Q. For a reaction $\frac{1}{2}A \rightarrow 2B$, rate of disappearance of ‘A’ is related to the rate of appearance of B by the expression
A) $- \frac{d\lbrack A\rbrack}{dt} = \frac{1}{2}\frac{d\lbrack B\rbrack}{dt}$
B) $- \frac{d\lbrack A\rbrack}{dt} = \frac{1}{4}\frac{d\lbrack B\rbrack}{dt}$
C) $- \frac{d\lbrack A\rbrack}{dt} = \frac{d\lbrack B\rbrack}{dt}$
D) $- \frac{d\lbrack A\rbrack}{dt} = 4\frac{d\lbrack B\rbrack}{dt}$
Explanation
(b)
$\frac{1}{2}A \rightarrow 2B$
Remember for $a\ A \rightarrow bB$
$- \frac{1}{a}\frac{d\lbrack A\rbrack}{dt} = \frac{1}{b}\frac{d\lbrack B\rbrack}{dt}$= Rate of reaction
For the given reaction
$- \frac{2d\lbrack A\rbrack}{dt} = \frac{1}{2}\frac{d\lbrack B\rbrack}{dt}$=rate of reaction
Rate of disappearance of A
$= - \frac{d\lbrack A\rbrack}{dt} = \frac{1}{2 \times 2}\frac{d\lbrack B\rbrack}{dt}$
$= \frac{1}{4}\frac{d\lbrack B\rbrack}{dt}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.