What is the mole fraction of solute in a 3.68 m aqueous solution?
The correct answer and explanation is :
To calculate the mole fraction of the solute in a solution, we need to understand a few concepts:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the molality is given as 3.68 m, meaning there are 3.68 moles of solute per 1 kilogram of solvent.
- Mole Fraction (X) is the ratio of the moles of solute to the total moles in the solution. It can be calculated using the formula:
[
X_{\text{solute}} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}}
]
Steps to find the mole fraction of solute:
- Determine the moles of solute:
The molality is 3.68 m, which means 3.68 moles of solute per 1 kilogram of solvent. So, we have 3.68 moles of solute. - Calculate the moles of solvent:
The solvent is water (H₂O). The molar mass of water is approximately 18.015 g/mol. Since there is 1 kg of solvent, we can convert the mass of solvent to moles:
[
\text{moles of solvent} = \frac{1000 \, \text{g}}{18.015 \, \text{g/mol}} = 55.51 \, \text{mol}
]
- Calculate the mole fraction of solute:
Now, we can calculate the mole fraction of the solute using the formula:
[
X_{\text{solute}} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} = \frac{3.68}{3.68 + 55.51}
]
[
X_{\text{solute}} = \frac{3.68}{59.19} = 0.0622
]
Conclusion:
The mole fraction of the solute in the 3.68 m aqueous solution is approximately 0.0622.
This result shows that the solute makes up only a small fraction of the total number of moles in the solution, which is expected for a dilute solution.