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

Options

A. `0.027`
B. `0.036`
C. `0.018`
D. `0.009`

Explanation

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

### Step 1: Understand the definition of a 1 molal solution
A 1 molal (1 m) solution contains 1 mole of solute dissolved in 1 kilogram (kg) of solvent (water in this case).

### Step 2: Determine the number of moles of solute
Since we have a 1 molal solution, the number of moles of solute is:
- Moles of solute = 1 mole

### Step 3: Calculate the number of moles of solvent
The mass of the solvent (water) is given as 1 kg, which is equivalent to 1000 grams. To find the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of water (H₂O) is calculated as follows:
- Molar mass of H = 1 g/mol (2 H atoms = 2 g)
- Molar mass of O = 16 g/mol
- Total molar mass of H₂O = 2 + 16 = 18 g/mol

Now, substituting the values:
\[ \text{Moles of solvent} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

### Step 4: Calculate the mole fraction of the solute
The formula for mole fraction (X) of the solute is:
\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} \]
Substituting the values we have:
\[ X_{\text{solute}} = \frac{1}{1 + 55.56} = \frac{1}{56.56} \approx 0.0177 \]

### Step 5: Final answer
Thus, the mole fraction of the solute in a 1 molal aqueous solution is approximately 0.0177.

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