This paper is one of a series exploring simple approaches for the estimation of lattice energy of ionic materials, avoiding elaborate computation. The readily accessible, frequently reported, and easily measurable (requiring only small quantities of inorganic material) property of density, rho(m), is related, as a rectilinear function of the form (rho(m)/M(m))(1/3), to the lattice energy U(POT) of ionic materials, where M(m) is the chemical formula mass. Dependence on the cube root is particularly advantageous because this considerably lowers the effects of any experimental errors in the density measurement used. The relationship that is developed arises from the dependence (previously reported in Jenkins, H. D. B.; Roobottom, H. K.; Passmore, J.; Glasser, L. Inorg. Chem. 1999, 38, 3609) of lattice energy on the inverse cube root of the molar volume. These latest equations have the form U(POT)/kJ mol(-1) = gamma(rho(m)/M(m))(1/3) + delta, where for the simpler salts (i.e., U(POT)/kJ mol(-1) < 5000 kJ mol(-1)), gamma and delta are coefficients dependent upon the stoichiometry of the inorganic material, and for materials for which U(POT)/kJ mol(-1) > 5000, gamma/kJ mol(-1) cm = 10(-7) AI(2IN(A))(1/3) and delta/kJ mol(-1) = 0 where A is the general electrostatic conversion factor (A = 121.4 kJ mol(-1)), I is the ionic strength = 1/2 the sum of n(i)z(i)(2), and N(A) is Avogadro's constant.
Standard absolute entropies of many inorganic materials are unknown; this precludes a full understanding of their thermodynamic stabilities. It is shown here that formula unit volume, V(m)(), can be employed for the general estimation of standard entropy, S degrees 298 values for inorganic materials of varying stoichiometry (including minerals), through a simple linear correlation between entropy and molar volume. V(m)() can be obtained from a number of possible sources, or alternatively density, rho, may be used as the source of data. The approach can also be extended to estimate entropies for hypothesized materials. The regression lines pass close to the origin, with the following formulas: For inorganic ionic salts, S degrees 298 /J K(-)(1) mol(-)(1) = 1360 (V(m)()/nm(3) formula unit(-)(1)) + 15 or = 2.258 [M/(rho/g cm(-)(3))] + 15. For ionic hydrates, S degrees 298 /J K(-)(1) mol(-)(1) = 1579 (V(m)()/nm(3) formula unit(-)(1)) + 6 or = 2.621 [M/(rho/g cm(-)(3))] + 6. For minerals, S degrees 298 /J K(-)(1) mol(-)(1) = 1262 (V(m)()/nm(3) formula unit(-)(1)) + 13 or = 2.095 [M/(rho/g cm(-)(3))] + 13. Coupled with our published procedures, which relate volume to other thermodynamic properties via lattice energy, the correlation reported here complements our development of a predictive approach to thermodynamics and ultimately permits the estimation of Gibbs energy data. Our procedures are simple, robust, and reliable and can be used by specialists and nonspecialists alike.
This chapter contains section titled: Case (i): Phase Behaviour of Normal Substances, for which: Vg ≫ Vl > Vs Prediction of General Form of Phase Diagram for Normal Substances: (Case (i)) Comparison with Experimental Phase Diagrams
An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
This chapter contains section titled: Chemical Potential, μ(real gas) for a Real (Non-Ideal) Gas. Fugacity, f Fugacity, f, Activity, a and Activity Coefficient, γ Model for a Real Gas by Correction of the Ideal Model Calculation of Fugacity, f, using the Virial Equation for a Gas at Moderate Pressures
This chapter contains section titled: Degrees of Freedom or Variance of a Thermodynamic System (F) Specification of Composition in a Mixture of Substances. Mole Fraction, x Independent and Dependent Variables The Phase Rule Application of the Phase Rule: f = c − p + 2
"Volume-based thermodynamics" (VBT) relates the thermodynamics of condensed-phase materials to their formula unit (or molecular) volumes, Vm. In order to secure the most accurate representation of these data, the volumes used are to be derived (in order of preference) from crystal structure data or from density or, in the absence of experimental data, estimated by ion-volume summation.
The structure of (NH 4 ) 2 Ge 7 O 15 recently described as being a microporous material containing rings, in which GeO 6 octahedra coexist with GeO 4 tetrahedra, is re-examined in the light of the Extended Zintl–Klemm Concept as applied to cations in oxides. The Ge [6] atoms together with the NH 4 + groups act as true cations, transferring their 6 valence electrons to the acceptor Ge 2 O 5 moiety, so converting it into the [Ge 6 O 15 ] 6− [triple-bond]3(Ψ-As 2 O 5 ) ion (where Ψ refers to a pseudo-lattice) and yielding threefold connectivity. The tetrahedral Ge network shows similarities with the Sb 2 O 3 analogue. At the same time, the Ge [6] atoms are connected to other Ge [4] atoms forming blocks that are part of a rutile-type GeO 2 structure. Such an analysis shows that both substructures (the Zintl polyanion and the rutile fragments) must be satisfied simultaneously as has already been illustrated in previous articles which considered stuffed-bixbyites [Vegas et al. (2009). Acta Cryst. B 65 , 11–21] as well as the compound FeLiPO 4 [Vegas (2011). Struct. Bond. 138 , 67–91]. This new insight conforms well to previous (differential thermal analysis) DTA–TGA (thermogravimetric analysis) experiments [Cascales et al. (1998). Angew. Chem. Int. Ed . 37 , 129–131], which show endothermic loss of NH 3 and H 2 O to give rise to the metastable structure Ge 7 O 14 , which further collapses to the rutile-type GeO 2 structure. We analyze the stability change in terms of ionic strength, I , and so provide a means of rationalizing the driving force behind this concept capable of explaining the atomic arrangements found in these types of crystal structures. Although the concept was formulated in 2003, later than the publication of the germanate structure, it was not used or else ignored by colleagues who solved this crystal structure.
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