Derive an intergrated rate for the first order reaction.

Explanation

Consider a first order reaction, `Rto` Products
Rate of reacton is given by
rate`=(d[R])/(dt)`=k[R] where k is the rate constant on rearranging, `(dp[R])/([R])=-k dt`
integrating both sides,
We get in R]=-kt+1
Where f is the constant of integration
when time, `t=0,[R]=[R]_0` the equation becomes, `1=In[R]_0`
Substituting the value of 1 in equation (1) we have in {R]=-kt+In`[R]_0`
Rearraging the above equation.
In`[R]_0-In[R]=kt`
`k=1/tIn([R]_0)/([R])`
`k=(2.303)/tlog([R]_0)/([R])`