Question

Half-life of first order reaction is 20 minutes. What is the time taken to reduce the initial concentration of the reactant to `1/10`th?

Options

• 66.56 min

• 6.6 min

• 150 min

• 79.68 min

Answer 1

66.56 min

Explanation:

For first order reaction,

k = `0.693/"t"_(1//2) = 0.693/20` = 0.0346 min^-1

Here, if [A]₀ = 1, [A]_t = `1/10`, t_1/10 = ?

k = `2.303/"t" log  (["A"]_0)/(["A"]_"t")`

`therefore "t"_(1//10) = 2.303/0.0346` log 10

= 66.56 min