Ionic hydrates, MipXq-nH2O:: Lattice energy and standard enthalpy of formation estimation

This paper is one of a series (see: Inorg. Chem. 1999, 38, 3609; J. Am. Chem. Soc. 2000, 122, 632; Inorg. Chem. 2002, 41, 2364) exploring simple approaches for the estimation of lattice energies of ionic materials, avoiding elaborate computation. Knowledge of lattice energy can lead, via thermochemical cycles, to the evaluation of the underlying thermodynamics involving the preparation and subsequent reactions of inorganic materials. A simple and easy to use equation for the estimation of the lattice energy of hydrate salts, U-POT(MpXq.nH(2)O) (and therefore for solvated salts, MpXq.nS, in general), using either the density or volume of the hydrate, or of another hydrate, or of the parent anhydrous salt or the volumes of the individual ions, is derived from first principles. The equation effectively determines the hydrate lattice energy, U-POT(MpXq.nH(2)O), from a knowledge of the (estimated) lattice energy, U-POT(MpXq), of the parent salt by the addition of ntheta(U) where theta(U)(H2O)/kJ mol(-1) = 54.3 and n is the number of water molecules. The average volume of the water molecule of hydration, V-m(H2O)/nm(3) = 0.0245, has been determined from data on a large series of hydrates by plotting hydrate/parent salt volume differences against n. The enthalpy of incorporation of a gaseous water molecule into the structure of an ionic hydrate, [Delta(1)Hdegrees (MpXq. nH(2)O,s) - Delta(1)Hdegrees (MpXq,s) - nDelta(f)Hdegrees (H2O,g)], is shown to be a constant, -56.8 kJ (mol of H2O)(-1). The physical implications with regard to incorporation of the water into various types of solid-state structures are considered. Examples are given of the use of the derived hydrate lattice energy equation, Standard enthalpies of formation of a number of hydrates are thereby predicted.