Question

The ratio of the time required for `3/4`th of the reaction of first order to complete to that required for half of the reaction is ______.

Options

• 4 : 3

• 3 : 2

• 2 : 1

• 1 : 2

Answer 1

The ratio of the time required for `3/4`th of the reaction of first order to complete to that required for half of the reaction is 2 : 1.

Explanation:

We are given a first-order reaction and asked to find the ratio:

`t_(3//4)/t_(1//2) = ?`

For a first-order reaction, the time required to reduce the concentration from [A]₀ to [A] is:

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

Time for half-reaction:

`t_(1//2) = 2.303/k log 2`

That means [A] = 14 [A]₀

`t_(3//4) = 2.303/k log([A]_0/([A]_0//4))`

= `2.303/k log 4`

By taking the ratio:

`t_(3//4)/t_(1//2) = (log 4)/(log 2)`

= `2/1`

= 2 : 1