Mass fraction (chemistry)

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

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

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.

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 ${\displaystyle \rho }$.

${\displaystyle w_{i}={\frac {\rho _{i}}{\rho }}.}$

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 is defined as the mass fraction multiplied by 100.

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

${\displaystyle x_{i}={\frac {w_{i}}{M_{i}}}{\bar {M}},}$

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

Replacing the expression of the molar-mass products,

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