# Mass fraction (chemistry)

In chemistry, the **mass fraction** is the ratio of one substance with mass to the mass of the total mixture , defined as^{[1]}

The symbol is also used to denote mass fraction. The sum of all the mass fractions is equal to 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). 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.

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]}

## Contents

## Terminology[edit]

"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). 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% = 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[edit]

The mass fraction is independent of temperature.

## Related quantities[edit]

### Mixing ratio[edit]

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[edit]

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[edit]

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

### Mass percentage[edit]

Multiplying mass fraction by 100 gives the mass percentage. It is sometimes called weight percent (wt%) or weight-weight percentage.

### Mole fraction[edit]

The mole fraction *x _{i}* can be calculated using the formula

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-products:

## Spatial variation and gradient[edit]

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

## References[edit]

**^**IUPAC,*Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "mass fraction".**^**Formula from Mass Composition**^**"How to Calculate Mass Percent Composition".*ThoughtCo*. Retrieved 2018-01-05.