Mass fraction (chemistry)

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 of them ${\displaystyle r_m=\frac{m_2}{m_1}}$. Then the mass fractions of the components will be

${\displaystyle \begin{array}{cc}{w}_1& =\frac{1}{1+r_m},\\ w_2& =\frac{r_m}{1+r_m}.\end{array}}$

The mass ratio equals the ratio of mass fractions of components:

${\displaystyle \frac{m_2}{m_1}=\frac{w_2}{w_1}}$

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 of solution ${\displaystyle \rho }$.

${\displaystyle w_i=\frac{{\rho }_i}{\rho }.}$

Molar concentration

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

${\displaystyle w_i=\frac{{\rho }_i}{\rho }=\frac{c_i{M}_i}{\rho },}$

where ${\displaystyle c_i}$ is the molar concentration, and ${\displaystyle M_i}$ is the molar mass of the component ${\displaystyle i}$.

Mass percentage

Mass percentage is defined as the mass fraction multiplied by 100.

Mole fraction

The mole fraction ${\displaystyle x_i}$ can be calculated using the formula

${\displaystyle x_i=\frac{w_i}{M_i}\overline{M},}$

where ${\displaystyle M_i}$ is the molar mass of the component ${\displaystyle i}$, and ${\displaystyle \overline{M}}$ is the average molar mass of the mixture.

Replacing the expression 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 non-uniform mixture, the mass fraction gradient gives rise to the phenomenon of diffusion.