In chemistry, the mass fraction $w\_i$ is the ratio of one substance with mass $m\_i$ to the mass of the total mixture $m\_\{tot\}$, defined as^{[1]}
- $w\_i\; =\; \backslash frac\; \{m\_i\}\{m\_\{tot\}\}$
The sum of all the mass fractions is equal to 1:
- $\backslash sum\_\{i=1\}^\{N\}\; m\_i\; =\; m\_\{tot\};\; \backslash sum\_\{i=1\}^\{N\}\; w\_i\; =\; 1$
Mass fraction is one way of expressing the composition of a mixture in a dimensionless size (mole fraction is another).
For elemental analysis, mass fraction (or "mass percent composition") can also refer to the ratio of the mass of one element to the total mass of a compound. It can be calculated for any compound using its empirical formula.^{[2]} or its chemical formula^{[3]}
Terminology
"Percent concentration" does not refer to this quantity. This improper name persists, especially in elementary textbooks. In biology, the unit "%" is sometimes (incorrectly) used to denote mass concentration, also called "mass/volume percentage." A solution with 1 g of solute dissolved in a final volume of 100 mL of solution would be labeled as "1 %" or "1 % m/v" (mass/volume). The notation is mathematically flawed because the unit "%" can only be used for dimensionless quantities. "Percent solution" or "percentage solution" are thus terms best reserved for "weight percent solutions" (mass/w = m% = mass solute/mass total solution after mixing), or "volume percent solutions" (v/v = v% = volume solute per volume of total solution after mixing). The very ambiguous terms "percent solution" and "percentage solutions" with no other qualifiers, continue to occasionally be encountered.
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
Mass concentration
The mass fraction of a component in a solution is the ratio of the mass concentration of that component $\backslash rho\_i$ (density of that component in the mixture) to the density of solution $\backslash rho$.
- $w\_i\; =\; \backslash frac\; \{\backslash rho\_i\}\{\backslash rho\}$
Molar concentration
The relation to molar concentration is like that from above substituting the relation between mass and molar concentration.
- $w\_i\; =\; \backslash frac\; \{\backslash rho\_i\}\{\backslash rho\}=\backslash frac\; \{c\_i\; M\_i\}\{\backslash rho\}$
Mass percentage
Multiplying mass fraction by 100 gives the mass percentage. It is sometimes called weight percent (wt%) or weight-weight percentage. However, since
mass and weight are different quantities, this is incorrect (see mass versus weight for details).
Mole fraction
The mole fraction $x\_i$ can be calculated using the formula
- $x\_i\; =\; w\_i\; \backslash cdot\; \backslash frac\; \{M\}\{M\_i\}$
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 produces:
- $x\_i\; =\; \backslash frac\; \{\backslash frac\{w\_i\}\{M\_i\}\}\{\backslash sum\_i\; \backslash frac\{w\_i\}\{M\_i\}\}$
Spatial variation and gradient
In a spatially non-uniform mixture, the mass fraction gradient triggers the phenomenon of diffusion.
References
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