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Derive the expression for integrated rate law (equation) for the first-order reaction.

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Consider the following first-order reaction, 

A → B 

The rate of the chemical reaction is given by the rate law expression as, 

Rate, 

R = k [A] where [A] is the concentration of the reactant A and k is the velocity constant or specific rate of the reaction. 

The instantaneous rate is given by,

If [A0] is the initial concentration of the reactant and [A]t at time t, then by integrating the above equation,

This is the integrated rate equation for the first order reaction. This is also called integrated rate law.

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