The decomposition of $\text{PCl}_5$ is represented below. $\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)$ A container with volume $1\ \text{dm}^3$ is filled with $1.0$ mol of $\text{PCl}_5(g)$, $1.0$ mol of $\text{PCl}_3(g)$ and $1.0$ mol of $\text{Cl}_2(g)$, then left at $250\,^{\circ}\text{C}$ until equilibrium is established. When equilibrium is reached at this temperature, the mixture contains $1.8$ moles of $\text{PCl}_3$. Determine the value of $K_c$ at $250\,^{\circ}\text{C}$?
- A$1$
- B$1.8$
- C$9$
- D$16.2$