We here present a first principles approach to calculate standard Gibbs energies and the corresponding observables (standard electrode potentials in the hydrogen scale E-SHE(0) and pK(a) values) of stoichiometric reactions involving electrons and/or protons as independent species in solution, from absolute electrochemical potentials defined according to quantum and statistical mechanics. In order to pass from the conventional electrodic and thermodynamic descriptions of electrochemistry to the first principles approach based on estimating absolute electrochemical potentials, we revisit the problem of the absolute and relative electrochemical scales from the macroscopic and microscopic viewpoints. A microscopic definition of the absolute electrochemical potential is presented in order to enable an identical thermodynamic treatment of any species in a given phase, i.e., electrons, protons, atoms, molecules, atomic and molecular ions, and electronically excited species. We show that absolute standard chemical potentials in the mole fraction scale can be easily computed with wave function and density functional theories in conjunction with self-consistent reaction field models. Based on Boltzmann and Fermi-Dirac statistics and experimental solvation data, we estimate an internally compatible set of absolute standard chemical and electrochemical potentials of protons and solvated electrons in the molality and molarity scales in aqueous solution at 298 K and 1 atm, within an absolute error of +/-0.5 kcal/mol. This scheme enables a consistent and simultaneous description of the Gibbs energy changes and the observables (E-SHE(0) and pK(a) 's) of electron, proton, and proton-coupled electron transfer reactions in aqueous solution at 298 K and 1 atm.