Q. A reaction was observed for 15 days and the percentage of the reactant remaining after the days indicated was recorded in the following table. [table] Time (days) | % Reactant remaining ; 0 | 100 ; 2 | 50 ; 4 | 39 ; 6 | 25 ; 8 | 21 ; 10 | 18 ; 12 | 15 ; 14 | 12.5 ; 15 | 10 [/table] Which one of following best describes the order and the half-life of the reaction? Reaction order Half-life (days)
A) First 2
B) First 6
C) Second 2
D) Zero 6
Explanation
(c)
$100\overset{2\ days\ }{\rightarrow}50$
$50\overset{4\ days\ }{\rightarrow}25$
$25\overset{8\ days\ }{\rightarrow}12.5$
Hence, the order of reaction is second.
For second order reaction,
$k = \frac{1}{2}\left\lbrack \frac{x}{a(a - x)} \right\rbrack = \frac{1}{2}\left\lbrack \frac{50}{100 \times 50} \right\rbrack$
$= \frac{1}{200}$
$t_{1/2} = \frac{1}{k.a}$
$\Rightarrow = \frac{1}{1/200.100}$
$= \frac{200}{100} = 2days$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.