Inchemistry andphysics, thedimensionlessmixing ratio is the abundance of one component of amixture relative to that of all other components. The term can refer either tomole ratio (seeconcentration) ormass ratio (seestoichiometry).^[1]

Inatmospheric chemistry, mixing ratio usually refers to themole ratior_i, which is defined as theamount of a constituentn_i divided by the total amount of allother constituents in a mixture:

${\displaystyle r_i=\frac{n_i}{n_{\mathrm{t}\mathrm{o}\mathrm{t}}-n_i}}$

The mole ratio is also calledamount ratio.^[2]Ifn_i is much smaller thann_tot (which is the case for atmospheric trace constituents), the mole ratio is almost identical to themole fraction.

Inmeteorology, mixing ratio usually refers to themass ratio of water${\displaystyle \zeta }$, which is defined as the mass of water${\displaystyle m_{\mathrm{H}2\mathrm{O}}}$ divided by the mass of dry air (${\displaystyle m_{\mathrm{a}\mathrm{i}\mathrm{r}}-m_{\mathrm{H}2\mathrm{O}}}$) in a given air parcel:^[3]

${\displaystyle \zeta =\frac{m_{\mathrm{H}2\mathrm{O}}}{m_{\mathrm{a}\mathrm{i}\mathrm{r}}-m_{\mathrm{H}2\mathrm{O}}}}$

The unit is typically given in${\displaystyle \mathrm{g}{\mathrm{k}\mathrm{g}}^{-1}}$. The definition is similar to that ofspecific humidity.

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

Themass fraction of the resulting solution from mixing solutions with massesm₁ andm₂ and mass fractionsw₁ andw₂ is given by:

${\displaystyle w=\frac{w_1{m}_1+w_2{m}_1{r}_m}{m_1+m_1{r}_m}}$

wherem₁ 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 densitiesρ_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 ratior_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

${\displaystyle r_{m1}=\frac{m_2}{m_1}{r}_{m2}=\frac{m_3}{m_1}}$

to be mixed giving:

${\displaystyle w=\frac{w_1{m}_1+w_2{m}_1{r}_{m1}+w_3{m}_1{r}_{m2}}{m_1+m_1{r}_{m1}+m_1{r}_{m2}}=\frac{w_1+w_2{r}_{m1}+w_3{r}_{m2}}{1+r_{m1}+r_{m2}}}$

The condition to get a partiallyideal solution on mixing is that the volume of the resulting mixtureV to equal double the volumeV_s of each solution mixed in equal volumes due to the additivity of volumes. The resulting volume can be found from themass balance equation involving densities of the mixed and resulting solutions and equalising it to 2:

${\displaystyle V=\frac{({\rho }_1+{\rho }_2)V_{\mathrm{s}}}{\rho },V=2V_{\mathrm{s}}}$

implies

${\displaystyle \frac{{\rho }_1+{\rho }_2}{\rho }=2}$

Of course for real solutions inequalities appear instead of the last equality.^{[citation needed]}

Mixtures of different solvents can have interesting features like anomalousconductivity (electrolytic) of particularlyonium ions andlyate ions generated bymolecular autoionization of protic and aprotic solvents due toGrotthuss mechanism of ion hopping depending on the mixing ratios. Examples may includehydronium andhydroxide ions in water and water alcohol mixtures, alkoxonium andalkoxide ions in the same mixtures,ammonium andamide ions in liquid and supercritical ammonia, and alkylammonium and alkylamide ions in ammines mixtures.^{[citation needed]}

• Chemical properties
• Dimensionless numbers of chemistry

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