Question

"A reaction is second order respect to the reactant A. If the reaction is 85% complete in 12 minutes, how long would it take for the reaction to be 15% complete?"

Answer 1

Answer:

0.3738 min

Explanation:

Integrated rate law for second order kinetics is:

$\frac{1}{[A_t]} = \frac{1}{[A]_0}+kt$

Where, $[A_t]$ is the final initial concentration

$[A_0]$ is the initial concentration

k is the rate constant

t is the time

Given that:-

85% is complete which means that 0.85 of $[A_0]$ is decomposed. So,

${[A_t]}$ = 1 - 0.85$[A_0]$  = $0.15[A_0]$

t = 12 minutes

$\frac{1}{0.15[A_0]} = \frac{1}{[A]_0}+k\times 12$

$\frac{5.6666}{[A_0]} =12k$  

$[A_0]=\frac{5.6666}{12k}$    -  1

Also,  

15 % is complete which means that 0.15 of $[A_0]$ is decomposed. So,

${[A_t]}$ = 1 - 0.15$[A_0]$  = $0.85[A_0]$

t = ?

$\frac{1}{0.85[A_0]} = \frac{1}{[A]_0}+kt$

$\frac{0.1765}{[A_0]} =tk$  

Applying value from 1

$\frac{0.1765}{\frac{5.6666}{12k}} =tk$  

$t=\frac{2.118}{5.6666}\ min=0.3738\ min$