In
chemistry, the mole fraction or molar fraction (''x
i'' or ) is defined as unit of the
amount
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit ...
of a constituent (expressed in
moles Moles can refer to:
* Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain
* The Moles (Australian band)
*The Moles, alter ego of Scottish band Simon Dupree and the Big Sound
People
*Abraham Moles, French engin ...
), ''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
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
s 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
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
letter (
chi) 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 lette ...
''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
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
of the United States prefers the term amount-of-substance fraction over mole fraction because it does not contain the name of the
unit
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in a theatrical presentation
Music
* ''Unit'' (a ...
mole.
Whereas mole fraction is a ratio of moles to moles,
molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of sol ...
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
In chemistry and fluid mechanics, the volume fraction φ''i'' is defined as the volume of a constituent ''V'i'' divided by the volume of all constituents of the mixture ''V'' prior to mixing:
:\phi_i = \frac
Being dimensionless, its unit is ...
(
percentage by volume, vol%) 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
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of sol ...
) 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 gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
es, the mole fraction can be expressed as the ratio of
partial pressure to total
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
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 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 plot
A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equ ...
s.
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
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of sol ...
''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
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
of the solution.
Mass and molar mass
The mole fraction can be calculated from the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
es ''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
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...
triggers the phenomenon of
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemica ...
.
References
{{Authority control
Chemical properties
Dimensionless numbers of chemistry