Predicting the Bond Lengths

6 Geometry of Valence Compounds 6.1 Predicting the Bond Lengths 

The ionic model can be used to derive a number of theorems that apply to valence 

The first is the electroneutrality rule (12). Because the atoms of the core-and-valence-shell model are all electrically neutral and all the charges have been conserved during the derivation of the ionic model, the array of charged ions in the ionic model must also be electrically neutral. 

In a valence compound, taking the cation valences as positive and the anion valences as negative, the sum of the valences (charges) of a the atoms (ions) is zero. 

More importantly, we can use the ionic model to predict the electrostatic flux or valence of the individual bonds, and from these we can predict their lengths. If the positions of the atoms are already known, the bond flux can, in principle, be calculated using Coulomb s law, but this is computationally intensive, and as it requires a prior knowledge of the structure, the result is not a prediction. Fortunately there is a simpler approach that requires no prior knowledge of the atomic positions. AU that is required is a knowledge of the bond network, that is, which atoms are linked by bonds. 

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Predict the bond length between carbon and fluorine in 1-chloro-l-fluoroetheylene (refer to Table 9-2) and predict if there is likely to be variation from your calculations. 

We may predict the bond length in a solid by minimizing the total energy, or maximizing the of Eq. (7-3), with respect to d. Thus, to the energy per atom labelled overlap in I ig. 7-1, from Hqs. (7-1) and (7-2) we add p , which docs not depend upon d, and —, which varies asd, at least near the equilibrium... 

The carbon-carbon bond length in C2H2 is 1.20 A, that in C2H4 is 1.34 A, and that in C2H5 is 1.53 A. Near which of these values would you predict the bond length of C2 to lie Is the experimentally observed value, 1.31 A, consistent with your prediction ... 

In most cases the number of bonds in the network exceeds the number of atoms (and hence the number of equations of type 10.5) and further constraints are needed to predict the bond lengths. By analogy with Kirchhoff s laws for the solution of electrical networks, these constraints are provided by Equation 10.6, which states that the sum of bond valences is zero around any loop in the graph [30]. 

In the above example of La2Ni04, not only the valence sum rule, but also the equal valence rule is clearly violated and the network equations cannot therefore be used to predict the bond lengths however, the network equations do give a set of ideal bond lengths, i.e. the lengths that the bonds would have if it were not for the constraints imposed by the translational symmetry of the crystal. This allows us to determine the sizes of the strains that such symmetry imposes, and allows us to understand why certain compounds undergo phase transitions as the temperature is reduced, and why they sometimes adopt unusual oxidation states and stoichiometries. 

Kunz and Brown (1995) have shown that it is possible to predict the bond lengths for the d° transition metal cations in octahedral coordination using weighted network equations ... 

The size of an atomic nucleus is on the order of 10 m. If two protons were able to make a bond, what would you predict the bond length to be ... 

Barium azide is 62.04% Ba and 37.96% N. Each azide km has a net charge of 1—. (a) Determine the chemical formula of the azide ion. (b) Write three resonance structures for the azide ion. (c) Which structure is most important (d) Predict the bond lengths in the ion. 

It was also found that although no data for metal-metal bonds were used in determining the parameters rand c, the values of /7/yobtained from equation (4) for metal-metal bonds, when used in equation (2) accurately predicted the bond lengths in metals with unambiguous valences (non-transition metals). 

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