Question

The rate of a first-order reaction is $0.04$ mol litre${}^{-1}$ s${}^{-1}$ at 10 minute and 0.03 mol litre${}^{-1}$ s${}^{-1}$ at 20 minute after initiation. The half-life of the reaction in minutes is ________.
Express the value of the nearest integer of the half-life in the form of $x+y$ if the integer is $xy.$

Answer 1

Rate of reaction at 10 seconds = 0.04 mol L${}^{-1}$ s${}^{-1}$

Rate of reaction at 20 seconds = 0.03 mol L${}^{-1}$ s${}^{-1}$

We have the equation for rate constant $k$ in the first order reaction:

$k=\frac{2.303}{t_2-t_1}\times log\left(\frac{A_1}{A_2}\right)$

$k=\frac{2.303}{20-10}\times log\left(\frac{0.04}{0.03}\right)$

$k=\frac{2.303}{10}\times 0.124$

$k=0.028mi{n}^{-1}$

We know that :

$t_{\frac{1}{2}}=\frac{0.693}{k}=24.1$ min

The half-life of the reaction is $24min$.
So, $x+y=2+4=6.$