Mole fraction

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, ntot:[1]

The sum of all the mole fractions is equal to 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.[1] 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.[2][3] For mixtures of gases, IUPAC recommends the letter y.[1]

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.[4]

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

Related quantities

Mass fraction

The mass fraction wi can be calculated using the formula

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:

Molar mixing ratio

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

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:

where M is the average molar mass of the mixture.

Molar concentration

The conversion to molar concentration ci is given by:

or

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: