(a) Derive the integrated rate equation for the rate constant of a first order reaction.
(b) What is pseudo first order reaction?

Explanation

(a) Consider a first order reaction,Rtoproducts.
Rate of reaction is given by.
`rate=(d[R])/([dt])=k[R]` where k is the rate constant.
on rearranging. `(d[R])/([R])=-K dt`
integrating both sides,
we get in [R] =- kt + L….(1)
where l is the constant of integration when time, `t = 0, [R] = [R]_(0)`, the equation becomes, `I = In [R]_(0)`,
  substituting the value of I in equation (1), we have In`[R]=-kt+In[R]_(0)`
Rearranging the above equation,
In `[R]_(0) – In [R] = kt`
`K=(1)/(t)In ([R]_(0))/([R])`
`K=(2.303)/(t)"log"([R]_(0))/([R])`
(b) Order of reaction is one and molecularity is two or more than two are called pseudo first order reactions.