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Mass fraction (chemistry)

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Fraction of one substance's mass to the mass of the total mixture

Not to be confused withMass concentration (chemistry).

"w/w" redirects here. For similarly named topics, seeWW (disambiguation).

Inchemistry, themass fraction of a substance within a mixture is the ratio $w_{i}$ (alternatively denoted $Y_{i}$ ) of the mass $m_{i}$ of that substance to the total mass $m_{\text{tot}}$ of the mixture.^[1] Expressed as a formula, the mass fraction is:

w_{i}={\frac {m_{i}}{m_{\text{tot}}}}.

Because the individual masses of the ingredients of a mixture sum to $m_{\text{tot}}$ , their mass fractions sum to unity:

\sum _{i=1}^{n}w_{i}=1.

Mass fraction can also be expressed, with adenominator of 100, aspercentage by mass (in commercial contexts often calledpercentage by weight, abbreviatedwt.%,% w/w orw/o; seemass versus weight). It is one way of expressing the composition of a mixture in adimensionless size;mole fraction (percentage bymoles, mol%) andvolume fraction (percentage by volume, vol%) are others.

When the prevalences of interest are those of individualchemical elements, rather than of compounds or other substances, the termmass fraction can also refer to the ratio of the mass of an element to the total mass of a sample. In these contexts an alternative term ismass percent composition. The mass fraction of an element in a compound can be calculated from the compound'sempirical formula^[2] or itschemical formula.^[3]

Terminology

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Inthermal engineering,vapor quality is used for the mass fraction of vapor in the steam.

In alloys, especially those of noble metals, the termfineness is used for the mass fraction of the noble metal in the alloy.

Properties

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The mass fraction is independent of temperature.

Related quantities

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Mixing ratio

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The mixing of two pure components can be expressed introducing the (mass)mixing ratio of them $r_{m}={\frac {m_{2}}{m_{1}}}$ . Then the mass fractions of the components will be

{\begin{aligned}w_{1}&={\frac {1}{1+r_{m}}},\\w_{2}&={\frac {r_{m}}{1+r_{m}}}.\end{aligned}}

The mass ratio equals the ratio of mass fractions of components:

{\frac {m_{2}}{m_{1}}}={\frac {w_{2}}{w_{1}}}

due to division of both numerator and denominator by the sum of masses of components.

Mass concentration

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The mass fraction of a component in a solution is the ratio of themass concentration of that componentρ_i (density of that component in the mixture) to thedensity of solution $\rho$ .

w_{i}={\frac {\rho _{i}}{\rho }}.

Molar concentration

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The relation to molar concentration is like that from above substituting the relation between mass and molar concentration:

w_{i}={\frac {\rho _{i}}{\rho }}={\frac {c_{i}M_{i}}{\rho }},

where $c_{i}$ is the molar concentration, and $M_{i}$ is the molar mass of the component $i {\displaystyle i}$ .

Mass percentage

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Mass percentage is defined as the mass fraction multiplied by 100.

Mole fraction

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Themole fraction $x_{i}$ can be calculated using the formula

x_{i}={\frac {w_{i}}{M_{i}}}{\bar {M}},

where $M_{i}$ is the molar mass of the component $i {\displaystyle i}$ , and ${\bar {M}}$ is the averagemolar mass of the mixture.

Replacing the expression of the molar-mass products,

x_{i}={\frac {\frac {w_{i}}{M_{i}}}{\sum _{j}{\frac {w_{j}}{M_{j}}}}}.

Spatial variation and gradient

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In aspatially non-uniform mixture, the mass fractiongradient gives rise to the phenomenon ofdiffusion.

References

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^IUPAC,Compendium of Chemical Terminology, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "mass fraction".doi:10.1351/goldbook.M03722
^Formula from Mass Composition Archived 2012-03-05 at theWayback Machine.
^"How to Calculate Mass Percent Composition".ThoughtCo. Archived fromthe original on 2011-07-07. Retrieved2018-01-05.

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Concentration and related quantities	Molar concentration Mass concentration Number concentration Volume concentration Normality Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio Ternary plot Total dissolved solids
Solubility	Solubility equilibrium Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart Miscibility
Solvent	(Category) Acid dissociation constant Protic solvent Polar aprotic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion Lyate ion