What substance has the lowest solubility product?

What substance has the lowest $K\_\mathrm{sp}$ and what is its value? The lowest I could find is $2.6\cdot 10^{-124}$ for cobalt(III) sulfide $\ce{Co2S3}$.




The $K\_\mathrm{sp}(\ce{Co2S3})$ value of magnitude of $10^{-124}$ appears in paper by Goates et al. [[1](https://doi.org/10.1021/ja01123a510)].
The refined "thermodynamic" value of $\pu{2.6E-124}$ that you've listed and is used by numerous textbook up to these days has been proposed by Waggoner [[2](https://doi.org/10.1021/ed035p339)].


However, thirty years later (late 1980s) there's been another study by Licht [[3](https://doi.org/10.1149/1.2095471)], which showed significant deviation from the previous studies due to two factors:


1. A new value of the free energy of sulfide ion formation for aqueous solutions has been used:


$$Δ\_\mathrm{f}G^\circ(\ce{S^2-(aq)}) = \pu{(111 ± 2) kJ mol-1}$$


Previous value [[1](https://doi.org/10.1021/ja01123a510)] was


$$Δ\_\mathrm{f}G^\circ(\ce{S^2-(aq)}) = \pu{20.64 kcal mol-1} \approx \pu{83.68 kJ mol-1}$$
2. Free sulfide activity $a(\ce{S^2-})$ used for $K\_\mathrm{sp}$ determination



> 
> $$
> \begin{align}
> \ce{M\_xS\_y &<=> x M^{$2y/x$+} + y S^2-} &\qquad K\_\mathrm{sp} &= a(\ce{M^{$2y/x$+}})^x \cdot a(\ce{S^2-})^y \\
> \ce{HS- &<=> H+ + S^2-} &\qquad K\_2 &= \frac{a(\ce{H+})\cdot a(\ce{S^2-})}{a(\ce{HS-})}
> \end{align}
> $$
> 
> 
> 


has also been misinterpreted in early studies by acidification of hydroxyl $\ce{OH-}$ instead, erroneously substituting $K\_2$ by $K\_\mathrm{w}.$


Table I from [[3](https://doi.org/10.1149/1.2095471)] lists more recent $\mathrm{p}K\_\mathrm{sp}$ values, among which the one for $\ce{Co2S3}$ that has increased significantly $(\mathrm{p}K\_\mathrm{sp}(\ce{Co2S3}) = 49.9,$ $K\_\mathrm{sp}(\ce{Co2S3}) \approx \pu{1.26E-50}).$
Five least soluble sulfides from that table are:


$$
\begin{array}{lrc}
\hline
\ce{M\_xS\_y} & \mathrm{p}K\_\mathrm{sp} & K\_\mathrm{sp} \\
\hline
\ce{Ir2S3} & 196.3 & \pu{5.0E-197} \\
\ce{Bi2S3} & 115.1 & \pu{7.9E-116} \\
\ce{Mo2S3} & 107.8 & \pu{1.6E-108} \\
\ce{Ni3S4} & 104.5 & \pu{3.2E-105} \\
\ce{In2S3} & 96.3 & \pu{5.0E-97} \\
\hline
\end{array}
$$


So that it seems like the new champion (at least among sulfides) is iridium(III) sulfide $\ce{Ir2S3}$ with $K\_\mathrm{sp} = \pu{5.0E-197}$.


### References


1. Goates, J. R.; Gordon, M. B.; Faux, N. D. Calculated Values for the Solubility Product Constants of the Metallic Sulfides. *Journal of the American Chemical Society* **1952**, 74 (3), 835–836. DOI: [10.1021/ja01123a510](https://doi.org/10.1021/ja01123a510).
2. Waggoner, W. H. Textbook Errors: Guest Column. The Solubility Product Constants of the Metallic Sulfides. *Journal of Chemical Education* **1958**, 35 (7), 339. DOI: [10.1021/ed035p339](https://doi.org/10.1021/ed035p339).
3. Licht, S. Aqueous Solubilities, Solubility Products and Standard Oxidation-Reduction Potentials of the Metal Sulfides. *Journal of The Electrochemical Society* **1988**, 135 (12), 2971. DOI: [10.1149/1.2095471](https://doi.org/10.1149/1.2095471).


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