Find the mole fraction of solute in its 3 molal aqueous solution.

Options

A. 0.0512
B. 0.0414
C. 0.0347
D. 0.0145

Explanation

To find the mole fraction of the solute in a 3 molal aqueous solution, 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 3 molal solution, which means there are 3 moles of solute in 1 kg of solvent (water).

### Step 2: Calculate the Moles of Solvent (Water)
To find the mole fraction, we need to know the number of moles of the solvent. The molar mass of water (H₂O) is approximately 18 g/mol. Since we have 1 kg of water, we convert this to grams:

\[ 1 \text{ kg} = 1000 \text{ g} \]

Now, we can calculate the moles of water:

\[ \text{Moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

### Step 3: Calculate the Total Moles
Now, we can find the total number of moles in the solution. The total moles is the sum of the moles of solute and the moles of solvent:

\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 3 + 55.56 \approx 58.56 \text{ moles} \]

### Step 4: Calculate the Mole Fraction of the Solute
The mole fraction of the solute (X_solute) is given by the formula:

\[ X_{\text{solute}} = \frac{\text{Moles of solute}}{\text{Total moles}} = \frac{3}{58.56} \]

Calculating this gives:

\[ X_{\text{solute}} \approx 0.0512 \]

### Final Result
Thus, the mole fraction of the solute in the 3 molal aqueous solution is approximately **0.0512**.

---