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

(a) 0.8 s

(b) t = 7.2 s

Step-by-step explanation:

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

`t_(1/2)=(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)=(1)/(1.25* 1.0)`

Half life = 0.8 s

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

`(1)/([A_t]) = (1)/([A]_0)+kt`

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

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

`[A_t]=\frac {10}{100}* 1.0=0.1\ M`

So,

`(1)/(0.1) = (1)/(1.0)+1.25t`

t = 7.2 s