Equilibrium distribution of polysulfide ions in aqueous solutions at 25°C: A new approach for the study of polysulfides' equilibria

A new approach based on rapid, chemical derivatization in a single phase was used to determine the disproportionation constants and the underlying thermodynamics of inorganic polysulfides in aqueous solutions. This method resolves the dispute over the existence of hexasulfide in aqueous solutions and establishes the presence of even higher polysulfide chains in water. The Gibbs free energies of formation (G_Sn^{o 2-}) for the polysulfide species are 77.4, 71.6, 67.4, 66.1, 67.2, 70.5, and 73.6 kJ/mol for n = 2-8, respectively. Our approach is based on single phase, fast methylation of polysulfides with methyl trifluoromethane-sulfonate (methyl triflate) and subsequent determination of the dimethylpolysulfides by HPLC. Two independent methods were used in order to confirm quantitative equivalence between the observed distribution of dimethylpolysulfides and the polysulfide distribution in the water: (i) Kinetic studies of each competing reaction step showed that the kinetics of the derivatization are faster than each of the competing reactions that may lead to disproportionation and deviation of the observed distribution of dimethylpolysulfides from that of the aqueous polysulfides. (ii) Determination of isotope mixing during the derivatization of a mixture of two solutions, one containing polysulfide of natural isotopic distribution and the second containing ³⁴S-rich polysulfide revealed that polysulfide mixing during derivatization is rather low. The systematic error due to redistribution of pentasulfide during derivatization is 3% based on isotope dilution tests and less than 5% of total zero-valent sulfur based on kinetic considerations.