Question

The rate of a first order reaction is 0.04 mol litre^-1 s^-1 at 10 minutes and 0.03 mol litre^-1 sec^-1 at 20 minutes after initiation. The half-life of the reaction is ______ min.

Options

• 24

• 10

• 36

• 30

Answer 1

The rate of a first order reaction is 0.04 mol litre^-1 s^-1 at 10 minutes and 0.03 mol litre^-1 sec^-1 at 20 minutes after initiation. The half-life of the reaction is 24 min.

Explanation:

Rate r = k[A]

0.04 = k [A₀]₁₀

0.03 = k [A]₂₀

`=> (["A"_0]_10)/(["A"]_20) = 0.04/0.03 = 4/3`

From t = `2.303/"k" log  (["A"]_10)/(["A"]_20)`

`=> 10 = 2.303/k log  4/3`

`=> 10 = 2.303/k (0.6020 - 0.4771)`

`=> k = 2.303/10 xx 0.1249`

= 2.876 × 10^-2 min^-1

`"t"_(1//2) = 0.693/k`

`= 0.693/(2.876 xx 10^-2)`

= `0.24 xx 10^2` min

= 24 min