For the given first order reaction A → B the half life of the...

Given $A \to B$ is a first order reaction

and $t\dfrac{1}{2} = 0 . 3010min$

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

We know the integrated rate equation for first order reaction

$K = \dfrac{2 . 303}{t}\log \left[\dfrac{{A}_{0}}{{A}_{t}}\right]$

$⇒ \dfrac{0 \cdot 693}{t\dfrac{1}{2}} = \dfrac{2 \cdot 303}{t}\log \left(\dfrac{{A}_{0}}{{A}_{t}}\right) ⇒ \dfrac{0 \cdot 693}{0 . 3010min} = \dfrac{2 \cdot 303}{2min}\log \left(\dfrac{{A}_{0}}{{A}_{t}}\right)$

$log\dfrac{{A}_{0}}{{A}_{t}} = 2$

$∴ \dfrac{{A}_{0}}{{A}_{t}} = {10}^{2} = 100$