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:
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. 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.
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:
Differential quotients can be formed at constant ratios like those above:
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:
The amount ratio equals the ratio of mole fractions of components:
Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent (abbreviated as n/n%).
The conversion to and from mass concentration ρi is given by:
where M is the average molar mass of the mixture.
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 mass
Spatial variation and gradient
- IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount fraction".
- Zumdahl, Steven S. (2008). Chemistry (8th ed.). Cengage Learning. p. 201. ISBN 0-547-12532-1.
- 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.
- 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.