3.2 molal aqueous solution will have mole fraction of solute equal to

Options

A. 0.1
B. 0.054
C. 0.3
D. 0.044

Answer

To find the mole fraction of solute in a 3.2 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 3.2 molal solution, which means there are 3.2 moles of solute in 1 kilogram (1000 grams) of solvent (water).

### Step 2: Calculate the Moles of Solvent (Water)
To find the mole fraction, we need to know the number of moles of the solvent (water). The molar mass of water (H₂O) is approximately 18 grams per mole.

\[ \text{Moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.55 \text{ moles} \]

### Step 3: Calculate the Total Moles
Now, we can calculate the total number of moles, which is the sum of the moles of solute and the moles of solvent.

\[ \text{Total moles} = \text{moles of solute} + \text{moles of solvent} = 3.2 + 55.55 = 58.75 \text{ moles} \]

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

\[ \chi_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles}} = \frac{3.2}{58.75} \]

Calculating this gives:

\[ \chi_{\text{solute}} \approx 0.054 \]

### Final Result
The mole fraction of the solute in the 3.2 molal aqueous solution is approximately **0.054**.

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