In a 500mL falsk, the degree of dissociation of `PCI_(5)` at equilibrium is `40%` and the initial amount is 5 moles. The value of equilibrium constant in mol `L^(-1)` for the decomposition of `PCI_(5)` is

Options

A. 2.33
B. 2.66
C. 5.32
D. 4.66

Explanation

To find the equilibrium constant (Kc) for the decomposition of PCl5, we will follow these steps:

### Step 1: Write the balanced chemical equation
The decomposition of phosphorus pentachloride (PCl5) can be represented as:

\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \]

### Step 2: Determine the initial moles and degree of dissociation
Given:
- Initial moles of PCl5 = 5 moles
- Degree of dissociation = 40%

### Step 3: Calculate the moles at equilibrium
The degree of dissociation tells us how many moles of PCl5 dissociate.

- Moles of PCl5 that dissociate = 40% of 5 moles = \( \frac{40}{100} \times 5 = 2 \) moles
- Moles of PCl5 remaining at equilibrium = Initial moles - Moles dissociated = \( 5 - 2 = 3 \) moles
- Moles of PCl3 formed = Moles of Cl2 formed = Moles dissociated = 2 moles (since the stoichiometry of PCl3 and Cl2 is 1:1)

### Step 4: Calculate the concentrations at equilibrium
The volume of the flask is 500 mL, which is equivalent to 0.5 L.

- Concentration of PCl5 at equilibrium:
\[ [\text{PCl}_5] = \frac{\text{moles of PCl}_5}{\text{volume}} = \frac{3 \text{ moles}}{0.5 \text{ L}} = 6 \text{ M} \]

- Concentration of PCl3 at equilibrium:
\[ [\text{PCl}_3] = \frac{\text{moles of PCl}_3}{\text{volume}} = \frac{2 \text{ moles}}{0.5 \text{ L}} = 4 \text{ M} \]

- Concentration of Cl2 at equilibrium:
\[ [\text{Cl}_2] = \frac{\text{moles of Cl}_2}{\text{volume}} = \frac{2 \text{ moles}}{0.5 \text{ L}} = 4 \text{ M} \]

### Step 5: Write the expression for the equilibrium constant (Kc)
The expression for Kc for the reaction is given by:

\[ K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]} \]

### Step 6: Substitute the equilibrium concentrations into the Kc expression
Substituting the values we calculated:

\[ K_c = \frac{(4)(4)}{6} \]

### Step 7: Calculate Kc
\[ K_c = \frac{16}{6} = \frac{8}{3} \approx 2.67 \text{ M} \]

### Conclusion
The value of the equilibrium constant \( K_c \) for the decomposition of PCl5 is approximately **2.67 mol L\(^{-1}\)**.

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