Question

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

• A. $0.5 \,mol^{-1}\, dm^3$
• B. $1.0 \,mol \,dm^{-3}$
• C. $1.5 \,mol \,dm^{-3}$
• D. $2.0\, mol^{-1}\, dm^3$

Answer 1

Answer: (A)

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