A sample of pure `PCl_(5)` was introduced into an evacuted vessel at `473 K`. After equilibrium was attained,concentration of `PCl_(5)` was found to be `0.5xx10^(-1)mol litre^(-1)`. If value of `K_(c)` is `8.3xx10^(-3) mol litre^(-1)`. What are the concentrations of `PCl_(3)` and `Cl_(2)` at equilibrium ?

Explanation

To solve the problem step by step, we will follow the reaction dynamics of the decomposition of phosphorus pentachloride (PCl₅) into phosphorus trichloride (PCl₃) and chlorine gas (Cl₂).

### Step 1: Write the balanced chemical equation
The decomposition reaction can be written as:
\[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \]

### Step 2: Define initial concentrations
Let the initial concentration of PCl₅ be \( A \) (in mol/L). At equilibrium, the concentration of PCl₅ is given as:
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