For which of the following reactions, the degree of dissociation cannot be calculated applying the formula: `alpha=(dt-d_(0))/((n-1)d_(0))`

Options

A. `PCl_(5)hArrPCl_(3)+Cl_(2)`
B. `2NH_(2)hArrN_(2)+3H_(2)`
C. `2HIhArrH_(2)+I_(2)`
D. `2KClO_(3)hArr2KCl+3O_(2)`

Answer

To determine for which reaction the degree of dissociation (α) cannot be calculated using the formula \( \alpha = \frac{(d_t - d_0)}{(n-1) d_0} \), we need to analyze the given reactions based on the change in the number of moles of reactants and products.

### Step-by-Step Solution:

1. **Understanding the Formula**: The formula for degree of dissociation is given as:
\[ \alpha = \frac{(d_t - d_0)}{(n-1) d_0} \]
where:
- \( d_t \) = concentration at time \( t \)
- \( d_0 \) = initial concentration
- \( n \) = total number of moles of products formed after the reaction.

2. **Analyzing the Reactions**:
- **Reaction 1**: \( \text{PCl}_5 \rightleftharpoons \text{PCl}_3 + \text{Cl}_2 \)
- Initial moles: 1 (PCl5)
- Final moles: 1 (PCl3) + 1 (Cl2) = 2
- Change in moles (\( \Delta n \)): \( 2 - 1 = 1 \) (not equal to 0)

- **Reaction 2**: \( \text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3 \)
- Initial moles: 1 (N2) + 3 (H2) = 4
- Final moles: 2 (NH3)
- Change in moles (\( \Delta n \)): \( 2 - 4 = -2 \) (not equal to 0)

- **Reaction 3**: \( 2\text{HI} \rightleftharpoons \text{H}_2 + \text{I}_2 \)
- Initial moles: 2 (HI)
- Final moles: 1 (H2) + 1 (I2) = 2
- Change in moles (\( \Delta n \)): \( 2 - 2 = 0 \) (equal to 0)

- **Reaction 4**: \( 2\text{KClO}_3 (s) \rightarrow 2\text{KCl} (s) + 3\text{O}_2 (g) \)
- Initial moles: 0 (since KClO3 is solid)
- Final moles: 0 (KCl is solid) + 3 (O2) = 3
- Change in moles (\( \Delta n \)): \( 3 - 0 = 3 \) (not equal to 0)

3. **Conclusion**: The only reaction where the change in the number of moles (\( \Delta n \)) is equal to 0 is the third reaction \( 2\text{HI} \rightleftharpoons \text{H}_2 + \text{I}_2 \). Therefore, the degree of dissociation cannot be calculated for this reaction using the given formula.

### Final Answer:
The degree of dissociation cannot be calculated for the reaction:
**\( 2\text{HI} \rightleftharpoons \text{H}_2 + \text{I}_2 \)** (Option 3).