# Pls derive expression for integrated rate law of zero,  first,  second and pseudo first order reaction!!

Dear Student,
• The Zero order reaction is independent of concentration of reactants. It is time dependent reaction.
So the integrated rate law will be  $\left[A\right]=\left[{A}_{0}\right]-kt$
• The first order reaction can be of following types

$A\to C\phantom{\rule{0ex}{0ex}}$
In the second case the concentration of B is in excess so the rate of reaction will be dependent only on concentration of A
The integrated rate law will be $rate=k\left[A{\right]}^{1}$
[A]=[A0] e-kt
• The second order reactions can be of following types

[A]=[A0] e-2kt
The pseudo first order reaction will be of the following type
$A+B\to C$
Here molecularity is 2 and order is 1
The integrated rate expression will be

For a first order reaction we have
$\to$

So
Integrating the above equation we have
loge[A] = kt +I
When t=0, [A] =[A]0

so I = -log e[A] 0
Putting the value of I in above equation we get
loge[A]= kt +[-loge[A]0]
log e$\frac{\left[A\right]}{\left[{A}_{0}\right]}={e}^{-kt}$
k =