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 °C in low-permittivity solvents such as tetrahydrofuran (THF, ε r = 7.58), 1,2-dimethoxyethane (DME, 7.2), chloroform (4.8), and ethyl acetate (6.0). Minima in the conductometric curves (Λ− C 1/2 ) were observed for concentrations which were dependent upon both the salt and the solvent, C min = 1.73 × 10 -4 mol dm -3 for 2,4-(NO 2 ) 2 C 10 H 5 OLi (lithium 2,4-dinitro-1-naphtholate) in THF and 2.56 × 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 - ⇌ MX, K 1 ), “symmetrical” triple ions (2M + + X - ⇌ M 2 X -, K 2; M + + 2X - ⇌ MX 2 -, K 3; K 2 = K 3 ), and (in some cases) additional formation of quadrupoles (2MX ⇌ M 2 X 2, 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., LiNO 3 in DME ( K 1 = 3.16 × 10 10, K 2 = 4.5 × 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 (R 4 N + ···X - ). However, coordination (or covalent) bonding forces as well as Coulombic forces had to be considered for the lithium salts except for LiClO 4 and LiBF 4 ). 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 (ε r = 7.58), the C min values of LiNO 3 and 2,4-(NO 2 ) 2 C 10 H 5 OLi increased with increasing contents of the hexanol, whereas the C min values of LiClO 4 and Bu 4 NX (X - = NO 3 -, 2,4-(NO 2 ) 2 C 10 H 5 O -, and ClO 4 - ) 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.