A) \[\frac{{{K}_{1}}K_{3}^{2}}{{{K}_{2}}}\]
B) \[\frac{{{K}_{2}}\,K_{3}^{3}}{{{K}_{1}}}\]
C) \[{{K}_{1}}\,{{K}_{2}}\,{{K}_{3}}\]
D) \[\frac{{{K}_{1}}\,{{K}_{2}}}{{{K}_{3}}}\]
Correct Answer: B
Solution :
For equilibrium \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)\],\[{{K}_{1}}=\frac{{{[N{{H}_{3}}]}^{2}}}{[{{N}_{2}}]{{[{{H}_{2}}]}^{3}}}\] ?(i) \[{{N}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g),\]\[{{K}_{2}}=\frac{{{[NO]}^{2}}}{[{{N}_{2}}]\,[{{O}_{2}}]}\] \[.....(ii)\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\rightleftharpoons {{H}_{2}}O(g),\]\[{{K}_{3}}=\frac{[{{H}_{2}}O]}{[{{H}_{2}}]\,{{[{{O}_{2}}]}^{1/2}}}.....(iii)\] For reaction, \[2N{{H}_{3}}(g)+\frac{5}{2}{{O}_{2}}(g)\rightleftharpoons 2NO(g)+3{{H}_{2}}O(g)\] \[K=\frac{{{[NO]}^{2}}\times {{[{{H}_{2}}O]}^{3}}}{{{[N{{H}_{3}}]}^{2}}\,{{[{{O}_{2}}]}^{5/2}}}....(iv)\] From equations number (i), (ii) and (ii) \[K=\frac{{{K}_{2}}\times {{K}_{3}}^{3}}{{{K}_{1}}}\]
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