The rate of a first order reaction is 0.4 mol `L^(-1)s^(-1)` at 10 minutes and 0.04 mol `L^(-1)s^(-1)` at 20 minutes after initiation. The half life of the reaction is

Options

A. 2 minutes
B. 6.9 minutes
C. 3 minutes
D. 3.3 minutes.

Answer

C

Explanation

Let the reaction start at 10 minutes.
`k=(2.303)/(t)log(a)/(a-x)`,(Time = 20-10=10 minutes)
`=(2.303)/(10)log(0.4)/(0.04)=(2.303)/(10)`
`t_(1//2)=(0.693)/(k)=(0.693xx10)/(2.303)`=3.0 minutes