Question

A first order reaction takes 40 minutes for 30% decomposition. What is the half-life of reaction?

Options

• 59.5 min

• 77.8 min

• 67.8 min

• 82.2 min

Answer 1

77.8 min

Explanation:

First order reaction,

t = 40 min

k = `2.303/40 log ["A"_0/("A"_0 - (30  "A"_0)/100)]`

= `2.303/40 log [(100  "A"_0)/(70  "A"_0)]`

= `2.303/40 (log  10/7)`

= 0.00892 min⁻¹

t_1/2 = `0.693/"k" = 0.693/0.00892` = 77.8 min⁻¹