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Chapter08.June02 - Chapter 8 Solid State Energetics The...

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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
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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 . 0 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. U o = 1389 o r ) 748 . 1 )( 1 )( 1 ( - + - 5 . 11 1 1 = - 632 kJ/mol; Solving for r o yields a value of 3.51Å r(Fr + ) + r(Cl - ) = r(Fr + ) + 1.67 = 3.51Å; therefore, r(Fr + ) = 1.84Å *8.5. (a) r(Bk 4+ ) = 0.97 = 0.77 which is consistent with a coordination number of 8 and r(O 2- ) 1.26 a fluorite lattice.
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