Mole fraction

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In chemistry, mole fraction x is a way of expressing the composition of a mixture. The mole fraction of each component i is defined as its amount of substance ni divided by the total amount of substance in the systemn


The sum is over all components, including the solvent in the case of a chemical solution. As an example, if a mixture is obtained by dissolving 10 moles of sucrose in 90 moles of water, the mole fraction of sucrose in that mixture is 0.1.

The same value for the mole fraction ratio is obtained using the number of molecules of i, Ni, and the total number of molecules of all kinds, N, since

where NA is the Avogadro constant ≈ 6.022×1023 mol–1. By definition, the sum of the mole fractions equals one, a normalization property.


Simple representation

The simple representation of examining the mole fraction is thinking in terms of A and B. The mole fraction of A would be moles of A divided by the moles of A and moles of B. This way, adding the two mole fractions together would equal one.

Another representation would be:

Where nA is the number of moles of substance A and nB is the number of moles of substance B

Notes and qualifications

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.

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 equilibrium or rate of a reaction. In practice (except for very dilute solutions or for gases 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. For mixtures of gases, it is more usual to use the letter y. The mole fraction of a substance in a reaction is also equal to the partial pressure of that substance.

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