Investigation of the composition and formation constant of molecular complexes.

It has been the purpose of the present paper to investigate and explore the conditions under which the linear relation between Delta/C(D) (0) and Delta in the Hanna-Ashbaugh-Foster-Fyfe equation for the evaluation of equilibrium constants holds, (C(D) (0) is initial concentration of a donor and Delta is the observed chemical shift relative to the chemical shift of the acceptor) to obtain the equation representing the exact linear relation between Delta/C(D) (0) and Delta, when the linear relation between Delta/C(D) (0) and Delta holds, and to discuss how to use the Job method in nuclear magnetic resonance measurements to determine the stoichiometry of molecular complexes. We have found that the conventional belief that C(D) (0) should always be chosen to be much greater than C(A) (0) (initial concentration of acceptor) is not necessarily always true and the exact linear relation between Delta/C(D) (0) and Delta is represented by the equation Delta/C(D) (0) = K(1)Delta(0)/(1 + K(1)C(A) (0)) - K(1)Delta/(1 + K(1)C(A) (0))(2), where K(1) is the formation constant of the complex. It is shown that in the Job method of nuclear magnetic resonance measurements one has to plot DeltaC(A) (0) against the mole fraction, and the mole fraction at the maximum should give us the composition of the complex. Theoretical results have been verified experimentally on the weak interaction between naphthalene and methyl iodide.