Find the mole fraction of solute in its 10 molal aqueous solution.

Options

A. 0.152
B. 0.215
C. 0.325
D. 0.485

Explanation

To find the mole fraction of the solute in a 10 molal aqueous solution, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we have a 10 molal solution, which means there are 10 moles of solute in 1 kg of solvent (water).

### Step 2: Calculate the moles of solvent (water)
The molar mass of water (H₂O) is approximately 18 g/mol. Since we have 1 kg of water, we need to convert this mass into grams:
- Mass of water = 1 kg = 1000 g

Now, we can calculate the moles of water:
\[ \text{Moles of water} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

### Step 3: Calculate the total moles of solution
The total moles of solution is the sum of the moles of solute and the moles of solvent:
\[ \text{Total moles of solution} = \text{Moles of solute} + \text{Moles of solvent} = 10 + 55.56 = 65.56 \text{ moles} \]

### Step 4: Calculate the mole fraction of solute
The mole fraction of solute (X_solute) is given by the formula:
\[ X_{\text{solute}} = \frac{\text{Moles of solute}}{\text{Total moles of solution}} = \frac{10}{65.56} \approx 0.152 \]

### Step 5: Conclusion
The mole fraction of the solute in the 10 molal aqueous solution is approximately 0.152.

---