Question

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

Answer: (A)

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