Find the mole fraction of solute in its 4 molal aqueous solution.

Options

A. 0.0672
B. 0.0468
C. 0.0347
D. 0.0125

Explanation

To find the mole fraction of solute in a 4 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 4 molal solution, which means there are 4 moles of solute in 1 kg of water (the solvent).

### Step 2: Identify the Moles of Solute
From the problem, we know:
- Moles of solute = 4 moles

### Step 3: Calculate the Moles of Solvent (Water)
To find the moles of solvent (water), we need to use the molar mass of water. The molar mass of water (H₂O) is approximately 18 g/mol.

Since we have 1 kg of water:
- Mass of water = 1000 g
- Moles of water = Mass of water (g) / Molar mass of water (g/mol)

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

### Step 4: Calculate the Total Moles in the Solution
Now, we can find the total number of moles in the solution by adding the moles of solute and the moles of solvent:
\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 4 + 55.56 = 59.56 \, \text{moles} \]

### Step 5: Calculate the Mole Fraction of Solute
The mole fraction of solute (X_solute) is calculated using the formula:
\[ X_{\text{solute}} = \frac{\text{Moles of solute}}{\text{Total moles}} \]
Substituting the values we have:
\[ X_{\text{solute}} = \frac{4}{59.56} \approx 0.0672 \]

### Final Answer
The mole fraction of solute in the 4 molal aqueous solution is approximately **0.0672**.

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