# Successive deprotonation - how far can it go?

It has been written that among the equilibria of the dissolution of $$\ce{SO_2}$$ in water, the dissociation of sulphur dioxide into $$\ce{HSO_3^-(aq) + H_3O^+(aq)}$$ is a complete dissociation. See the answer of S R Maiti to this question:

Can physical absorption happen despite the formation of products?

However, in principle, couldn't $$\ce{HSO_3-(aq)}$$ deprotonate once more? According to this site, it does.

If it doesn't, why would it? In general, how far does deprotonation go?

It depends on the pH value of the solution / the (remaining) presence of a base sufficiently strong if you have a significant concentration of $$\ce{H2SO3}$$ (note the note), $$\ce{HSO^-_3}$$, and $$\ce{SO^{2-}_3}$$ because they are connected by chemical equilibria:

$$\ce{H2SO3 + H2O <=> H3O+ + HSO^-_3}$$ $$\ce{HSO^-_3 + H2O <=> H3O+ + SO^{2-}_3}$$

Note: Similar to $$\ce{CO2}$$ in water / $$\ce{H2CO3}$$, there however is an other (more) important equilibrium to consider, about $$\ce{SO2}$$ merely dissolved as a gas in water

$$\ce{SO2 + H2O <<=> H2SO3} \quad K \ll 10^{-9}$$

Hence the description $$\ce{H2SO3 <=> H+ + HSO^-_3 <=> 2 H+ + SO^{2-}_3}$$ with

$$K_1 = \frac{[\ce{H+}] [\ce{HSO^-_3}]} {[\ce{H2SO3}]} = 1.54 \times 10^{-2}$$

and

$$K_2 = \frac{[\ce{H+}] [\ce{SO^{2-}_3}]} {[\ce{HSO^-_3}]} = 1.02 \times 10^{-7}$$

for aqueous solutions at $$\pu{18 ^\circ{}C}$$ (values by Holleman) has to be read with $$[\ce{H2SO3}]$$ as the total of the concentration of the anhydride ($$\ce{SO2}$$) plus the one of undissociated acid $$\ce{H2SO3}$$ you can't isolate from water. (For comparison, values by Housecroft for $$\pu{298 K}$$: $$\mathrm{p}K_a(1) = 1.82$$, $$\mathrm{p}K_a(2) = 6.92$$) Hence, sulfurous acid is a "special aqueous acid" (to cite Jolly, $$\ce{H2O + SO2 <=> H+ + HSO^-_3}$$, $$K_1 = 1.2 \times 10^{-3}$$).

Though a showcase about $$\ce{H3PO4}$$, Wikipedia's diagram about polyprotic acids describes this with the following plot:

(source: Acid dissociation constant)

With the thermodynamic values in hand, it is possible to compute these dissociations / plot the corresponding curves by help of a computer. Curtipot is an example freely available since 1992 to work with MS Excel.

edit: substitute sulfuric acid ($$\ce{H2SO4}$$, initial form of the answer) by sulfurous acid ($$\ce{H2SO3}$$).

references:

Band 1 Grundlagen Und Hauptgruppenelemente; Holleman, A. F., Ed.; De Gruyter, 2016. https://doi.org/10.1515/9783110495850, page 649 (German)

Housecroft, C. E.; Sharpe, A. G. Inorganic Chemistry, 2nd ed.; Pearson Prentice Hall: Upper Saddle River, N.J, 2005. Here, table 15.8 / p. 458, accessed on archive.org

Jolly, W. L. Customized modern inorganic chemistry, 2nd ed.; MacGraw Hill: New York, 1998. pp. 226 accessed on archive.org (requires their free library card)

• Note that, in contrary to carbonic acid, detection of presence of sulfurous acid (Raman IR) has not been confirmed in water solutions, but just hydrated SO2. $\ce{SO2(aq) + H2O <=> HSO3-(aq) + H+(aq)}$ May 13 at 11:27
• @Poutnik interesting contrast with carbon dioxide, which does seem to form carbonic acid as a minor species. Molecular sulfurous acid does exist in the gas phase, however. May 14 at 16:00
• @OscarLanzi It is similar for carbonic acid too. Many unstable things are willing to exist in gas or vacuum, where they are bored, nothing to react with. May 14 at 16:04
• @Poutnik p 296 of Miessler (by 2014) introduces sulfites as conjugate base to hydrogensulfites when SO2 is dissolved in water (with a login on archive.org). Housecroft (by 2005) on p. 457 describes sulfourous acid with 2 pKa the next page's table (on archive.org). German Holleman (doi.org/10.1515/9783110495850 by 2016) on page 649 with cross-reference to CO2 and H2CO3(aq). So there is an edit. May 14 at 17:45

Citric acid represents a surprising example of nedium-dependent deprotonation. Ordinarily this acid, $$\ce{H3C6H5O7}$$, has three dissociable hydrogen atoms from its carboxyl groups. But a fourth dissociation is possible from an alcoholic hydroxyl group under strongly basic conditions. [Silva et al. 1] have measured the dissociation constant of the alcoholic hydroxyl group in citric acid, obtaining $$\pu{pK}_{a4}=14.4$$. Thus in $$0.1$$ molar sodium hydroxide solution several percent of citrate ions would undergo the extra dissociation to form $$\ce{C6H4O7^{4-}}$$. This is appreciably more acidic than is typically found in alcoholic hydroxyl groups, and a similar enhancement is observed in the alcoholic hydroxyl protons of malic and lactic acids. The easier displacement of this hydrogen facilitates chelation of the anions on these acids with metal ions in biochemical systems.

The authors identify a hydrogen-bonding interaction between the deprotonated alcoholic oxygen and the methylene hydrogens attached to the carboxylate groups. Negative conjugation between the methylene $$\ce{C - H}$$ bonds and the carboxylate $$\pi^*$$ orbitals polarizes the former and makes the methylene hydrogens sufficiently protic to form such hydrogen bonds. The interaction may be represented in the case of citrate by a cobtributing valence-bond structure*:

*Yes, using a picture isn't preferred. Unfortunately, limited drawing options on my device prevent my rendering the structures electronically.

Reference

1. Silva, A.M.N., Kong, X. & Hider, R.C. (2009). "Determination of the pKa value of the hydroxyl group in the α-hydroxycarboxylates citrate, malate and lactate by 13C NMR: implications for metal coordination in biological systems". Biometals 22, 771–778. https://doi.org/10.1007/s10534-009-9224-5