Q34 / 180 · KCET 2021 · Chemistry

If the rate constant for a first order reaction is $k$, the time $(t)$ required for the completion of $99 \%$ of the reaction is given by

  • Correct answer
    A
    $t=\frac{4.606}{k}$
  • B
    $t=\frac{2303}{k}$
  • C
    $t=\frac{0.693}{k}$
  • D
    $t=\frac{6.909}{k}$

Solution

Given, for a first order reaction, let initial concentration $=\left[R_{0}\right]$ After $99 \%$ completion, concentration $\begin{aligned} {[R] } &=R_{0}-0.99 R_{0} \\ &=0.1 R_{0} \end{aligned}$ Using formula, $t=\frac{2303}{k} \log \frac{\left[R_{0}\right]}{[R]}$ $=\frac{2303}{k} \log \frac{100}{1}=\frac{4.606}{k}$

Hence, the correct answer is option: 'A'.

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