Question

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

• A. $3.0$
• B. $2.303$
• C. $4.89$
• D. $0.477$

Answer 1

Answer: (C)

$4.89$

For a first order reaction,
$t=\frac{2.303}{\lambda }{\log }_{10}\frac{a}{a-x}$

Let, initial amount of reactant is $100$.
$\frac{t_1}{t_2}=\frac{\log \left(\frac{100}{100-75}\right)}{\log \left(\frac{100}{100-25}\right)}$

$=\frac{\log \left(4\right)}{\log \left(\frac{4}{3}\right)}=\frac{0.6020}{0.1249}=4.8$