To solve the problem of determining the correct order of vapor pressure of the solutions formed by mixing 10 g of solutes A, B, and C in 180 g of water, we will use the concept of colligative properties, specifically the relative lowering of vapor pressure.
### Step-by-Step Solution:
1. **Understanding the Problem**:
We have 180 g of water and we are adding 10 g of three different solutes (A, B, and C) separately. We need to find out the order of their vapor pressures after mixing.
2. **Molecular Masses**:
- Molecular mass of A (MMA) = 100 g/mol
- Molecular mass of B (MMB) = 150 g/mol
- Molecular mass of C (MMC) = 125 g/mol
3. **Calculating Moles of Solute**:
The number of moles of each solute can be calculated using the formula:
\[
\text{Number of moles} = \frac{\text{mass (g)}}{\text{molecular mass (g/mol)}}
\]
- Moles of A (nA) = \( \frac{10 \, \text{g}}{100 \, \text{g/mol}} = 0.1 \, \text{mol} \)
- Moles of B (nB) = \( \frac{10 \, \text{g}}{150 \, \text{g/mol}} = \frac{1}{15} \, \text{mol} \approx 0.0667 \, \text{mol} \)
- Moles of C (nC) = \( \frac{10 \, \text{g}}{125 \, \text{g/mol}} = 0.08 \, \text{mol} \)
4. **Calculating Moles of Solvent (Water)**:
The number of moles of the solvent (water) can be calculated as:
\[
n_{water} = \frac{180 \, \text{g}}{18 \, \text{g/mol}} = 10 \, \text{mol}
\]
5. **Relative Lowering of Vapor Pressure**:
The relative lowering of vapor pressure (RLVP) can be expressed as:
\[
\text{RLVP} = \frac{P_0 - P}{P_0} = \frac{n_{solute}}{n_{solute} + n_{solvent}}
\]
Since the number of moles of solvent is the same for all solutions, we can simplify our comparison to just the number of moles of solute.
6. **Comparing Moles of Solute**:
- For A: \( n_A = 0.1 \, \text{mol} \)
- For B: \( n_B \approx 0.0667 \, \text{mol} \)
- For C: \( n_C = 0.08 \, \text{mol} \)
7. **Determining the Order of Vapor Pressure**:
The solution with the highest number of moles of solute will have the greatest lowering of vapor pressure, and thus the lowest vapor pressure. Conversely, the solution with the least number of moles of solute will have the least lowering of vapor pressure, and thus the highest vapor pressure.
- A has the highest moles (0.1 mol) → Lowest vapor pressure
- C has the next highest moles (0.08 mol) → Middle vapor pressure
- B has the lowest moles (0.0667 mol) → Highest vapor pressure
Therefore, the order of vapor pressure from highest to lowest is:
\[
\text{B} > \text{C} > \text{A}
\]
### Final Answer:
The correct order of vapor pressure of the solutions is: **B > C > A**.
