# What substance has the lowest Kₛₚ value?

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 $$\ce{Co2S3}$$.

• Could you add a reference for this extreme value of the solubility product of cobalt(III) sulfide? – user45298 Jul 18 '17 at 16:46
• This is somewhatartificial. The $K_ {sp}$ value for mercury (II) sulfide involves two ion terms and the one for cobalt (III) sulfide has five. On a per-ion basis, assuming (not really accurate) a simple dissociation reaction when the solid dissolves, mercury (II) sulfide beats cobalt (III) sulfide. – Oscar Lanzi Mar 18 at 11:21

The $$K_\mathrm{sp}(\ce{Co2S3})$$ value of magnitude of $$10^{-124}$$ appears in paper by Goates et al. [1]. 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 in [2].

However, thirty years later (late 1980s) there's been another study by Licht [3], 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:

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

Previous value [1] was

$$ΔG_\mathrm{f}^\circ(\ce{S^2-(aq)}) = \pu{20.64 kcal mol-1} \approx \pu{83.68 kJ mol-1}$$

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 $$K_\mathrm{w}$$.

That's being said, Table I from [3] 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:

$$\begin{array}{lcc} \hline \ce{M_xS_y} & \mathrm{p}K_\mathrm{sp} & K_\mathrm{sp} \\ \hline \ce{Ir2S3} & 196.3 & \pu{5.0e-197} \\ \ce{Bi2S3} & 115.1 & \pu{7.9e-116} \\ \ce{Mo2S3} & 107.8 & \pu{1.6e-108} \\ \ce{Ni3S4} & 104.5 & \pu{3.2e-105} \\ \ce{In2S3} & 96.3 & \pu{5.0e-97} \\ \hline \end{array}$$

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. 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. 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. https://doi.org/10.1149/1.2095471.