From definition of pH is known that an activity of hydrogen ions is 10^(-pH). The activity of substance is activity coeficient multiplied by physical concentration (in units "mol/mol").
So if we assume that behind all activity of hydrogen ion in water solution is hydronium (H3O+) with activity coeficient γ then the concentration of hydronia in „mol/L“ should be calculated as (10‑pH/γ)*ρ/MM, where ρ is solution density and MM is molar mass of solution.
For example in solution with pH=7, γ =1, MM=18 g/mol, ρ=1000 g/L (as pure water) the concentration of H3O+ shoud be (10-7) [mol/mol] * 55.6 [mol/L] = 5.56 μmol/L ?
And in solution with pH=7.4, γ=0.73, MM=20 g/mol, ρ=1025 g/L (as blood plasma) should be (10-7.4)/0.73 [mol/mol] * 52 [mol/L] = 2.8 μmol/L ?
Are these calculations correct?
Can I assume that almost all active H+ in water solution are in form of H30+ ? Can be the pH connected this way with physical “mol/mol”-concentration of H30+ ? Are all authors talking about 40 nmol/L as equivalent of pH=7.4 wrong?