One mole of SO₃ was placed in a litre reaction flask at a given temperature when the reaction equilibrium was established in the reaction.

$2{\mathrm{SO}}_3\rightleftharpoons 2{\mathrm{SO}}_2+{\mathrm{O}}_2$

the vessel was found to contain 0.6 mol of SO₂. The value of the equilibrium constant is

$$\begin{gathered} 2{\mathrm{SO}}_{3 }\rightleftharpoons 2{\mathrm{SO}}_{2 }+ {\mathrm{O}}_2 \\ \mathrm{Initial} 1 0 0 \\ \mathrm{At} \mathrm{equilibrium} 1 - 2\mathrm{x} 2\mathrm{x} \mathrm{x} \\ \begin{array}{l}\therefore 2\mathrm{x}=0.6,\therefore \mathrm{x}=0.3\\ \left[{\mathrm{SO}}_3\right]=1-2\mathrm{x}=1-0.6=0.4\\ \left[{\mathrm{SO}}_2\right]=2\mathrm{x}=0.6\\ \left[{\mathrm{O}}_2\right]=\mathrm{x}=0.3\\ \mathrm{K}=\frac{\mathrm{x}\times (2\mathrm{x}{)}^2}{(1-2\mathrm{x}{)}^2}=\frac{0.3\times 0.6\times 0.6}{0.4\times 0.4}=0.675\end{array} \end{gathered}$$