# Influence of solubility on the complexation constants at different pH values

Given some small chemical compounds whose solubility varies with pH, and in the case of compounds that can form complexes, I have seen that the complexation constant varies with pH.

I think there might be two main reasons for this:

1. Chemical structure of the host system is affected by pH (for instance, protonation) and therefore it affects complexation constant;
2. It might be related to the small chemical compound, since its solubility might vary according to pH.

So I guess that in this case there are many chemical/physical equilibria involved, in this case mainly phase solubility and protonation for both species. I wonder what is the best approach for describing this, perhaps one can use different equilibrium constants for the mentioned equilibria, and from there derive a global constant that depends on pH. How do these two factors (protonation and phase/solvation) influence the value of the complexation constant?

As a particular case, I am mostly interested in complexation of flavonoids with cyclodextrins.

• This is a much more focused question about solubility, pH, and complexation constants. I have edited the last line to make it clearly a question, since it reads like an invitation to discussion. An example of the types of molecules you are looking at would make this a great question. I know from your previous questions that you are interested in flavonoids. Is that true here also? – Ben Norris Feb 27 '13 at 12:30

It is possible to calculate out all of the complexation and speciation reactions using the concepts of Aquatic Chemistry. I’m a PhD student in environmental chemistry and I TA a course in Aquatic Chemistry. Usually, when pH matters it’s because the protonation state controls the chemistry and can be described using equilibrium constants. I bet that your solubility issue is related to the deprotonated form being an anion and thus more soluble in water than the protonated, neutral form (very common for organic compounds). The protonation state can be calculated from the $\mathrm{p}K_\text{a}$:

$$\ce{L- + H+ <=> HL}\\ K_\text{a}=10^{-\mathrm{p}K_\text{a}}=\dfrac{[\ce{L-}][\ce{H+}]}{[\ce{HL}]}$$

Where $K_\text{a}$ is the equilibrium constant, and L is your compound. I would guess that your flavanoids and cyclodextrins might have multiple $\mathrm{p}K_\text{a}$s, you can write an expression like this for each one.

Complexation reactions can be written in a similar way. Let’s say that $\ce{Y}$ is the molecule your $\ce{L}$ molecule complexes with, and it is neutral when protonated ($\ce{HY}$).

$$\ce{L- + HY <=> HLY-}\\ K=\dfrac{[\ce{L-}][\ce{HY}]}{[\ce{HLY-}]}$$

Where $K$ is the equilibrium constant for this complexation reaction. Keep in mind that which species (protonation state) is in the expression matters, the value for the equilibrium constant is only valid for those species. Above, I’ve written that the deprotonated form of L ($\ce{L-}$) complexes with the protonated form of Y ($\ce{HY}$). This is where pH comes in. pH controls how much of L is deprotonated and how much of Y is deprotonated and able to participate in complexation, and $K$ controls how much of the available $\ce{L-}$ and $\ce{HY}$ form the complex. Complexes themselves can also have $\mathrm{p}K_\text{a}$s the one above ($\ce{HLY-}$) could probably be protonated to a neutral form $\ce{H2LY}$.

You might be able to guess that the mathematics gets a little complex at this point. It is possible to do these calculations by hand, but there are computer programs that can handle them. The most easily accessible one is Visual MinTEQ. The other hard part is having the data for the equilibrium constants, there may be data for your system, but you’ll have to look.

Just to summarize. Complexation constants don’t change with pH (they are, in fact, constant) it’s just that the speciation matters, and speciation is controlled by pH. The ‘global constant’ you refer to is pH, not something else.

• excellent answer! thanks a lot. Could you also recommenda good book about aquatic chemistry? – Open the way Mar 7 '13 at 10:25
• W. Stumm and J. J. Morgan, Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters Is the "classic" text for Aquatic Chemistry. J. F. Pankow, Aquatic Chemistry Concepts is also good. – Phillip Mar 8 '13 at 18:24