Q. What is the two third life of a first order reaction having $k = 5.48 \times 10^{- 14}\ s^{- 1}?$
A) $2.01 \times 10^{13}\ s$
B) $2.01 \times 10^{12}\ s$
C) $4.02 \times 10^{13}\ s$
D) $4.02 \times 10^{26}\ s$
Explanation
(a)
For 2/3 of a reaction
$\lbrack A\rbrack_{0} = a,\ \lbrack A\rbrack = a - \frac{2}{3}\ a = \frac{a}{3}$
$\because t_{2/3} = \frac{2.303}{k}\log\frac{\lbrack A\rbrack_{0}}{\lbrack A\rbrack}$
$\ = \frac{2.303}{5.48 \times 10^{- 14}}\log\frac{a}{a/3}$
$= \frac{2.303}{5.48 \times 10^{- 14}}\log 3$
$t_{2/3} = 2.01 \times 10^{13}\ s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.