The rate of first-order reaction is 0.04 mol/l/s at 10 sec and 0.03 mol/L/s at 20 sec after intiation of the reaction. What is the half-life period of the reaction?

The half-life period of the reaction is given as:

$k=frac{2.303}{t_{2}-t_{1}}logfrac{[A]_{1}}{[A]_{2}}$ $k=frac{2.303}{t_{2}-t_{1}}logfrac{(rate)_{1}}{(rate)_{2}}$

This is because rate is proportional to [A] $k=frac{2.303}{20-10}logfrac{0.04}{0.03}=0.0287 sec^{-1}$ $t_{1/2}=frac{0.693}{k}=frac{0.693}{0.0287sec^{-1}}=24.14 sec$