A general method is described for obtaining the relaxation times, normal coordinates and normal modes of reaction of a non-ideal chemical system. The normal modes are obtained as a set of orthonormal reactions, though the orthonormality condition is more complicated than in dilute solution. Earlier results for the properties of an orthonormal set of reactions (not necessarily the normal modes) in dilute solution hold with but slight modification in the non-ideal case. In particular, the affinity of the kth orthonormal reaction is independent of the extents of reaction of the remaining reactions and is given by -RT& where & is the extent of the kth reaction, in mol/rnol of solvent, measured from equilibrium.

The method described previously for obtaining the relaxation times, normal coordinates and normal modes of relaxation of a non-ideal chemical system at constant temperature and pressure is extended to relaxation under adiabatic conditions and/or at constant volume; in each case the normal modes of relaxation are obtained as an orthonormal set satisfying orthonorinality conditions similar to those pertaining to constant temperature and pressure. First-order perturbation theory is used for evaluating the various corrections required when the simple dilute-solution theory is used at concentrations which are too high for the theory to be strictly applicable.

The mean square length and mean square radius of gyration of 1,4′‐polysaccharides and of cis‐ and trans‐polybutadiene were calculated by an extension of the method of Eyring and Benoit, the results being expressed in terms of the degree of polymerization and of certain parameters of physical significance connected with the rotations about the various single bonds in these molecules. The calculations were based on the simplifying assumptions that no correlation exists between rotations about bonds separated by at least one pyranose ring or double bond and that the polysaccharide molecules are made up of pyranose rings in the “chair” form. The excluded volume effect was neglected throughout. The results obtained show that, if the mean square length is plotted against the degree of polymerization, n, then the deviations for small n from the limiting straight line obtained for larger n will have the form of a damped vibration, n appearing instead of the time. In certain cases, however, the results for odd and even n fall on different curves.

The dipole moments of the eight α,ω-dibromoparaffins from dibromopropane to dibromodecane together with those of n-propyl and n-butyl bromide have been determined at 25° and 64°C in benzene solution. The results obtained are in good quantitative agreement with the theory developed previously on the assumption that the flexibility of these molecules is due to independent restricted rotations about the various C–C bonds. The data obtained were insufficient for determining the form of the potential barriers restricting these rotations, but could be interpreted in terms of the usual picture of gauche-trans rotational isomerism on the assumption that the energy of a gauche isomer is 0.40±0.12 kcal/mole more than that of the corresponding trans isomer, except for the rotations of the CH2Br groups when the energy difference is somewhat less, 0.34±0.14 kcal/mole.

The relaxation times and normal modes of reaction of a chemical system in dilute solution are discussed and compared with the normal frequencies and normal modes of vibration of a polyatomic molecule. The normal modes of reaction are orthogonal and hence can be written as an orthonormal set satisfying Cvkivli/Ei = &I, where vki is the stoichiometric coefficient of the ith substance in the kth normal mode of reaction while mi is the number of moles of the ith substance, per mole of solvent, at equilibrium. The use of such an orthonormal set of reactions (not necessarily the normal modes of reaction) simplifies the thermodynamics of the system and facilitates the treatment of the effects of instantaneous temperature and pressure changes (7'-jumps and p-jumps). The application of these results to chemical relaxation shows that the use of normalized normal modes of reaction simplifies the usual equations for T-jump, p-jump, and sound-absorption experiments.