The half life period of a substance is 50 minutes at a certain initial concentration. When the concentration is reduced to one half of the initial value, the half-life period is 25 minutes. Calculate the order of the reaction.

Explanation

Let us suppose that the initial concentration in the first case is a `molL^(-1)`. According to available data,
When `[A_(0)]_(1) = a,(t_(1//2))_(1)` = 50 minutes.
When `[A_(0)]_(2) = a//2,(t_(1//2))_(2)= 25` minutes.
We know that for the nth order
`t_(1//2) propto 1/[A_(0)]^(n-1)`
`(t_(1//2))_(1)/((t_(1//2))_(2)) = [A_(0)]_(2)^(n-1)/[A_(0)]_(1)^(n-1)={[A_(0)]_(2)/[[A_(0)]_(1)}}^(n-1)`
On substituting the values,
`(50 "minutes")/(25 "minutes") = ((a//2)/(a))^(n-1)` or `2/1 = (1//2)^(n-1)` or `(2/1)^(1) = (2/1)^(1-n)`