Find the mole fraction of solute in its 9 molal aqueous solution.

Explanation

To find the mole fraction of solute in a 9 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 9 molal solution, which means there are 9 moles of solute in 1 kg of solvent (water).

### Step 2: Calculate the moles of solvent
Since the solvent is water, we need to calculate the number of moles of water in 1 kg (1000 grams). The molar mass of water (H₂O) is approximately 18 g/mol.

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

### Step 3: Calculate 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.

\[ \text{Total moles} = \text{moles of solute} + \text{moles of solvent} = 9 + 55.56 \approx 64.56 \text{ moles} \]

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

\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles of solution}} = \frac{9}{64.56} \approx 0.139 \]

### Final Answer
The mole fraction of the solute in the 9 molal aqueous solution is approximately **0.139**.

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