Q34 / 120 · VITEEE 2018 · Chemistry

Given that the equilibrium constant for the reaction $2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$ has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature? $$ \mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) $$

  • A
    $1.8 \times 10^{-3}$
  • B
    $3.6 \times 10^{-3}$
  • Correct answer
    C
    $6.0 \times 10^{-2}$
  • D
    $1.3 \times 10^{-5}$

Solution

$$ \begin{array}{l} 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{SO}_{3} \quad \mathrm{~K}=278 \text { (given) } \\ \mathrm{SO}_{3} \rightleftharpoons \mathrm{SO}_{2}+\frac{1}{2} \mathrm{O}_{2} \quad \mathrm{~K}^{\prime}=\left(\sqrt{\frac{1}{\mathrm{~K}}}\right) \\ =\sqrt{\frac{1}{278}}=\sqrt{35.97 \times 10^{-4}}=6 \times 10^{-2} \end{array} $$

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

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