The molality (in mol kg^-1) of 1 mole of solute in 50 g of solvent is

CONCEPT:

Molality (m)

• Molality (m) is a measure of the concentration of a solute in a solution.
• It is defined as the number of moles of solute per kilogram of solvent.
• The formula for molality is:

  m = (moles of solute) / (mass of solvent in kg)

EXPLANATION:

• Given data:
  • Moles of solute = 1 mole
  • Mass of solvent = 50 g
• Convert mass of solvent to kilograms:
  • 50 g = 50 / 1000 kg = 0.05 kg
• Using the molality formula:
  • m = (moles of solute) / (mass of solvent in kg)
  • = 1 mole / 0.05 kg
  • = 20 mol kg^-1

Therefore, the molality of 1 mole of solute in 50 g of solvent is 20 mol kg^-1.

Other Options Explanation:

• Option 1 (10 mol kg^-1):
  • This would be the result if the mass of the solvent was 100 g (0.1 kg) instead of 50 g.
  • m = 1 mole / 0.1 kg = 10 mol kg^-1
• Option 3 (30 mol kg^-1):
  • This would be the result if the mass of the solvent was approximately 33.33 g (0.03333 kg).
  • m = 1 mole / 0.03333 kg ≈ 30 mol kg^-1
• Option 4 (40 mol kg^-1):
  • This would be the result if the mass of the solvent was 25 g (0.025 kg).
  • m = 1 mole / 0.025 kg = 40 mol kg^-1