A) \[\frac{{{K}_{2}}K_{3}^{2}}{{{K}_{1}}}\]
B) \[\frac{K_{2}^{2}{{K}_{3}}}{{{K}_{1}}}\]
C) \[\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{3}}}\]
D) \[\frac{{{K}_{2}}K_{3}^{3}}{{{K}_{1}}}\]
Correct Answer: D
Solution :
[d] Given, \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}};\,\,\,\,{{K}_{1}}\] ....(i) \[{{N}_{2}}+{{O}_{2}}2NO;\,\,\,\,{{K}_{2}}\] .?(ii) \[{{H}_{2}}+\frac{1}{2}{{O}_{2}}{{H}_{2}}O;\,\,\,\,{{K}_{3}}\] ....(iii) We have to calculate \[4N{{H}_{3}}+5{{O}_{2}}\xrightarrow{{}}4NO+6{{H}_{2}}O;\,\,\,\,K=?\] or \[2N{{H}_{3}}+\frac{5}{2}{{O}_{2}}\xrightarrow{{}}2NO+3{{H}_{2}}O\] For this equation, \[K=\frac{{{[NO]}^{2}}\,\,{{[{{H}_{2}}O]}^{3}}}{{{[N{{H}_{3}}]}^{2}}\,\,{{[{{O}_{2}}]}^{5/2}}}\] but \[{{K}_{1}}=\frac{{{[N{{H}_{3}}]}^{2}}}{[{{N}_{2}}]\,\,{{[{{H}_{2}}]}^{3}}},\] \[{{K}_{2}}=\frac{{{[NO]}^{2}}}{[{{N}_{2}}]\,\,[{{O}_{2}}]}\] & \[{{K}_{3}}=\frac{[{{H}_{2}}O]}{[{{H}_{2}}]\,\,{{[{{O}_{2}}]}^{1/2}}}\] or \[{{K}_{3}}=\frac{{{[{{H}_{2}}O]}^{3}}}{{{[{{H}_{2}}]}^{3}}\,\,{{[{{O}_{2}}]}^{3/2}}}\] Now operate, \[\frac{{{K}_{2}}.{{K}_{3}}^{3}}{{{K}_{1}}}\] \[=\frac{{{[NO]}^{2}}}{[{{N}_{2}}]\,\,[{{O}_{2}}]}\times \frac{{{[{{H}_{2}}O]}^{3}}}{{{[{{H}_{2}}]}^{3}}\,\,{{[O]}^{3/2}}}.\frac{[{{N}_{2}}]\,\,{{[{{H}_{2}}]}^{3}}}{{{[N{{H}_{3}}]}^{2}}}\] \[=\frac{{{[NO]}^{2}}\,\,{{[{{H}_{2}}O]}^{3}}}{{{[N{{H}_{3}}]}^{2}}\,\,{{[{{O}_{2}}]}^{5/2}}}=K\]| \[\therefore K=\frac{{{K}_{2}}.{{K}_{3}}^{3}}{{{K}_{1}}}\] |
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