A) \[r=k[A][B]\]
B) \[r=k[AB][B]\]
C) \[r=k[A]{{[B]}^{2}}\]
D) \[r=k{{[A]}^{2}}[B]\]
Correct Answer: C
Solution :
Mechanism, \[A+B\overset{{{k}_{1}}}{\mathop{\rightleftharpoons }}\,AB\,\,\,(fast)\] \[AB+B\overset{{{k}_{2}}}{\mathop{\rightleftharpoons }}\,A+{{B}_{2}}\,\,\,(slow)\] rate law \[={{k}_{2}}[AB][B]\] For fast reaction (steady state step) \[{{k}_{1}}[A][B]={{k}_{1}}[AB]\] \[[AB]=\frac{{{k}_{1}}[A][B]}{{{k}_{-1}}}\] The value of \[[AB]\] put into rate law Rate law\[=\frac{{{k}_{2}}{{k}_{1}}}{{{k}_{-1}}}[A]{{[B]}^{2}}\] \[=k[A]{{[B]}^{2}}\]
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