For which of the following reactions, the degree of dissociation cannot be calculated from the vapour density data.
I. `2HI_((g))hArrH_(2(g))+I_(2(g))`
II. `2NH_(3(g))hArrN_(2(g))+3H_(2(g))`
III. `2NO_((g))hArrN_(2(g))+O_(2(g))`
IV. `PCl_(5(g))hArr PCl_(3(g))+Cl_(2(g))`

Options

A. I and III
B. III and IV
C. I and II
D. II and III

Answer

To determine for which of the given reactions the degree of dissociation cannot be calculated from the vapor density data, we need to analyze each reaction based on the change in the number of moles of reactants and products.

### Step-by-step Solution:

1. **Understanding Degree of Dissociation**:
- The degree of dissociation (α) is defined as the fraction of the original substance that has dissociated into products at equilibrium.
- It can be calculated using the formula:
\[ \alpha = \frac{\text{moles dissociated}}{\text{initial moles}} = \frac{p}{1} = p \]
- The total moles at equilibrium will be the sum of the moles of reactants and products.

2. **Identifying the Change in Moles**:
- For a reaction, if the change in moles (Δn) is zero (i.e., the number of moles of products equals the number of moles of reactants), we cannot calculate the degree of dissociation from vapor density data.

3. **Analyzing Each Reaction**:
- **Reaction I**: \(2HI \rightleftharpoons H_2 + I_2\)
- Initial moles: 2 (HI)
- Final moles: 2 (1 H2 + 1 I2)
- Change in moles (Δn) = 2 - 2 = 0
- **Conclusion**: Degree of dissociation cannot be calculated.

- **Reaction II**: \(2NH_3 \rightleftharpoons N_2 + 3H_2\)
- Initial moles: 2 (NH3)
- Final moles: 4 (1 N2 + 3 H2)
- Change in moles (Δn) = 4 - 2 = 2
- **Conclusion**: Degree of dissociation can be calculated.

- **Reaction III**: \(2NO \rightleftharpoons N_2 + O_2\)
- Initial moles: 2 (NO)
- Final moles: 3 (1 N2 + 1 O2)
- Change in moles (Δn) = 3 - 2 = 1
- **Conclusion**: Degree of dissociation can be calculated.

- **Reaction IV**: \(PCl_5 \rightleftharpoons PCl_3 + Cl_2\)
- Initial moles: 1 (PCl5)
- Final moles: 2 (1 PCl3 + 1 Cl2)
- Change in moles (Δn) = 2 - 1 = 1
- **Conclusion**: Degree of dissociation can be calculated.

4. **Final Conclusion**:
- The reactions for which the degree of dissociation cannot be calculated from vapor density data are:
- **Reaction I** and **Reaction III**.

### Answer:
The degree of dissociation cannot be calculated from the vapor density data for reactions I and III.