mass percent

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In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...
, the mass 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 $m_\text$ of the mixture. Expressed as a formula, the mass fraction is: : $w_i = \frac .$ Because the individual masses of the ingredients of a mixture sum to $m_\text$, their mass fractions sum to unity: : $\sum_^ w_i = 1.$ 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%''; see
mass versus weight In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Nevertheless, one object will always weigh more than a second object, if the first object has greater mass, and t ...
). It is one way of expressing the composition of a mixture in a dimensionless size;
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of substance, amount of a constituent (expressed in mole (unit), moles), ''ni'', divided by the total amount of all constituents in a mixture (also expr ...
(percentage by moles, mol%) and
volume fraction In chemistry and fluid mechanics, the volume fraction φ''i'' is defined as the volume of a constituent ''V'i'' divided by the volume of all constituents of the mixture ''V'' prior to mixing: :\phi_i = \frac Being dimensionless quantity, dim ...
( percentage by volume, vol%) are others. When the prevalences of interest are those of individual
chemical elements A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
, 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 In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
.

# 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 1g of solute dissolved in a final volume of 100mL of solution would be labeled as "1%" or "1% m/v" (mass/volume). This is incorrect because the unit "%" can only be used for dimensionless quantities. Instead, the concentration should simply be given in units of g/mL. ''Percent solution'' or ''percentage solution'' are thus terms best reserved for ''mass percent solutions'' (m/m, m%, or mass solute/mass total solution after mixing), or ''volume percent solutions'' (v/v, v%, or 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 In physics, a vapor (American English American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. English is the Languages of ...
is used for the mass fraction of vapor in the steam. In alloys, especially those of noble metals, the term
fineness The fineness of a precious metal Precious metals are rare, naturally occurring metallic chemical elements of high Value (economics), economic value. Chemically, the precious metals tend to be less reactivity (chemistry), reactive than mos ...
is used for the mass fraction of the noble metal in the alloy.

# Properties

The mass fraction is independent of temperature until phase change occurs.

# Related quantities

## Mixing ratio

The mixing of two pure components can be expressed introducing the (mass)
mixing ratio In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to Mole (unit), mole ratio (see concentration) or mass ratio (see Mass rati ...
of them $r_m = \frac$. Then the mass fractions of the components will be : $\begin w_1 &= \frac, \\ w_2 &= \frac. \end$ The mass ratio equals the ratio of mass fractions of components: : $\frac = \frac$ 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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...
of solution $\rho$. : $w_i = \frac.$

## Molar concentration

The relation to molar concentration is like that from above substituting the relation between mass and molar concentration: : $w_i = \frac = \frac,$ where $c_i$ is the molar concentration, and $M_i$ is the molar mass of the component $i$.

## Mass percentage

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

## Mole fraction

The
mole fraction In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of substance, amount of a constituent (expressed in mole (unit), moles), ''ni'', divided by the total amount of all constituents in a mixture (also expr ...
$x_i$ can be calculated using the formula : $x_i = \frac \bar,$ where $M_i$ is the molar mass of the component $i$, and $\bar$ is the average
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in mole (unit), moles. The molar mass is a bulk, not ...
of the mixture. Replacing the expression of the molar-mass products, : $x_i = \frac.$

In a spatially non-uniform mixture, the mass fraction
gradient In vector calculus, the gradient of a scalar-valued function, scalar-valued differentiable function of Function of several variables, several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "d ...
gives rise to the phenomenon of
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
.