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

For a first order reaction, A→ Products  and  for concentration of the reactant at two different times,k=2.303t2-t1log[A]1[A]2∴ k=2.303t2-t1log( rate )1( rate )2 (∵ rate ∝[A])k=2.303(20-10)log0.040.03=0.0287sec-1t1/2=0.693k=0.6930.0287sec-1=24.14sec