Mole fraction

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]

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

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 ${\displaystyle {\mathsf {N}}/{\mathsf {N}}}$ 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:

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

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.