To find the mole fraction of solute in a
5m (molal) solution, we first need to understand what molality means. Molality
(m) is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water, and we have a 5 molal solution, which means there are 5 moles of solute per kilogram of water.
First, let's calculate the mass of
1‌kg of water in grams because the moles of water need to be in grams. Since the density of water is approximately
1g∕mL,
1‌kg of water is 1000 grams.
The molar mass of water
(H2O) is approximately
18g∕mol. To find the moles of water, divide the mass of water by its molar mass:
‌ Moles of water ‌=‌≈55.56‌molGiven the molality of the solution, you have 5 moles of solute. Now, calculate the total moles in the solution (which is the sum of moles of solute and solvent):
Total moles
=5 moles of solute +55.56 moles of solvent
≈60.56 moles
The mole fraction of solute (
χ‌solute ‌) is then calculated as the number of moles of solute divided by the total moles in the solution:
χ‌solute ‌=‌≈0.082Thus, the mole fraction of solute in a
5m aqueous solution is approximately 0.082. The correct option is: