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):[1]
It is
denoted xi (lowercase Roman letter x), sometimes χi (lowercase Greek letter chi).[2][3] (For mixtures of gases, the letter y is recommended.[1][4]
)
It is a
dimension
of and
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
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:
Mole fraction is numerically identical to the number fraction, which is defined as the
) 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 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 (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 ternary mixture one can express mole fractions of a component as functions of other components mole fraction and binary mole ratios:
Differential quotients can be formed at constant ratios like those above:
or
The ratios X, Y, and Z 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
Related quantities
Mass fraction
The mass fractionwi can be calculated using the formula
where Mi is the molar mass of the component i and M̄ is the average molar mass of the mixture.
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:
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 of phase diagrams using, for instance, ternary plots.
Mixing binary mixtures with a common component to form ternary mixtures
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.
Mole percentage
Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent [abbreviated as (n/n)% or mol %].