Q80 / 180 · JIPMER 2017 · Chemistry

A first order reaction is $50 \%$ completed in $1.26 \times 10^{14} \mathrm{~s}$. How much time would it takes for 100\% completion?

  • A
    $1.26 \times 10^{15} \mathrm{~s}$
  • B
    $2.52 \times 10^{14} \mathrm{~s}$
  • C
    $2.52 \times 10^{28} \mathrm{~s}$
  • Correct answer
    D
    Infinite

Solution

$k$-for first order. $\frac{0.693}{t_{1 / 2}}=\frac{0.693}{1.26 \times 10^{14}}$ for $100 \%$ completion. $\because t=\frac{2.303}{k} \log \frac{a}{a-x}$ $t=\frac{2.303 \times 1.26 \times 10^{14}}{0.693} \log \frac{100}{0}$ $\therefore t=\infty$

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

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