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. 3.0
• B. 2.303
• C. 4.8
• D. 0.477

Answer 1

Answer: (C)

For a first order reaction,
$t=\frac{2.303}{k}lo{g}_{10}\frac{a}{a-x}$
Let initial amount of reactant is 100.
$\frac{t_1}{t_2}=\frac{log\frac{100}{100-75}}{log\frac{100}{100-25}}[\therefore kremainsconstant]$
$=\frac{log\frac{100}{25}}{log\frac{100}{75}}=\frac{log4}{log4/3}$
$=\frac{log4}{log4-log3}$
$=\frac{2\times 0.3010}{2\times 0.3010-0.4771}$
$=\frac{0.6020}{0.1249}=4.81$