Q22 / 180 · KCET 2022 · Chemistry

A first order reaction is half completed in $45 \mathrm{~min}$. How long does it need $99.9 \%$ of the reaction to be completed ?

  • Correct answer
    A
    7.5 Hours
  • B
    10 Hours
  • C
    20 Hours
  • D
    5 Hours

Solution

$t_{1 / 2}$ for first order reaction is $45^{\circ} \mathrm{min}$ $$ t_{1 / 2}=\frac{0.693}{k} \Rightarrow k=\frac{0.693}{I_{1 / 2}}=\frac{0.693}{45} $$ $$ \begin{aligned} t & =\frac{2.303}{k} \log \frac{a}{a-x}=\frac{2.303}{0.693} \times 45 \log \frac{100}{0.1} \\ & =448 \text { min } \approx 7.5 \mathrm{hrs} . \end{aligned} $$

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

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