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Question:
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Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively,
$$
\begin{aligned}
&\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g) \\
&2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)
\end{aligned}
$$
The equilibrium constants are related as
Options:
$$
\begin{aligned}
&\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g) \\
&2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)
\end{aligned}
$$
The equilibrium constants are related as
Solution:
2262 Upvotes
Verified Answer
The correct answer is:
$K_{1}^{2}=\frac{1}{K_{2}}$
$\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)$
... (i) $K_{1}$ Equation (i) is reversed and multiplied by 2 $2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \quad$ (i) $\frac{1}{K_{1}^{2}}$ $2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$
(ii) $K_{2}$ $\therefore \quad K_{2}=\frac{1}{K_{1}^{2}}$
$$
K_{1}^{2}=\frac{1}{K_{2}}
$$
... (i) $K_{1}$ Equation (i) is reversed and multiplied by 2 $2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \quad$ (i) $\frac{1}{K_{1}^{2}}$ $2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$
(ii) $K_{2}$ $\therefore \quad K_{2}=\frac{1}{K_{1}^{2}}$
$$
K_{1}^{2}=\frac{1}{K_{2}}
$$
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