Are there separate quantity symbols for the pKa of a substance and the pKa of its conjugate acid?

For polyprotic acids, we distinguish the different deprotonation equilibria and their equilibrium constants by indices, e.g. phosphoric acid dissociation is described by $K\_1$, $K\_2$, and $K\_3$. Considering the acid/base properties of water, there are two relevant equilibria (protonating or deprotonating water once) and equilibria with at least two other species ($\ce{H4O^2+}$ and $\ce{O^2-})$. Is there a systematic nomenclature for these equilibria, maybe something like $K\_1$, $K\_2$, and $K\_{-1}$ and $K\_{-2}$?


In tables (typically in organic chemistry), molecules are often listed alongside with the $\mathrm{p}K\_\mathrm{a}$ values of the conjugate acid, e.g. comparing the basicity of amines and amides. There is potential confusion with the $\mathrm{p}K\_\mathrm{a}$ values of the species listed (giving a measure of how acidic they are).


Is there are good way of symbolically distinguishing the $\mathrm{p}K\_\mathrm{a}$ values of the substance itself and that of its conjugate acid?




Clayden et al. [1, p. 174] suggest to use $\mathrm{p}K\_\mathrm{aH}$ (however, they merely introduce the symbol once and never use it again in the book relying solely on $\mathrm{p}K\_\mathrm{a}$):



> 
> **The ‘$\mathrm{p}K\_\mathrm{a}\text{s}$’ of bases**
> 
> 
> Chemists often say things like ‘the $\mathrm{p}K\_\mathrm{a}$ of triethylamine is about 10.’ (It’s actually 11.0 but 10 is a good number to remember for typical amines).
> This may surprise you as triethylamine has no acidic hydrogens.
> What they mean is of course this: ‘the $\mathrm{p}K\_\mathrm{a}$ of the conjugate acid of triethylamine is about 10.’
> Another way to put this is to write ‘the $\mathrm{p}K\_\mathrm{aH}$ of triethylamine is about 10.’
> The subscript ‘$\mathrm{aH}$’ refers to the conjugate acid.
> 
> 
> 


Note that older literature used $\mathrm{p}K\_\mathrm{b}$ written for the equilibrium


$$\ce{B + H2O <=> BH+ + OH-}\quad K\_\mathrm{b} = \frac{[\ce{BH+}][\ce{OH-}]}{[\ce{B}]}\tag{1}$$


instead of uniform equilibrium with conjugate acid


$$\ce{BH+ <=> B + H+}\quad K\_\mathrm{a} = \frac{[\ce{B}][\ce{H+}]}{[\ce{BH+}]}\tag{2}$$


and suggesting to use a relation


$$\mathrm{p}K\_\mathrm{a} + \mathrm{p}K\_\mathrm{b} = \mathrm{p}K\_\mathrm{w} = 14.00~(\text{at}~\pu{25 °C}),\tag{3}$$


which was not only inconvenient for comparison between two scales for acidity (for example, see [What is the importance of using a pKa value instead of a pKb value when describing drug chemistry?](https://chemistry.stackexchange.com/questions/7522)), but was a source of errors when one didn't pay attention for what temperature the value was reported (i.e. at $\pu{20 °C}$ $\mathrm{p}K\_\mathrm{w}$ is $14.17,$ not $14.00).$
There is also a conceptual flaw in using $\mathrm{p}K\_\mathrm{b}$ [2, pp. 195–196]:



> 
> Today the use of $K\_\mathrm{b}$ is avoided because it does not touch the heart of the matter, namely: an acid produces hydrogen ions and a base receives them.
> Thus both acids and bases are best related in terms of a single quantity, their affinity for the hydrogen ion.
> Such a relationship requires the use of the acidic constant $(K\_\mathrm{a})$ for *both* acids and bases.
> 
> 
> 


### References


1. Clayden, J.; Greeves, N.; Warren, S. G. *Organic Chemistry*, 2nd ed.; Oxford University Press: Oxford; New York, **2012**. ISBN 978-0-19-927029-3.
2. Albert, A. *The Determination of Ionization Constants: A Laboratory Manual*, 3rd ed.; Springer Netherlands: Dordrecht, **1984**. ISBN 978-94-009-5548-6.


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