The mole fraction of solute in 2.5 m aqueous solution is

Options

A. 0.055
B. 0.043
C. 0.86
D. 0.25

Explanation

To find the mole fraction of the solute in a 2.5 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, a 2.5 molal solution means there are 2.5 moles of solute in 1 kg of solvent (water).

### Step 2: Calculate the Moles of Solvent
Since the solvent is water (H₂O), we need to calculate the number of moles of water in 1 kg (1000 g):
- Molar mass of water (H₂O) = 2(1) + 16 = 18 g/mol
- Moles of water = mass of water (g) / molar mass (g/mol) = 1000 g / 18 g/mol = 55.56 moles (approximately).

### Step 3: Calculate the Total Moles in the Solution
Now, we need to find the total number of moles in the solution, which includes both the solute and the solvent:
- Moles of solute = 2.5 moles
- Moles of solvent = 55.56 moles
- Total moles = moles of solute + moles of solvent = 2.5 + 55.56 = 58.06 moles (approximately).

### Step 4: Calculate the Mole Fraction of the Solute
The mole fraction (X) of the solute is calculated using the formula:
\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles}} \]
Substituting the values:
\[ X_{\text{solute}} = \frac{2.5}{58.06} \approx 0.043 \]

### Final Answer
The mole fraction of the solute in the 2.5 molal aqueous solution is approximately 0.043.

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