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Formulas & Remarks Relating to Unified Acidity


The defintion of the pHabs is:

pH abs = − µ abs ( H+  ) R T ln10

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

pH abs = − solv G ° H+  R T ln10 + pH S

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:
  HA + S =  HS+  + A  (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:
p K a < 0: c(H+) = c0(HA)  (4)
0 < p K a < 4.5: c(H+) =  − K a 2 + K a 2 4 + K a c 0 (HA)  (5)
4.5 < p K a < 9.5: c(H+) = K a c 0 (HA)  (6)
9.5 < p K a : c(H+) = K a c 0 (HA)+ K solv  (7)

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

  HS + HS =  H 2 S++  S  (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:


pHabsH2O = pHabs − 193.5


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.

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