Answer to Question #228651 in Math for yarris

Question

The rate equation for a reaction: A → B is r=K[A]⁰ . If the initial concentration of the reactant is a moldm^-3 , the half-life period of the reaction is?

Answer 1

Given:

The rate equation for the reaction is r=k[A]⁰_.

Initial concentration of the reactant = a moldm^-3

The rate law of the reaction is expressed as:

Rate=k[A]^x

Here, x is the order of the reaction and k is the rate constant for the reaction.

According to the given rate law, r=k[A]⁰, the order of the reaction is zero order.

For a zero order reaction, the rate constant is given by:

$k=\frac{[A]o−[A]}{t}......(1)$

Here, [A]_o is the initial concentration of the reactant and [A]

A is the final concentration of the reactant after time t.

Half-life period is the time period at which the final concentration of reactant becomes half of the initial concentration of the reactant. Hence,$[A]=\frac{1}{2}[A]_o.$

Substitute the given values in equation (1).

$k=\frac{[A]_o−\frac{[A]_o}{2}}{t_{\frac{1}{2}}}\\k=\frac{2[A]_o−[A]_o}{2t_{\frac{1}{2}}}\\t_{\frac{1}{2}}=\frac{[A]_o}{2k}\\t_{\frac{1}{2}}=\frac{a}{2k}$

Therefore, the half-life period of the reaction is $\frac{a}{ 2k}.$