Find the mole fraction of solute in its 14 molal aqueous solution.

Options

A. 0.102
B. 0.201
C. 0.301
D. 0.014

Explanation

To find the mole fraction of solute in a 14 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 14 molal solution, which means there are 14 moles of solute in 1 kg of solvent (water).

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

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

### 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.

\[ \text{Total moles of solution} = \text{moles of solute} + \text{moles of solvent} = 14 + 55.56 \approx 69.56 \text{ moles} \]

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

\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles of solution}} = \frac{14}{69.56} \approx 0.201 \]

### Final Answer
The mole fraction of solute in the 14 molal aqueous solution is approximately **0.201**.

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