For the given first order reaction A → B the half life of the reaction is 0 . 3010   min . The…

Given $\mathrm{A}\to \mathrm{B}$ is a first order reaction 

and   ${\mathrm{t}}_{\frac{1}{2}}=0.3010 \min$

$\frac{{\mathrm{A}}_{\mathrm{o}}}{{\mathrm{A}}_{\mathrm{t}}}$ at time $2 \min =$?

We know the integrated rate equation for first order reaction

$\mathrm{K}=\frac{2.303}{\mathrm{t}}\log \left[\frac{{\mathrm{A}}_0}{ {\mathrm{A}}_{\mathrm{t}}}\right]$

$$\begin{gathered} \Rightarrow \frac{0·693}{{\mathrm{t}}_{\frac{1}{2}}}=\frac{2·303}{\mathrm{t}}\log \left(\frac{{\mathrm{A}}_0}{ {\mathrm{A}}_{\mathrm{t}}}\right) \\ \Rightarrow \frac{0·693}{0.3010 \min }=\frac{2·303}{2 \min }\log \left(\frac{{\mathrm{A}}_0}{ {\mathrm{A}}_{\mathrm{t}}}\right) \end{gathered}$$

$\log \frac{{\mathrm{A}}_0}{{\mathrm{A}}_{\mathrm{t}}}=2$

$\therefore \frac{{\mathrm{A}}_0}{{ \mathrm{A}}_{\mathrm{t}}}={10}^2=100$