# Mass Fraction

In chemistry , the mass fraction of a substance within a mixture is the ratio of (optionally denoted ) the mass of that substance to the total mass of the mixture.  Expressed as a formula, the mass fraction is:    {\displaystyle w_{i}={\frac {m_{i}}{m_{\text{tot}}}}.}


Since the components of a mixture have different mass sums , their mass fractions are the sum of unity: {\displaystyle \sum _{i=1}^{n}w_{i}=1.}


The mass fraction can also be expressed as a percentage of mass , with a denominator of 100 (in commercial contexts often called percentage by weight , abbreviated wt% ; see mass versus weight ). It is a way of expressing the composition of a mixture in a dimensionless shape ; Mole fraction ( percentage by moles , mol%) and volume fraction ( percentage by volume, vol%) are others.

When the generality of interest is individual chemical elements rather than compounds or other substances, the term mass fraction can also refer to the ratio of an element’s mass to the total mass of a sample. An alternative term in these contexts is the mass percentage composition . The mass fraction of an element in a compound can be calculated from the compound’s empirical formula  or its chemical formula .

## Glossary

Percent concentration does not refer to this quantity. This remains an inappropriate name, especially in primary textbooks. In biology, the unit “%” is sometimes (incorrectly) used to denote mass concentration, also known as mass/volume percentage . A solution containing 1 g of solute dissolved in a final volume of  100 mL of solution will 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 be given in units of g/mL only. Percent Solution or Percent Solution Thus the mass percentage solution (m/m, m%,The volume percentage is best reserved for the solution (v/v, v%, or volume of solute per volume). of the total solution after mixing). Very vague term percentage solution and percentage solution without any other qualification are sometimes encountered.

In thermal engineering , vapor quality is the term used for the mass fraction of steam in steam.

In alloys, especially noble metals, the term fineness is used for the mass fraction of the noble metal in the alloy.

## Property

The mass fraction is independent of temperature until the phase change occurs.

## related quantity

### mixing ratio

A mixture of two pure components can be expressed by introducing their (mass) mixture ratio . Then the mass fractions of the components will be

{\displaystyle r_{m}={\frac {m_{2}}{m_{1}}}}
{\displaystyle {\begin{aligned}w_{1}&={\frac {1}{1+r_{m}}},\\w_{2}&={\frac {r_{m}}{1+r_{m}}}.\end{aligned}}}


The mass ratio is equal to the ratio of the mass fractions of the components:

{\displaystyle {\frac {m_{2}}{m_{1}}}={\frac {w_{2}}{w_{1}}}}


Because of the division of both the numerator and the denominator by the sum of the masses of the components.

### mass concentration

The mass fraction of a component in a solution is the ratio of the mass concentration of that component i (the density of that component in the mixture ) to the density of the solution . {\displaystyle w_{i}={\frac {\rho _{i}}{\rho }}.}


### molar concentration

The relation to molar concentration is such as substituting the relation between mass and molar concentration from above:

{\displaystyle w_{i}={\frac {\rho _{i}}{\rho }}={\frac {c_{i}M_{i}}{\rho }},}


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

Percentage by mass can also be expressed as a percentage of weight , abbreviated wt% , or weight-by-weight percentage.

### mole fraction

The mole fraction can be calculated using the formula {\displaystyle x_{i}={\frac {w_{i}}{M_{i}}}{\bar {M}},}

where is the molar mass of the component , and is the mean molar mass of the mixture .   the expression space of the molar-mass products,

{\displaystyle x_{i}={\frac {\frac {w_{i}}{M_{i}}}{\sum _{j}{\frac {w_{j}}{M_{j}}}}}.}


## spatial variation and gradient

In a spatially unequal mixing, the mass fraction gradient gives rise to the phenomenon of diffusion .