The mole fraction of the solute in one molal aqueous solution is:

Options

A. `0.009`
B. `0.0018`
C. `0.027`
D. `0.036`

Explanation

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

### Step 2: Calculate Moles of Solvent
To find the mole fraction, we need to calculate the number of moles of the solvent (water). The molecular weight of water (H₂O) is approximately 18 g/mol. Since we have 1 kg (or 1000 g) of water:

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

### Step 3: Calculate Total Moles
Now we can find the total number of moles in the solution. We have 1 mole of solute and approximately 55.56 moles of solvent. Therefore, the total moles in the solution is:

\[ \text{Total moles} = \text{moles of solute} + \text{moles of solvent} = 1 + 55.56 = 56.56 \, \text{moles} \]

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

\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles}} = \frac{1}{56.56} \approx 0.0177 \]

### Step 5: Final Answer
Thus, the mole fraction of the solute in a one molal aqueous solution is approximately 0.0177.

### Summary of Steps:
1. Define molality and identify the number of moles of solute.
2. Calculate the moles of solvent using its mass and molecular weight.
3. Find the total moles in the solution.
4. Use the formula for mole fraction to calculate the mole fraction of the solute.