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# Formulas & Remarks Relating to Unified Acidity

The defintion of the pHabs is:

${\mathrm{\text{pH}}}_{\mathrm{\text{abs}}}$

(1)

Under standard conditions the absolute chemical potential of the proton equals the Standard Gibbs energy of solvation and therefore the pHabs is calculable via:

${\mathrm{\text{pH}}}_{\mathrm{\text{abs}}}$

(2)

Whereby pHS ist the pH value in the pH scale of the solvent S. The pHS is calculable conventionally using the pKa of an acid HA for the solvent S and the reaction:
$\mathrm{\text{−}}$  (3)

Generally, pHS = −log(a(H+)) = −log(c(H+) f±(H+A)) with f±(H+A) is the mean acitivity coefficient of H+ and A in the solvent S. For ideal solutions (c0 < 10−3 mol L−1; f±(H+A) ≈ 1), therefore pHS = −log(c(H+)), one can distinct following cases:

${\mathrm{\text{p}}K}_{\mathrm{\text{a}}}\mathrm{<}0:$ c(H+) = c0(HA)  (4)

${\mathrm{0}<\mathrm{\text{p}}K}_{\mathrm{\text{a}}}\mathrm{<}\mathrm{4.5:}$ c(H+)  (5)

${\mathrm{\text{4.5}}<\mathrm{\text{p}}K}_{\mathrm{\text{a}}}\mathrm{<}\mathrm{9.5:}$ c(H+) $\mathrm{\text{=}}\sqrt{{K}_{\mathrm{\text{a}}}^{}\mathrm{\bullet }{c}_{0}\mathrm{\text{(HA)}}}$  (6)

${\mathrm{\text{9.5}}<\mathrm{\text{p}}K}_{\mathrm{\text{a}}}:$ c(H+) $\mathrm{\text{=}}\sqrt{{K}_{\mathrm{\text{a}}}^{}\mathrm{\bullet }{c}_{0}\mathrm{\text{(HA)+}}{K}_{\mathrm{\text{solv}}}^{}}$  (7)

Ksolv is the autoprotolysis constant of the solvent S, i.e. for the reaction:

$-{\mathrm{\text{}}}^{\mathrm{\text{}}}$  (8)

For non-ideal solutions one can replace c(H+) by a(H+)/f±(H+A) in equations (4 - 7) without obtaining analytical solutions (f(HA) of the undissociated acid is 1 since it is uncharged).

The zero point of the absolute pH scale pHabs 0 is assigned to the ideal proton gas at 1 bar and 298.15 K. Here the chemical potential of the proton is 0 kJ mol−1.

The pHabsH2O is the alignment of the zero values of the pHabs scale and the water acidity scale pHH2O:

 ${\mathrm{\text{pHabsH2O}}}_{\mathrm{\text{}}}$$\mathrm{\text{= pHabs − 193.5}}$ (9)

Note, that not the refence states are aligned but only the zero values are, i.e. the pHabsH2O can be regarded as the thermochemical well founded continuation of the water pH scale.