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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,

mole fraction | |
---|---|

Other names | molar fraction, amount fraction, amount-of-substance fraction |

Common symbols | x |

SI unit | 1 |

Other units | mol/mol |

It is denoted * x_{i}* (lowercase Roman letter

It is a dimensionless quantity with dimension of 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

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 number of particles (molecules) of a constituent *N _{i}* divided by the total number of all molecules

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:

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

The mass fraction *w _{i}* can be calculated using the formula

where *M _{i}* is the molar mass of the component

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 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.

Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent [abbreviated as (n/n)% or mol %].

The conversion to and from mass concentration *ρ _{i}* is given by:

where *M̄* is the average molar mass of the mixture.

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.

The mole fraction can be calculated from the masses *m _{i}* and molar masses

In a spatially non-uniform mixture, the mole fraction gradient triggers the phenomenon of diffusion.

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^{a}^{b}^{c}IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount fraction". doi:10.1351/goldbook.A00296 **^**Zumdahl, Steven S. (2008).*Chemistry*(8th ed.). Cengage Learning. p. 201. ISBN 978-0-547-12532-9.**^**Rickard, James N.; Spencer, George M.; Bodner, Lyman H. (2010).*Chemistry: Structure and Dynamics*(5th ed.). Hoboken, N.J.: Wiley. p. 357. ISBN 978-0-470-58711-9.- ^
^{a}^{b}"ISO 80000-9:2019 Quantities and units — Part 9: Physical chemistry and molecular physics".*ISO*. 2013-08-20. Retrieved 2023-08-29. **^**"SI Brochure".*BIPM*. Retrieved 2023-08-29.- ^
^{a}^{b}Thompson, A.; Taylor, B. N. (2 July 2009). "The NIST Guide for the use of the International System of Units". National Institute of Standards and Technology. Retrieved 5 July 2014.