For the given reaction: $\text{PCl}_5 \rightleftharpoons \text{PCl}_3 + \text{Cl}_2$

The expression for the equilibrium constant $K_c$ is: $K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]}$

Given equilibrium concentrations: $[\text{PCl}_5] = 1.40\text{ M}$ $[\text{Cl}_2] = 1.60\text{ M}$ $[\text{PCl}_3] = 1.60\text{ M}$

Substituting these values into the equilibrium expression: $K_c = \frac{1.60 \times 1.60}{1.40}$ $K_c = \frac{2.56}{1.40} \approx 1.83$

Therefore, the value of $K_c$ is $1.83$.