Answer to Question #180842 in Chemistry for Joy

Question

For a solution of acetic acid (HC₂H₃O₂) to be called vinegar it must contain 5% acetic acid by mass. If the vinegar is made up of only of acetic acid, density of the solution = 1.006g/ml. Find mol fraction of solute and solvent, M, m of the solution.

Answer 1

Solution:

Vinegar is an aqueous solution of acetic acid.

acetic acid - HC₂H₃O₂ = C₂H₄O₂

The molar mass of C₂H₄O₂ is 60.052 g/mol.

The molar mass of H₂O is 18.015 g/mol.

Let's assume that the volume of the solution is 1 L (1000 mL).

Thus,

Mass of 1 L C₂H₄O₂ solution = Solution volume × Density = 1000 mL × 1.006 g/mL = 1006 g

Mass of C₂H₄O₂ = (%C₂H₄O₂ × Mass of solution) / 100% = (5% × 1006 g) / 100% = 50.3 g C₂H₄O₂

Mass of solvent (H₂O) = Mass of solution - Mass of C₂H₄O₂ = 1006 g - 50.3 g = 955.7 g H₂O

Moles of C₂H₄O₂ = Mass of C₂H₄O₂ / Molar mass of C₂H₄O₂ = 50.3 g / 60.052 g mol^-1 = 0.8376 mol

Moles of H₂O = Mass of H₂O / Molar mass of H₂O = 955.7 g / 18.015 g mol^-1 = 53.0502 mol

Mole Fraction (χ):

Mole fraction (χ) is the ratio of moles of one substance in a mixture to the total number of moles of all substances.

Total number of moles = Moles of C₂H₄O₂ + Moles of H₂O = 0.8376 mol + 53.0502 mol = 53.8878 mol

χ_solute = χ_C2H4O2 = Moles of C₂H₄O₂ / Total number of moles = 0.8376 mol / 53.8878 mol = 0.016

χ_solute = 0.016

χ_solvent = χ_H2O = Moles of H₂O / Total number of moles = 53.0502 mol / 53.8878 mol = 0.984

χ_solvent = 0.984

Molarity (M):

Molarity or molar concentration is the number of moles of solute per liter of solution.

Molarity of solution = Moles of C₂H₄O₂ / Volume of solution

Molarity of solution = 0.8376 mol / 1 L = 0.8376 mol/L = 0.8376 M = 0.838 M

Molarity of solution = 0.838 M

Molality (m):

Molality of a solution is the moles of solute divided by the kilograms of solvent.

Mass of solvent (H₂O) = 955.7 g = 0.9557 kg

Molality of solution = Moles of C₂H₄O₂ / Kilograms of solvent

Molality of solution = 0.8376 mol / 0.9557 kg = 0.8764 mol/kg = 0.8764 m = 0.876 m

Molality of solution = 0.876 m

Answers:

χ_solute = 0.016

χ_solvent = 0.984

Molarity of solution = 0.838 M

Molality of solution = 0.876 m