Mole Fraction Calculator
What is Mole Fraction?
Mole fraction describes the amount proportion of one component relative to the total amount in a mixture.
Definition:
χi = ni / ntotal
χi = ni / ntotal
- Range: 0 to 1
- Unit: dimensionless
- Sum: Σχi = 1
Formulas
Mole fraction:
χi = ni / ntotal
χi = ni / ntotal
Moles from χ:
ni = χi · ntotal
ni = χi · ntotal
Sum rule:
Σχi = 1
Σχi = 1
Mass fraction (approx.):
wi = (χiMi)/Σ(χjMj)
wi = (χiMi)/Σ(χjMj)
Examples
Binary mixture
n(A)=2 mol, n(B)=3 mol → ntotal=5 mol
χ(A)=2/5=0.4, χ(B)=3/5=0.6
n(A)=2 mol, n(B)=3 mol → ntotal=5 mol
χ(A)=2/5=0.4, χ(B)=3/5=0.6
Air (simplified)
χ(O₂)≈0.21, χ(N₂)≈0.79
χ(O₂)≈0.21, χ(N₂)≈0.79
Back calculation
χ(A)=0.25, ntotal=8 mol
n(A)=0.25·8=2 mol
χ(A)=0.25, ntotal=8 mol
n(A)=0.25·8=2 mol
Check
χ(A)+χ(B)+χ(C)=1
χ(A)+χ(B)+χ(C)=1
Technical Background
Use in thermodynamics
Mole fractions are used in Raoult’s law, Dalton’s law, and activity models for solutions.
Gas mixtures
For ideal gases: χi = pi / ptotal. Mole fraction equals pressure fraction.
Solutions
- Foundation for vapor-liquid equilibrium
- Important for mixing enthalpies and chemical potential
- Independent of chosen mass/volume units
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