Q15 / 180 · KCET 2013 · Chemistry

If $50 \%$ of the reactant is converted into a product in a first order reaction in $25 \mathrm{~min}$, how much of it would react in $100 \mathrm{~min}$ ?

  • Correct answer
    A
    $93.75 \%$
  • B
    87.5\%
  • C
    $75 \%$
  • D
    100\%

Solution

Number of half-lives $=\frac{100}{25}=4$, i.e., $n=4$ Amount of the substance left after 4 half-lives $\begin{aligned} &=\frac{A^{0}}{2^{n}} \\ &=\frac{A^{0}}{2^{4}}=\frac{A^{0}}{16}=\frac{100}{16}=6.25 \% \end{aligned}$ $(\because n=4)$ $\therefore$ Amount of the substance converted into the product in $100 \mathrm{~min}=100-6.25=93.75 \%$

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

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