Q. For a reaction of the type $A + B \rightarrow x$ products, it is observed that doubling the concentration of $A$ causes the reaction rate $\left( k_{1} \right)$ to be four times as great but doubling the amount of $B$ does not affect the rate $\left( k_{2} \right).$ The rate equation is
Explanation
(b)
For this reaction
$2A + B_{2} \rightleftharpoons 2AB$
$k = \frac{\lbrack AB\rbrack^{2}}{\lbrack A\rbrack^{2}\left\lbrack B_{2} \right\rbrack}$
For this reaction,
$A + B_{2} \rightleftharpoons AB + B$
$k_{1} = \frac{\lbrack AB\rbrack\lbrack B\rbrack}{\lbrack A\rbrack\left\lbrack B_{2} \right\rbrack}$
For this reaction,
$A + B \rightleftharpoons AB$
$k_{2} = \frac{\lbrack AB\rbrack}{\lbrack A\rbrack\lbrack B\rbrack}$
$k_{1} \times k_{2} = \frac{\lbrack AB\rbrack\lbrack B\rbrack}{\lbrack A\rbrack\left\lbrack B_{2} \right\rbrack} \times \frac{\lbrack AB\rbrack}{\lbrack A\rbrack\lbrack B\rbrack}$
$= \frac{\lbrack AB\rbrack^{2}}{\lbrack A\rbrack^{2}\left\lbrack B_{2} \right\rbrack}$
$\therefore k_{1} \times k_{2} = k$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.