Question

What is the mole fraction of the solute in a $1.00\, m$ aqueous solution ?

• A. 0.0354
• B. 0.0177
• C. 0.177
• D. 1.77

Answer 1

The Correct Option is B

To find the mole fraction of the solute in a 1.00\, m (molal) aqueous solution, we need to follow these steps:

1. Understand Molality: Molality (\(m\)) is defined as the number of moles of solute per kilogram of solvent.

2. Define the Given: A 1.00\, m solution means there is 1 mole of solute in 1 kg of water (the solvent).

3. Calculate Mole Fraction: Mole fraction of solute is calculated using the formula:

   \[\text{Mole fraction of solute} = \frac{\text{Moles of solute}}{\text{Moles of solute} + \text{Moles of solvent}}\]

4. Calculate Moles of Solvent (Water): The molar mass of water is approximately \(18.01528 \, \text{g/mol}\). Therefore, moles of solvent (water) in 1 kg (1000 g) is:

   \[\text{Moles of water} = \frac{1000 \, \text{g}}{18.01528 \, \text{g/mol}} = 55.51 \, \text{mol}\]

5. Substitute and Solve: Substitute the calculated values into the mole fraction formula:

   \[\text{Mole fraction of solute} = \frac{1 \, \text{mol}}{1 \, \text{mol} + 55.51 \, \text{mol}} = \frac{1}{56.51} = 0.0177\]

Hence, the mole fraction of the solute in the 1.00\, m aqueous solution is 0.0177. This matches the given correct answer.