A predominance diagram purports to show the conditions of concentration and pH where a

chemical species A chemical species is a chemical substance or ensemble composed of chemically identical molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. These energy levels determine the wa ...

has the highest concentration in solutions in which there are multiple acid-base equilibria. The lines on a predominance diagram indicate where adjacent species have the same concentration. Either side of such a line one species or the other predominates, that is, has higher concentration relative to the other species. Predominance diagram Cr

To illustrate a predominance diagram, part of the one for chromate is shown at the right. pCr stands for minus the logarithm of the chromium concentration and pH stands for minus the logarithm of the

hydrogen ion A hydrogen ion is created when a hydrogen atom loses or gains an electron. A positively charged hydrogen ion (or proton) can readily combine with other particles and therefore is only seen isolated when it is in a gaseous state or a nearly particle ...

concentration. There are two independent equilibria, with

equilibrium constants The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...

defined as follows. A third equilibrium constant can be derived from ''K''₁ and ''K''_D. The species and are only formed at very low pH so they do not appear on this diagram. Published values for log ''K''₁ and log ''K''_D are 5.89 and 2.05, respectively. Using these values and the equality conditions, the concentrations of the three species, chromate , hydrogen chromate and dichromate can be calculated, for various values of pH, by means of the equilibrium expressions. The chromium concentration is calculated as the sum of the species' concentrations in terms of chromium content. :

\qquad p\ce=-\log_\ce

The three species all have concentrations equal to at pH = p''K''₁, for which r= . The three lines on this diagram meet at that point. ; Green line: Chromate and hydrogen chromate have equal concentrations. Setting [] equal to [] in eq. , [] = , or pH = log ''K''₁. This relationship is independent of pCr, so it requires a vertical line to be drawn on the predominance diagram. ; Red line: Hydrogen chromate and dichromate have equal concentrations. Setting [] equal to [] in Eq. , [] = ; from Eq. , then, [] = . ; Blue line: Chromate and dichromate have equal concentrations. Setting [] equal to [] in Eq. gives [] = . The predominance diagram is interpreted as follows. The chromate ion is the predominant species in the region to the right of the green and blue lines. Above pH ~6.75 it is always the predominant species. At pH < 5.89 (pH < p''K''₁) the hydrogen chromate ion is predominant in dilute solution but the dichromate ion is predominant in more concentrated solutions. Predominance diagrams can become very complicated when many polymeric species can be formed as, for example, with

vanadate In chemistry, a vanadate is an anionic coordination complex of vanadium. Often vanadate refers to oxoanions of vanadium, most of which exist in its highest oxidation state of +5. The complexes and are referred to as hexacyanovanadate(III) and no ...

, p. 984

molybdate In chemistry a molybdate is a compound containing an oxoanion with molybdenum in its highest oxidation state of 6. Molybdenum can form a very large range of such oxoanions which can be discrete structures or polymeric extended structures, altho ...

and

tungstate In chemistry, a tungstate is a compound that contains an oxyanion of tungsten or is a mixed oxide containing tungsten. The simplest tungstate ion is , "orthotungstate". Many other tungstates belong to a large group of polyatomic ions that are ...

. Another complication is that many of the higher polymers are formed extremely slowly, such that equilibrium may not be attained even in months, leading to possible errors in the equilibrium constants and the predominance diagram.

References

{{DEFAULTSORT:Predominance Diagram Acid–base chemistry Equilibrium chemistry Oxyanions