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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.

For more information concerning unified Brønsted acidity click here: onlinelibrary.wiley.com/doi/full/10.1002/anie.201709057

German version: onlinelibrary.wiley.com/doi/10.1002/ange.201709057