# Mole fraction

In chemistry, the mole fraction or molar fraction (xi) is defined as the amount of a constituent (expressed in moles), ni, divided by the total amount of all constituents in a mixture (also expressed in moles), ntot:[1]

${\displaystyle x_{i}={\frac {n_{i}}{n_{\mathrm {tot} }}}}$

The sum of all the mole fractions is equal to 1:

${\displaystyle \sum _{i=1}^{N}n_{i}=n_{\mathrm {tot} };\;\sum _{i=1}^{N}x_{i}=1}$

The same concept expressed with a denominator of 100 is the mole percent or molar percentage or molar proportion (mol%).

The mole fraction is also called the amount fraction.[1] It is identical to the number fraction, which is defined as the number of molecules of a constituent Ni divided by the total number of all molecules Ntot. The mole fraction is sometimes denoted by the lowercase Greek letter χ (chi) instead of a Roman x.[2][3] For mixtures of gases, IUPAC recommends the letter y.[1]

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.[4]

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.

## PropertiesEdit

Mole fraction is used very frequently in the construction of phase diagrams. It has a number of advantages:

• it is not temperature dependent (such as 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:

${\displaystyle x_{1}={\frac {1-x_{2}}{1+{\frac {x_{3}}{x_{1}}}}}}$

${\displaystyle x_{3}={\frac {1-x_{2}}{1+{\frac {x_{1}}{x_{3}}}}}}$

## Related quantitiesEdit

### Mass fractionEdit

The mass fraction wi can be calculated using the formula

${\displaystyle w_{i}=x_{i}\cdot {\frac {M_{i}}{M}}}$

where Mi is the molar mass of the component i and M is the average molar mass of the mixture.

Replacing the expression of the molar mass:

${\displaystyle w_{i}=x_{i}\cdot {\frac {M_{i}}{\sum _{i}x_{i}M_{i}}}}$

### Molar mixing ratioEdit

The mixing of two pure components can be expressed introducing the amount or molar mixing ratio of them ${\displaystyle r_{n}={\frac {n_{2}}{n_{1}}}}$ . Then the mole fractions of the components will be:

${\displaystyle x_{1}={\frac {1}{1+r_{n}}}}$
${\displaystyle x_{2}={\frac {r_{n}}{1+r_{n}}}}$

### Mole percentageEdit

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

### Mass concentrationEdit

The conversion to and from mass concentration ρi is given by:

${\displaystyle x_{i}={\frac {\rho _{i}}{\rho }}\cdot {\frac {M}{M_{i}}}}$

where M is the average molar mass of the mixture.

${\displaystyle \rho _{i}=x_{i}\rho \cdot {\frac {M_{i}}{M}}}$

### Molar concentrationEdit

The conversion to molar concentration ci is given by:

${\displaystyle c_{i}={\frac {x_{i}\cdot \rho }{M}}=x_{i}c}$

or

${\displaystyle c_{i}={\frac {x_{i}\cdot \rho }{\sum _{i}x_{i}M_{i}}}}$

where M 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 massEdit

The mole fraction can be calculated from the masses mi and molar masses Mi of the components:

${\displaystyle x_{i}={\frac {\frac {m_{i}}{M_{i}}}{\sum _{i}{\frac {m_{i}}{M_{i}}}}}}$