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How to Go From Percentage by Mass to a Mole Fraction

A weight percentage expresses the composition of a mixture of substances or a concentration of a dissolved compound in the solution. This quantity is the ratio of the compound mass to total mass of the mixture or the solution. Moles are a unit of quantity in chemistry that are necessary for many quantitative calculations. A mole fraction is another way to express the mixture composition; it is the ratio of the number of moles of a substance to the total moles of the mixture.

Things You'll Need

Calculator

Instructions

- 1
  Write down the mixture composition. For example, the mixture consists of two salts, sodium chloride (NaCl) and magnesium chloride (MgCl2), and their respective weight percentages are 60 and 40.
- 2
  Multiply the mass of the mixture by the weight percentage of the first component, and then divide by 100 to calculate the weight of the first component in the mixture. In this example, if the mixture weight is 100 grams, then the mass of sodium chloride is (100 x 60) / 100 = 60 g.
- 3
  Multiply the mass of the mixture by the weight percentage of the second component, and then divide by 100 to calculate the weight of the second component in the mixture. In this example, the mass of magnesium chloride is (100 x 40) / 100 = 40 g.
- 4
  Obtain atomic weights of elements that compose compounds in the mixture from the Periodic Table of Elements. In this example, such elements are sodium (Na), magnesium (Mg) and chlorine (Cl), and their atomic weights are 23, 24 and 35.5.
- 5
  Calculate the molecular weight of the first component of the mixture by multiplying the atomic weight of each element in the molecule by the number of the respective atoms, and then adding up these products. In this example, the molecular weight of sodium chloride is (23 x 1) + (35.5 x 1) = 58.5.
- 6
  Calculate the molecular weight of the second component of the mixture; in this example, the molecular weight of magnesium chloride, MgCl2, is (24 x 1) + (35.5 x 2) = 95.
- 7
  Divide the mass of the first component by its molecular weight to compute the number of moles. In this example, the number of moles of sodium chloride is 60 / 58.5 = 1.026 moles.
- 8
  Divide the mass of the second component by its molecular weight to calculate the number of moles. In this example, the number of moles of magnesium chloride is 40 / 95 = 0.421 moles.
- 9
  Add up the moles of all components to calculate the total number of moles in the mixture. In this example, the mixture has 1.026 + 0.421 = 1.447 moles.
- 10
  Divide the number of moles of the first component by the total number of moles to calculate the mole fraction for this component. In this example, the mole fraction of sodium chloride is 1.026 / 1.447 = 0.709.
- 11
  Divide the number of moles of the second component by the total number of moles to calculate the mole fraction for this component. In this example, the mole fraction of magnesium chloride is 0.421 / 1.447 = 0.291.

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