Complexity in Acid–Base Titrations: Multimer Formation Between Phosphoric Acids and Imines

Solutions of Brønsted acids with bases in aprotic solvents are not only common model systems to study the fundamentals of proton transfer pathways but are also highly relevant to Brønsted acid catalysis. Despite their importance the light nature of the proton makes characterization of acid-base aggregates challenging. Here, we track such acid-base interactions over a broad range of relative compositions between diphenyl phosphoric acid and the base quinaldine in dichloromethane, by using a combination of dielectric relaxation and NMR spectroscopy. In contrast to what one would expect for an acid-base titration, we find strong deviations from quantitative proton transfer from the acid to the base. Even for an excess of the base, multimers consisting of one base and at least two acid molecules are formed, in addition to the occurrence of proton transfer from the acid to the base and simultaneous formation of ion pairs. For equimolar mixtures such multimers constitute about one third of all intermolecular aggregates. Quantitative analysis of our results shows that the acid-base association constant is only around six times larger than that for the acid binding to an acid-base dimer, that is, to an already protonated base. Our findings have implications for the interpretation of previous studies of reactive intermediates in organocatalysis and provide a rationale for previously observed nonlinear effects in phosphoric acid catalysis.