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In chemistry, the mole fraction $x_i$ is defined as the amount of a constituent $n_i$ divided by the total amount of all constituents in a mixture $n_{tot}$:

$x_i=\frac{n_i}{n_{tot}}$

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

$\sum _{i=1}^N{n}_i=n_{tot};\sum _{i=1}^N{x}_i=1$

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 $N_{tot}$. It is one way of expressing the composition of a mixture with a dimensionless quantity (mass fraction is another). The mole fraction is sometimes denoted by the lowercase Greek letter $\chi$ (chi) instead of a Roman $x$. For mixtures of gases, IUPAC recommends the letter $y$.

Properties

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.

Related quantities

Mass fraction

The mass fraction $w_i$ can be calculated using the formula

$w_i=x_i\cdot \frac{M_i}{M}$

where $M_i$ 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:

$w_i=x_i\cdot \frac{M_i}{\sum _i{x}_i{M}_i}$

Mole percentage

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

Mass concentration

The conversion to and from mass concentration ${\rho }_i$ is given by:

$x_i=\frac{{\rho }_i}{\rho }\cdot \frac{M}{M_i}$

where $M$ is the average molar mass of the mixture.

${\rho }_i=x_i\rho \cdot \frac{M_i}{M}$

Molar concentration

The conversion to molar concentration $c_i$ is given by:

$c_i=\frac{x_i\cdot \rho }{M}=x_{i}c$

or

$c_i=\frac{x_i\cdot \rho }{\sum _i{x}_i{M}_i}$

where $M$ is the average molar mass of the solution, c total molar concentration and $\rho$ is the density of the solution .

Mass and molar mass

The mole fraction can be calculated from the masses $m_i$ and molar masses $M_i$ of the components:

$x_i=\frac{\frac{m_i}{M_i}}{\sum _i\frac{m_i}{M_i}}$

Spatial variation and gradient

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

References

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