Question

A first order reaction takes 100 minutes for completion of 60 per cent of reaction. Find the time when 90% of the reaction will be completed.

Answer 1

Given: For first-order reaction:

Time to complete 60% = 100 minutes

Time for 90% completion = ?

Using first-order rate law:

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

⇒ t = `2.303/k log(1/(1 - x))`

Where x = fraction of reaction completed.

At 60% completion:

x = 0.90

⇒ `[A]_0/([A]) = 1/0.10`

= 10

`t = 2.303/0.009164 log (10)`

= `(2.303 xx 1)/(0.009164)`

= `2.303/0009164`

= 251.3 minutes