Question

For the given first order reaction
$A\to B$
the half life of the reaction is $0.3010\min$. The ratio of the initial concentration of reactant to the concentration of reactant at time $2.0min$ will be equal to ___(Nearest integer)

Answer 1

Answer: 100

$A\to B$
$t_{1/2}=0.3010\min$
$A_0/A_t\text{ at time }2\min =\text{ ? }$
$K=\frac{2.303}{t}\log \left[\frac{A_0}{A_t}\right]$
$\Rightarrow \frac{0\cdot 693}{t_{\frac{1}{2}}}=\frac{2\cdot 303}{2}\log \left(\frac{A_0}{A_t}\right)$
$\text{ Or }\frac{2.303\times 0.3010}{0.3010}=\frac{2.303}{2}\log \frac{A_0}{A_t}$
$\log \frac{A_0}{A_t}=2$
$\therefore \frac{A_0}{A_t}=10^2=100$