| A hypothetical reaction: |
| \[{{A}_{2}}+{{B}_{2}}\xrightarrow{{}}2AB\] follows mechanism as given below: |
| \[{{A}_{2}}A+A\]............ (fast) |
| (\[{{k}_{c}}\] is equilibrium constant) |
| \[{{A}_{2}}+{{B}_{2}}\xrightarrow{{{k}_{1}}}AB+B\] ..............(slow) |
| (\[{{k}_{1}}\] rate constant) |
| \[A+BAB\] .................. (fast) |
| (\[{{k}_{2}},{{k}_{3}}\] are rate constant) |
| Give the rate law. |
A) \[r={{k}_{1}}\sqrt{{{k}_{c}}}\,{{[{{A}_{2}}]}^{1/2}}[{{B}_{2}}]\]
B) \[r=\frac{{{k}_{1}}}{{{k}_{c}}}\,{{[{{A}_{2}}]}^{1/2}}[{{B}_{2}}]\]
C) \[r=\sqrt{{{k}_{1}}{{k}_{c}}}\,\,{{[{{A}_{2}}]}^{1/2}}[{{B}_{2}}]\]
D) \[r=\frac{{{k}_{1}}}{\sqrt{{{k}_{c}}}}\,{{[{{A}_{2}}]}^{1/2}}[{{B}_{2}}]\]
Correct Answer: A
Solution :
| [a] | |
| Rate is governed by slowest step | |
| \[A+{{B}_{2}}\xrightarrow{{{k}_{1}}}AB+B\] | |
| \[r={{k}_{1}}\,[A]\,\,[{{B}_{2}}]\] | (i) |
| From \[{{A}_{2}}A+A\] | |
| \[{{k}_{c}}=\frac{{{[A]}^{2}}}{[{{A}_{2}}]}\] | (ii) |
| \[[A]=\sqrt{{{k}_{c}}}\,\,{{[{{A}_{2}}]}^{1/2}}\] | |
| \[r={{k}_{1}}\sqrt{{{k}_{c}}}\,\,{{[{{A}_{2}}]}^{1/2}}\,[{{B}_{2}}]\] order is \[=\frac{1}{2}+1=\frac{3}{2}\]. | |
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