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Mole fraction
In chemistry, the mole fraction or molar fraction (<math>x_i</math>) is defined as the amount of a constituent (expressed in moles), <math>n_i</math>, divided by the total amount of all constituents in a mixture, <math>n_{tot}</math>:^{[1]}
 <math>x_i = \frac{n_i}{n_{tot}}</math>
The sum of all the mole fractions is equal to 1:
 <math>\sum_{i=1}^{N} n_i = n_{tot} ; \; \sum_{i=1}^{N} x_i = 1</math>
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 <math>N_i</math> divided by the total number of all molecules <math>N_{tot}</math>. The mole fraction is sometimes denoted by the lowercase Greek letter <math alt="χ">\chi</math> (chi) instead of a Roman <math>x</math>.^{[2]}^{[3]} For mixtures of gases, IUPAC recommends the letter <math>y</math>.^{[1]}
The National Institute of Standards and Technology of the United States prefers the term amountofsubstance 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 ratio 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.
Contents
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 <math>w_i</math> can be calculated using the formula
 <math>w_i = x_i \cdot \frac {M_i}{M}</math>
where <math>M_i</math> is the molar mass of the component <math>i</math> and <math>M</math> is the average molar mass of the mixture.
Replacing the expression of the molar mass:
 <math>w_i = x_i \cdot \frac {M_i}{\sum_i x_i M_i}</math>
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 <math>\rho_i</math> is given by:
 <math>x_i = \frac{\rho_i}{\rho} \cdot \frac{M}{M_i}</math>
where <math>M</math> is the average molar mass of the mixture.
 <math>\rho_i = x_i \rho \cdot \frac{M_i}{M}</math>
Molar concentration
The conversion to molar concentration <math>c_i</math> is given by:
 <math>c_i = \fracTemplate:X i \cdot \rhoṃ = x_i c </math>
or
 <math>c_i = \fracTemplate:X i \cdot \rhoTemplate:\sum i x i M i </math>
where <math>M</math> is the average molar mass of the solution, c total molar concentration and <math>\rho</math> is the density of the solution .
Mass and molar mass
The mole fraction can be calculated from the masses <math>m_i</math> and molar masses <math>M_i</math> of the components:
 <math> x_i= \frac{{\fracTemplate:M iTemplate:M i}}{{\sum_i \fracTemplate:M iTemplate:M i}}</math>
Spatial variation and gradient
In a spatially nonuniform mixture, the mole fraction gradient triggers the phenomenon of diffusion.
References
 ^ ^{a} ^{b} ^{c} IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount fraction".
 ^ Zumdahl, Steven S. (2008). Chemistry (8th ed. ed.). Cengage Learning. p. 201. ISBN 0547125321.
 ^ Rickard, James N. Spencer, George M. Bodner, Lyman H. (2010). Chemistry : structure and dynamics. (5th ed. ed.). Hoboken, N.J.: Wiley. p. 357. ISBN 9780470587119.
 ^ Thompson, A.; Taylor, B. N. "The NIST Guide for the use of the International System of Units". http://physics.nist.gov/Pubs/SP811/sec08.html. National Institute of Standards and Technology. Retrieved 5 July 2014.

