Find the mole fraction of solute in its 8 molal aqueous solution.

Options

A. 0.212
B. 0.125
C. 0.222
D. 0.025

Explanation

To find the mole fraction of the solute in an 8 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 an 8 molal solution, which means there are 8 moles of solute in 1 kg of solvent (water).

### Step 2: Calculate the number of moles of solvent (water)
To find the number of moles of water, we use the formula:
\[ \text{Moles of water} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} \]
The molar mass of water (H₂O) is approximately 18 g/mol. Since we have 1 kg of water, which is 1000 g:
\[ \text{Moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 3: 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:
\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 8 + 55.56 \approx 63.56 \, \text{moles} \]

### Step 4: Calculate the mole fraction of the solute
The mole fraction (X) of the solute is given by the formula:
\[ X_{\text{solute}} = \frac{\text{Moles of solute}}{\text{Total moles of solution}} \]
Substituting the values we have:
\[ X_{\text{solute}} = \frac{8}{63.56} \approx 0.125 \]

### Conclusion
The mole fraction of the solute in the 8 molal aqueous solution is approximately 0.125.

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