Q. Mathematical expression for $t_{1/4}$ i.e., when (1/4)th reaction is over following first order kinetics can be given by
A) $t_{1/2} = \frac{2.303}{k}\log 4$
B) $t_{1/2} = \frac{2.303}{k}\log 2$
C) $t_{1/2} = \frac{2.303}{k}\log\frac{4}{3}$
D) $t_{1/2} = \frac{2.303}{k}\log\frac{3}{4}$
Explanation
(c)
$t = \frac{2.303}{k}\log\frac{a}{(a - x)}$
If $t = t_{1/4};\ \ \ x = a/4$
$\therefore t_{1/4} = \frac{2.303}{k}\log\frac{a}{(a - 1/4)}$
$\frac{2.303}{k}\log\frac{4}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.