The half-life of a zero order reaction is x second. If the reaction takes `t_(1)` second to complete, calculate `t_(1)` in terms of x.

Explanation

The integrated rate equation of a zero order reaction is : `[A]=[A]_(0)-kt,` where `[A]_(0)` = initial concentration of the reactant [A] = concentration of the reactant after time't' (from the start of the reaction) and k = rate constant.
(1) when, `t=x,[A]=([A]_(0))/(2)`
`therefore([A]_(0))/(2)=[A]_(0)-kxthereforex=([A]_(0))/(2k) " " ...[1]`
If the reaction takes time `t_(1)` to reach completion,
as this time , `[A]=0and 0 = [A]_(0)-kt_(1)`
or, `t_(1)=([A]_(0))/(k) " "..[2]`
From equations [1] and [2] we get,
`x=(1)/(2)([A]_(0))/(k)=(1)/(2)t_(1) therefore t_(1)=2xx"x"`