Two gaseous equilibria S O_ 2(g) + 1 2 O_ 2(g) S O_ 3(g) and 2S O… - Vidyadip

MCQ

Two gaseous equilibria $S{O_{2(g)}} + \frac{1}{2}{O_{2(g)}}$ $\rightleftharpoons$ $S{O_{3(g)}}$ and $2S{O_{3(g)}}$ $\rightleftharpoons$ $2S{O_{2(g)}} + {O_{2(g)}}$ have equilibrium constants ${K_1}$ and ${K_2}$ respectively at $298\,K$. Which of the following relationships between ${K_1}$ and ${K_2}$ is correct

A
${K_1} = {K_2}$
B
${K_2} = K_1^2$
✓
${K_2} = \frac{1}{{K_1^2}}$
D
${K_2} = \frac{1}{{{K_1}}}$

✓

Answer

Correct option: C.

${K_2} = \frac{1}{{K_1^2}}$

(c)${{K}_{1}}=\frac{[S{{O}_{3}}]}{[S{{O}_{2}}]\,\,{{[{{O}_{2}}]}^{{1}/{2}\;}}}$ and ${{K}_{2}}=\frac{{{[S{{O}_{2}}]}^{2}}[{{O}_{2}}]}{{{[S{{O}_{3}}]}^{2}}}$ ; ${{K}_{2}}=\frac{1}{K_{1}^{2}}$

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