A sealed container with a volume of $1.00\,\text{dm}^3$ initially contains 0.200 mol of sulfur dioxide and 0.200 mol of oxygen. The gases are left to react until equilibrium is established. $\text{2SO}_2 + \text{O}_2 \rightleftharpoons \text{2SO}_3$ When equilibrium is reached, the amount of $\text{SO}_3$ in the container is $0.100$ mol. Calculate the value of $K_c$.
- A$0.150\,\text{mol dm}^{-3}$
- B$0.800\,\text{mol dm}^{-3}$
- C$1.25\,\text{mol}^{-1}\text{dm}^3$
- D$6.67\,\text{mol}^{-1}\text{dm}^3$