The rate of the first-order reaction $\mathrm{X}\to$products is $7.5\times {10}^{-4} \mathrm{mol} {\mathrm{L}}^{-1} {\min }^{-1}$. What will be the value of rate constant when the concentration of X is 0.5 mol ${\mathrm{L}}^{-1}$? 

Rate of reaction $=7.5\times {10}^{-4} \mathrm{mol} {\mathrm{L}}^{-1} {\min }^{-1}$

                         $=\frac{7.5\times {10}^{-4}}{60}\mathrm{mol} {\mathrm{L}}^{-1} {\mathrm{s}}^{-1}$

                       $=1.25\times {10}^{-5} \mathrm{mol} {\mathrm{L}}^{-1} {\sec }^{-1}$

Rate of reaction = k [concentration of reactant X] 

or $\mathrm{k}=\frac{1.25\times {10}^{-5}}{0.5}=2.5\times {10}^{-5}{\mathrm{s}}^{-1}$