Question

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. $t_{1/4}=\frac{2.303}{K}log1/4$
• C. $t_{1/4}=\frac{2.303}{K}log2$
• D. $t_{1/4}=\frac{2.303}{K}log\frac{4}{3}$

Answer 1

The correct option is D $t_{1/4}=\frac{2.303}{K}log\frac{4}{3}$

As we know, for a first order reaction,

$t=\frac{2.303}{K}log\frac{a}{(a-x)}$

If $t=t_{1/4};x=\frac{a}{4}$

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