Find the mole fraction of solute in its 5 molal aqueous solution.

Options

A. 0.0826
B. 0.0425
C. 0.0325
D. 0.0125

Explanation

To find the mole fraction of solute in a 5 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 5 molal solution, which means there are 5 moles of solute in 1 kg of water (the solvent).

### Step 2: Calculate Moles of Solvent
The solvent in this case is water. We need to calculate the number of moles of water present in 1 kg.

- Molar mass of water (H₂O) = 18 g/mol
- 1 kg of water = 1000 g

Now, we can calculate the moles of water:

\[ \text{Moles of water} = \frac{\text{mass of water (g)}}{\text{molar mass of water (g/mol)}} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 3: Calculate Total Moles
Now, we can find the total number of moles in the solution. The total moles will be the sum of the moles of solute and the moles of solvent:

\[ \text{Total moles} = \text{Moles of solute} + \text{Moles of solvent} = 5 + 55.56 \approx 60.56 \, \text{moles} \]

### Step 4: Calculate Mole Fraction of Solute
The mole fraction of solute (X_solute) is calculated using the formula:

\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles}} = \frac{5}{60.56} \]

Calculating this gives:

\[ X_{\text{solute}} \approx 0.0826 \]

### Conclusion
The mole fraction of the solute in a 5 molal aqueous solution is approximately **0.0826**.

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