Derive an intergrated rate for the first order reaction.

Explanation

Consider a first order reaction, R to product 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 + 1 ` .......(1) where I is the constant of integration When time, ` t = 0, [R] = [R]_0,` the equation becomes, I` = In [R]_0 ` substiuting the value of l in equation (1), we have `I_n [R] = -kt + I_n [R]o` 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]`