derive the unit s of rate constants k for the first and second order reaction

Hey Rajveer

Rate constant of a first order reaction: The reaction in which, the overall rate of the reaction is proportional to the first power of concentration of one of the reactants only are called first order reaction.
A→k1 products
Rate of reaction =dt−d[A]=k1[A]10
where k1 is the rate constant of the first order reaction.
At the beginning of the reaction, time ′t′=0, let the concentration of A be 'a' mole lit−1. After the reaction has proceeded for some time 't', let the concentration of A that has reacted be x mole lit−1. The concentration of unreacted A remaining at time 't' will be (a−x) mole lit−1. The rate of the reaction will be dx/dt. For a first order reaction,
rate =dx/dt=k1(a−x) ...... (1)
Integrating (1), both sides
∫(a−x)dx=k1∫dt
Which is −ln(a−x)=k1t+c ...... (2)
C= integration constant.
at time, t=0,x=0
In equation (2)
−ln(a−0)=k1×0+c
or
c=ln a
Substituting c value in equation (2)
−ln(a−x)=k1t−ln a
rearranging,
k1=t1lna−xa
k1=t2.303loga−xa
Unit of k1 is sec−1
This equation is known as the first order rate constant equation.

The unit for the rate constant of a second order reaction is Lmol−1s−1.
For a second order reaction, rate=k[A]2
molL−1s−1=k(molL−1)2
k=Lmol−1s−1

Hope this will help you.

GOOD LUCK.