In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio (see concentration) or mass ratio (see stoichiometry).^[1]

In atmospheric chemistry and meteorology

Mixing ratio of mixtures or solutions

Two binary solutions of different compositions or even two pure components can be mixed with various mixing ratios by masses, moles, or volumes.

The mass fraction of the resulting solution from mixing solutions with masses m₁ and m₂ and mass fractions w₁ and w₂ is given by:

${\displaystyle w={\frac {w_{1}m_{1}+w_{2}m_{1}r_{m}}{m_{1}+m_{1}r_{m}}}}$

where m₁ can be simplified from numerator and denominator

${\displaystyle w={\frac {w_{1}+w_{2}r_{m}}{1+r_{m}}}}$

and

${\displaystyle r_{m}={\frac {m_{2}}{m_{1}}}}$

is the mass mixing ratio of the two solutions.

By substituting the densities ρ_i(w_i) and considering equal volumes of different concentrations one gets:

${\displaystyle w={\frac {w_{1}\rho _{1}(w_{1})+w_{2}\rho _{2}(w_{2})}{\rho _{1}(w_{1})+\rho _{2}(w_{2})}}}$

Considering a volume mixing ratio r_V(21)

${\displaystyle w={\frac {w_{1}\rho _{1}(w_{1})+w_{2}\rho _{2}(w_{2})r_{V}}{\rho _{1}(w_{1})+\rho _{2}(w_{2})r_{V}}}}$

The formula can be extended to more than two solutions with mass mixing ratios

${\displaystyle r_{m1}={\frac {m_{2}}{m_{1}}}\quad r_{m2}={\frac {m_{3}}{m_{1}}}}$

to be mixed giving:

${\displaystyle w={\frac {w_{1}m_{1}+w_{2}m_{1}r_{m1}+w_{3}m_{1}r_{m2}}{m_{1}+m_{1}r_{m1}+m_{1}r_{m2}}}={\frac {w_{1}+w_{2}r_{m1}+w_{3}r_{m2}}{1+r_{m1}+r_{m2}}}}$

References