Mole Fraction Formula and Calculation

In chemistry, the mole fraction is a unit of concentration that is the number of moles of a component divided by the total number of moles of a solution or mixture. The mole fraction is a dimensionless number. The sum of all of the mole fractions equals 1. The symbol for mole fraction is the capital letter X or the lowercase Greek letter chi (χ). The terms “amount fraction” or “amount-of-substance fraction” mean the same as mole fraction.

Mole Fraction Formula

The formula for mole fraction is the moles of one component divided by the total number of moles:

X_A = moles A / total moles

How to Calculate Mole Fraction

For example, in a mixture consisting of 0.25 moles of component A and 0.40 moles of component B, you can find the mole fractions of A and B.

X_A = moles A / total moles = 0.25 / (0.25 + 0.40) = 0.38 (rounded)

X_B = moles B / total moles = 0.40 / (0.25 + 0.40) = 0.62 (rounded)

Remember, adding up the mole fractions equals 1.

X_A + X_B = 1

0.38 + 0.62 = 1

If the mixture consists of more than two components, the same rules apply.

Mole Percent

A related term is mole percent. Mole percent or mole percentage is the mole fraction multiplied by 100%.

mol% = X_A x 100%

The sum of all of the mole percents of a mixture equals 100%

Mole Fraction Properties and Advantages

The mole fraction offers advantages over some of the other units of concentration.

• Unlike molarity, mole fraction is not temperature dependent.
• Preparing a solution using mole fraction is easy because you simply weigh the masses of the components and then combine them.
• There is no confusion over which component is the solvent and which is the solute. The unit is symmetric in this respect because the roles of solute and solvent are reversible, depending on the mole fraction.
• In a mixture of ideal gases or most real gases, the mole fraction is the same as the ratio of partial pressure of a gas to the total pressure of the mixture. In other words, mole fraction follows Dalton’s law of partial pressure.

Example Calculations

Simple Example

For example, find the mole fraction of carbon tetrachloride in a mixture consisting of 1 mole benzene, 2 moles carbon tetrachloride, and 7 moles acetone.

X_A = moles A / total moles

X_CCl4 = 2 / (1 + 2 + 7) = 2/10 = 0.2

Mole Fraction From Grams

Find the mole fraction of formaldehyde (CH₂O) when you dissolve 25.7 grams of CH₂O in 3.25 moles of carbon tetrachloride (CCl₄).

Here, the amount of CCl₄ is already in moles, but you can’t find mole fraction until you convert grams of CH₂O into moles, too. Look up the atomic masses of carbon, hydrogen, and oxygen on the periodic table and use the chemical formula for formaldehyde to calculate the number of moles.

1 mole CH₂O = 12.01 g + 2×1.01 g + 16.00 g = 30.03 g

Use this relationship and find the number of moles of CH₂O.

moles CH₂O = 25.7 g x (1 mol/30.03 g) = 0.856 mol

Now, solve for mole fraction.

X_A = moles A / total moles

X_A = 0.856 moles CH₂O / (0.856 moles CH₂O + 3.25 moles CCl₄) = 0.208

How to Find Mole Fraction From Molality

Molality (m) is the moles of solute per kilogram of solvent. Using these units, you can calculate mole fraction if you know molality. For example, find the mole fraction of table sugar or sucrose (C₆H₁₂O₆) in a 1.62 m solution of sucrose in water.

Given the definition of molality, you know the following:

1.2 m sucrose = 1.62 moles sucrose / 1 kg water

Next, find how many moles there are of water. Use the atomic masses from the periodic table and find that the molar mass of water is 18.0 (2×1.01 + 16.00).

1 kg = 1000 g = 1 mol / 18.0 g = 55.5 moles H₂O

Knowing the moles of sucrose and the moles of water, find the mole fraction of sucrose.

X_A = moles A / total moles

X_sucrose = moles sucrose / total moles = 1.62 / (1.62 + 55.5) = 0.0284

With small numbers like this, it’s often better expressing mole fraction as mole percent. The solution is 2.84% sugar in water.

References

• IUPAC (1997). “Amount fraction.” Compendium of Chemical Terminology (the “Gold Book”) (2nd ed.). Blackwell Scientific Publications. ISBN 0-9678550-9-8. doi:10.1351/goldbook.A00296
• Rickard, James N.; Spencer, George M.; Bodner, Lyman H. (2010). Chemistry: Structure and Dynamics (5th ed.). Hoboken, N.J.: Wiley. ISBN 978-0-470-58711-9.
• Thompson, A.; Taylor, B. N. (2009). “Special Publication 811.” The NIST Guide for the use of the International System of Units. National Institute of Standards and Technology.
• Zumdahl, Steven S. (2008). Chemistry (8th ed.). Cengage Learning. ISBN 978-0-547-12532-9.