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Mole Fraction and Mole Percent

Key Concepts

  • Mole fraction and mole percent are ways of expressing the concentration of a solution.

Mole Fraction

  • Mole fraction is the ratio of moles of one compound to the total number of moles present.

  • Mole fraction is represented by the symbol Χ

  • Χa = na ÷ (na + nb + nc + .....)
        Χa = mole fraction of component a
        na = moles of component a
        nb = moles of component b
        nc = moles of component c

  • For a two component system, one component is the solute and the other is the solvent:
        Χ(solute) = n (solute) ÷ (n(solute) + n(solvent))
        Χ(solvent) = n (solvent) ÷ (n(solvent) + n(solute))

  • The sum of the mole fractions for each component in a solution will be equal to 1.
        For a solution containing 2 components, solute and solvent,
        Χsolute + Χsolvent = 1

Mole Percent

  • Mole percent is the percentage of the total moles that is of a particular component.

  • Mole percent is equal to the mole fraction for the component multiplied by 100:
        mol % a = Χa x 100

  • The sum of the mole percents for each component in a solution will be equal to 100.
        For a solution containing 2 components, solute and solvent,
        mol % solute + mol % solvent = 100

Example: Calculating Mole Fraction of Solute and Solvent

What is the mole fraction and mole percent of sodium chloride and the mole fraction and mole percent of water in an aqueous solution containing 25.0g water and 5.0g sodium chloride?
  1. Identify the components making up the solution: NaCl (solute) and H2O (solvent)

  2. Χ(NaCl) = n(NaCl) ÷ (n(NaCl) + n(H2O))             and             Χ(H2O) = 1 - Χ(NaCl)

  3. Calculate the moles of each component:

    moles of solute (NaCl):
    n(NaCl) = mass ÷ molecular mass
    mass (NaCl) = 5.0g
    MM (NaCl) = 22.99 + 35.45 = 58.44g/mol
    n (NaCl) = 5.0 ÷ 58.44 = 0.08556mol
    moles of solvent (H2O):
    n(H2O) = mass ÷ molecular mass
    mass (H2O) = 25.0g
    MM (H2O) = 2 x 1.008 + 16.00 = 18.016g/mol
    n (H2O) = 25.0 ÷ 18.016 = 1.3877mol

  4. Calculate the mole fraction of sodium chloride:
    Χ(NaCl) = n(NaCl) ÷ (n(NaCl) + n(H2O)) = 0.08556 ÷ (0.08556 + 1.3877) = 0.058

  5. Calculate mole percent of NaCl = 100 x Χ(NaCl) = 100 x 0.058 = 5.8%

  6. Mole fraction of solvent (water) = 1 - Χ(H2O) = 1 - 0.058 = 0.942

  7. Calculate mole percent of H2O = 100 x Χ(H2O) = 100 x 0.942 = 94.2%

Example: Calculating Mass of Solute or Solvent

A particular aqueous solution contains 7.5 moles of water and a mole fraction of sodium chloride of 0.125.
How many grams of sodium chloride are present in the solution?
  1. Re-arrange the equation Χ(NaCl) = n(NaCl) ÷ (n(NaCl) + n(H2O)) to find n(NaCl):
    Multiply both sides by (n(NaCl) + n(H2O)):
    Χ(NaCl) x (n(NaCl) + n(H2O)) = n(NaCl)

    Expand the expression on the left hand side:
    (NaCl) x n(NaCl)) + (Χ(NaCl) x n(H2O)) = n(NaCl)

    Collect like terms (n(NaCl)):
    Χ(NaCl) x n(H2O) = n(NaCl) - (Χ(NaCl) x n(NaCl))

    Re-arrange the expression for n(NaCl)
    Χ(NaCl) x n(H2O) = n(NaCl)(1 - Χ(NaCl))

    Divide throughout by (1 - Χ(NaCl)) to get an expression for n(NaCl):
    (NaCl) x n(H2O)) ÷ (1 - Χ(NaCl)) = n(NaCl)

  2. Calculate n(NaCl):
    n(NaCl) = (Χ(NaCl) x n(H2O)) ÷ (1 - Χ(NaCl)) = (0.125 x 7.5) ÷ (1 - 0.125) = 1.071mol

  3. Calculate mass of NaCl:
    n(NaCl) = mass(NaCl) ÷ MM(NaCl)
    So mass(NaCl) = n(NaCl) x MM(NaCl) = 1.071 x 58.44 = 62.6g


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