Mole fraction

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In chemistry, the mole fraction of a component in a mixture is the relative proportion of molecules belonging to the component to those in the mixture, by number of molecules. It is one way of measuring concentration. It provides the most symmetrical way of representing thermodynamic functions of mixtures. For each component $i$ , the mole fraction $x i$ is the number of moles $n i$ divided by the total number of moles in the system, $n$ .

$x_i \ \stackrel{\mathrm{def}}{=}\ \frac{n_i}{n} = \frac{N_i}{N}$

where

$n = \sum_j n_j \,$

The sum is over all components, including the solvent in the case of a chemical solution. As indicated above, the same ratio is obtained using the number of molecules of $i$ , $N i$ , and the total number of molecules of all kinds, $N$ .

$N_i = n_i \times N_A$

where $N A$ is Avogadro's number ≈ 6.022 x 10²³. By definition, the sum of the mole fractions equals one, a normalization property.

$\sum_i x_i \ \stackrel{\mathrm{def}}{=}\ 1 \,$

Mole fractions are one way of representing the concentrations of the various chemical species. They are an ideal-mixture approximation to the effect of concentration on the equilbrium or rate of a reaction. In practice (except for very dilute solutions or for gasses at atmospheric pressure, all measures of concentration must be multiplied by correction factors called activity coefficients in order to yield accurate results.

The mole fraction is sometimes denoted by the lower case Greek letter $χ$ (chi) instead of a Roman $x$ .

Mole fractions are dimensionless numbers. Other ways of representing concentrations, e.g., molarity and molality, yield dimensional quantities (per litre, per kilogram, etc.). When chemical formulas seem to be taking the logarithms of dimensional quantities, there is an implied ratio, and such expressions can always be rearranged so that the arguments of the logarithms are dimensionless numbers, as they must be.

As an example, if a mixture is obtained by dissolving 10 moles of NaCl in 90 moles of water, the mole fraction of NaCl in that mixture is 0.1.

For mixtures of molecules of differing sizes, see: volume fraction.