Question

derive integrated rate law for the first order reaction.

Answer 1

Let the reaction be

$$A\overset{k}{\to} product$$

Initial amount of of A be $A_°$

Rate law eqn will be

$$\frac{dA}{dt}= -kA$$

Seperating variables

We get

$$dA= -kAdt$$

Integrating it $From \ A_°\ to \ A$

We get

$$[lnA\underset{A_°}{\overset{A}{]}}= -kt\\lnA-lnA_°= -kt\\ln\frac{A}{A_°}= -kt\\A= A_°e^{-kt}$$

This is the integrated rate law for first order reaction.