Chapter 12, Problem 126MP

Consider the following reaction:

${\text{CH}}_{\text{3}}\text{X}+\text{Y}\to {\text{CH}}_{\text{3}}\text{Y}+\text{X}$

At 25°C, the following two experiments were run, yielding the following data:

Experiment 1: [Y]₀ = 3.0 M

[CH3X] (mol/L)	Time(h)
7.08 × 10−3	1.0
4.52 × 10−3	1.5
2.23 × 10−3	2.3
4.76 × 10−4	4.0
8.44 × l0−5	5.7
2.75 × l0−5	7.0

Experiment 2: [Y]₀ = 4.5 M

[CH3X] (mol/L)	Time(h)
4.50 × 10−3	0
1.70 × 10−3	1.0
4.19 × 10−4	2.5
1.11 × 10−4	4.0
2.81 × l0−5	5.5

Experiments also were run at 85°C. The value of the rate constant at 85°C was found to be 7.88 × 10⁸ (with the time in units of hours), where [CH₃X]₀ = 1.0 × 10⁻² M and [Y]₀ = 3.0 M.

a. Determine the rate law and the value of k for this reaction at 25°C.

b. Determine the half-life at 85°C.

c. Determine E_a for the reaction.

d. Given that the C8X bond energy is known to be about 325 kJ/mol, suggest a mechanism that explains the results in parts a and c.