HOME

TheInfoList



OR:

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, proper ...
, 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 la, fractus, "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 ...
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 (percentage by
moles Moles can refer to: * Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain *The Moles (Australian band) *The Moles, alter ego of Scottish band Simon Dupree and the Big Sound People * Abraham Moles, French engin ...
, mol%) and volume fraction ( 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 nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler su ...
, 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, would simply be SO, as is the ...
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 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 engineer ...
, 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 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 ...
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 letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
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 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 moles. The molar mass is a bulk, not molecular, ...
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 of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...
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 ...
.


See also

* Mass-flux fraction


References

{{Chemical solutions Chemical properties Dimensionless numbers of chemistry Combustion