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Problem: I want to create minimum solubility plots for a series of metal hydrolysis species against pH (below). But I cannot reconcile literature stability constants and equilibrium constants.

Context: Finding out a potential pH-range where certain metals (in mine wastewater) precipitate as hydroxides (adjustment with NaOH).

log-concentration of al hydrolysis species vs pH

The plot above I created from equilibrium constants $log K$ found in Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters by Stumm and Morgan 1996.

Table 6.3 from Aquatic chemistry.

Equations of concentration for hydrolysis species base on pH

But the literature values you find for these hydrolysis reactions are instead the stability constants $\beta_{p,q}$, for example here: https://www.cost-nectar.eu/pages/wg1_period.html that has compiled data from books books such as The Hydrolysis of Cations by Baes and Mesmer 1976 and Hydrolysis of Metal Ions by Brown and Ekberg 2016.

I know that the stability constant should the log-sum of the equilibrium constants leading up to that reaction. However I cannot seem to get the numbers right. Basically, my calculations of $\beta_n = \sum_{1}^{n}K_n$ in log-space for the tabulated values does not make sense. Below is a table of the equilibrium constants from Stumm and Morgan and the stability constants from Ekberg and Brown (with comma as decimal mark). I accept that there might be some numerical discrepancies since Ekberg & Brown are doing some quality assessment of previously reported values.

enter image description here

Note that aluminium is only used as an example here, since I had both data to create the plot from one source and the stability constants from another source. But I would like to create plots of 5-8 metals for which I have stability constants.

I feel I might be missing something really basic, but I have spent so much time reading the books and I thought perhaps someone could point it out easily.

Take $Al(OH)_{2}^{+}$ for example. From Stumm and Morgan 1996, the linear equation becomes: $$log[Al(OH)_{2}^{+}] = -0.8 - pH$$ But calculating with the stability constants, I get: $$log[Al(OH)_{2}^{+}] = -2.88 - pH$$

A fairly large discrepancy. The complete plot is: enter image description here

What am I missing here? (I want to go from the stability constants $\beta$ to the linear equation systems)

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  • $\begingroup$ The table containing data from both authors is confusing because it's unclear what the reactant is in two important rows. For the copy of the Stumm and Morgan data, the reactant is always solid aluminum hydroxide and the product varies. One product is aqueous aluminum hydroxide with a log K of –6.5, but this is mislabeled in the table as a solid. For Brown and Ekberg, what is the reactant? I thought for hydrolysis products, the bare metal ion would be the reactant, but if that's the case then the Al3+ row would be blank. $\endgroup$
    – Marc Shelikoff
    Commented Dec 20, 2023 at 13:19

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