For a first order reaction, $$A \to B,$$  the reaction rate at reactant concentration of $$0.01\,M$$  is found to be $$2.0 \times {10^{ - 5}}mol\,{L^{ - 1}}{s^{ - 1}}.$$     The half-life period of the reaction is

Solution :
$$\eqalign{ & {\text{For first order reaction,}} \cr & A \to B \cr & {\text{rate}} = k \times \left[ A \right] \cr & {\text{Rate}} = 2.0 \times {10^{ - 5}}mol\,{L^{ - 1}}{s^{ - 1}} \cr & \left[ A \right] = 0.01\,M \cr & {\text{So,}}\,\,{\text{2}}{\text{.0}} \times {\text{1}}{{\text{0}}^{ - 5}} = k \times 0.01 \cr & k = \frac{{2.0 \times {{10}^{ - 5}}}}{{0.01}}\,{s^{ - 1}} \cr & = 2.0 \times {10^{ - 3}}{s^{ - 1}} \cr & {\text{For first order reaction,}} \cr & {t_{\frac{1}{2}}} = \frac{{0.693}}{k} = \frac{{0.693}}{{2.0 \times {{10}^{ - 3}}}} \cr & = 346.5 \approx 347\,s \cr} $$