Question

A first order reaction is 20% complete in 10 minutes. Calculate the time taken for the reaction to go to 80% completion.

Answer 1

Given:

A first-order reaction

20% complete in 10 minutes

Need to calculate time for 80% completion

By using first-order rate law

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

For 20% completion

[A] = 80% of [A]₀

`k = 2.303/10 log (100/80)`

= `(2.303/10) log(1.25)`

`k = (2.303 xx 0.0969)/10`    ...(log 1.25 = 0.0969)

k = 0.02233 min⁻¹

For 80% completion

[A] = 20% of [A]₀

`t = 2.303/k log (100/20)`

`t = (2.303/0.02233) log 5`

`t = (2.303 xx 0.6990)/0.02233`    ...(log 5 = 0.6990)

t = 1.610/0.02233`

= 72.1 minutes