Mole fraction

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^[1]:

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

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.^[2] 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 in a dimensionless size (mass fraction is another). The mole fraction is sometimes denoted by the lower case Greek letter χ (chi) instead of a Roman x. For mixtures of gases, the letter y is recommended.

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.

Mole percentage

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

References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "mole fraction".
2. ^ http://goldbook.iupac.org/A00296.html