# Problem: The reaction A =&gt; B + C is second order in A. When the initial [A] = 0.100 M, the reaction is 20.0% complete in 26.2 minutes. Calculate the value of the rate constant (in L/min·mol).a. 8.22x10-2 b. 9.54x10-2c. 1.53d. 1.05e. 0.91

###### FREE Expert Solution

We’re being asked to determine the rate constant (k) of a second-order reaction:

B + C

The concentration of A decreases by 80% (from 100% - 20% = 80%) starting 0.1 M in 26.2 minutes. 80% of 0.1 M is:

0.1 M x 0.8 = 0.08 M

The integrated rate law for a second-order reaction is as follows:

$\overline{)\frac{\mathbf{1}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{t}}}{\mathbf{=}}{\mathbf{kt}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}}}$

where:

[A]t = concentration at time t

k = rate constant

t = time

[A]0 = initial concentration

###### Problem Details

The reaction A => B + C is second order in A. When the initial [A] = 0.100 M, the reaction is 20.0% complete in 26.2 minutes. Calculate the value of the rate constant (in L/min·mol).

a. 8.22x10-2

b. 9.54x10-2

c. 1.53

d. 1.05

e. 0.91