Question

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

• A. 3
• B. 2.303
• C. 4.8
• D. 0.477

Answer 1

Answer: (C)

4.8

Answer 2

For a first order reaction,
\hspace25mm t =\frac{2.303}{k} \, log_{10} \, \frac{a}{a-x}
Let initial amount of reactant is 100.
\hspace20mm \frac{t_1}{t_2} = \frac{log \frac{100}{100-75}}{log \frac{100}{100-25}} \, [\therefore \, k \, remains \, constant]
\hspace20mm =\frac{log \frac{100}{25}}{log \frac{100}{75}} = \frac{log \, 4}{log \, 4/3}
\hspace20mm =\frac{log \, 4}{log \, 4 - log \, 3}
\hspace20mm =\frac{2 \times 0.3010}{2 \times 0.3010-0.4771}
\hspace20mm = \frac{0.6020}{0.1249} = 4.81