| (I) \[{{N}_{2}}+2{{O}_{2}}\rightleftharpoons 2N{{O}_{2}}\] |
| (II) \[2N{{O}_{2}}\rightleftharpoons {{N}_{2}}+2{{O}_{2}}\] |
| (III) \[N{{O}_{2}}\rightleftharpoons \frac{1}{2}{{N}_{2}}+{{O}_{2}}\] |
| The correct relation from the following is |
A) \[{{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{K}_{3}}}\]
B) \[{{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{({{K}_{3}})}^{2}}}\]
C) \[{{K}_{1}}=\sqrt{{{K}_{2}}}={{K}_{3}}\]
D) \[{{K}_{1}}=\frac{1}{{{K}_{2}}}={{K}_{3}}\]
Correct Answer: B
Solution :
[b]| \[\begin{matrix} (I) & {{N}_{2}}+2{{O}_{2}}\overset{{{K}_{1}}}{\mathop{\rightleftharpoons }}\,2N{{O}_{2}} \\ \end{matrix}\] |
| \[{{K}_{1}}=\frac{{{[N{{O}_{2}}]}^{2}}}{[{{N}_{2}}]{{[{{O}_{2}}]}^{2}}}\] ....(i) |
| \[\begin{matrix} (II) & 2N{{O}_{2}}\overset{{{K}_{2}}}{\mathop{\rightleftharpoons }}\,{{N}_{2}}+2{{O}_{2}} \\ \end{matrix}\] |
| \[{{K}_{2}}=\frac{[{{N}_{2}}]{{[{{O}_{2}}]}^{2}}}{{{[N{{O}_{2}}]}^{2}}}\] ...(ii) |
| \[\begin{matrix} (III) & N{{O}_{2}}\overset{{{K}_{3}}}{\mathop{\rightleftharpoons }}\,\frac{1}{2}{{N}_{2}}+{{O}_{2}} \\ \end{matrix}\] |
| \[{{K}_{3}}=\frac{{{[{{N}_{2}}]}^{1/2}}[{{O}_{2}}]}{[N{{O}_{2}}]}\] |
| \[\therefore {{({{K}_{3}})}^{2}}=\frac{[{{N}_{2}}]{{[{{O}_{2}}]}^{2}}}{{{[N{{O}_{2}}]}^{2}}}\] ....(iii) |
| \[\therefore \] from equation (i), (ii) and (iii) \[{{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{({{K}_{3}})}^{2}}}\] |
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