Osmometric analysis of quasi-indefinite mixed associations of the first kind

Mixed associations of the type A + B----AB, A + AB----A2B, ..., A + Ai-1 B----AiB, ... are readily analyzed by osmometric methods. The equilibrium molar concentration of A, mA, is obtained very simply from mA = meq-m0B; here meq = c/Meqn is the equilibrium molar concentration of all associating species and m0B denotes the stoichiometric or original molar concentration of B. The quantity mB can then be obtained from methods developed by Steiner. The value of the binding polynomial lambda is given by lambda = m0B/mB; lambda is a function of mA only. In principle, one can evaluate the equilibrium constants (kA,B,etc.) by fitting lambda to the appropriate polynomial in mA of degree n (n = 2, 3, ...). The binding polynomial lambda is analogous to polynomials encountered in the analysis of self-associations. By making some simple assumptions one can develop four analogs of two sequential, equal equilibrium constant (SEK) or two attenuated equilibrium constant (AK) models. With the aid of r (the number average degree of binding), g (the osmotic coefficient), lambda, as well as mA and mB, one can evaluate the equilibrium constant or constants. The methods developed here can be extended to the nonideal case.