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Mole fraction

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In chemistry, the mole fraction or molar fraction (xi) is defined as the amount of a constituent (expressed in moles), ni, divided by the total amount of all constituents in a mixture (also expressed in moles), ntot:

Contents

x i = n i n t o t

The sum of all the mole fractions is equal to 1:

∑ i = 1 N n i = n t o t ; ∑ i = 1 N x i = 1

The same concept expressed with a denominator of 100 is the mole percent or molar percentage or molar proportion (mol%).

The mole fraction is also called the amount fraction. It is identical to the number fraction, which is defined as the number of molecules of a constituent Ni divided by the total number of all molecules Ntot. The mole fraction is sometimes denoted by the lowercase Greek letter χ (chi) instead of a Roman x. For mixtures of gases, IUPAC recommends the letter y.

The National Institute of Standards and Technology of the United States prefers the term amount-of-substance fraction over mole fraction because it does not contain the name of the unit mole.

Whereas mole fraction is a ratio of moles to moles, molar concentration is a quotient of moles to volume.

The mole fraction is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and volume fraction (percentage by volume, vol%) are others.

Properties

Mole fraction is used very frequently in the construction of phase diagrams. It has a number of advantages:

  • it is not temperature dependent (such as molar concentration) and does not require knowledge of the densities of the phase(s) involved
  • a mixture of known mole fraction can be prepared by weighing off the appropriate masses of the constituents
  • the measure is symmetric: in the mole fractions x = 0.1 and x = 0.9, the roles of 'solvent' and 'solute' are reversed.
  • In a mixture of ideal gases, the mole fraction can be expressed as the ratio of partial pressure to total pressure of the mixture

    • Mass fraction

    The mass fraction wi can be calculated using the formula

    w i = x i ⋅ M i M

    where Mi is the molar mass of the component i and M is the average molar mass of the mixture.

    Replacing the expression of the molar mass:

    w i = x i ⋅ M i ∑ i x i M i

    Molar mixing ratio

    The mixing of two pure components can be expressed introducing the amount or molar mixing ratio of them r n = n 2 n 1 . Then the mole fractions of the components will be:

    x 1 = 1 1 + r n x 2 = r n 1 + r n

    Mole percentage

    Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent (abbreviated as n/n%).

    Mass concentration

    The conversion to and from mass concentration ρi is given by:

    x i = ρ i ρ ⋅ M M i

    where M is the average molar mass of the mixture.

    ρ i = x i ρ ⋅ M i M

    Molar concentration

    The conversion to molar concentration ci is given by:

    c i = x i ⋅ ρ M = x i c

    or

    c i = x i ⋅ ρ ∑ i x i M i

    where M is the average molar mass of the solution, c is the total molar concentration and ρ is the density of the solution.

    Mass and molar mass

    The mole fraction can be calculated from the masses mi and molar masses Mi of the components:

    x i = m i M i ∑ i m i M i

    Spatial variation and gradient

    In a spatially non-uniform mixture, the mole fraction gradient triggers the phenomenon of diffusion.

    References

    Mole fraction Wikipedia
    (Text) CC BY-SA