# PRINCIPLES OF CHEMISTRY II CHEM 1212 CHAPTER 13

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PRINCIPLES OF CHEMISTRY II CHEM 1212 CHAPTER 13
DR. AUGUSTINE OFORI AGYEMAN Assistant professor of chemistry Department of natural sciences Clayton state university

CHAPTER 13 CHEMICAL KINETICS

RATES OF REACTIONS each other and interact to form products
- Chemical reactions occur when reactant species strike each other and interact to form products Reaction kinetics is studied to - improve production of materials - increase quality and quantity of products - increase energy efficiency - minimize pollution etc

RATES OF REACTIONS Rate = change per unit time Rate of reaction = change in concentration per unit time

RATES OF REACTIONS For a chemical reaction Reactant → Product
- Rate at which reactants are consumed or products are formed in a given period of time is given as Units: M/s Square brackets represent molar concentrations [reactant] = reactant concentration [product] = product concentration

RATES OF REACTIONS Rate of appearance of product = rate of disappearance of reactant - Reactant concentration decreases during reaction ∆[reactant] is negative - Product concentration increases during reaction ∆[product] is positive - Rate is always positive - Rate can be measured by following the concentrations of reactants or products

INSTANTANEOUS AND AVERAGE RATES
- Rate of reaction is generally not constant - Rate of reaction changes over the course of reaction - Concentration of reactants or products are measured at regular time intervals - A graph of concentration vs time may be plotted - Instantaneous rate at a given time is the slope of the tangent to the curve at that time - Average rate is measured rate over a time interval

INSTANTANEOUS AND AVERAGE RATES
∆y ∆x

REACTION STOICHIOMETRY
- Rate depends on stoichiometry of the reaction - Rate is the ratio of rate of change of a substance to its coefficient Consider the reaction 2HBr(g) → H2(g) + Br2(g) 2 mol HBr : 1 mol of each product

REACTION STOICHIOMETRY
For the decomposition of HBr 2HBr(g) → H2(g) + Br2(g) If HBr concentration is decreasing at a rate of 0.52 M/s What is the rate of the reaction? What is the rate of appearance of H2 and Br2?

Factors Affecting Rate of Chemical Reaction
RATES OF REACTIONS Factors Affecting Rate of Chemical Reaction - Concentration of reactants - Reaction temperature - Physical nature of reactants - Catalysts

Concentration of Reactants
RATES OF REACTIONS Concentration of Reactants - An increase in the concentration of reactants causes an increase in the rate of reaction - Collisions are more frequent in a given time for higher concentrations

RATES OF REACTIONS Reaction Temperature
- An increase in temperature of a system increases the average kinetic energy of the reacting molecules - An increase in kinetic energy results in an increase in collisions in a given time - The rate of a chemical reaction normally doubles for every 10 oC raise in temperature

Physical State of Reactants: solid, liquid, or gas
RATES OF REACTIONS Physical State of Reactants: solid, liquid, or gas solid-state reactants liquid-state reactants gaseous-state reactants < < Increasing rate of reaction

RATES OF REACTIONS Physical State of Reactants: solid, liquid, or gas
- Most frequent collisions occur in the gaseous state (the most freedom of movement of particles) Solid-State Particle Size - Smaller particles have larger surface area and higher reaction rates - Extremely small particles may result in very fast reaction rates and may lead to explosion

Catalysts increase the rate of a reaction without being used up
RATES OF REACTIONS Catalysts Catalysts increase the rate of a reaction without being used up

RATE LAW - Rate of reaction is strongly influenced by concentrations
of reacting species - Rate is proportional to the product of the concentrations of the reactants each raised to some power aA + bB → cC + dD Rate = k[A]x[B]y x and y are usually positive integers k = rate constant

RATE LAW aA + bB → cC + dD Rate = k[A]x[B]y
- x and y are not necessarily coefficients of A and B - x and y are the orders of the reaction - Described as xth order in A and yth order in B If x = 1 and y = 2 The reaction is first order in A and second order in B Overall order = = 3

The reaction is first order in NO2 and first order in F2
RATE LAW Example For the reaction 2NO2(g) + F2(g) → 2NO2F(g) Rate = k[NO2][F2] The reaction is first order in NO2 and first order in F2

INITIAL RATE OF REACTION
The decomposition of nitrosyl chloride was studied: 2NOCl(g) ↔ 2NO(g) + Cl2(g) The following data were obtained [NOCl]0 (molecules/cm3) 3.0 x 1016 2.0 x 1016 1.0 x 1016 4.0 x 1016 Initial Rate (molecules/cm3·s) 5.98 x 104 2.66 x 104 6.64 x 103 1.06 x 105 What is the rate law? Calculate the rate constant Rate = k[NOCl]2, k = 6.64 x cm3/molecules∙s

INITIAL RATE OF REACTION
The reaction below was studied at -10 oC 2NO(g) + Cl2(g) → 2NOCl(g) The following data were obtained [NO]0 (mol/L) 0.10 0.20 [Cl2]0 (mol/L) 0.10 0.20 Initial Rate (mol/L) 0.18 0.36 1.45 What is the rate law? Calculate the rate constant Rate = k[NO]2[Cl2], k = 1.8 x 102 L2/mol2

CONCENTRATION AND TIME
- Rate of reaction decreases with time - Rate of reaction eventually goes to zero - Concentrations of reactants decrease - Concentrations of products increase

ZERO-ORDER RATE LAW - Rates are independent of the concentrations of the reactants R → product Rate = k[R]0 Rate = k - Called differential rate law Unit of k = unit of reaction rate = M/s

- Graph of concentration vs time
ZERO-ORDER RATE LAW - Graph of concentration vs time Concentration Time

ZERO-ORDER RATE LAW - Rates are independent of the concentrations of the reactants R → product [R]t = [R]0 - kt - Called integrated rate law Unit of k = unit of reaction rate = M/s Examples Metabolism of ethyl alcohol in the body Biochemical reactions involving enzymes

- Graph of concentration vs time is a straight line
ZERO-ORDER RATE LAW - Graph of concentration vs time is a straight line Concentration Slope = −k Intercept = [R]0 Time

ZERO-ORDER RATE LAW HALF - LIFE
- A large value of k implies a fast reaction - The half-life (t1/2) is also used to describe the speed of a reaction - Half-life is the time needed for the concentration of a reactant to decrease to half its original value - A short half-life indicates a fast reaction

ZERO-ORDER RATE LAW HALF - LIFE
At t = 0 Initial concentration = [R]0 At half-life t = t1/2 [R]t = ½[R]0 - Substitute in zero-order equation and simplify

ZERO-ORDER RATE LAW HALF - LIFE
- Using the zero-order rate equation [R]t = [R]0 – kt - Simplifying gives - Half-life for zero-order depends on concentration

ZERO-ORDER RATE LAW The reaction A → B + C
is known to be zero order in A and to have a rate constant of 5.0 x 10-2 mol/L·s at 25 oC. An experiment was run at 25 oC where [A]0 = 1.0 x 10-3 M. a) What is the integrated rate law for this reaction? b) Calculate the half-life for the reaction. c) Calculate the concentration of B after 5.0 x 10-3 s has elapsed. a) [A] = [A]0 - kt b) 1.0 x 10-2 s c) 2.5 x 10-4 M

FIRST-ORDER RATE LAW - Rate is proportional to the concentration of the reactant R → product - Called the differential form of the rate law - Relates differences in concentration and time Unit of k = s-1

- A graph of concentration vs time describes an exponential decay
FIRST-ORDER RATE LAW - A graph of concentration vs time describes an exponential decay Concentration Time

FIRST-ORDER RATE LAW - Rate is proportional to the concentration of the reactant R → product - Called the integrated form of the rate law (describes an exponential decay) - Relates instantaneous concentrations [R]t = concentration of R at any time [R]0 = initial concentration at t = 0 e = base of natural logarithms ≈ 2.718

FIRST-ORDER RATE LAW From the first-order rate equation
Take natural logarithm on both sides and simplify or

A graph of ln[R]t vs time is a straight line
FIRST-ORDER RATE LAW A graph of ln[R]t vs time is a straight line ln[Concentration] Slope = −k Intercept = ln[R]0 Time

FIRST-ORDER RATE LAW HALF - LIFE
At t = 0 Initial concentration = [R]0 At half-life t = t1/2 [R]t = ½[R]0 Substitute in first-order equation and simplify

FIRST-ORDER RATE LAW HALF - LIFE
From the first-order rate equation Substitute and simplify

FIRST-ORDER RATE LAW HALF - LIFE
- Half-life of a first-order reaction is independent of the concentration of the reactant - Depends on only the rate constant (k) - Constant half-life from concentration vs time plot indicates first-order reaction Example Radioactive decay processes

FIRST-ORDER RATE LAW The radioactive isotope 32P decays by first-order kinetics and has a half-life of 14.3 days. How long does it take for 95% of a sample of 32P to decay? k = /day t = 61.8 days

FIRST-ORDER RATE LAW A first-order reaction is 75.0% complete in 320 second. a) What are the first and second half-lives for this reaction? b) How long does it take for 90% completion? a) 160 s for both first and second half-lives b) 532 s

FIRST-ORDER RATE LAW Calculate the half-life of a first order reaction if the concentration of the reactant is M at 30.5 seconds after the reaction starts and is M at 45.0 seconds after the reaction starts. How many seconds after the start of the reaction does it take for the reactant concentration to decrease to M? a) 29.5 s b) 94.9 s

SECOND-ORDER RATE LAW - Rate is proportional to the concentration of the reactant raised to the second power R → product - Called the differential form of the rate law - Relates differences in concentration and time Unit of k = M-1s-1 or L/mol·s

- Graph of concentration vs time
SECOND-ORDER RATE LAW - Graph of concentration vs time Concentration Time

SECOND-ORDER RATE LAW - Rate is proportional to the concentration of the reactant raised to the second power R → product - Called the integrated form of the rate law Unit of k = M-1s-1 or L/mol·s

- A graph of 1/concentration vs time is a straight line
SECOND-ORDER RATE LAW - A graph of 1/concentration vs time is a straight line 1/[Concentration] Slope = k Intercept = 1/[R]0 Time

Half-life depends on starting concentration
SECOND-ORDER RATE LAW HALF-LIFE Half-life depends on starting concentration

SECOND-ORDER RATE LAW For the reaction A → products
successive half-lives are observed to be 10.0, 20.0, and 40.0 min for an experiment in which [A]0 = 0.10 M. Calculate the concentration of A at a) 30.0 min b) 70.0 min c) 80.0 min a) M b) M c) M

SECOND-ORDER RATE LAW Consider the following initial rate data for the decomposition of compound AB to give A and B [AB]0, mol/L: Initial rate, mol/L·s: x x x 10-2 Determine the half-life for the decomposition reaction initially having 1.00 M AB present Rate = k[AB]2 k = L/mol·s t1/2 = 12.5 s

RATE AND TEMPERATURE - Almost all reactions go faster at higher temperatures - The rate of most reactions increase at increasing temperature - The order of the reaction usually does not change with temperature

RATE AND TEMPERATURE Example For the reaction
NO(g) + O3(g) → NO2(g) + O2(g) The rate constant increases with increasing temperature k (L/mol·s) T (K)

COLLISION THEORY - Explains the rate of reactions in terms of molecular-scale collisions - The basic assumption is that molecules must collide to react - The collision frequency (Z) is the number of collisions per second - Z depends on the concentrations of the reacting species

COLLISION THEORY - The collision frequency (Z) between two molecules is proportional to the product of their concentrations - For two reacting molecules XY and AB Z α [XY][AB] Z = Z0[XY][AB] Z0 = is the proportionality constant Z0 depends on sizes and speed of reacting species

COLLISION THEORY - Collision frequency increases with increasing temperature as molecules move faster - However, the increase in collision frequency cannot account for the temperature dependence of reaction rate - Not every collision results in a chemical reaction

ACTIVATION ENERGY (Ea)
- Not all collisions result in the formation of products (by Svante Arrhenius) - Molecules must collide with enough energy to rearrange the bonds - Molecules bounce off if the total energy of colliding species is not enough - Activation energy (Ea) is the minimum collision energy required for a reaction to occur

THE ACTIVATED COMPLEX - Is a transition state
- The least stable or highest energy transition state - Very unstable and concentration is extremely small - The energy needed to from the activated complex from the reactants is the activation energy - Reactions with high activation energies are generally slower than reactions with low activation energies

ENERGY LEVEL DIAGRAM Activated complex potential energy Ea Reactants
Products Reaction coordinate

EFFECT OF TEMPERATURE - The effect of temperature on reaction rate is influenced by the magnitude of the activation energy - The number of molecules with high enough kinetic energies to initiate a reaction is directly related to temperature - The fraction of collisions (fr) with energy in excess of Ea R is the gas constant = J/mol·K T is the temperature in Kelvin

EFFECT OF TEMPERATURE - fr is between 0 and 1
- fr gets closer to 1 as T increases - Ea does not change with T - Number of collisions exceeding Ea increases exponentially with T

ENERGY DISTRIBUTION IN GAS MOLECULES
Low Temperature Gas Fraction High Temperature Gas Ea Energy

EFFECT OF TEMPERATURE Rate of reaction = (collision frequency) x (fraction exceeding Ea) Rate = Z x fr Z = Z0[XY][AB] Experimental rate = k[XY][AB] k is the rate constant

STERIC FACTOR - The expression predicts faster rates than experimentally observed - Not all collisions with energies greater than Ea result in a reaction - The correct orientation of reactants is an important factor - The steric factor (p) expresses the need for the correct orientation Rate = (steric factor) x (collision frequency) x (fraction exceeding Ea)

STERIC FACTOR A = pZo A is known as the pre-exponential term
The Arrhenius equation - A includes the steric factor and cannot be predicted by theory - A can only be determined by experiment

THE ARRHENIUS EQUATION
Take natural log of both sides For an Arrhenius plot - That is a graph of ln k versus 1/T Slope = -Ea/R Intercept = ln A

THE ARRHENIUS EQUATION
Consider rate constants k1 and k2 at temperatures T1 and T2

THE ARRHENIUS EQUATION
The activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186 kJ/mol. The rate constant at 555 K is 3.52 x 10-7 L/mol·s. What is the rate constant at 645 K? 9.60 x 10-5 L/mol·s

THE ARRHENIUS EQUATION
A first order reaction has rate constant of 4.6 x 10-2 s-1 and 8.1 x 10-2 s-1 at 0 oC and 20 oC, respectively. What is the value of the activation energy? Ea = 19 kJ/mol

THE ARRHENIUS EQUATION
A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from 22 oC to a higher temperature, the rate constant increases by a factor of Calculate the higher temperature. T2 = 324 K or 51 oC

CATALYSIS Rate of reaction can be increased in two ways
1) Increase the temperature 2) Reduce the activation energy or increase the steric factor (addition of catalyst) - A catalyst is a substance that increases the rate of reaction but is not consumed in the reaction - A catalyzed reaction generally has lower activation energy

CATALYSIS - Catalysts increase the rate of a reaction without being used up - Provide alternative reaction pathways with lower activation energies Uncatalyzed reaction: X + Y → XY Catalyzed reaction: Step X + C → XC Step XC + Y → XY + C

CATALYSIS uncatalyzed activation energy potential energy catalyzed
Reaction pathway

HOMOGENEOUS CATALYSIS
- Present in the same phase as the reactants Example N2(g) + O2(g) → 2NO(g) The formation of ozone

HETEROGENEOUS CATALYSIS
- Present in a different phase from the reactants Examples Use of solid metal catalysts such as platinum, nickel, palladium, titanium Use of platinum catalyst for the production of methanol from hydrogen and carbon monoxide 2H2(g) + CO(g) → CH3OH(g) - Catalysts can determine the nature of products formed Platinum catalyst produces methanol Nickel catalyst produces methane and water

ENZYME CATALYSIS - Enzymes are large molecules that catalyze specific
biochemical reactions - An enzyme is specifically tailored to facilitate a given reaction - Enzymes increase the rate of reaction by increasing the steric factor rather than decreasing the activation energy - Enzymes are generally named after the reactions they catalyze (that is their functions) Examples Carboxypeptidase-A, Alcohol dehydrogenase (ADH)

COLLISIONS BETWEEN MOLECULES
- The sequence of steps leading from reactants to products is known as the reaction mechanism - Some reactions require only one step (a single collision) - Other reactions require more than one collisions leading to the formation of intermediates

INTERMEDIATES - Compounds that are produced in one step and consumed in another - Not observed among the products of the reaction - Differ from activated complex - An intermediate is in a shallow minimum in the energy level diagram - An activated complex occurs at the maximum in the

ENERGY LEVEL DIAGRAM potential energy Intermediates Reactants Products
Reaction coordinate

ELEMENTARY STEP - Chemical equation that describes an actual molecular-level event - The overall reaction is the sum of the elementary reactions Example NO2 + NO2 → NO3 + NO step 1 NO3 + CO → NO2 + CO2 step 2 NO2 + CO → NO + CO2 overall NO3 is an intermediate

RATE LAW FOR ELEMENTARY STEP
- Rate law of an elementary step can be written directly from the stoichiometry of that step Consider an elementary step iA + jB → products Rate = k[A]i[B]j - The rate law for an overall reaction cannot be determined from the stoichiometry

RATE LAW FOR ELEMENTARY STEP
Molecularity - The number of species involved in a single elementary step Unimolecular Step - Involves the spontaneous decomposition of a single molecule - First-order rate law describes the kinetics HCl → H + Cl Bimolecular Step - Involves the collision of two species - Second-order rate law describes the kinetics NO2 + NO2 → N2O4

RATE LAW FOR ELEMENTARY STEP
Termolecular Step - Involves the collision of three species - Third-order rate law describes the kinetics - Uncommon NO2 + NO + O2 → NO3 + NO2 - Collisions involving four or more species are very rare

RATE-LIMITING STEP - The slowest elementary step in a given reaction
- The rate of a chemical reaction is limited by the rate of the slowest step - The rate law of the slowest step is consistent with the experimental rate law of the overall reaction Example 2NO ↔ N2O2 fast, reversible N2O2 + Cl2 → 2NOCl slow step (rate limiting)

COMPLEX REACTION MECHANISMS
- Reactions in which the rate limiting step is not the first step - Reaction rate may depend on intermediates - Intermediates are unstable and their concentrations are difficult to measure - Rate laws are not written in terms of intermediates - Other complex reactions contain rapid and reversible steps before the rate-limiting step

ENZYME METABOLISM - Many enzyme catalyzed reactions follow the
Michaelis-Menten mechanism E + S ↔ ES → E + P - Rate of reaction is zero order in substrate (S) Substrate - The compound on which the enzyme acts - Product (P) does not bind to enzyme (E) - First step is fast and reversible - Second step is irreversible