Question

Under the same reaction conditions, the initial concentration of 1.386 mol $d{m}^{-3}$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively.

The ratio $(k_1/k_0$) of the rate constants for first order $\left(k_1\right)$ and zero order $\left(k_0\right)$of the reaction is

• A. $0.5$
• B. $1.0$
• C. $1.5$
• D. $2.0$

Answer 1

The correct option is A $0.5$

For the first order reaction,the rate constant

$k_1=\frac{0.693}{t_{1/2}}=\frac{0.693}{40}$

For zero order reaction, the rate constant

$k_0=\frac{A_0}{2\times t_{1/2}}=\frac{1.386}{2\times 20}$

Hence,

$\frac{k_1}{k_0}=\frac{0.693}{1.386}=0.5$