Q10 / 160 · WBJEE 2011 · Chemistry

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

  • Correct answer
    A
    \(\mathrm{K}_2=\left(\frac{1}{\mathrm{~K}_1}\right)^2\)
  • B
    \(K_1=\left(\frac{1}{K_2}\right)^3\)
  • C
    \(K_2=\left(\frac{1}{K_1}\right)\)
  • D
    \(K_2=\left(K_1\right)^2\)

Solution

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 \(\mathrm{K}_2=\left(\frac{1}{\mathrm{~K}_1}\right)^2\)

Hence, the correct answer is option: 'A'.

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