In chemistry, the mass fraction of a substance within a mixture is the ratio w i {\displaystyle w_{i}} (alternatively denoted Y i {\displaystyle Y_{i}} ) of the mass m i {\displaystyle m_{i}} of that substance to the total mass m tot {\displaystyle m_{\text{tot}}} of the mixture. Expressed as a formula, the mass fraction is:
w i = m i m tot . {\displaystyle w_{i}={\frac {m_{i}}{m_{\text{tot}}}}.}
Because the individual masses of the ingredients of a mixture sum to m tot {\displaystyle m_{\text{tot}}} , their mass fractions sum to unity:
∑ i = 1 n w i = 1. {\displaystyle \sum _{i=1}^{n}w_{i}=1.}
Mass fraction can also be expressed, with a denominator of 100, as percentage by mass (in commercial contexts often called percentage by weight, abbreviated wt.%, % w/w or w/o; see mass versus weight). It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction (percentage by volume, vol%) are others. When the prevalences of interest are those of individual chemical elements, rather than of compounds or other substances, the term mass 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 is mass percent composition. The mass fraction of an element in a compound can be calculated from the compound's empirical formula or its chemical formula.
Terminology In thermal engineering, vapor quality is used for the mass fraction of vapor in the steam. In alloys, especially those of noble metals, the term fineness is used for the mass fraction of the noble metal in the alloy.
Properties The mass fraction is independent of temperature.
Related quantities
Mixing ratio The mixing of two pure components can be expressed introducing the (mass) mixing ratio of them r m = m 2 m 1 {\displaystyle r_{m}={\frac {m_{2}}{m_{1}}}} . Then the mass fractions of the components will be
w 1 = 1 1 + r m , w 2 = r m 1 + r m . {\displaystyle {\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:
m 2 m 1 = w 2 w 1 {\displaystyle {\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 The mass fraction of a component in a solution is the ratio of the mass concentration of that component ρi (density of that component in the mixture) to the density of solution ρ {\displaystyle \rho } .
w i = ρ i ρ . {\displaystyle w_{i}={\frac {\rho _{i}}{\rho }}.}
Molar concentration The relation to molar concentration is like that from above substituting the relation between mass and molar concentration:
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