Mole fraction calculator
This mole fraction calculator gives each substance’s share of the total amount in a mixture. Example: 2 mol of A and 3 mol of B give x(A) = 0.4 and x(B) = 0.6.
Example: What is given: Amounts in mol · Substance 1: amount n₁ 2 mol · Substance 2: amount n₂ 3 mol · Substance 3: amount n₃ 0 mol → Result: x₁ = 0.4 · x₂ = 0.6. Source: IUPAC Green Book (Quantities, Units and Symbols in Physical Chemistry), „amount fraction“ x_B = n_B / n. Updated: .
How it is calculated
The mole fraction x (amount fraction) states what fraction of the total number of particles a substance makes up in a mixture. It is dimensionless, lies between 0 and 1, and all fractions of a mixture add up to 1.
Formula
x(i) = n(i) / n(total), where n(total) is the sum of all amounts. If only masses are known, convert first: n(i) = m(i) / M(i) with the molar mass M in g/mol. Multiplied by 100 you get the share in percent (mol %).
Worked example
A mixture holds 2 mol of A and 3 mol of B: n(total) = 5 mol, so x(A) = 2/5 = 0.4 and x(B) = 3/5 = 0.6. From masses: 100 g of ethanol (46.07 g/mol) gives n = 2.17061 mol, 100 g of water (18.015 g/mol) gives n = 5.55093 mol. With n(total) = 7.72154 mol, x(ethanol) = 0.281111 (28.11 %) and x(water) = 0.718889 (71.89 %). Three substances with 1, 1 and 2 mol give 0.25, 0.25 and 0.5.
- The mass fraction of ethanol here would be 50 %, but its mole fraction only about 28 % – water has the much smaller molar mass.
- The mole fraction is used in Raoult’s law and for partial pressures of ideal gas mixtures.
- Enter nothing or 0 for substance 3 if there are only two components.
Frequently asked questions
What is the difference between mole fraction and mass fraction?
The mole fraction counts particles (mol), the mass fraction weighs grams. For 100 g of ethanol and 100 g of water it is 50 % by mass but only 28.11 % by amount for ethanol.
How do I calculate the mole fraction from grams?
First divide each mass by its molar mass (n = m / M), then divide each amount by the total amount. For 100 g of ethanol this gives x = 0.281111.
Must the fractions always add up to 1?
Yes. The mole fractions of a mixture always sum to exactly 1 or 100 %. The calculator shows this check sum in the table.
Sources and legal basis
- IUPAC Green Book (Quantities, Units and Symbols in Physical Chemistry), „amount fraction“ x_B = n_B / n
- IUPAC Gold Book: mole fraction
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