Molar volumes of metal complex ions in water

Part 2. Hexahalogeno, hexacyano and tris(ethane-1,2-dioate) complexes

Abstract

The partial molar volumes at infinite dilution in water, V̄°, of [MB₆]^z− have been determined at 25 °C and are discussed, together with the V̄° of [MB₆]^z+ reported earlier. M is the metal ion; 1 ⩽ z ⩽ 4; A is F⁻, Cl⁻, CN⁻ or alkanedioato ion/2; B is NH₃ or diamine/2. The intrinsic volumes of [ML₆]^{z ±} , V_cav(ML₆), were obtained from V̄° − kz², where L is A or B, kz² is the electrostatic effect of charge on V_cav(ML₆) and k is −7.2 cm³ mol⁻¹ for [MF₆]^z− and −5.0 cm³ mol⁻¹ for other [ML₆]^{z ±} . Linear relationships are observed between V_ar(ML₆) and r_MX which change over a small range for [ML₆]^{z ±} having an identical L, r_MX being the bond distance between M and the coordination atoms X. dV_cav(ML₆)/dr_MX is independent of the magnitude of V_cav(ML₆) and increases as r_MX increases. These facts are explained by using the model of the MX₆ core where the sphere M* (radius r_M^*) is overlapped by six spheres of X (radii r_X) whose centres are at a distance r_MX from the centre of M*. Assuming that r_M^* = (r_MX + r_X)cos θ, a self-consistent set of r_M^* and θ is determined from the experimental value of dV_cav(ML₆)/dr_MX on the basis of scaled particle theory (SPT). θ is the angle between the MX bond and the centres of solvent water molecules (as spheres) which are nearest to M and in contact with X. Thus V_cav(ML₆) is given by

V_cav(ML₆) = V_cav(M_sphere^*) + 6V_cav(X_seg) + 6V_cav(L_excX)

where V_cav(M_sphere^*), V_cav(X_seg) and V_cav(L_excX) are the intrinsic volumes of M*, the segment of X which does not overlap with M* and the ligand excluding the X atom, respectively. It is found that all plots of V_cav(ML₆) vs. r_M^* for [ML₆]^{z ±} parallel the plot of V_cav(M_sphere^*) calculated by SPT, vs. r_M^*. A very similar relationship is observed for MO₄^z− using the MX₄ model.