# Mole Fraction and Mole Percent

## Key Concepts

### 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
etc
• 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 × 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

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## Example: Calculating Mole Fraction of Solute and Solvent

Question: 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 25.0 g water and 5.0 g sodium chloride?

Solution:

1. Identify the components making up the solution:
solute = sodium chloride = NaCl
solvent = water = H2O (because this is an aqueous solution)
2. Write the equation for finding the mole fraction of solute:
Χ(NaCl) = n(NaCl) ÷ (n(NaCl) + n(H2O))
3. Calculate the moles of each component:

 moles of solute (NaCl):n(NaCl) = mass ÷ molar mass mass (NaCl) = 5.0 g molar mass (NaCl) = 22.99 + 35.45 = 58.44 g mol-1 n (NaCl) = 5.0 ÷ 58.44 = 0.08556 mol moles of solvent (H2O):n(H2O) = mass ÷ molar mass mass (H2O) = 25.0 g molar mass (H2O) = 2 × 1.008 + 16.00 = 18.016 g mol-1 n (H2O) = 25.0 ÷ 18.016 = 1.3877 mol

4. Calculate the mole fraction of sodium chloride:
Χ(NaCl) = n(NaCl) ÷ (n(NaCl) + n(H2O))
Χ(NaCl) = 0.08556 ÷ (0.08556 + 1.3877)
Χ(NaCl) = 0.058
5. Calculate mole percent of NaCl:
mole percent of NaCl = 100 × Χ(NaCl)
mole percent of NaCl= 100 × 0.058
mole percent of NaCl= 5.8%
6. Write the equation for finding the mole fraction of solvent:
Χ(H2O) = 1 - Χ(NaCl)
7. Calculate the mole fraction of solvent (water):
mole fraction of solvent (water) = 1 - Χ(NaCl)
mole fraction of solvent (water) = 1 - 0.058
mole fraction of solvent (water) = 0.942
8. Calculate mole percent of H2O
mole percent of H2O = 100 × Χ(H2O)
mole percent of H2O = 100 × 0.942
mole percent of H2O = 94.2%

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## Example: Calculating Mass of Solute or Solvent

Question: 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?

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) × (n(NaCl) + n(H2O)) = n(NaCl)

Expand the expression on the left hand side:

(NaCl) × n(NaCl)) + (Χ(NaCl) × n(H2O)) = n(NaCl)

Collect like terms (n(NaCl)):

Χ(NaCl) × n(H2O) = n(NaCl) - (Χ(NaCl) × n(NaCl))

Re-arrange the expression for n(NaCl)

Χ(NaCl) × n(H2O) = n(NaCl)(1 - Χ(NaCl))

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

(NaCl) × n(H2O)) ÷ (1 - Χ(NaCl)) = n(NaCl)

2. Calculate moles of NaCl:
n(NaCl) = (Χ(NaCl) × n(H2O)) ÷ (1 - Χ(NaCl))
n(NaCl) = (0.125 × 7.5) ÷ (1 - 0.125)
n(NaCl) = 1.071 mol
3. Calculate mass of NaCl:
n(NaCl) = mass(NaCl) ÷ molar mass(NaCl)
mass(NaCl) = n(NaCl) × molar mass(NaCl)
mass(NaCl) = 1.071 × 58.44
mass(NaCl) = 62.6 g

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