Mass fraction (chemistry)

In chemistry, the mass fraction w_i is the fraction of one substance with mass m_i to the mass of the total mixture m_tot, defined as ^[1]:

$w_i = \frac {m_i}{m_{tot}}$

The sum of all the mass fractions is equal to 1:

$\sum_{i=1}^{N} m_i = m_{tot} ; \sum_{i=1}^{N} w_i = 1$

It is one way of expressing the composition of a mixture in a dimensionless size (mole fraction is another).

For elemental analysis, mass fraction (or "mass percent composition") can also refer to the fraction of the mass of one element to the total mass of a compound. It can be calculated for any compound using its empirical formula^[2] or its chemical formula^[3].

Related quantities

Mass concentration

The mass fraction of a component in a solution is the ratio of the mass concentration of that component ρ_i (partial density of that component) to the density of solution ρ:

$w_i = \frac {\rho_i}{\rho}$

Molar concentration

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

$w_i = \frac {c_i M_i}{\rho}$

Mass percentage

Multiplying mass fraction by 100 gives the mass percentage, sometimes referred to by the obsolete term weight-weight percentage or weight percent (abbreviated as w/w% or wt%).

Mole fraction

The mole fraction x_i can be calculated using the formula

$x_i = w_i \cdot \frac {M}{M_i}$

where M_i is the molar mass of the component i and M is the average molar mass of the mixture.

References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "mass fraction".
2. ^ Formula from Mass Composition
3. ^ http://chemistry.about.com/od/workedchemistryproblems/a/mass-percent-worked-problem.htm