[2] If ni is much smaller than ntot (which is the case for atmospheric trace constituents), the mole ratio is almost identical to the mole fraction.
Two binary solutions of different compositions or even two pure components can be mixed with various mixing ratios by masses, moles, or volumes.
By substituting the densities ρi(wi) and considering equal volumes of different concentrations one gets: Considering a volume mixing ratio rV(21) The formula can be extended to more than two solutions with mass mixing ratios to be mixed giving: The condition to get a partially ideal solution on mixing is that the volume of the resulting mixture V to equal double the volume Vs of each solution mixed in equal volumes due to the additivity of volumes.
The resulting volume can be found from the mass balance equation involving densities of the mixed and resulting solutions and equalising it to 2: implies Of course for real solutions inequalities appear instead of the last equality.
Mixtures of different solvents can have interesting features like anomalous conductivity (electrolytic) of particular lyonium ions and lyate ions generated by molecular autoionization of protic and aprotic solvents due to Grotthuss mechanism of ion hopping depending on the mixing ratios.
Examples may include hydronium and hydroxide ions in water and water alcohol mixtures, alkoxonium and alkoxide ions in the same mixtures, ammonium and amide ions in liquid and supercritical ammonia, alkylammonium and alkylamide ions in ammines mixtures, etc....