Question

A hypothetical reaction $ {{A}_{2}}+{{B}_{2}}\to 2AB $ follows the mechanism as given below, $ {{A}_{2}}\rightleftharpoons A+A(fast) $ $ A+{{B}_{2}}\xrightarrow{{}}AB+B(slow) $ $ A+B\xrightarrow{{}}AB(fast) $ The order of the overall reaction is

• A. $ 2 $
• B. $ 1 $
• C. $ 1\frac{1}{2} $
• D. $ 0 $

Answer 1

Answer: (C)

From slow step, rate $ =k[{{B}_{2}}][A] $ From 1st equation $ {{K}_{eq}}=\frac{{{[A]}^{2}}}{[{{A}_{2}}]} $ or $ [A]=\sqrt{{{K}_{eq}}[{{A}_{2}}]}=K_{eq}^{1/2}A_{2}^{1/2} $ Hence, rate $ =k[{{B}_{2}}]K_{eq}^{1/2}{{[{{A}_{2}}]}^{1/2}} $ $ =k{{[{{A}_{2}}]}^{1/2}}[{{B}_{2}}] $ . Hence, order $ =1\frac{1}{2} $