`3.00` mol of `PCl_(5)` kept in `1L` closed reaction vessel was allowed to attain equilibrium at `3.80 K`. Calculate composition of the mixture at equilibrium `K_(c) = 1.80`

Explanation

To solve the problem step by step, we will analyze the equilibrium situation for the reaction of phosphorus pentachloride (PCl₅) dissociating into phosphorus trichloride (PCl₃) and chlorine gas (Cl₂).

### Step 1: Write the balanced chemical equation.
The dissociation of phosphorus pentachloride can be represented as:
\[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \]

### Step 2: Set up the initial concentrations.
Given that we have 3.00 moles of PCl₅ in a 1 L vessel, the initial concentration of PCl₅ is:
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