Physical Chemistry Third Edition

532 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms

Solution reactions that are much slower than diffusion-limited reactions are called

activation-limited reactions. After an encounter occurs, the molecules undergo numer-

ous collisions inside a “cage” of other molecules before finally reacting. The rate of

collisions is very large (see Example 9.12), but only a small fraction of them will

lead to reaction. If this fraction depends only on the temperature, the rate will be

proportional to the number of encounters as well as to the fraction of collisions that lead

to reaction. Since the number of 2–3 encounters is proportional to the number of type

2 molecules and the number of type 3 molecules, an activation-limited bimolecular

elementary reaction is first order with respect to each reactant and second order

overall, just as with a diffusion-limited reaction and a gas-phase reaction. The rate of

a reaction between molecules of the same substance is second order with respect to

that substance, and its temperature dependence should be similar to that of a gas-phase

reaction.

Termolecular and Unimolecular Liquid-Phase Reactions

The rates of diffusion-limited termolecular elementary processes in liquid phases

are proportional to the number of encounter pairs (pairs of molecules in the midst

of an encounter) and also to the number of “third” molecules present to diffuse

into the same cage as the encounter pair. Therefore, diffusion-limited termolecular

elementary processes are third order, just as in the gas phase. Activation-limited

termolecular elementary reactions in liquids are also third order if the fraction of

collisions that lead to reaction is independent of the concentration. We assume further

that unimolecular elementary processes in liquids exhibit first-order kinetics, as in

the gas phase. We can now summarize the facts for elementary processes in both

liquids and gases:The molecularity of a substance in an elementary process is equal

to its order, and the overall order is equal to the sum of the orders of the individual

substances.

PROBLEMS

Section 12.2: Elementary Processes in Liquid Solutions

12.1 The reaction

2I−→I 2

is diffusion-controlled in carbon tetrachloride and also in

water. Estimate the rate constant of the reaction in water at

20 ◦C from data in Example 12.3 and from viscosities in

Table A.18 of Appendix A.

12.2 The reaction in aqueous solution

NH+ 4 +OH−−→NH 3 +H 2 O

is diffusion-controlled with rate constant equal to

1. 0 × 1010 L mol−^1 s−^1 at some temperature. Estimate the

sum of the diffusion coefficients of NH+ 4 and OH−at this

temperature.

12.3 Compute the reaction diameterd 12 for the reaction

CH 3 CO− 2 +H+−→CH 3 CO 2 H

for whichk 4. 5 × 1010 L mol−^1 s−^1. Use the values of

the ion mobilities from Table A.20 of Appendix A.

12.4 a.The reaction

2CH 3 −→C 2 H 6

in toluene is diffusion-controlled. The viscosity of

toluene at 30◦C is equal to 5. 236 × 10 −^4 kg m−^1 s−^1.

Estimate the rate constant of the reaction. State any

assumptions.

b.The viscosity of toluene at 20◦C is equal to 5. 9 ×

10 −^4 kg m−^1 s−^1. Estimate the activation energy of the