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

- The Zero order reaction is independent of concentration of reactants. It is time dependent reaction.

- 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 $rate=k[A{]}^{1}$

[A]=[A

_{0}] e

^{-kt}

- The second order reactions can be of following types

[A]=[A

_{0}] 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

$rate=k[A{]}^{1}$

For a first order reaction we have

A $\to $C

$\frac{-d\left[A\right]}{dt}=k\left[A\right]$

So $\frac{-d\left[A\right]}{\left[A\right]}=kdt\phantom{\rule{0ex}{0ex}}$

Integrating the above equation we have

log

_{e}[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

log

_{e}[A]= kt +[-log

_{e}[A]

_{0}]

log

_{e}$\frac{\left[A\right]}{\left[{A}_{0}\right]}={e}^{-kt}$

k = $\frac{2.303}{t}\times \mathrm{log}{}_{10}\frac{\left[{A}_{0}\right]}{\left[A\right]}$

Kindly ask the remaining derivations in a separate thread.

Regards!

**
**