The mole fraction of solute in one molal aqueous solution is ………… .

Answer

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

### Step-by-Step Solution:

1. **Understand the Definition of Molality**:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent. A one molal solution means there is 1 mole of solute in 1 kg (1000 g) of solvent.

2. **Identify Moles of Solute**:
- Since we have a one molal solution, the moles of solute (n_solute) = 1 mole.

3. **Calculate Moles of Solvent**:
- The solvent is water, and the molar mass of water (H₂O) is approximately 18 g/mol.
- To find the moles of solvent (n_solvent), we use the formula:
\[ n_{\text{solvent}} = \frac{\text{mass of solvent (g)}}{\text{molar mass of solvent (g/mol)}} \]
- For 1000 g of water:
\[ n_{\text{solvent}} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

4. **Calculate Total Moles**:
- Total moles = moles of solute + moles of solvent:
\[ n_{\text{total}} = n_{\text{solute}} + n_{\text{solvent}} = 1 + 55.56 = 56.56 \text{ moles} \]

5. **Calculate Mole Fraction of Solute**:
- The mole fraction of solute (X_solute) is given by:
\[ X_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{total}}} \]
- Substituting the values:
\[ X_{\text{solute}} = \frac{1}{56.56} \approx 0.0177 \]

### Final Answer:
The mole fraction of solute in a one molal aqueous solution is approximately **0.0177**.

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