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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:[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.



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
  • In a ternary mixture one can express mole fractions of a component as functions of other components mole fraction and binary mole ratios:



Related quantitiesEdit

Mass fractionEdit

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 ratioEdit

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 percentageEdit

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

Mass concentrationEdit

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


where M is the average molar mass of the mixture.


Molar concentrationEdit

The conversion to molar concentration ci is given by:




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 massEdit

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


Spatial variation and gradientEdit

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


  1. ^ a b c IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "amount fraction".
  2. ^ Zumdahl, Steven S. (2008). Chemistry (8th ed.). Cengage Learning. p. 201. ISBN 0-547-12532-1. 
  3. ^ Rickard, James N.; Spencer, George M.; Bodner, Lyman H. (2010). Chemistry: Structure and Dynamics (5th ed.). Hoboken, N.J.: Wiley. p. 357. ISBN 978-0-470-58711-9. 
  4. ^ Thompson, A.; Taylor, B. N. "The NIST Guide for the use of the International System of Units". National Institute of Standards and Technology. Retrieved 5 July 2014.