Half lives of first order and a zero order reaction are same. Ass… - Vidyadip

MCQ

Half lives of first order and a zero order reaction are same. Assume that initial concentration of reactant is same for both reactions, then the ratio of initial rates of first order reaction to that of zero order reaction is

A
$\frac{1}{{0.693}}$
✓
$2\, \times \,0.693$
C
$0.693$
D
$\frac{2}{{0.693}}$

✓

Answer

Correct option: B.

$2\, \times \,0.693$

b
${\left( {{{\text{t}}_{1/2}}} \right)_{{1^{st}}}} = {\left( {{{\text{t}}_{1/2}}} \right)_{zero}}$

$\frac{{0.693}}{{{{\text{k}}_1}}} = \frac{{{{\text{C}}_0}}}{{2{{\text{k}}_0}}}$ $ \Rightarrow \frac{{{{\text{k}}_1}}}{{{{\text{k}}_0}}} = \frac{{2 \times 0.693}}{{{{\text{C}}_0}}}$

$\mathrm{r}_{1}=\mathrm{k}_{1} \times\left[\mathrm{C}_{0}\right]^{1}$

$\mathrm{r}_{0}=\mathrm{k}_{0} \times\left[\mathrm{C}_{0}\right]^{0}$

$\frac{\mathrm{r}_{1}}{\mathrm{r}_{0}}=\frac{\mathrm{k}_{1}\left[\mathrm{C}_{0}\right]}{\mathrm{k}_{0}}=2 \times 0.693$

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