Question

A second-order reaction has a rate constant of 1.25 M-1 s-1. If the initial reactant concentration is 1.0 M (a) determine the half-life of this reaction (b) calculate the time required for 90% reaction

Answer 1

Answer:

(a) 0.8 s

(b) t = 7.2 s

Explanation:

(a) Half life expression for second order kinetic is:

$t_{1/2}=\frac{1}{k[A_o]}$

Where,

$[A_o]$ is the initial concentration = 1.0 M

k is the rate constant = 1.25 M⁻¹s⁻¹

So,

$t_{1/2}=\frac{1}{1.25\times 1.0}$

Half life = 0.8 s

(b) Integrated rate law for second order kinetic is:

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

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

For 90% completion, 10% is left. so,

$[A_t]=\frac {10}{100}\times 1.0=0.1\ M$

So,

$\frac{1}{0.1} = \frac{1}{1.0}+1.25t$

t = 7.2 s