home test drill game contact

# 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
Practice Questions Homework Checker
For AUS-e-TUTE members:
1. Click on the Mole Fraction drill link:
Mole Fraction drill
3. Click the "New Question" button to begin the drill.
4. Worked solutions are provided if you need some help!

Not an AUS-e-TUTE Member?

For AUS-e-TUTE members:

 Moles of solute: Moles solvent: Click Calculate: Mole fraction = Mole % solute = % To start again, click Reset:

# Search this Site

You can search this site using a key term or a concept to find, tutorials, tests, exams, learning activities (games), drills, worksheet and quiz wizards.

# Subscribe to our Free Newsletter

Email to
subscribe to AUS-e-TUTE's free quarterly newsletter, AUS-e-NEWS.

AUS-e-NEWS is emailed out in
December, March, June, and September.

# Ask Chris, the Chemist, a Question

The quickest way to find the definition of a term is to ask Chris, the AUS-e-TUTE Chemist.

Chris can also send you to the relevant
AUS-e-TUTE tutorial topic page.

# Bookmark AUS-e-TUTE

Bookmark this site!