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Question:
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If the equilibrium constants of the following equilibria
\(\mathrm{SO}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{SO}_3 \text { and } 2 \mathrm{SO}_3 \rightleftharpoons 2 \mathrm{SO}_2+\mathrm{O}_2\)
are given by \(\mathrm{K}_1\) and \(\mathrm{K}_2\) respectively, which of the following relations is correct
Options:
\(\mathrm{SO}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{SO}_3 \text { and } 2 \mathrm{SO}_3 \rightleftharpoons 2 \mathrm{SO}_2+\mathrm{O}_2\)
are given by \(\mathrm{K}_1\) and \(\mathrm{K}_2\) respectively, which of the following relations is correct
Solution:
1884 Upvotes
Verified Answer
The correct answer is:
\(\mathrm{K}_2=\left(\frac{1}{\mathrm{~K}_1}\right)^2\)
Hints: \(\mathrm{K}_1=\frac{\left[\mathrm{SO}_3\right]}{\left[\mathrm{SO}_2\right]\left[\mathrm{O}_2\right]^{1 / 2}}\)
\(\mathrm{K}_2=\frac{\left[\mathrm{SO}_2\right]^2\left[\mathrm{O}_2\right]}{\left[\mathrm{SO}_3\right]^2}\)
Thus \(\mathrm{K}_2=\left(\frac{1}{\mathrm{~K}_1}\right)^2\)
\(\mathrm{K}_2=\frac{\left[\mathrm{SO}_2\right]^2\left[\mathrm{O}_2\right]}{\left[\mathrm{SO}_3\right]^2}\)
Thus \(\mathrm{K}_2=\left(\frac{1}{\mathrm{~K}_1}\right)^2\)
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