For a first order reaction A B , the reaction rate at reactant...

For first order reaction $A \longrightarrow B$ Given that rate $=k \times[A]$ Rate $=2.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} [A]=$ Conc. of $A=0.01 \mathrm{M}$ So, $2.0 \times 10^{-5}=k \times 0.01$$\begin{aligned} k & =\frac{2.0 \times 10^{-5}}{0.01} \mathrm{~s}^{-1} \\ & =2.0 \times 10^{-3} \mathrm{~s}^{-1}\end{aligned}$$$For first order reaction$$\begin{aligned} T_{1/2} & =\frac{0.693}{k}=\frac{0.693}{2.0 \times 10^{-3}} \\ & =346.5 \approx 347 \mathrm{~s}\end{aligned}$$