Study Guide to Chemical Kinetics

 

DISCLAIMER: This Guide is not meant to be exhaustive. That is, I have tried to summarize the essential points of the lectures on this topic. The presence of a topic here does not guarantee a related question on an exam, nor are exam topics limited to what appears in this Guide. As with any Chemistry class, you are responsible for ALL of the assigned readings, problems and lecture material. Lectures will often contain information not covered or given less emphasis in the text. 

 
 
 

Text Reading

Chapter 15 (pages 703-749)

Chapter 5, Section 6 (pages 154-162)

 
 

What should you learn from this section of the course?

The lectures will initially be concerned with basic concepts such as rate constants, orders of reaction, integral and differential rate laws for simple first and second order reactions and half-lives. We shall then focus on more interesting aspects of kinetics. The extraction of a plausible mechanism from the rate law and the use of a fast pre-equilibrium or the steady state assumption to give physical meaning to kinetic mechanisms is an important topic for any chemical or biochemical scientist. You also need to be able to apply these concepts, and to that end you should be familiar with whatever applications we discuss in class (a subset of the possibilities: chain reactions, enzyme kinetics and surface reactions) and ready to tackle any new application using the knowledge you have gained.  We will also examine how temperature affects rate constants.  In order to gain this understanding, we will need to recall (in a qualitative way) the distribution of speeds and energies of atoms/molecules as a function of temperature (Chapter 5).

 

               General

o      Definitions of kinetic terms such as reaction order, rate and rate constant

o      Difference between elementary reactions and mechanisms

o      Using experimental data to obtain rate constants and/or half-lives

o      Be able to plot kinetic data

o      Understand how speed and energy depend on temperature

 

               Rate Laws and Mechanisms

o      Differential and integral rate laws for reversible first order reactions

o      Difference between prior equilibrium and steady state (SSA) assumptions

o      Use SSA to obtain rate law from mechanism 

 

               Temperature Dependence of Rate Constants

o      Arrhenius model

o      Collision theory model 

 

               Applications (as time allows)

o      Chain reactions

o      Enzyme kinetics

o      Surface reactions

o      Unimolecular Chemistry

 

 

 

Recommended Problems

Chapter 15 Problems

Reaction Rates: 11, 13.  Rate laws: 15, 21, 25, 27, 33.  Mechanisms: 43, 45, 47, 51.  Temp. Dependence:  55, 57, 59, 63, 65.  Mixed Concepts:  73, 75, 79, 85, 87

Chapter 5 Problems

Kinetic Theory of Gases:  63, 65, 67, 127

 
 
 

Additional Problems

1.  Consider the hydrolysis of acetyl chloride (CH3COCl) to produce acetic acid (CH3COOH) and hydrochloric acid (HCl).  Note: water is the solvent.

CH3COCl  +  H2O -> CH3COOH  +  HCl

Experimentally the rate law is found to be

     d[CH3COCl]/dt  =  k [CH3COCl] [H2O]

At the beginning of the reaction, the concentration of CH3COCl is 0.10 M.

(i)   At the beginning of the reaction, what is the concentration of H2O?

(ii)  If the reaction proceeds to completion what is the final concentration of H2O?

(iii) If k = 1.16 x 103  M1 s1, how long will it take for the concentration of CH3COCl to be reduced to 0.05 M?

 

2.   The gas phase reaction of nitric oxide, NO, with chlorine, Cl2, occurs according to the equation:

                        2 NO  +  Cl2 -> 2 NOCl

      The experimental rate law is:

                        (1/2) d[NOCl]/dt  =  k [NO]2 [Cl2] 

      A possible reaction mechanism is:

      (i)               2 NO -> N2O2                             (fast, at equilibrium)

      (ii)              N2O2 +  Cl2 -> 2 NOCl                (slow)

      Identify the rate determining step (rds), show that this mechanism is consistent with the rate law, and express the experimental rate constant, kexp, in terms of the rate constants for the elementary processes. 

 

3.   An alternative mechanism for the reaction considered in Problem #2 is:

      (i)               NO  +  Cl2 -> NOCl2                  (fast, at equilibrium)

      (ii)              NOCl2  +  NO -> 2NOCl            (slow)

      Identify the rds, derive an expression for the rate of production of nitrosyl chloride, NOCl, and hence express the experimental rate constant, k'exp, in terms of the rate constants for the elementary processes.  Could kinetic data alone distinguish between the mechanism proposed in this problem and that proposed in Problem #2?

 

4.   The mechanism for the decomposition  2 NO2Cl -> 2 NO2  +  Cl2 is:

                        (i)                     NO2Cl -> NO2  +  Cl

                        (ii)                    NO2Cl  +  Cl -> NO2  +  Cl2

      If step (i) is at equilibrium and fast relative to step (ii), show that the rate of disappearance of NO2Cl is given by:

       d[NO2Cl]/dt  =  2 k2 K [NO2Cl]2 [NO2]-1

 

5. The rate law of the reaction

                        2 NO(g) + H2(g) ---> N2O(g) + H2O(g)

      is investigated at a certain temperature under pseudo-first-order conditions.  The following two experiments are performed:

     (1) 2.0 mol/L of NO is mixed with 0.010 mol/L of H2, and the time dependence of [H2] is determined, with the following results:

time(s)                              [H2] (M)

0                                     1.0x10-2

10                                    6.2x10-3

20                                    3.8x10-3

30                                    2.4x10-3

 

      (2) 2.0 mol/L of H2 is mixed with 0.010 mol/L of NO, and the time dependence of [NO] is determined, with the following results:

time(s)                              [NO] (M)

0                                     1.0x10-2

1000                                8.1x10-3

2000                                6.8x10-3

3000                                5.8x10-3

 

       Determine the rate law of the reaction and the value of the rate constant.

 

6. The following mechanism has been proposed for the decomposition of O3(g) to O2(g):

                        (i)                     O3 -> O2  +  O                  (fast, at equilibrium); K = k1/k-1

                        (ii)                    O  +  O3 -> 2 O2               (slow)

      Identify the rds, derive an expression for the overall rate of production of O2, and hence express the experimental rate constant kexp in terms of the rate constants for the elementary processes. 

 

7.  The following data were obtained in a study of the temperature dependence of the rate constant for the reaction:   N2O5 -> 2 NO2 + (1/2) O2.  Plot these data and calculate the activation energy for this process.

T(K)

338

328

318

308

298

273

k (s-1)

4.8x10-3

1.50x10-3

4.98x10-4

1.35x10-4

3.46x10-5

7.87x10-7

 

8.  The rate of the second-order decomposition of acetaldehyde, CH3CHO, was measured over the temperature range 700 - 1000 K, and the rate constants are reported in the table below.  By plotting these data determine (a) the activation energy Ea and (b) the pre-exponential (frequency) factor A.

T(K)

700

730

760

790

810

840

910

1000

k (M-1s-1)

0.011

0.035

0.105

0.343

0.789

2.17

20.0

145

 

9.  The mechanism for the reaction

                                              2NO(g) + O2(g)  ----> 2NO2(g)

is believed to involve the following steps:

                                               

(a) Derive a 3rd-order rate law consistent with this mechanism.

(b) The rate of the reaction decreases with increasing temperature.  Explain this unusual behavior on the basis of the postulated mechanism, the derived rate law, and the fact that the reaction in Step 1 is exothermic

 

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