Mole fraction of a solute in 2.5 molal aqueous solution is

Options

A. `0.43`
B. `0.043`
C. `4.3`
D. `43`

Answer

To find the mole fraction of a solute in a 2.5 molal aqueous solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Molality**:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent.
- Given that the solution is 2.5 molal, this means there are 2.5 moles of solute in 1 kg of solvent (water).

2. **Identify the Number of Moles of Solvent**:
- Since the solvent is water and we have 1 kg of it, we need to convert this mass into grams for easier calculations:
\[ \text{Mass of solvent} = 1 \text{ kg} = 1000 \text{ g} \]
- To find the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
- The molar mass of water (H₂O) is calculated as follows:
- Hydrogen (H): 2 atoms × 1 g/mol = 2 g/mol
- Oxygen (O): 1 atom × 16 g/mol = 16 g/mol
- Total = 2 + 16 = 18 g/mol
- Therefore, the number of moles of water is:
\[ \text{Number of moles of water} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.55 \text{ moles} \]

3. **Calculate the Total Number of Moles**:
- The total number of moles in the solution is the sum of the moles of solute and the moles of solvent:
\[ \text{Total moles} = \text{moles of solute} + \text{moles of solvent} = 2.5 + 55.55 = 58.05 \text{ moles} \]

4. **Calculate the Mole Fraction of the Solute**:
- The mole fraction of the solute (denoted as \( x_{\text{solute}} \)) is given by:
\[ x_{\text{solute}} = \frac{\text{moles of solute}}{\text{total moles}} = \frac{2.5}{58.05} \]
- Performing the calculation:
\[ x_{\text{solute}} \approx 0.043 \]

5. **Final Answer**:
- The mole fraction of the solute in the 2.5 molal aqueous solution is approximately **0.043**.