Let's say we have some neutral molecule A and its protonated form, A+. The pKa of molecule A is known, but we do not know the pKa of molecule A+. Can the pKa of molecule A+ be determined only knowing the pka of molecule A? For example, is there an expression that relates the pKa values of arginine together? (For reference, arginine's pKa values are are 2, 9, 12.5.)
The context of this question lies in trying to understand how the protonation state of molecule A+ will change in an inhomogeneous environment (for example, a lipid bilayer). The pKa of molecule A+ is estimated to change +2 pK units in the bilayer relative to in aqueous solution. The pKa of molecule A is known to be 7.09, but the pKa of molecule A+ is not known. How can any change in protonation state of molecule A+ be predicted given only this information?
Note that this question is NOT asking the protonation state of a molecule if we know THAT molecule's pKa and if we know how ITS pKa changes (for example, as was asked previously).