To solve the question regarding the effect of adding 1 mole of \( I_2 \) (solid) to a 1 M, 1 liter KI solution, we will analyze the changes in colligative properties, which include osmotic pressure, freezing point, relative lowering of vapor pressure, and boiling point.
### Step-by-Step Solution:
1. **Understanding Colligative Properties**:
- Colligative properties depend on the number of solute particles in a solution, not on the identity of the solute. The main colligative properties include osmotic pressure, freezing point depression, boiling point elevation, and relative lowering of vapor pressure.
2. **Adding \( I_2 \) to KI Solution**:
- When 1 mole of \( I_2 \) (solid) is added to the KI solution, it does not dissociate into ions because it is a molecular solid. KI, on the other hand, dissociates into \( K^+ \) and \( I^- \) ions in solution.
3. **Effect on Osmotic Pressure**:
- The osmotic pressure (\( \Pi \)) of a solution is given by the formula:
\[
\Pi = iCRT
\]
where \( i \) is the van 't Hoff factor (number of particles the solute dissociates into), \( C \) is the molarity, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
- Since \( I_2 \) does not dissociate, it adds 1 mole of solute particles, increasing the osmotic pressure.
4. **Effect on Freezing Point**:
- The freezing point depression (\( \Delta T_f \)) is given by:
\[
\Delta T_f = iK_f m
\]
where \( K_f \) is the freezing point depression constant and \( m \) is the molality of the solution.
- Adding \( I_2 \) increases the total number of solute particles, leading to a greater depression of the freezing point. Thus, the freezing point of the solution decreases.
5. **Effect on Relative Lowering of Vapor Pressure**:
- The relative lowering of vapor pressure is given by:
\[
\Delta P = \frac{n_{solute}}{n_{solution}}
\]
where \( n_{solute} \) is the number of moles of solute and \( n_{solution} \) is the total number of moles in the solution.
- Adding \( I_2 \) increases the number of solute particles, leading to an increase in the relative lowering of vapor pressure.
6. **Effect on Boiling Point**:
- The boiling point elevation (\( \Delta T_b \)) is given by:
\[
\Delta T_b = iK_b m
\]
where \( K_b \) is the boiling point elevation constant.
- Similar to freezing point, the addition of \( I_2 \) increases the number of solute particles, resulting in an elevation of the boiling point.
### Summary of Changes:
- **Osmotic Pressure**: Increases
- **Freezing Point**: Decreases (the freezing point of the solution decreases)
- **Relative Lowering of Vapor Pressure**: Increases
- **Boiling Point**: Increases
### Conclusion:
The correct statement regarding the changes in colligative properties when adding 1 mole of \( I_2 \) to the KI solution is that the osmotic pressure increases, the freezing point decreases, and the relative lowering of vapor pressure increases. The boiling point also increases.
