Half-lives of first-order and zeroth order reactions are same. Ratio of rates at the start of nreaction is

Half-lives of first-order and zeroth order reactions are same. Ratio of rates at the start of nreaction is
  1. $0.693$
  2. $\frac{1}{0.693}$
  3. $2 \times 0.693$
  4. $\frac{2}{0693}$

Solution

$T_{50}($ zeroth $)=\frac{a}{2 k_{0}}$
$T_{50}($ first $)=\frac{0.693}{k_{1}}$
$\frac{a}{2 k_{0}}=\frac{0.693}{k_{1}}$
$\therefore \frac{k_{1}}{k_{0}}=\frac{2 \times 0.693}{a}$
$\frac{\left(\frac{d x}{d t}ight)_{1}}{\left(\frac{d x}{d t}ight)_{0}}=\frac{k_{1} a}{k_{0}}=2 \times 0.693$ /

Asked in: JEE-TOPICTESTS-CHEMISTRY

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