Reliable data describing acidity of 2,4,6-trinitrobenzenesulfonic acid

I wonder what is the $\mathrm{p}K\_\mathrm{a}$ or the value of Hammett's $H\_0$ function of 2,4,6-trinitrobenzenesulfonic acid? [PubChem](https://pubchem.ncbi.nlm.nih.gov/compound/2_4_6-Trinitrobenzenesulfonic-acid#section=Dissociation-Constants) gives $\mathrm{p}K\_\mathrm{a} = 0.13,$ but doesn't specify the solvent. Even if it's real value I doubt it's the value for water. Why? For starter even aliphatic sulfonic acids are strong, and with electron withdrawing groups, even stronger.


Guthrie reports gives $\mathrm{p}K\_\mathrm{a} = -4.0$ for *p*-nitrosulfonic acid [[1](https://doi.org/10.1139/v78-385@cjc-csc.issue01)]. Even if resonance of *o*-nitro groups is blocked, it doesn't negate inductive effects. Reasoning with solvation effects also seems dubious — nitro groups aren't hydrophobic at all. Is there some reliable data for this, rather obscure, acid?


### Reference


1. Guthrie, J. P. Hydrolysis of Esters of Oxy Acids: $\mathrm{p}K\_\mathrm{a}$ Values for Strong Acids; Brønsted Relationship for Attack of Water at Methyl; Free Energies of Hydrolysis of Esters of Oxy Acids; and a Linear Relationship between Free Energy of Hydrolysis and $\mathrm{p}K\_\mathrm{a}$ Holding over a Range of 20 $\mathrm{p}K$ Units. *E. Can. J. Chem.* **1978**, 56, 2342–2354. DOI: [10.1139/v78-385@cjc-csc.issue01](https://doi.org/10.1139/v78-385@cjc-csc.issue01). ([PDF](http://www.nrcresearchpress.com/doi/pdf/10.1139/v78-385))




The reference for the [PubChem entry for picryl sulfonic acid](https://pubchem.ncbi.nlm.nih.gov/compound/11045) is: 



> 
> Serjeant, E.P., Dempsey B.; Ionisation Constants of Organic Acids in Aqueous Solution. International Union of Pure and Applied Chemistry (IUPAC). IUPAC Chemical Data Series No. 23, 1979. New York, New York: Pergamon Press, Inc., p. 40
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So, yes that is the value of the pKa for picryl sulfonic acid (2,4,6-trinitrobenzenesulfonic acid) in water. 


The pKa of [benzenesulfonic acid](https://pubchem.ncbi.nlm.nih.gov/compound/7371) is 2.554, although the reference does not specify a solvent. The pKa of [methanesulfonic acid](https://pubchem.ncbi.nlm.nih.gov/compound/6395) is -1.86, with the same reference as picrylsulfonic acid. 


The difference between methanesulfonic acid and the arylsulfonic acids might be the ability of water to solvate the anion. The aryl groups are less polar and more hydrophobic. They are also large. This same reason (decreased solvation of the anion) is invoked as the explanation for the difference in acidity between [primary, secondary, and tertiary alcohols](https://chemistry.stackexchange.com/questions/14767/steric-hindrance-and-bronsted-basicity). The magnitude of the effect in alcohols is a few pKa units, which appears to be of a similar scale for the same effect in sulfonic acids.


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