# First order reaction

**Question**

The time taken for !!90%!! of a first order reaction to complete is approximately.

(a) !!(ln 0.1)/ (ln 0.5)!! times of half life

(b) !!(ln 0.5)/(ln 0.1) !! times of half life

(c) !!(ln 0.9)/(ln 0.5) !! times of half life

(d) !!(ln 0.5)/(ln 0.9)!! times of half life

**Solution**

For first order reaction, we know

!!C = C_0 e^(-kt)!!

Half life time !!t_(1/2)= (ln2)/k= - (ln 0.5)/k...(1)!!

According to the question suppose !!C_0=100!!, then !!C= 10!!

!!=> 10= 100 e^(-kt)!!

!!=> t = - (ln 0.1)/k....(2)!!

From equation (1) and (2), we get

!!-(ln 0.1)/t = -(ln 0.5)/t_(1/2)!!

!!=> t =(ln 0.1)/(ln 0.5) t_(1/2)!!

Therefore option (a) is correct.