Q. For a reaction$\ \ A + B \rightarrow C + D$, if the concentration of A is doubled without altering the concentration of B, the rate gets doubled. If the concentration of B is increased by nine times without altering the concentration of A, the rate gets tripled. The order of the reaction is
A) 2
B) 1
C) 3/2
D) 4/3
Explanation
(c)
$A + B \rightarrow C + D$
Rate (𝑟)=𝑘$\lbrack A\rbrack^{a}\lbrack B\rbrack^{b}$ …(i)
2𝑟=𝑘$\lbrack 2A\rbrack^{a}\lbrack B\rbrack^{b}\ \ \ \ \ \ \ \ldots(ii)$
3𝑟=𝑘$\lbrack A\rbrack^{a}\lbrack 9B\rbrack^{b}$ …(iii)
Dividing eq.(ii) by eq.(i)
$2 = 2^{a}$or a=1
Dividing eq (iii)by eq.(i)
$3 = 9^{b}\ or\ 3 = 3^{2b}\ \ or\ 2b = 1\ or\ b = 1/2$
So order of reaction $= 1 + \frac{1}{2} = \frac{3}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.