Mole fraction

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Mole fraction

In chemistry, the mole fraction xi is defined as the amount of a constituent ni divided by the total amount of all constituents in a mixture ntot[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 Ni divided by the total number of all molecules Ntot. 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 wi can be calculated using the formula

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

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

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

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