A $1.00\text{ dm}^3$ sealed container is charged with $0.200$ mol of sulfur dioxide and $0.200$ mol of oxygen. The gases are then left to react until equilibrium is attained. $2\text{SO}_2 + \text{O}_2 \rightleftharpoons 2\text{SO}_3$ When equilibrium is established, the container contains $0.100$ mol of $\text{SO}_3$. 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$6.67\ \text{mol}^{-1}\text{ dm}^3$