Relationship between triple ion formation constants and the salt concentration of the minimum in the conductometric curves in low-permittivity solvents

Conductivities of a number of uni-univalent salts, including tetrabutylammonium and lithium nitrophenolates, were measured at 25.0 degrees C in low-permittivity solvents such as tetrahydrofuran (THF, epsilon(r) = 7.58), 1,2-dimethoxyethane (DME, 7.2), chloroform (4.8), and ethyl acetate (6.0). Minima in the conductometric curves (Lambda-C-1/2) were observed for concentrations which were dependent upon both the salt and the solvent, C-min = 1.73 x 10(-4) mol dm(-3) for 2,4-(NO2)(2)C10H5OLi (lithium 2,4-dinitro-1-naphtholate) in THF and 2.56 x 10(-2) mol dm(-3) for LiPic (lithium picrate) in DME. The observed molar conductivities including C-min could be completely explained by the formation of ion pairs (M+ + X- reversible arrow MX, K-1), ''symmetrical'' triple ions (2M(+) + X- reversible arrow M2X-, K-2; M+ + 2X(-) MX2-, K-3; K-2 = K-3), and (in some cases) additional formation of quadrupoles (2MX reversible arrow M2X2,K-41). A linear relationship (the slope of -1) between the triple ion formation constants (log(K-2/K-1)) and the salt concentrations at the minimum (log C-min) was given for all the salts in the various solvents, except for some systems in which a distinct formation of quadrupole takes place, e.g., LiNO3 in DME (K-1 = 3.16 x 10(10), K-2 = 4.5 x 10(13), and K-41 = 35). The formation of triple ions might be attributed to the ion sizes in solutions in which Coulombic interactions were the only main forces between ions (R4N+... X-). However, coordination (or covalent) bonding forces as well as Coulombic forces had to be considered for the lithium salts except for LiClO4 and LiBF4). Gutmann's donor and acceptor numbers of solvents (and not the permittivity) accounted for the larger difference of C-min, of lithium salts in THF and DME. In mixed solvents of THF and 2-ethyl-1-hexanol (epsilon(r) = 7.58), the C-min values of LiNO3 and 2,4-(NO2)(2)C10H5OLi increased with increasing contents of the hexanol, whereas the C-min values of LiClO4 and Bu4NX (X- = NO3-, 2,4-(NO2)(2)C10H5O-, and ClO4-) remained constant for 0-30 vol % hexanol added to THF. The positive shifts in C-min were explained quantitatively by the decrease in triple ion formation constants and/or by an increase in the quadrupole formation constants.