Question #228651

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?


1
Expert's answer
2021-09-07T14:39:44-0400

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=[A]o[A]t......(1)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]=12[A]o.[A]=\frac{1}{2}[A]_o.


Substitute the given values in equation (1).

k=[A]o[A]o2t12k=2[A]o[A]o2t12t12=[A]o2kt12=a2kk=\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 a2k.\frac{a}{ 2k}.


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