The rate of a first-order reaction is 0.04 mol L⁻¹s⁻¹ at 10 seconds and 0.03 mol L⁻¹s⁻¹ at 20 seconds after initiation of the reaction. The half-life period of the reaction is :

Let the rate=k[A]
At t=10 seconds, 0.04=k[A1]
At t=20 seconds, 0.03=k[A2]
∴, in 10 seconds concentration of A decreases by 0.01
k[M]
Using first order kinetics equation,
10×k=ln(0.04/0.03)
10×k=0.2877
k=0.02877
Half life of first order reaction=ln 2/k
t1/2=ln 2/0.02877=24.1 seconds