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https://openchemistryhelp.blogspot.com/2013/02/solvent-levelling.html

I learned the concept of solvent theory and solvent leveling of acid and base,but couldn't understand what the graph below says

enter image description here

I thought since the pKa of ammonium ion(NH4+) in water is 9.24 and pKa of ammonia in water is 38, the line shows the interval between these pKa.

But as I searched for more information I found out that pKa of sulfuric acid in weter is -2.8, which doesn't correspond the graph.

Could someone explain what this graph means?

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    $\begingroup$ This graph is hard to understand, apart from water and ammonia. For example, the pKa of hydrofluoric acid is known to be $3.17$. It is not a strong acid. In the graph, the blue domain of HF goes from $-21$ to $-4$, which is typical of very strong acids. These limits have nothing to do with $3.17$. What does it mean? Same thing for acetic acid, whose pKa is $4.75$. In the graph, the blue domain of acetic acid (ethanoic acid) goes from $-2$ to $+12$. What is the meaning of this blue domain ? $\endgroup$
    – Maurice
    Commented Aug 2, 2023 at 8:44
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    $\begingroup$ @Maurice HF is rather exception. Very concentrated HF solution converges to becoming a superacid and liquid HF definitely is, due 3 HF <-> H2F+ + HF2^-. H2F+ is acting acidic agent of fluoroantimonic acid ( HF + SbF5) $\endgroup$
    – Poutnik
    Commented Aug 2, 2023 at 8:47
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    $\begingroup$ @Poutnik. The abscissa does not speak of pH in concentrated solutions. It is "Effective pH in water". $\endgroup$
    – Maurice
    Commented Aug 2, 2023 at 8:50
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    $\begingroup$ @Maurice It was comment to your comment, not to the question. By other words, pKa of diluted HF in water is very different than pKa of liquid HF, because there is a side fluorine chemistry behind the simple HA <=> H+ + A-. $\endgroup$
    – Poutnik
    Commented Aug 2, 2023 at 8:52
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    $\begingroup$ About the H2SO4, it is not about the acidity of H2SO4 in water, but about acidity of H2SO4 and H3SO4+ in pure sulphuric acid. Hammett function value for sulfuric acid -12 quite matches the range on the chart. $\endgroup$
    – Poutnik
    Commented Aug 2, 2023 at 10:32

1 Answer 1

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In my understanding "the effective pH in water" is nothing else but the Hammett acidity function, which is extension of the classical $\text{pH}$ quantity to non-aqueous solutions. The blue ranges are then available Hammett function values for the given protic solvent, similarly as there is range of available pH values for water solutions.

The respective dissolved conjugate acid/base pairs can have in other then water protic solvents such activity ratios that would hypothetically belong to the "effective pH in water", if such ratio should be achieved in water solution.

E.g. $\ce{HNO3}$ has reportedly $\mathrm{p}K_\mathrm{a} = -1.5$. If it was dissolved in glacial acetic acid(preferred IUPAC name over the IUPAC systematic name ethanoic acid) and the solution was adjusted in a way $\ce{HNO3}$ : $\ce{NO3-}$ ratio was 1:1, then the solution in acetic acid would have the "effective pH in water" equal to -1.5.

IF the conjugate acid/pair activity ratio belonged to the effective value out of the blue range, it would be the acid is stronger than protonated solvent and it would protonate the solvent. Or, the base is stronger base than the deprotonated solvent and would deprotonate it:

\begin{align} \ce{HA(solv) + Solv(l) &<=> A-(solv) + HSolv+(solv)}\\ \ce{B(solv) + HSolv(l) &<=> BH+(solv) + Solv-(solv)} \end{align}

The left edge of blue ranges maps itself to the case $\ce{HA(solv)}$ and $\ce{HSolv+(solv)}$ are equally strong acids.

The right edge of blue ranges maps itself to the case $\ce{B(solv)}$ and $\ce{Solv-(solv)}$ are equally strong bases.

The edge values can be considered as $\mathrm{p}K_\mathrm{a}$ of protonated(left) and not protonated(right) solvent.

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    $\begingroup$ @MaxW Thanks you for the edit. I am not sure if glacial acetic acid is the IUPAC preferred name for the pure acetic acid. I have meant that acetic acid as the compound name is preferred by IUPAC over ethanoic acid as the established non-systematic name. $\endgroup$
    – Poutnik
    Commented Aug 2, 2023 at 14:00
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    $\begingroup$ Poutnik - I realize I went overboard on glacial acetic acid but I was trying to make it absolutely clear that you weren't referring to an aqueous solution. When I read your original post I absolutely understood you, but I didn't think the OP would. - Nice answer by the way... $\endgroup$
    – MaxW
    Commented Aug 3, 2023 at 0:08
  • $\begingroup$ @Poutnik Thank you for you thourough explanation about the graph. I didn't know about hammett acidity function. About the last sentence of your answer, is it correct to consider that the edge values are pKa of protonated(left) and not protonated(right) solvent "in water"? $\endgroup$
    – satoru kurita
    Commented Aug 3, 2023 at 21:29
  • $\begingroup$ Well, yes and no. Yes in sense it matches the idea of pKa in water. No in sense the molecular entity in the solvent has often different pKa than the same in water. Typical cases are those with very different solvent interactions, like for HF. It is also related to the solvent autoionization constant HS + HS <=> S- + H2S+, defining acidity ratio of H2S+ versus HS. $\endgroup$
    – Poutnik
    Commented Aug 4, 2023 at 10:36

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