# Mole fraction

In chemistry, the **mole fraction** or **molar fraction** (* x_{i}*) is defined as the amount of a constituent (expressed in moles),

*n*, divided by the total amount of all constituents in a mixture,

_{i}*n*

_{tot}:

^{[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 *N _{i}* divided by the total number of all molecules

*N*

_{tot}. 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 *w _{i}* can be calculated using the formula

where *M _{i}* 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 *ρ _{i}* is given by:

where *M* is the average molar mass of the mixture.

### Molar concentration

The conversion to molar concentration *c _{i}* 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 *m _{i}* and molar masses

*M*of the components:

_{i}## Spatial variation and gradient

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

## References

- 1 2 3 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.