Find the mole fraction of solute in its 12 molal aqueous solution.

Options

A. 0.717
B. 0.177
C. 0.215
D. 0.256

Explanation

To find the mole fraction of solute in a 12 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 12 molal solution, which means there are 12 moles of solute in 1 kg of solvent (water).

### Step 2: Calculate Moles of Solvent (Water)
We need to calculate the number of moles of water (the solvent). The molar mass of water (H₂O) is approximately 18 g/mol. Since we have 1 kg (or 1000 g) of water, we can calculate the moles of water as follows:

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

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

\[ \text{Total moles of solution} = \text{moles of solute} + \text{moles of solvent} = 12 + 55.56 \approx 67.56 \, \text{moles} \]

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

\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles of solution}} = \frac{12}{67.56} \approx 0.177 \]

### Conclusion
The mole fraction of solute in the 12 molal aqueous solution is approximately **0.177**.

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