Question

Half-lives of a first order and a zero order reactions are same. Then, the ratio of the initial rates of first order reaction to that of the zero order reaction is

• A. $\frac{1}{0.93}$
• B. $2\times 0.693$
• C. $0.693$
• D. $\frac{2}{0.693}$

Answer 1

Answer: (B)

$2\times 0.693$

Answer 2

${{t}_{1/2}}$ for zero order reaction
$=\frac{{{[A]}_{0}}}{2k}$
${{t}_{1/2}}$ for first order reaction
$=\frac{0.693}{k}$ Rate of zero order reaction,
${{r}_{0}}=k\frac{{{[A]}_{0}}}{2.{{t}_{1/2}}}$ Rate of first order reaction,
${{r}_{1}}=k({{A}_{0}})=\frac{0.693}{{{t}_{1/2}}}{{[A]}_{0}}$
$\Rightarrow$ $\frac{{{r}_{1}}}{{{r}_{0}}}=\frac{0.693{{[A]}_{0}}}{{{t}_{1/2}}}\times \frac{2\times {{t}_{1/2}}}{{{[A]}_{0}}}$
$=2\times 0.693$