At a particular temperature, solid ammonium chloride breaks down in a $0.500\,\text{dm}^3$ vessel to produce ammonia and hydrogen chloride. $\text{NH}_4\text{Cl}(s) \rightleftharpoons \text{NH}_3(g) + \text{HCl}(g)$ The starting amount of ammonium chloride was $1.00\,\text{mol}$, and after equilibrium was established, $0.300\,\text{mol}$ of ammonium chloride remained. Calculate the numerical value of $K_c$ for this reaction under these conditions?
- A$0.490$
- B$1.63$
- C$1.96$
- D$3.27$