclear reactions are accompanied by large changes in energy, which result in detectable changes in mass.The relationship between mass, m, and energy, E, is expressed in the equation E = mc2, where c is the speed of light (2.998 x 108 m/s), and energy and mass are expressed in units of joules and kilograms, respectively.Every mass has an associated energy, and any reaction that involves a change in energy must be accompanied by a change in mass.Large changes in energy in nuclear reactions are reported in units of keV or MeV; a change in energy that accompanies a nuclear reaction can be calculated from the change in mass (1 amu = 931 MeV).Chemical reactions are accompanied by changes in mass, but these changes are too small to be detected
404 Nuclear Binding Energies The mass of an atom is always less than the sum of the masses of its component particles; the only exception is hydrogen-1.The difference between the sum of the masses of the components and the measured atomic mass is called the mass defect of the nucleus.The amount of energy released when a nucleus forms from its component nucleons is the nuclear binding energy.The magnitude of the mass defect is proportional to the nuclear binding energy, so both values indicate the stability of the nucleus.
405 Nuclear Binding Energies Not all nuclei are equally stable; the relative stability of different nuclei are described by comparing the binding energy per nucleon, which is obtained by dividing the nuclear binding energy by the mass number A of the nucleus.The binding energy per nucleon increases rapidly with increasing atomic number until Z = 26, where it levels off and then decreases slowly.
406 Nuclear Fission and Fusion The splitting of a heavy nucleus into two lighter onesNucleus usually divides asymmetrically rather than into equal parts, and the fission of a given nuclide does not give the same products every timeIn a typical nuclear fission reaction, more than one neutron is released by each dividing nucleus; when these neutrons collide with and induce fission in other neighboring nuclei, a self-sustaining series of nuclear fission reactions known as a nuclear chain reaction can resultEach series of events is called a generationThe minimum mass capable of supporting sustained fission is called the critical mass
408 Nuclear Fission and Fusion If the mass of the fissile isotope is greater than the critical mass, then under the right conditions, the resulting supercritical mass can release energy explosively• Nuclear fusionTwo light nuclei combine to produce a heavier, more stable nucleus and is the opposite of a nuclear fission reactionThe positive charge on both nuclei results in a large electrostatic energy barrier to fusion; barrier can be overcome if one or both particles have sufficient kinetic energy to overcome the electrostatic repulsions, allowing the two nuclei to approach close enough for a fusion reaction to occur
410 Chemistry: Principles, Patterns, and Applications, 1e 20.5 Applied Nuclear Chemistry
411 Nuclear ReactorsWhen a critical mass of a fissile isotope has been achieved, the resulting flux of neutrons can lead to a self-sustaining reaction; a variety of techniques can be used to control the flow of neutrons, which allows nuclear fission reactions to be maintained at safe levelsMany levels of control are required, along with a fail-safe design; otherwise, the chain reaction can accelerate so rapidly that it releases enough heat to melt or vaporize the fuel and the container, causing the release of enough radiation to contaminate the surrounding areaIf the neutron flow in a reactor is carefully regulated so that only enough heat is released to boil water, then the resulting steam can be used to produce electricity
412 Nuclear Reactors Light-water reactors Used to produce electricity Fuel rods containing a fissile isotope in a structurally stabilized form (uranium oxide pellets encased in a corrosion-resistant zirconium alloy) are suspended in a cooling bath that transfers the heat generated by the fission reaction to a secondary cooling systemHeat is used to generate steam for the production of electricityControl rods are utilized to absorb neutrons and control the rate of the nuclear chain reactionPulling the control rods out increases the neutron flow, allowing the reactor to generate more heat; inserting the rods completely stops the reaction
414 Nuclear Reactors Heavy-water reactors Deuterium (2H) absorbs neutrons less effectively than does hydrogen (1H), but it is about twice as effective at scattering neutronsA nuclear reactor that uses D2O instead of H2O as the moderator is so efficient that it can use unenriched uranium as fuel, which reduces the operating costs and eliminates the need for plants that produce enriched uranium
415 Nuclear Reactors Breeder reactors A nuclear fission reactor that produces more fissionable fuel than it consumes; the fuel produced is not the same as the fuel consumedOverall reaction is the conversion of nonfissile 238U to fissile 239Pu, which can be isolated chemically and used to fuel a new reactor
416 Nuclear Reactors Nuclear fusion reactors Nuclear fusion reactions are thermodynamically spontaneous, but the positive charge on both nuclei results in a large electrostatic energy barrier to the reaction; high temperatures are required to overcome the electrostatic repulsions and initiate a fusion reactionAchieving these temperatures, controlling the materials to be fused, and extracting the energy released by the fusion reaction are difficult problemsThese nuclear reactions are called thermonuclear reactions because a great deal of thermal energy must be invested to initiate the reaction; amount of heat released by the reaction is several orders of magnitude greater than the energy needed to initiate it
417 Uses of RadioisotopesRadiation is destructive to rapidly dividing cells such as tumor cells and bacteria, so it has been used medically to treat cancer; many radioisotopes are available for medical use, and each has specific advantages for certain applicationsRadiation therapyRadiation is delivered by a source planted inside the body, or in some cases, physicians take advantage of the body’s own chemistry to deliver a radioisotope to the desired locationIn cases where a tumor is surgically inaccessible, an external radiation source is used to aim a tightly focused beam of rays at it
418 Uses of Radioisotopes Medical imaging A radioisotope is temporarily localized in a particular tissue or organ where its emissions provide a map of the tissue or organPositron emission tomography (PET) is an imaging technique that produces remarkably detailed three-dimensional images; biological molecules that have been tagged with a positron-emitting isotope can be used to probe the functions of organs
419 Uses of Radioisotopes• Ionizing radiation is used in the irradiation of food to kill bacteria• In addition to the medical uses of radioisotopes, radioisotopes have hundreds of other uses: smoke alarms, dentistry, detectors, and gauges
420 Chemistry: Principles, Patterns, and Applications, 1e 20.6 The Origin of the Elements
421 Relative Abundances of the Elements on Earth and in the Universe • The relative abundances of the elements in the universe and on Earth relative to silicon are shown in the following figure
422 Relative Abundances of the Elements on Earth and in the Universe • Data are estimates based on the characteristic emission spectra of the elements in stars, the absorption spectra of matter in clouds of interstellar dust, and the approximate composition of Earth as measured by geologists• Data illustrate two pointsExcept for hydrogen, the most abundant elements have even atomic numbersThe relative abundances of the elements in the universe and on Earth are very different
423 Relative Abundances of the Elements on Earth and in the Universe • All the elements originally present on Earth were synthesized from hydrogen and helium nuclei in the interiors of the stars that have long since exploded and disappeared• Six of the most abundant elements in the universe (carbon, oxygen, neon, magnesium, silicon, and iron) have nuclei that are integral multiples of the helium-4 nucleus, which suggests that helium-4 is the primary building block for heavier nuclei
424 Synthesis of the Elements in Stars • Elements are synthesized in discrete stages during the lifetime of a star, and some steps occur only in the most massive stars knownAll stars are formed by the aggregation of interstellar dust, which is mostly hydrogenAs the cloud of dust slowly contracts due to gravitational attraction, its density reaches 100g/cm3 and the temperature increases to 1.5 x 107 K, forming a dense plasma of ionized hydrogen nucleiSelf-sustaining nuclear reactions begin and the star ignites, creating a yellow starIn the first stages of life, the star is powered by a series of nuclear fusion reactions that convert hydrogen to helium
425 Synthesis of the Elements in Stars Overall reaction is the conversion of four hydrogen nuclei to a helium-4 nucleus, accompanied by the release of two positrons, two rays, and a great deal of energyWhen large amounts of helium-4 have been formed, they become concentrated in the core of the star, which slowly becomes denser and hotterAt a temperature of 2 x 108 K, the helium-4 nuclei begin to fuse, producing beryllium-8, which is unstable and decomposes in 10–16 s, long enough for it to react with a third helium-4 nucleus to form the stable carbon-12
426 Synthesis of the Elements in Stars Sequential reactions of carbon-12 with helium-4 produce the elements with even numbers of protons and neutrons up to magnesium-24So much energy is released by these reactions that it causes the surrounding mass of hydrogen to expand, producing a red giant that is 100 times larger than the original yellow starAs the star expands, the heavier nuclei accumulate in its core, which contracts to a density of 50,000 g/cm3 and becomes hotter
427 Synthesis of the Elements in Stars At a temperature of 7 x 108 K, carbon and oxygen nuclei undergo nuclear fusion reactions to produce sodium and silicon nucleiAt these temperatures, carbon-12 reacts with helium-4 to initiate a series of reactions that produce more oxygen-16, neon-20, magnesium-24, and silicon-28, as well as heavier nuclides such as sulfur-32, argon-36, and calcium-40Energy released by these reactions causes a further expansion of the star to form a red supergiant
428 Synthesis of the Elements in Stars Core temperature increases steadily, at a temperature of 3 x 109 K, the nuclei that have been formed exchange protons and neutrons freelyThis equilibration process forms heavier elements up to iron-56 and nickel-58, which have the most stable nuclei known
429 Formation of Heavier Elements in Supernovas • All naturally occurring elements heavier than nickel are formed in the rare but spectacular cataclysmic explosions called supernovas
430 Formation of Heavier Elements in Supernovas Fuel in the core of a massive star is consumed, so its gravity causes it to collapse in about 1 sAs the core is compressed, the iron and nickel nuclei within it disintegrate to protons and neutrons, and many of the protons capture electrons to form neutronsThe resulting neutron star is so dense that atoms no longer existThe energy released by the collapse of the core causes the supernova to explode in a violent event
431 Formation of Heavier Elements in Supernovas Force of the explosion blows the star’s matter into space, creating a gigantic and rapidly expanding dust cloud called a nebulaThe concentration of neutrons is so great that multiple neutron-capture events occur, leading to the production of the heaviest elements and many of the less-stable nuclidesForce of the explosion distributes these elements throughout the galaxy surrounding the supernova and are eventually captured in the dust that condenses to form new stars
433 CHAPTER OBJECTIVESTo be able to describe the physical and chemical properties of hydrogen and to predict its reactivityTo be able to describe how the alkali and alkaline earth metals are isolatedTo become familiar with the reactions, compounds, and complexes of the alkali and alkaline earth metalsTo know some of the uses of the alkali and alkaline earth metalsTo become familiar with the role of the s-block elements in biology
434 Chemistry: Principles, Patterns, and Applications, 1e 21.1 Overview of Periodic Trends
435 21.1 Overview of Periodic Trends • The single most important unifying principle in understanding the chemistry of the elements is the systematic increase in atomic number, accompanied by the orderly filling of atomic orbitals by electrons, which leads to periodicity in such properties as atomic and ionic size, ionization energy, electronegativity, and electron affinitySame factors lead to periodicity in valence-electron configurations, which for each group results in similarities in oxidation states and the formation of compounds with common stoichiometries
436 21.1 Overview of Periodic Trends The most important periodic trends in atomic properties are summarized in the following table:
437 21.1 Overview of Periodic Trends These trends are based on periodic variations in a single fundamental property, the effective nuclear charge (Zeff), which increases from left to right and from bottom to top in the periodic tableThe diagonal line separates the metals (to the left of the line) from the nonmetals (to the right)1. Metals have low electronegativities; they tend to lose electrons in chemical reactions to form compounds in which they have positive oxidation states2. Nonmetals have high electronegativities; they tend to gain electrons in chemical reactions to form compounds in which they have negative oxidation states
438 21.1 Overview of Periodic Trends The semimetals lie along the diagonal line dividing metals and nonmetals; they exhibit properties and reactivities intermediate between those of metals and nonmetalsElements of Groups 13, 14, and 15 span the diagonal line separating metals and nonmetals, and their chemistry is more complex than predicted based solely on their valence-electron configuration
439 Unique Chemistry of the Lightest Elements The chemistry of the second-period element of each group (n = 2; Li, Be, B, C, N, O, and F) differs in many important aspects from that of the heavier members, or congeners, of the groupThe elements of the third period (n = 3; Na, Mg, Al, Si, P, S, and Cl) are generally more representative of the group to which they belong