# Mass fraction (chemistry)

In chemistry, the **mass fraction** of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. Expressed as a formula, the mass fraction is:

Because the individual masses of the ingredients of a mixture sum to , their mass fractions sum to unity:

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.%* or *% w/w*; 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

*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** 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 until phase change occurs.

## Related quantities

### Mixing ratio

The mixing of two pure components can be expressed introducing the (mass) mixing ratio of them . Then the mass fractions of the components will be

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

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 *ρ _{i}* (density of that component in the mixture) to the density of solution .

### Molar concentration

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

where is the molar concentration, and is the molar mass of the component .

### Mass percentage

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

### Mole fraction

The mole fraction can be calculated using the formula

where is the molar mass of the component , and is the average molar mass of the mixture.

Replacing the expression of the molar-mass products,

## Spatial variation and gradient

In a spatially non-uniform mixture, the mass fraction gradient gives rise to the phenomenon of diffusion.