Question

Under the same reaction conditions, initial concentration of 1.386 $mold{m}^{-3}$ of a substance becomes half in 40 s amd 20 s through first order and zero order kinetics respectively. Ratio $\left(\frac{k_1}{k_0}\right)$ of the rate constants for first order $\left(k_1\right)$ and zero order $\left(k_0\right)$ of the reaction is:

• A. $0.5mo{l}^{-1}d{m}^3$
• B. $1.0mold{m}^{-3}$
• C. $1.5mold{m}^{-3}$
• D. $2.0mo{l}^{-1}d{m}^3$

Answer 1

The correct option is A

$0.5mo{l}^{-1}d{m}^3$

For first order reaction $t_{1/2}=\frac{In2}{k_1}=40s$ $\cdots \left(i\right)$
For zero order reaction $t_{1/2}=\frac{[A{]}_0}{2k_0}=20s$ $\cdots \left(ii\right)$
$\Rightarrow Eq.\left(ii\right)/\left(i\right)=\frac{1}{2}=\frac{[A{]}_0}{2k_0}\times \frac{k_1}{In2}$
$\Rightarrow \frac{k_1}{k_0}=\frac{In2}{[A{]}_0}=\frac{0.693}{1.386}=0.5$