Question

For the given first order reaction
$A \rightarrow B$
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 $2.0 min$ will be equal to ___(Nearest integer)

Answer 1

$ A \rightarrow 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$