One for all! On the basis of the absolute chemical potential of the proton, a unified absolute pH scale is introduced that is universally applicable in the gas phase, in solution, and in the solid state. With this scale, it is possible to directly compare acidities in different media, and to give a thermodynamically meaningful definition of superacidity. This scale can be used in all areas with variable proton activity.

The COSMO cluster-continuum (CCC) solvation model is introduced for the calculation of standard Gibbs solvation energies of protons. The solvation sphere of the proton is divided into an inner proton-solvent cluster with covalent interactions and an outer solvation sphere that interacts electrostatically with the cluster. Thus, the solvation of the proton is divided into two steps that are calculated separately: 1) The interaction of the proton with one or more solvent molecules is calculated in the gas phase with high-level quantum-chemical methods (modified G3 method). 2) The Gibbs solvation energy of the proton-solvent cluster is calculated by using the conductor-like screening model (COSMO). For every solvent, the solvation of the proton in at least two (and up to 11) proton-solvent clusters was calculated. The resulting Gibbs solvation energies of the proton were weighted by using Boltzmann statistics. The model was evaluated for the calculation of Gibbs solvation energies by using experimental data of water, MeCN, and DMSO as a reference. Allowing structural relaxation of the proton-solvent clusters and the use of structurally relaxed Gibbs solvation energies improved the accordance with experimental data especially for larger clusters. This variation is denoted as the relaxed COSMO cluster-continuum (rCCC) model, for which we estimate a 1σ error bar of 10 kJ mol(-1) . Gibbs solvation energies of protons in the following representative solvents were calculated: Water, acetonitrile, sulfur dioxide, dimethyl sulfoxide, benzene, diethyl ether, methylene chloride, 1,2-dichloroethane, sulfuric acid, fluorosulfonic acid, and hydrogen fluoride. The obtained values are absolute chemical standard potentials of the proton (pH=0 in this solvent). They are used to anchor the individual solvent specific acidity (pH) scales to our recently introduced absolute acidity scale.

We introduce the protoelectric potential map (PPM) as a novel, two-dimensional plot of the absolute reduction potential (peabs scale) combined with the absolute protochemical potential (Brønsted acidity: pHabs scale). The validity of this thermodynamically derived PPM is solvent-independent due to the scale zero points, which were chosen as the ideal electron gas and the ideal proton gas at standard conditions. To tie a chemical environment to these reference states, the standard Gibbs energies for the transfer of the gaseous electrons/protons to the medium are needed as anchor points. Thereby, the thermodynamics of any redox, acid-base or combined system in any medium can be related to any other, resulting in a predictability of reactions even over different media or phase boundaries. Instruction is given on how to construct the PPM from the anchor points derived and tabulated with this work. Since efforts to establish "absolute" reduction potential scales and also "absolute" pH scales already exist, a short review in this field is given and brought into relation to the PPM. Some comments on the electrochemical validation and realization conclude this concept article.

Arrhenius, [1] Brønsted [2] und Lowry [3] definierten Säuren als Protonendonoren und Basen als Protonenakzeptoren. Dieses heutzutage als Brønsted-Acidität bekannte Konzept wird in praktisch allen mit der Chemie verwandten Fachgebieten [4] genutzt, darunter Materialwissenschaften, [5] Energiespeicherung, [6] Katalyse, [7,8] Umweltwissenschaften [9] und Molekularbiologie.[ Um die Acidität stark saurer Flüssigkeiten -beispielsweise reiner Mineralsäuren -zu beschreiben, wurden die Hammett-Funktion und der H 0 -Wert [14] eingeführt. Für wässrige Lösungen starker Säuren kann die H 0 -Skala als Fortführung der konventionellen pH-Skala in den negativen Bereich betrachtet werden. Der H 0 -Wert ist gegenwärtig der gebräuchlichste Parameter für die Quantifizierung der Acidität superacider Medien, [15] also solcher Brønsted-Säuren, die acider als 100-prozentige Schwefelsäure sind. [16] Indessen verkörpern H 0 -Werte, obwohl weit verbreitet, keine "thermodynamische" Aciditätsskala, die zum Beispiel durch elektrochemische Messungen oder (computergestützte) Rechnungen validierbar sein sollte. Die Unzulänglichkeiten der H 0 -Werte sind mannigfaltig, [17] vor allem infolge ihrer Unabhängigkeit von der Protonenaktivität. Erste Ideen für eine vereinheitlichte Aciditätsskala, die die Möglichkeit bietet, Aciditäten in verschiedenen Medien quantitativ zu vergleichen, datieren zurück auf die 1950er Jahre.[18] Ansätze hin zu thermodynamischen Aciditätswerten wurden von Izmailov, [19] Alexandrov [20] und Strehlow [21] entwickelt. Diese fanden aber, obwohl in ihrem Wesen korrekt, unter anderem wegen experimenteller Schwierigkeiten keine verbreitete Anwendung.Hier schlagen wir eine vereinheitlichte Brønsted-Aciditätsskala auf der Grundlage des absoluten chemischen Potentials des Protons in einem beliebigen Medium vor. In dieser Skala definieren wir als Referenzzustand maximaler Acidität das Proton in der Gasphase und setzen dessen absolutes chemisches Standardpotential m abs A(H +

Although receiving large interest over the last years, some fundamental aspects of Brønsted acidity in ionic liquids (ILs) have up to now been insufficiently highlighted. In this work, standard states, activity, and activity coefficient definitions for IL solvent systems were developed from general thermodynamic considerations and then extended to a general mixed solvent standard state. By using the bromide/bromoaluminate systems as representative ILs, formulae for thermodynamically consistent pH scales for ILs with simple (Br(-) ) and complex ([Aln Br3n+1 ](-) ) anions were derived on the basis of the chemical potential of the proton. Supported by quantum chemical [ccsd(t)/MP2/DFT/COSMO-RS] calculations, Gibbs solvation energies of the proton were calculated, which allowed the ILs to be ranked in absolute acidity, that is, pHabs or μabs (H(+) , IL), and additionally allowed their acidity to be compared with molecular Brønsted acid systems. It was shown that bromoaluminate ILs are suited for reaching superacidic conditions. The complexity of autoprotolysis processes in C6 MIM(+) [AlBr4 ](-) (C6 MIM=1-hexyl-3-methylimidazolium) with or without the addition of basic (i.e. Br(-) ) or acidic (AlBr3 and/or HBr) solutes was examined in detail by model calculations, and they indicated a large thermodynamic influence of small deviations from the exact stoichiometric composition.