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, ni (expressed in unit of moles, symbol mol), and the total amount of all constituents in a mixture, ntot (also expressed in moles):
x i = n i n t o t {\displaystyle x_{i}={\frac {n_{i}}{n_{\mathrm {tot} }}}}
It is denoted xi (lowercase Roman letter x), sometimes χi (lowercase Greek letter chi). (For mixtures of gases, the letter y is recommended.) It is a dimensionless quantity with dimension of N / N {\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). 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) and amount-of-substance fraction by the U.S. National Institute of Standards and Technology (NIST). This nomenclature is part of the International System of Quantities (ISQ), as standardized in ISO 80000-9, which deprecates "mole fraction" based on the unacceptability of mixing information with units when expressing the values of quantities. The sum of all the mole fractions in a mixture is equal to 1:
∑ i = 1 N n i = n t o t ; ∑ i = 1 N x i = 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 Ni divided by the total number of all molecules Ntot. 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.
Properties Mole fraction is used very frequently in the construction of phase diagrams. It has a number of advantages:
it is not temperature dependent (as is 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 In a ternary mixture one can express mole fractions of a component as functions of other components mole fraction and binary mole ratios:
x 1 = 1 − x 2 1 + x 3 x 1 x 3 = 1 − x 2 1 + x 1 x 3 {\displaystyle {\begin{aligned}x_{1}&={\frac {1-x_{2}}{1+{\frac {x_{3}}{x_{1}}}}}\\[2pt]x_{3}&={\frac {1-x_{2}}{1+{\frac {x_{1}}{x_{3}}}}}\end{aligned}}}
Differential quotients can be formed at constant ratios like those above:
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