How much `PCI_5` must be taken in a 9.2 L vessel to get 0.5 moles of `Cl_2` at a particular temperature? The value of equilibrium constant `(K_c)` at the given temperature is 0.0414.

Explanation

To solve the problem of how much \( PCl_5 \) must be taken in a 9.2 L vessel to get 0.5 moles of \( Cl_2 \) at a particular temperature, we can follow these steps:

### Step 1: Write the balanced chemical equation
The dissociation reaction of \( PCl_5 \) can be represented as:
\[ PCl_5 \rightleftharpoons PCl_3 + Cl_2 \]

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