For the reaction \(A + B \longrightarrow C + D\), doubling the concentration of A without changing the concentration of B doubles the rate. Increasing the concentration of B nine times without changing the concentration of A triples the rate. The overall order of the reaction is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{3}{2}\)
The order of a reaction is the sum of the powers of the concentration terms in the rate law. Let the rate law be:
\( \displaystyle \text{Rate}=k[\mathrm{A}]^{x}[\mathrm{B}]^{y} \)
Order in A: doubling [A] doubles the rate, so \( 2^{x}=2 \) and x = 1.
Order in B: making [B] nine times larger triples the rate, so \( 9^{y}=3 \), that is \( 3^{2y}=3^{1} \) and y = ½.
\( \displaystyle \text{Overall order}=x+y=1+\frac{1}{2}=\frac{3}{2} \)