Derive an intergrated rate for the first order reaction.

Explanation

Consider a first order reaction ,
R to products
Rate of reacrtion is given by
`rate =(d[R])/dt=K[R]` where k is the rate constant on rearranging.
`(d[R])/[R]=-kdt`
intergrating both sides
We get In [R] =-kt+I…..(1),
Where I is the constant of intergration when time, t=0
[R]=[R]0.
the equation becomes
I=in[R]0
subsituting the value of i in equation
(1), we have `I_n[R]=+kt+I_n[R]_(0)`
Rearranging the above equation
In `[R]0-In[R]=kt`
k=1/t In `[R]-kt` `k=1/iIn([R])_0/([R])` `k=1/iIn([R])_0/([R])`