Editing Mole fraction (section)

==Related quantities==
===Mass fraction===
The [[mass fraction (chemistry)|mass fraction]] ''w<sub>i</sub>'' can be calculated using the formula
:<math>w_i = x_i \frac{M_i}{\bar{M}} = x_i \frac {M_i}{\sum_j x_j M_j}</math>

where ''M<sub>i</sub>'' is the molar mass of the component ''i'' and ''M̄'' is the average [[molar mass]] of the mixture.

=== Molar mixing ratio ===
The mixing of two pure components can be expressed introducing the amount or molar [[mixing ratio]] of them <math>r_n = \frac{n_2}{n_1}</math>. Then the mole fractions of the components will be:
:<math>\begin{align}
  x_1 &= \frac{1}{1 + r_n} \\[2pt]
  x_2 &= \frac{r_n}{1 + r_n}
\end{align}</math>

The amount ratio equals the ratio of mole fractions of components:

:<math>\frac{n_2}{n_1} = \frac{x_2}{x_1}</math>

due to division of both numerator and denominator by the sum of molar amounts of components. This property has consequences for representations of [[phase diagram]]s using, for instance, [[ternary plot]]s.

====Mixing binary mixtures with a common component to form ternary mixtures====
Mixing binary mixtures with a common component gives a ternary mixture with certain mixing ratios between the three components. These mixing ratios from the ternary and the corresponding mole fractions of the ternary mixture x<sub>1(123)</sub>, x<sub>2(123)</sub>, x<sub>3(123)</sub> can be expressed as a function of several mixing ratios involved, the mixing ratios between the components of the binary mixtures and the mixing ratio of the binary mixtures to form the ternary one.
:<math>x_{1(123)} = \frac{n_{(12)} x_{1(12)} + n_{13} x_{1(13)}}{n_{(12)} + n_{(13)}}</math>

===Mole percentage===
Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent [abbreviated as (n/n)% or mol %].

===Mass concentration===
The conversion to and from [[mass concentration (chemistry)|mass concentration]] ''ρ<sub>i</sub>'' is given by:
:<math>\begin{align}
                     x_i &= \frac{\rho_i}{\rho} \frac{\bar{M}}{M_i} \\[3pt]
  \Leftrightarrow \rho_i &= x_i \rho \frac{M_i}{\bar{M}}
\end{align}</math>

where ''M̄'' is the average molar mass of the mixture.

===Molar concentration===
The conversion to [[molar concentration]] ''c<sub>i</sub>'' is given by:
:<math>\begin{align}
  c_i &= x_i c \\[3pt]
      &= \frac{x_i\rho}{\bar{M}} = \frac{x_i\rho}{\sum_j x_j M_j}
\end{align}</math>

where ''M̄'' is the average molar mass of the solution, ''c'' is the total molar concentration and ''ρ'' is the [[density]] of the solution.

===Mass and molar mass===
The mole fraction can be calculated from the [[mass]]es ''m<sub>i</sub>'' and [[molar mass]]es ''M<sub>i</sub>'' of the components:
:<math>x_i = \frac{\frac{m_i}{M_i}}{\sum_j \frac{m_j}{M_j}}</math>