Molar volumes of metal complex ions in water Part 2.Hexahalogeno, hexacyano and tris(ethane-1,2-dioate) complexes

The partial molar volumes at infinite dilution in water, (V) over bar degrees, of [MB6](z-) have been determined at 25 degrees C and are discussed, together with the (V) over bar degrees of [MB6](z+) reported earlier. M is the metal ion; 1 less than or equal to z less than or equal to 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 (V) over bar degrees - kz(2), where L is A or B, kz(2) is the electrostatic effect of charge on V-cav(ML6) and k is -7.2 cm(3) mol(-1) for [MF6](z-) and -5.0 cm(3) 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 theta, a self-consistent set of r(M*) and theta is determined from the experimental value of dV(cav)(ML6)/dr(MX) on the basis of scaled particle theory (SPT). a 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 MO4z- using the MX4 model.