Mole fraction

mole fraction
mole fraction
Other names	molar fraction, amount fraction, amount-of-substance fraction
Common symbols	x
SI unit	1
Other units	mol/mol

In chemistry, the mole fraction or molar fraction, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, n_i (expressed in unit of moles, symbol mol), and the total amount of all constituents in a mixture, n_tot (also expressed in moles):^[1]

x_{i}={\frac {n_{i}}{n_{\mathrm {tot} }}}

It is denoted x_i (lowercase Roman letter x), sometimes $χ i$ (lowercase Greek letter chi).^[2]^[3] (For mixtures of gases, the letter y is recommended.^[1]^[4])

It is a dimensionless quantity with dimension of ${\mathsf {N}}/{\mathsf {N}}$ and dimensionless unit of moles per mole (mol/mol or mol ⋅ mol^-1) or simply 1; metric prefixes may also be used (e.g., nmol/mol for 10^-9).^[5] When expressed in percent, it is known as the mole percent or molar percentage (unit symbol %, sometimes "mol%", equivalent to cmol/mol for 10^-2). The mole fraction is called amount fraction by the International Union of Pure and Applied Chemistry (IUPAC)^[1] and amount-of-substance fraction by the U.S. National Institute of Standards and Technology (NIST).^[6] This nomenclature is part of the International System of Quantities (ISQ), as standardized in ISO 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:

\sum _{i=1}^{N}n_{i}=n_{\mathrm {tot} };\ \sum _{i=1}^{N}x_{i}=1.

Mole fraction is numerically identical to the number fraction, which is defined as the number of particles (molecules) of a constituent N_i divided by the total number of all molecules N_tot. 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 a dimensionless quantity are mass fraction and volume fraction are others.

^ ^a ^b ^c IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount fraction". doi:10.1351/goldbook.A00296
^ Zumdahl, Steven S. (2008). Chemistry (8th ed.). Cengage Learning. p. 201. ISBN 978-0-547-12532-9.
^ 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.
^ ^a ^b "ISO 80000-9:2019 Quantities and units — Part 9: Physical chemistry and molecular physics". ISO. 2013-08-20. Retrieved 2023-08-29.
^ "SI Brochure". BIPM. Retrieved 2023-08-29.
^ ^a ^b Thompson, A.; Taylor, B. N. (2 July 2009). "The NIST Guide for the use of the International System of Units". National Institute of Standards and Technology. Retrieved 5 July 2014.

[goldbook-1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount fraction". doi:10.1351/goldbook.A00296

[2] Zumdahl, Steven S. (2008). Chemistry (8th ed.). Cengage Learning. p. 201. ISBN 978-0-547-12532-9.

[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.

[ISO-4] "ISO 80000-9:2019 Quantities and units — Part 9: Physical chemistry and molecular physics". ISO. 2013-08-20. Retrieved 2023-08-29.

[BIPM_c402-5] "SI Brochure". BIPM. Retrieved 2023-08-29.

[NIST-6] Thompson, A.; Taylor, B. N. (2 July 2009). "The NIST Guide for the use of the International System of Units". National Institute of Standards and Technology. Retrieved 5 July 2014.

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