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Unformatted text preview: 48 Chapter 8 Solid State Energetics The sections and subsections in this chapter are listed below. 8.1 Lattice Energy: A Theoretical Evaluation 8.2 Lattice Energy: Thermodynamic Cycles Electron Affinities Heats of Formation for Unknown Compounds Thermochemical Radii 8.3 Lattices Energies and Ionic Radii: Connecting Crystal Field Effects with Solid State Energetics Chapter 8 Objectives You should be able to • define and discuss both the electrostatic and short-range repulsive forces that contribute to the overall lattice energy of an ionic compound • derive and discuss the components of the Born-Landé equation for the lattice energy of an ionic compound • discuss the role of charge density as a factor in determining the magnitude of the lattice energy of a compound • discuss the role of Kapustinskii equation in estimating the lattice energy of an ionic compound • write a Born-Haber thermodynamic cycle that can be used to derive a value of the lattice energy of an ionic compound • discuss the conditions under which significant covalent contributions to lattice energy would be expected • use thermodynamic cycles and the Born-Landé or Kapustinskii equations to estimate values of electron affinity, heats of formation for unknown compounds, and thermochemical radii • account qualitatively and quantitatively for the role of crystal field effects in determining the cationic radii and lattice energies of transition metal salts 49 Solutions to Odd-Numbered Problems 8.1. (a) r(Rb + ) = 1.66 = 0.91 r(Br- ) 1.82 This radius ratio is consistent with a coordination number of eight. Therefore, a reasonable * unit cell would be that of cesium chloride, that is, a simple cubic array of bromide ions with rubidium cations in the center of each cell. A sketch of such a cell is found at right. ( * The actual unit cell of RbBr is rock salt, but CsCl is a reasonable structure nevertheless for this compound.) (b) U o = 1389 o- r M Z Z + - n 1 1 = 1389 1.82) (1.66 ) 763 . 1 )( 1 )( 1 ( +- + - 10 1 1 = - 633 kJ/mol 8.3. There are two reasonable approaches to this problem. (1) Since we do not know the crystal structure, we can simply use the Kapustinskii Equation and solve for r(Fr + ).- 632 kJ/mol = 1202 o r ) 1 )( 1 )( 2 (- + - o r 345 . 1 Solving for r o yields a value of 3.42Å; 3.42Å = r(Fr + ) + r(Cl- ) = r(Fr + ) + 1.67 Therefore, r(Fr + ) = 1.75Å (2) A second approach: since all the other alkali halides assume the rock salt structure, it would be logical to assume that FrCl does also. In that case we can use the Born-Landé Equation with n = 14 for Fr + , which has a [Rn] shell (the value of 14 was obtained by extrapolating from the data given in Table 8.2), n = 9 for Cl- which has an [Ar] shell. The average value of n is 11.5....
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This note was uploaded on 04/06/2010 for the course CHEMISTRY CHM 3610 taught by Professor Dr.kavallieratos during the Spring '10 term at FIU.
- Spring '10