Question

A second order reaction is 50% complete in 15 min. How long after the start of the 10 reaction will it be 85% complete?

Answer 1

Answer: 85 minutes

Explanation:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

Half life for second order kinetics is given by:

$t_{\frac{1}{2}=\frac{1}{k\times a_0}$

$t_{\frac{1}{2}$ = half life = 15 min

k = rate constant =?

$a_0$ = initial concentration = 100 (say)

$15min=\frac{1}{k\times 100}$

$k=\frac{1}{1500}$

Integrated rate law for second order kinetics is given by:

$\frac{1}{a}=kt+\frac{1}{a_0}$

a= concentration left after time t = $100-\farc{85}{100}\times 100=15$

$\frac{1}{15}=\frac{1}{1500}\times t+\frac{1}{100}$

$t=85min$

Thus after 85 minutes after the start of the reaction, it will be 85% complete.