For a first order reaction $\mathrm{A} \rightarrow \mathrm{B}$ the reaction rate at reactant concentration…
For a first order reaction $\mathrm{A} \rightarrow \mathrm{B}$ the reaction rate at reactant concentration of $0.01 \mathrm{M}$ is found to be $2.0 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1}$ $\mathrm{s}^{-1}$. The half life period of the reaction is:
$30 \mathrm{~s}$
$220 \mathrm{~s}$
$300 \mathrm{~s}$
$347 \mathrm{~s}$
Solution
$\begin{aligned}
& \text { rate of reaction }=2 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \\
& \Rightarrow \text { order of reaction is } n=1 \\
& \text { rate }=\mathrm{K}[\mathrm{A}]^n \\
& {[\mathrm{~A}] }=0.01 \mathrm{M} \\
& \Rightarrow \quad \mathrm{K}=\frac{2 \times 10^{-5}}{0.01}=2 \times 10^{-3} \\
& \mathrm{~K}=\frac{0.693}{t_{1 / 2}} \\
& t_{1 / 2}=\frac{0.693}{2 \times 10^{-3}}=346.5 \mathrm{~s}
\end{aligned}$
Related Theory
For a first-order reaction, a graph plotted with $\ln [A]$ on the $Y$-axis and time on the $X$-axis, will be a straight line with a slope of $-k$.
