The mole fraction of solvent in 0.1 molal aqueous solution is

Options

A. `0.9982`
B. `0.0017`
C. `0.017`
D. `0.17`

Explanation

To find the mole fraction of the solvent in a 0.1 molal aqueous solution, we can follow these steps:

### Step 1: Understand Molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we have a 0.1 molal solution, which means there are 0.1 moles of solute in 1 kg of solvent.

### Step 2: Identify the Solvent
The solvent in this case is water. We know that the mass of the solvent (water) is 1 kg, which is equivalent to 1000 grams.

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

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

### Step 4: Calculate Total Moles in the Solution
Now, we need to calculate the total number of moles in the solution, which includes both the moles of solute and the moles of solvent.

\[ \text{Total moles} = \text{Moles of solvent} + \text{Moles of solute} = 55.56 + 0.1 = 55.66 \text{ moles} \]

### Step 5: Calculate Mole Fraction of Solvent
The mole fraction of the solvent (water) is given by the formula:

\[ \text{Mole fraction of solvent} = \frac{\text{Moles of solvent}}{\text{Total moles}} = \frac{55.56}{55.66} \approx 0.9982 \]

### Conclusion
The mole fraction of the solvent in a 0.1 molal aqueous solution is approximately 0.9982.

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