Question

The mathematical expression for $t_{1/4}$ i.e., when $(1/4{)}^{th}$ reaction is over following first-order kinetics can be given by:

• A. $t_{1/4}=\frac{2.303}{K}log4$
• B. $t_{1/4}=\frac{2.303}{K}log2$
• C. $t_{1/4}=\frac{2.303}{K}log\frac{4}{3}$
• D. $t_{1/4}=\frac{2.303}{K}log\frac{3}{4}$

Answer 1

Answer: (C)

$t_{1/4}=\frac{2.303}{K}log\frac{4}{3}$

As we know,
for first order reaction,
$t=\frac{2.303}{K}log\frac{a}{(a-x)}$
if $t=t_{1/4};x=a/4$
$\therefore t_{1/4}=\frac{2.303}{K}log\frac{a}{a-a/4}$
$=\frac{2.303}{K}log\frac{4}{3}$.