To aqueous solution of Nal increasing amounts of solid `HgI_2` is added. The vapor pressure of the solution

Options

A. decrease to a constant value
B. increase to a constant value
C. increases first and then decreases
D. remains constant because `HgI_2` is sparingly soluble in water

Explanation

To solve the problem regarding the vapor pressure of an aqueous solution of NaI when increasing amounts of solid HgI2 are added, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Solution**:
- The initial solution contains NaI, which dissociates completely in water.
- The dissociation of NaI can be represented as:
\[ \text{NaI} \rightarrow \text{Na}^+ + \text{I}^- \]
- For every 1 mole of NaI, we get 2 moles of ions (1 Na⁺ and 1 I⁻). Therefore, if we have 2 moles of NaI, we will have 4 moles of ions (2 Na⁺ and 2 I⁻).

2. **Calculating the Van't Hoff Factor (i)**:
- The Van't Hoff factor (i) is the number of particles the solute breaks into. For NaI:
\[ i = 2 \quad (\text{for 1 NaI} \rightarrow 2 \text{ ions}) \]
- Thus, for 2 moles of NaI, \(i = 4\).

3. **Adding HgI2**:
- When HgI2 is added, it is only sparingly soluble in water. The reaction can be represented as:
\[ 2 \text{NaI} + \text{HgI}_2 \rightarrow \text{Na}_2\text{HgI}_4 \]
- The complex Na₂HgI₄ dissociates into:
\[ \text{Na}_2\text{HgI}_4 \rightarrow 2 \text{Na}^+ + \text{HgI}_4^{2-} \]
- This results in a total of 3 moles of ions (2 Na⁺ and 1 HgI₄²⁻).

4. **New Van't Hoff Factor (i)**:
- After the addition of HgI2, the new Van't Hoff factor becomes:
\[ i = 3 \quad (\text{for Na}_2\text{HgI}_4 \rightarrow 3 \text{ ions}) \]

5. **Effect on Vapor Pressure**:
- The vapor pressure of a solution is related to the number of solute particles. According to Raoult's Law:
\[ \frac{P_0 - P}{P_0} = i \cdot \chi_{\text{solute}} \]
- As the Van't Hoff factor decreases from 4 to 3, the vapor pressure of the solution will increase because the number of solute particles is decreasing.

6. **Conclusion**:
- Initially, as HgI2 is added, the vapor pressure increases until a certain point where the reaction reaches completion and the vapor pressure stabilizes at a constant value.

### Final Answer:
- The vapor pressure of the solution **increases to a constant value**.