Chapter 12, Problem 104CP

Two isomers (A and B) of a given compound dimerize as follows:

$\begin{array}{l}\text{2A}\stackrel{k_1}{\to }{\text{A}}_{\text{2}}\\ \text{2B}\stackrel{k_2}{\to }{\text{B}}_{\text{2}}\end{array}$

Both processes are known to be second order in reactant, and k₁

is known to be 0.250 L/mol · s at 25°C. In a particular experiment A and B were placed in separate containers at 25°C, where [A]₀ = 1.00 × 10⁻²M and [B]₀ = 2.50 × 10⁻² M. It was found that after each reaction had progressed for 3.00 min, [A] = 3.00[B]. In this case the rate laws are defined as

$\begin{array}{l}\text{Rate}=-\frac{\Delta [A]}{\Delta t}=k_1{[A]}^2\\ Rate=-\frac{\Delta [\text{B}]}{\Delta t}=k_2{[\text{B}]}^2\end{array}$

a. Calculate the concentration of A₂ after 3.00 min.

b. Calculate the value of k₂ .

c. Calculate the half-life for the experiment involving A.