Chapter 13: Rates of Reaction 309
CHAPTER 13
Rates of Reaction
Chapter Terms and Definitions
Numbers in parentheses after definitions give the text sections in which the terms are explained. Starred terms are italicized in the text. Where a term does not fall directly under a text section heading, additional information is given for you to locate it.
chemical kinetics* study of reaction rates, how they change under varying reaction conditions, and what molecular events occur during the overall reaction (13.1, introductory section)
catalyst substance that increases the rate of a reaction without being consumed in the overall reaction (13.1, introductory section)
reaction rate increase in molar concentration of product of a reaction per unit time or decrease in molar concentration of reactant per unit time (13.1)
average (rate)* rate of reaction over a time interval ∆t (13.1)
instantaneous (rate)* rate of reaction at a particular instant of time; also the value of Δ[x]/Δt for the tangent to the concentration-versus-time curve at a given instant (13.1)
rate law equation that relates the rate of a reaction to the concentrations of reactants (and catalyst) raised to various powers (13.3)
rate constant (k) proportionality constant in the relationship between rate and reactant concentrations (13.3)
reaction order experimentally determined exponent of the concentration of a species in a rate law (13.3)
overall order of a reaction sum of the exponents in a rate law (13.3)
isomerization* reaction in which one geometric isomer of a compound is converted to another (13.3)
initial-rate method* process of determining reaction orders by varying the starting concentrations of reactants (13.3)
integrated rate law a mathematical relationship between concentration and time (13.4)
half-life (t1/2) time required for the reactant concentration to decrease to one-half its initial value (13.4)
collision theory model that assumes that for reaction to occur, reactant molecules must collide with an energy greater than some minimum value and with the proper orientation (13.5)
activation energy (Ea) minimum energy that two molecules must possess in order to react on collision (13.5)
transition-state theory model that considers the collision of two reactant molecules in terms of an unstable grouping (activated complex) that can break up to form products (13.5)
activated complex (transition state) in transition-state theory, an unstable grouping of atoms that can break up to form products (13.5)
Arrhenius equation k = ; mathematical equation that expresses the dependence of the rate constant on temperature (13.6)
frequency factor symbol A, a constant in the Arrhenius equation related to the frequency of collisions with proper orientation (13.6)
elementary reaction single molecular event, such as a collision of molecules, resulting in a reaction (13.7)
reaction mechanism set of elementary reactions whose overall effect is given by the net chemical equation (13.7)
reaction intermediate species produced during a reaction that does not appear in the net equation because it reacts in a subsequent step in the mechanism (13.7)
molecularity number of molecules on the reactant side of an elementary reaction (13.7)
unimolecular reaction elementary reaction involving one reactant molecule (13.7)
bimolecular reaction elementary reaction involving two reactant molecules (13.7)
termolecular reaction elementary reaction involving three reactant molecules (13.7)
rate-determining step slowest step of a reaction mechanism, the rate of which governs the overall rate of reaction (13.8)
dynamic equilibrium* state in which the rates of the forward and reverse reactions are equal (13.8)
enzymes* proteins that catalyze biochemical processes (13.9)
homogeneous catalysis use of a catalyst that is in the same phase as the reacting species (13.9)
heterogeneous catalysis use of a catalyst (usually a solid) that is in a different phase from the reacting species (13.9)
adsorption* attraction of molecules to a surface (13.9)
physical adsorption* attraction of molecules to a surface through weak intermolecular forces (13.9)
chemisorption binding of one substance to the surface of another owing to chemical bonding forces between the surfaces of both substances (13.9)
catalytic hydrogenation* addition of hydrogen to carbon–carbon multiple bonds of an organic compound in the presence of a catalyst (13.9)
contact process* industrial method of preparing sulfuric acid by the catalytic oxidation of sulfur dioxide (13.9)
substrate substance whose reaction an enzyme catalyzes (13.9)
active site* in an enzyme-catalyzed reaction, the particular place on the enzyme where the substrate binds and the catalysis takes place (13.9)
pump pulse* laser pulse used to excite a reactant molecule to a higher energy state (A Chemist Looks at: Seeing Molecules React)
probe pulse* laser pulse of properly chosen wavelength used to detect a molecule as it transforms to products (A Chemist Looks at: Seeing Molecules React)
Chapter Diagnostic Test
1. Determine whether each of the following statements is true or false. If the statement is false, change it so that it is true.
a. An isotope with a decay constant of 7.32 ´ 10-4 /s has a half-life of 5.07 ´ 10-4 s. True/False: ______
______
b. The exponents of concentrations in the rate-law expression are determined by the stoichiometry of the chemical reaction. True/False:______
______
c. A catalyst operates by reducing the value of DH of a reaction. True/False ______
______
d. In gas-phase kinetics, the molecularity is limited to bimolecular reactions. True/False: ______
______
e. The rate-law expression of rate = 0.91[SO3][F2]2 indicates that the rate law is second order with respect to F2 and third order overall. True/False: ______
______
f. The existence of an activated complex can be substantiated by isolating the species at extremely low temperature. True/False: ______
______
g. When a reaction is influenced by a homogeneous catalyst, the reaction-rate expression is a function of catalyst concentration. True/False: ______
______
2. For the following reactions and data, provide the missing information.
a. Reaction: 2NO(g) + H2(g) ® N2O(g) + H2O(g)
Rate law: Rate = k[H2][NO]2
Order with respect to H2: ______
N2O: ______
NO: ______
H2O: ______
Overall order: ______
b. Reaction: 2H2 + O2 ® 2H2O
Rate law: Rate = ______
Order with respect to H2: second
O2: first
H2O: zero
Overall order: ______
c. Reaction: 2NO2(g) + F2(g) ® 2NO2F(g)
Rate law: Rate = k[NO2] [F2]
Order with respect to NO2: ______
F2: ______
NO2F: ______
Overall order: second
3. The decomposition of acetaldehyde, CH3CHO, has an activation energy of 188.3 kJ/mol and occurs by the mechanism
CH3CHO ® CH3CHO2+ ® CH4 + CO
When this reaction is carried out in the presence of iodine, the activation energy is 138.1 kJ/mol. Sketch the potential-energy diagram for these two cases on the same graph as the reaction progresses. Identify the following on the curves: reactant, product, activation energy, activated complex.
4. Determine which of the following is a correct expression for the average rate of the reaction
aA + bB ® eE + fF
a. Rate =
b. Rate = –f
c. Rate = –
d. Rate =
e. None of the above
5. The debromination of stilbene dibromide by SnCl2 occurs according to the following overall stoichiometry:
(C6H5CHBr)2 + SnCl2 ® (C6H5CH)2 + SnCl2Br2
Kinetic studies indicate that the reaction mechanism entails the following elementary reactions:
(C6H5CHBr)2 + SnCl2 / + SnCl2Br+ / (slow)+ Br– / (fast)
(fast)
SnCl2Br+ + Br– / SnCl2Br2 / (fast)
On the basis of this information, predict the rate-law expression for the debromination reaction and give the order of reaction.
6. The following concentration data were collected for the reaction F2 + 2ClO2 2FClO2 at 350°C and various times.
Rate of formation of FClO2 (M/s) / [F2](M) / [ClO2](M)1.6 ´ 10–3 / 0.15 / 0.015
4.8 ´ 10–3 / 0.15 / 0.045
6.4 ´ 10–3 / 0.15 / 0.060
9.6 ´ 10–3 / 0.30 / 0.045
1.9 ´ 10–2 / 0.60 / 0.045
Calculate the rate constant and order of this reaction.
7. The hydrolysis of (CH2)6CClCH3 is first order. Using the following data, calculate the rate constant k.
t(s) / [(CH2)6CClCH3] (M)0 / 0.650
184 / 0.613
293 / 0.592
314 / 0.588
495 / 0.555
8. Which of the following statements is true?
a. Knowledge of a rate law is useful in understanding how a reaction takes place at the molecular level.
b. A plot of concentration versus time for a first-order reaction is linear.
c. The overall order of a reaction equals the largest exponent in the rate-law expression.
d. A catalyst increases the reaction rate by increasing the activation energy of the reaction.
e. None of the above.
9. When heated, ammonium cyanate, NH4CNO, forms urea, (NH2)2CO, according to the following stoichiometry:
NH4+ + CNO– → (NH2)2CO
The assumed mechanism encompasses the following elementary reactions:
NH4+ + CNO– / NH3 + HCNO / (fast, equilibrium)NH3 + HCNO / (NH2)2CO / (slow)
Verify that the mechanism agrees with the experimentally determined rate law:
Rate = kobs[NH4+][CNO–]
10. Acetonecarbonic acid decomposes to dimethylketone and carbon dioxide. The rate constants for the decomposition were measured at 283 K and 323 K and found to be 1.08 ´ 106/s and 1.85 ´ 108/s, respectively. Calculate the activation energy for this reaction.
11. A substance decomposes according to the first-order rate law. With a rate constant of 4.80 ´ 10-4/s at 45°C, calculate the following:
a. Half-life of the substance
b. Concentration after 725 s if the initial concentration is 0.0824 M
c. Time required for concentration of the substance to decrease to 20.0%
12. The rate constant for the decomposition of PH3 is 0.024 s-1. What is the half-life for the decomposition reaction?
13. The reaction between the hydroxyl radical and carbon monoxide, which is important in atmospheric chemistry, is proposed to occur through the following elementary reactions:
3OH + 3CO 3HOCO*
HOCO* OH + CO
HOCO* H + CO2
HOCO* + M HOCO + M
HOCO H + CO2
Write the overall chemical equation for the hydroxyl radical -CO reaction.
14. Write the rate equation for each elementary reaction in Problem 13 and indicate the molecularity of each.
Answers to Chapter Diagnostic Test
If you missed an answer, study the text section and problem-solving skill (PS Sk.) given in parentheses after the answer.
1.
a. False. An isotope with a decay constant of 7.32 ´ 10-4 /s has a half-life of 9.47 ´ 102 s. (13.4, PS Sk. 6)
b. False. The exponents of concentrations in the rate-law expression are determined experimentally. (13.3)
c. False. A catalyst operates by providing a mechanism in which the energy of activation Ea is lower than in the uncatalyzed reaction. (13.9)
d. False. In gas-phase kinetics, the molecularity is limited to intermolecular reactions. (13.7)
e. True (13.3, PS Sk. 3)
f. False. The activated complex cannot be isolated because it is an unstable species. (13.5)
g. True (13.9)
2.
a. Order with respect to H2: first
N2O: zero
NO: second
H2O: zero
Overall order: third
b. Rate law: Rate = k[H2]2[O2]
Overall order: third
c. Order with respect to NO2: first
F2: first
NO2F: zero (13.3, PS Sk. 3)
3.
(13.5, 13.9)
4. d (13.1, PS Sk. 1)
5. Rate = kobs[(C6H5CHBr)2][SnCl2]; reaction is second order (13.3, 13.8, PS Sk. 11)
6. k = 7.1 ´ 10-1/(M ∙ s); reaction is second order (13.2, 13.3, PS Sk. 4)
7. k = 3.20 ´ 10-4 /s (13.2, 13.4, PS Sk. 5)
8.
a. (13.8); sections for other responses are
b. (13.4)
c. (13.3)
d. (13.9)
9. According to the mechanism, the rate-determining step is the reaction of NH3 and HCNO. The rate-law expression is
Rate = k2[NH3][HCNO]
The concentration of NH3 and that of HCNO are related to NH4CNO by the fast equilibrium reaction with the equilibrium expression
=
In terms of the product, [NH3][HCNO],
[NH3][HCNO] = [NH4+][CNO–]
Substituting this into the rate-law expression gives
Rate = [NH4+][CNO–]
The rate law derived from the mechanism agrees with the experimentally observed rate law, if = kobs. (13.8, PS Sk. 11)
10. 9.77 ´ 104 J (13.6, PS Sk. 7)
11.
a. 1.44 ´ 103 s
b. 0.0582 M
c. 3.35 ´ 103 s (13.4, PS Sk. 5, 6)
12. 29 s (13.4, PS Sk. 6)
13. OH + CO H + CO2 (13.7, PS Sk. 8)
14. Rate = k[OH][CO], bimolecular
Rate = k[HOCO*], unimolecular
Rate = k[HOCO*], unimolecular
Rate = k[HOCO*][M], bimolecular
Rate = k[HOCO], unimolecular (13.7, 13.8, PS Sk. 9, 10)
Summary of Chapter Topics
Chemical kinetics requires a good deal of mathematical computation—involving calculus and logarithms—to answer questions related to reaction rates. Coverage of this topic in your text and this study guide, and in most freshman chemistry courses, does not use calculus but does use logarithms. You were introduced to the use of natural logarithms in Section 11.2 of this study guide. You may wish to look back for a review.
13.1 Definition of a Reaction Rate
Learning Objectives
· Define reaction rate.
· Explain instantaneous rate and average rate of a reaction.
· Explain how the different ways of expressing reaction rates are related. (Example 13.1)
· Calculate average reaction rate. (Example 13.2)
Problem-Solving Skills
1. Relating the different ways of expressing reaction rates. Given the balanced equation for a reaction, relate the different possible ways of defining the rate of the reaction (Example 13.1).
2. Calculating the average reaction rate. Given the concentration of reactant or product at two different times, calculate the average rate of reaction over that time interval (Example 13.2).
Exercise 13.1
For the reaction given in Example 13.1, how is the rate of formation of NO2F related to the rate of reaction of NO2?
Known: By definition, the rate of formation of NO2F is
and the rate of reaction of NO2 is
–
Solution: Divide each rate by the coefficient of the appropriate substance in the reaction, and set these expressions equal:
= –
which can be written as
= –
In words this reads, “The rate of formation of NO2F is equal to the rate of reaction of NO2.”
Exercise 13.2
Iodide ion is oxidized by hypochlorite ion in basic solution.
I–(aq) + ClO–(aq) Cl–(aq) + IO–(aq)
In 1.00 M NaOH at 25°C, the iodide ion concentration (equal to the ClO– concentration) at different times was as follows: