Spectrophotometric and Partition Methods of Determining Association Constants of 1 :1 Charge-Transfer Complexes

Abstract

The spectrophotometric method of determining the association constant of a complex AB when A, B, and the solvent have appreciable optical absorption is discussed, and the influence of the ratio of the concentrations of A and B examined. The formation of termolecular complexes such as A2B and of self-complexes such as A2 is found to affect the spectrophotometric method but not the partition method of determining association constants, whereas nonideality of the solutions affects both methods. The significance of the spectrophotometric method when applied to a completely general system including contact charge-transfer absorption is examined by means of Hill's statistical thermodynamic method of treating solutions. The results obtained are applied to three simple quasi-crystalline models. The experimental fact that spectrophotometric association constants are usually smaller than those determined by the partition method is shown to indicate that the attractive forces causing the formation of 1:1 complexes are probably not completely saturated in these complexes. In particular, for the extreme case in which the tendency of one side of an aromatic compound to complex formation is not affected by complex formation on its other side, it is shown that the spectrophotometric association constant would have only half the value found by the partition method. The experimental values in the literature for the association constants of a number of alkyl naphthalene-picric acid complexes are in good agreement with this view.