The half-life of the reaction $$X \to Y,$$  following first order kinetics, when the initial concentration of $$X$$ is $$0.01\,mol\,{L^{ - 1}}$$   and initial rate is \[0.00352\,mol\,{{L}^{-1}}\,{{\min }^{-1}}\]     will be

Solution :
$$\eqalign{ & \frac{{dx}}{k} = k\left[ X \right]\,{\text{(For a first order reaction)}} \cr & 0.00352 = k \times 0.01 \Rightarrow k = 0.352 \cr & {t_{\frac{1}{2}}} = \frac{{0.693}}{k} = \frac{{0.693}}{{0.352}} = 1.969\,\min . \cr} $$