Q. The thermal decomposition of a compound is of first order. If a sample of the compound decompose 50% in 120 min. What time will it take to undergo 90% decomposition?
A) Nearly 400 min
B) Nearly 45 min
C) Nearly 480 min
D) Nearly 240 min
Explanation
(a)
For first order reaction :
$t = \frac{2.303}{k}\log\frac{a}{a - x}$
For Ist case :
$a = 100,\ x = 50,\ t = 120\ \min$
$k = \frac{2.303}{120}\log\frac{100}{100 - 50}$
$= \frac{2.303}{120}\log 2$
$k = \frac{2.303 \times 0.3010}{120}$
$k = 0.0057\ \min^{- 1}$
For the IInd case :
$t = \frac{2.303}{0.0057}\log\frac{100}{100 - 90}$
$= \frac{2.303}{0.0057}\log 10$
$t = 404\ \min$
$\ \approx 400\ \min$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.