Q. What is the two third life of a first order reaction having $= 5.48 \times 10^{- 14}s^{- 1}$ ?
A) $2.01 \times 10^{11}s$
B) $2.01 \times 10^{13}s$
C) $8.08 \times 10^{13}s$
D) $16.04 \times 10^{11}s$
Explanation
(b)
for two-third of a reaction ,
${\lbrack A\rbrack}_{0} = a,\lbrack A\rbrack = a - \frac{2}{3}a = \frac{a}{3}$
$t_{2/3} = \frac{2.303}{k}\log\frac{{\lbrack A\rbrack}_{0}}{\lbrack A\rbrack}$
$= \frac{2.303}{k}\log\frac{a}{\frac{a}{3}} = \frac{2.303}{k}\log 3$
$t_{2/3} = \frac{2.303 \times 0.4771}{5.48 \times 10^{- 14}} = 2.01 \times 10^{13}s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.