Find the mole fraction of solute in its 7 molal aqueous solution.

Options

A. 0.112
B. 0.221
C. 0.212
D. 0.125

Explanation

To find the mole fraction of solute in a 7 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 7 molal solution, which means there are 7 moles of solute in 1 kg of water (the solvent).

### Step 2: Calculate the Moles of Solvent (Water)
To find the moles of water, we can use the formula:
\[ \text{Moles of water} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} \]
Given that the mass of water is 1000 g (1 kg) and the molar mass of water is approximately 18 g/mol, we can calculate:
\[ \text{Moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 3: Calculate the Total Moles in the Solution
The total moles in the solution is the sum of the moles of solute and the moles of solvent:
\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 7 + 55.56 \approx 62.56 \, \text{moles} \]

### Step 4: Calculate the Mole Fraction of Solute
The mole fraction of solute (X_solute) is calculated using the formula:
\[ X_{\text{solute}} = \frac{\text{Moles of solute}}{\text{Total moles in solution}} \]
Substituting the values we have:
\[ X_{\text{solute}} = \frac{7}{62.56} \approx 0.112 \]

### Conclusion
The mole fraction of the solute in the 7 molal aqueous solution is approximately **0.112**.

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