Mass fraction (chemistry)
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 (frequently, though erroneously, called percentage by weight, abbreviated wt%). 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. or its chemical formula
"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 alloys, especially those of noble metals, the term fineness is used for the mass fraction of the noble metal in the alloy.
The mass fraction is independent of temperature.
The relation to molar concentration is like that from above substituting the relation between mass and molar concentration.
Multiplying mass fraction by 100 gives the mass percentage. It is sometimes called weight percent (wt%) or weight-weight percentage. However, since mass and weight are different quantities, this is incorrect (see mass versus weight for details).
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-produces:
Spatial variation and gradient