Q36 / 160 · AP EAMCET 2009 · Chemistry

For a first order reaction at $27^{\circ} \mathrm{C}$, the ratio of time required for $75 \%$ completion to $25 \%$ completion of reaction is

  • A
    3.0
  • B
    2.303
  • Correct answer
    C
    4.8
  • D
    0.477

Solution

For a first order reaction, $t=\frac{2.303}{\lambda} \log _{10} \frac{a}{a-x}$ Let initial amount of reactant is 100 . $\begin{aligned} \frac{t_1}{t_2}= & \frac{\log \frac{100}{100-75}}{\log \frac{100}{100-25}} \\ & =\frac{\log \frac{100}{25}}{\log \frac{100}{75}} \end{aligned}$ $\begin{aligned} & =\frac{\log 4}{\log 4 / 3} \\ & =\frac{\log 4}{\log 4-\log 3} \\ & =\frac{2 \times 0.3010}{2 \times 0.3010-0.4771} \\ & =\frac{0.6020}{0.1249} \\ & =4.81\end{aligned}$

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

Relevant Questions