Mole fraction

In chemistry, the mole fraction or molar fraction (x_i) is defined as the amount of a constituent (expressed in moles), n_i, divided by the total amount of all constituents in a mixture, n_tot:^[1]

x_{i}={\frac {n_{i}}{n_{\mathrm {tot} }}}

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

\sum _{i=1}^{N}n_{i}=n_{\mathrm {tot} };\;\sum _{i=1}^{N}x_{i}=1

The same concept expressed with a denominator of 100 is the mole percent or molar percentage or molar proportion (mol%).

The mole fraction is also called the amount fraction.^[1] 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. The mole fraction is sometimes denoted by the lowercase Greek letter χ (chi) instead of a Roman x.^[2]^[3] For mixtures of gases, IUPAC recommends the letter y.^[1]

The National Institute of Standards and Technology of the United States prefers the term amount-of-substance fraction over mole fraction because it does not contain the name of the unit mole.^[4]

Whereas mole fraction is a ratio of moles to moles, molar concentration is a quotient of moles to volume.

The mole fraction is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and volume fraction (percentage by volume, vol%) are others.

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}}}

Molar mixing ratio

The mixing of two pure components can be expressed introducing the amount or molar mixing ratio of them $r_{n}={\frac {n_{2}}{n_{1}}}$ . Then the mole fractions of the components will be:

x_{1}={\frac {1}{1+r_{n}}}

x_{2}={\frac {r_{n}}{1+r_{n}}}

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 ρ_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

c_{i}={\frac {x_{i}\cdot \rho }{\sum _{i}x_{i}M_{i}}}

where M is the average molar mass of the solution, c is the total molar concentration and ρ 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

1 2 3 IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount fraction".
↑ Zumdahl, Steven S. (2008). Chemistry (8th ed.). Cengage Learning. p. 201. ISBN 0-547-12532-1.
↑ Rickard, James N.; Spencer, George M.; Bodner, Lyman H. (2010). Chemistry: Structure and Dynamics (5th ed.). Hoboken, N.J.: Wiley. p. 357. ISBN 978-0-470-58711-9.
↑ Thompson, A.; Taylor, B. N. "The NIST Guide for the use of the International System of Units". National Institute of Standards and Technology. Retrieved 5 July 2014.

Mole concepts

Physical quantities	Mass concentration Molar concentration Molality Mass Volume Density Mole fraction Mass fraction Amount of substance Molar mass Atomic mass Particle number Avogadro constant Pressure Kelvin temperature Gas constant Molar volume Specific volume

Laws	Charles's law Boyle's law Gay-Lussac's law Combined gas law Ideal gas law

Articles related to solutions

Solution	Ideal solution Aqueous solution Solid solution Buffer solution Flory–Huggins Mixture Suspension Colloid Phase diagram Eutectic point Alloy Saturation Supersaturation Serial dilution Dilution (equation) Apparent molar property Miscibility gap

Concentration and related quantities	Molar concentration Mass concentration Number concentration Volume concentration Normality Percentage solution Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio

Solubility	Solubility equilibrium Total dissolved solids Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart

Solvent	(Category) Acid dissociation constant Protic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion

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