chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

, 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 A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, thre ...

of 100, as percentage by mass (in commercial contexts often called ''percentage by weight'', abbreviated ''wt.%'' or ''% w/w''; 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 another with less mass if both are subject to the same g ...

). 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, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, ''ni'' (expressed in unit of moles, symbol mol), and the to ...

(percentage by moles, mol%) and

volume fraction In chemistry and fluid mechanics, the volume fraction \varphi_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: :\varphi_i = \frac . Being dimensionless quantit ...

( percentage by volume, vol%) are others. When the prevalences of interest are those of individual

chemical elements A chemical element is a chemical substance whose atoms all have the same number of protons. The number of protons is called the atomic number of that element. For example, oxygen has an atomic number of 8: each oxygen atom has 8 protons in i ...

, 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 In chemistry, the empirical formula of a chemical compound is the simplest whole number ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulfur monoxide, or SO, is simply SO, as is the empir ...

or its

chemical formula 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, such as pare ...

Terminology

thermal engineering Thermal engineering is a specialized sub-discipline of mechanical engineering that deals with the movement of heat energy and transfer. The energy can be transferred between two mediums or transformed into other forms of energy. A thermal engin ...

vapor quality In thermodynamics, vapor quality is the mass fraction in a saturated mixture that is vapor; in other words, saturated vapor has a "quality" of 100%, and saturated liquid has a "quality" of 0%. Vapor quality is an intensive property which ca ...

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 object (coin, bar, jewelry, etc.) represents the weight of ''fine metal'' therein, in proportion to the total weight which includes alloying base metals and any impurities. Alloy metals are added to increase hard ...

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 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 ratio (see concentration) or mass ratio (see stoichiometry). In a ...

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 ''ρ_i'' (density of that component in the mixture) to the

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

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

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 () (sometimes called molecular weight or formula weight, but see related quantities for usage) of a chemical substance ( element or compound) is defined as the ratio between the mass () and the amount of substance ...

of the mixture. Replacing the expression of the molar-mass products, :

x_i = \frac.

Spatial variation and gradient

In a spatially non-uniform mixture, the mass fraction

gradient In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The g ...

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 ...

References

{{Chemical solutions Combustion Dimensionless quantities of chemistry