| mole fraction | |
|---|---|
Other names | molar fraction, amount fraction, amount-of-substance fraction |
Common symbols | x |
| SI unit | 1 |
Other units | mol/mol |
Inchemistry, themole fraction ormolar fraction, also calledmole proportion ormolar proportion, is aquantity defined as theratio between theamount of a constituent substance,ni (expressed inunit ofmoles, symbol mol), and the total amount of all constituents in a mixture,ntot (also expressed in moles):[1]
It isdenotedxi (lowercaseRoman letterx), sometimesχi (lowercaseGreek letterchi).[2][3] (For mixtures of gases, the lettery is recommended.[1][4])
It is adimensionless quantity withdimension of anddimensionless unit ofmoles per mole (mol/mol ormol⋅mol−1) or simply 1;metric prefixes may also be used (e.g., nmol/mol for10−9).[5]When expressed inpercent, it is known as themole percent ormolar percentage (unit symbol %, sometimes "mol%", equivalent to cmol/mol for10−2).The mole fraction is calledamount fraction by theInternational Union of Pure and Applied Chemistry (IUPAC)[1] andamount-of-substance fraction by the U.S.National Institute of Standards and Technology (NIST).[6] This nomenclature is part of theInternational System of Quantities (ISQ), as standardized inISO 80000-9,[4] which deprecates "mole fraction" based on the unacceptability of mixing information with units when expressing the values of quantities.[6]
The sum of all the mole fractions in a mixture is equal to 1:
Mole fraction is numerically identical to thenumber fraction, which is defined as thenumber of particles (molecules) of a constituentNi divided by the total number of all moleculesNtot. Whereas mole fraction is a ratio of amounts to amounts (in units of moles per moles),molar concentration is a quotient of amount to volume (in units of moles per litre).Other ways of expressing the composition of a mixture as adimensionless quantity aremass fraction andvolume fraction.
Mole fraction is used very frequently in the construction ofphase diagrams. It has a number of advantages:
Differential quotients can be formed at constant ratios like those above:
or
The ratiosX,Y, andZ of mole fractions can be written for ternary and multicomponent systems:
These can be used for solving PDEs like:
or
This equality can be rearranged to have differential quotient of mole amounts or fractions on one side.
or
Mole amounts can be eliminated by forming ratios:
Thus the ratio of chemical potentials becomes:
Similarly the ratio for the multicomponents system becomes
Themass fractionwi can be calculated using the formula
whereMi is the molar mass of the componenti andM̄ is the averagemolar mass of the mixture.
The mixing of two pure components can be expressed introducing the amount or molarmixing ratio of them. Then the mole fractions of the components will be:
The amount ratio equals the ratio of mole fractions of components:
due to division of both numerator and denominator by the sum of molar amounts of components. This property has consequences for representations ofphase diagrams using, for instance,ternary plots.
Mixing binary mixtures with a common component gives a ternary mixture with certain mixing ratios between the three components. These mixing ratios from the ternary and the corresponding mole fractions of the ternary mixture x1(123), x2(123), x3(123) can be expressed as a function of several mixing ratios involved, the mixing ratios between the components of the binary mixtures and the mixing ratio of the binary mixtures to form the ternary one.
Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent [abbreviated as (n/n)% or mol %].
The conversion to and frommass concentrationρi is given by:
whereM̄ is the average molar mass of the mixture.
The conversion tomolar concentrationci is given by:
whereM̄ is the average molar mass of the solution,c is the total molar concentration andρ is thedensity of the solution.
The mole fraction can be calculated from themassesmi andmolar massesMi of the components:
In aspatially non-uniform mixture, the mole fractiongradient triggers the phenomenon ofdiffusion.
