In
chemistry, the mole fraction or molar fraction (''x
i'' or ) is defined as unit of the
amount of a constituent (expressed in
moles), ''n
i'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''
tot.
This expression is given below:
:
The sum of all the mole fractions is equal to 1:
:
The same concept expressed with a
denominator
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
of 100 is the mole percent, molar percentage or molar proportion (mol%).
The mole fraction is also called the amount fraction.
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 (
chi
Chi or CHI may refer to:
Greek
*Chi (letter), the Greek letter (uppercase Χ, lowercase χ);
Chinese
* ''Chi'' (length) (尺), a traditional unit of length, about ⅓ meter
* Chi (mythology) (螭), a dragon
*Chi (surname) (池, pinyin: ''chí' ...
) instead of a
Roman
Roman or Romans most often refers to:
* Rome, the capital city of Italy
* Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*''Epistle to the Romans'', shortened to ''Romans'', a lett ...
''x''. For mixtures of gases,
IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
recommends the letter ''y''.
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.
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 diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseou ...
s. 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:
*:
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 fraction ''w
i'' can be calculated using the formula
:
where ''M
i'' is the molar mass of the component ''i'' and ''M̄'' is the average
molar mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
of the mixture.
Molar mixing ratio
The mixing of two pure components can be expressed introducing the amount or molar
mixing ratio
In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio (see concentration) or mass ratio (see stoichiometry).
In a ...
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 diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseou ...
s 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 x
1(123), x
2(123), x
3(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
bbreviated as (n/n)% or mol %
Mass concentration
The conversion to and from
mass concentration ''ρ
i'' is given by:
:
where ''M̄'' is the average molar mass of the mixture.
Molar concentration
The conversion to
molar concentration ''c
i'' is given by:
:
where ''M̄'' 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 mass
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...
es ''M
i'' of the components:
:
Spatial variation and gradient
In a
spatially non-uniform mixture, the mole fraction
gradient triggers the phenomenon of
diffusion.
References
{{Authority control
Chemical properties
Dimensionless numbers of chemistry