Distribution of Osmium Tetraoxide between Carbon Tetrachloride and Water:

In the aqueous phase, osmium tetraoxide exists as a dibasic acid, H2OsO5, which partially dissociates as shown below:

OsO₄ ↔ H₂OsO₅

H₂OsO₅ ↔     H⁺ +HOsO ^- ₅

HOsO₅^- ↔     H⁺ + OsO₅^2-  

In the organic phase, osmium tetraoxide forms a tetramer

4 OsO₄ ↔ (OsO₄)₄

If we analyse the total scenario with regard to the presence of osmium in its different forms in the two phases, it is not simple. Osmium tetraoxide monomer will be the only species present in both the phases. H₂OsO₅ and the charged species, HOsO₅^-, OsO₅^2-  will remain totally in the aqueous phase while (OsO₄)₄, the tetramer, will remain in the organic phase.

D =   Total concentration of osmium in the organic phase/Total concentration of osmium in aqueous phase                                                  ... (2.12)

D =      [OsO ₄ ]_o  + 4[(OsO ₄ ) ₄ ]_o/[OsO ₄ ]_a+ [H₂ OsO ₅ ]_a+ [HOsO ^- ]+ [OsO₅^2- ]

The value of D or the total osmium concentration in the two phases can be calculated if the values of equilibrium constants of the reactions listed above are known.

In the two equilibria, one of benzoic acid and the other of osmium tetraoxide, the distribution ratios have been presented in terms of concentration of certain species. The expressions can be simplified by bringing in certain equilibrium constants and minimum number of variables. Finally, the effect of variables on distribution ratio can be experimentally verified. For reference, see answer of Terminal Question 1.