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. $\frac{2}{0.693}$
• E. $6.93$

Answer 1

Answer: (B)

$t_{1/2}$ 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,
$r_1=k(A_0)=\frac{0.693}{t_{1/2}}{[A]}_0$
$\Rightarrow$ $\frac{r_1}{r_0}=\frac{0.693{[A]}_0}{t_{1/2}}\times \frac{2\times t_{1/2}}{{[A]}_0}$
$=2\times 0.693$