Calculate mole fraction of solute in its 2 molal aqueous solution .

Explanation

To calculate the mole fraction of a solute in a 2 molal aqueous solution, we will 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 2 molal solution, which means there are 2 moles of solute in 1 kg (1000 g) of solvent (water).

### Step 2: Calculate the number of moles of solute
Given that the solution is 2 molal, we can directly state:
- Moles of solute = 2 moles

### Step 3: Calculate the mass of the solvent
The mass of the solvent is given as 1000 g (1 kg) since we are dealing with a 2 molal solution.

### Step 4: Calculate the number of moles of solvent
To find the number of moles of solvent (water), we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass of solvent (g)}}{\text{Molar mass of solvent (g/mol)}} \]
The molar mass of water (H₂O) is approximately 18 g/mol. Therefore:
\[ \text{Moles of solvent} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \]

### Step 5: Calculate the total number of moles in the solution
The total number of moles in the solution is the sum of the moles of solute and the moles of solvent:
\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 2 + 55.56 = 57.56 \text{ moles} \]

### Step 6: Calculate the mole fraction of the solute
The mole fraction (X) of the solute is calculated using the formula:
\[ X_{\text{solute}} = \frac{\text{Moles of solute}}{\text{Total moles of solution}} \]
Substituting the values we have:
\[ X_{\text{solute}} = \frac{2}{57.56} \approx 0.0347 \]

### Final Answer
The mole fraction of the solute in the 2 molal aqueous solution is approximately **0.0347**.

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