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8 Chemical Bonding Solutions to Exercises 8.79 (a) Lattice energy is proportional to Q₁Q₂/d. For each of these compounds, is the same. The anion H⁻ is present in each compound, but the ionic radius of the cation increases going from Be to Ba. Thus, the value of d (the cation-anion separation) increases and the ratio Q₁Q₂/d decreases. This is reflected in the decrease in lattice energy going from BeH₂ to BaH₂. (b) Again, Q₁Q₂ for ZnH₂ is the same as that for the other compounds in the series and the anion is H⁻. The lattice energy of ZnH₂, 2870 kJ, is closest to that of MgH₂, 2791 kJ. The ionic radius of Zn²⁺ is similar to that of Mg²⁺. 8.80 (a) Lattice Lattice Compound Energy (kJ) Compound Energy (kJ) NaCl 788 56 kJ LiCl 834 55 kJ 106 kJ NaBr 732 104 kJ LiBr 779 Na I 682 Li I 730 The difference in lattice energy between LiCl and Lil is 104 kJ. The difference between NaCl and Nal is 106 kJ; the difference between NaCl and NaBr is 56 kJ, or 53% of the difference between NaCl and Nal. Applying this relationship to the Li salts, 0.53(104 kJ) = 55 kJ difference between LiCl and LiBr. The approximate lattice energy of LiBr is (834 - 55) kJ = 779 kJ. (b) Lattice Lattice Compound Energy (kJ) Compound Energy (kJ) NaCl 788 56 kJ CsCl 657 30 kJ 106 kJ NaBr 732 57 kJ CsBr 627 Na I 682 Cs I 600 By analogy to the Na salts, the difference between lattice energies of CsCl and CsBr should be approximately 53% of the difference between CsCl and Csl. The lattice energy of CsBr is approximately 627 kJ. (c) Lattice Lattice Compound Energy (kJ) Compound Energy (kJ) MgO 3795 381 kJ MgCl₂ 2326 131 kJ 578 kJ CaO 3414 199 kJ CaCl₂ 2195 SrO 3217 SrCl₂ 2127 By analogy to the oxides, the difference between the lattice energies of MgCl₂ and CaCl₂ should be approximately 66% of the difference between MgCl₂ and SrCl₂. That is, 0.66(199 kJ) = 131 kJ. The lattice of CaCl₂ is approximately (2326 131) kJ = 2195 kJ. 8.81 The charge on M is likely to be 3+. According to Table 8.2, the lattice energy for an ionic compound with the general formula MX and a charge of 2+ on the metal will be in the range of 3-4 X 10³ kJ/mol. The charge on M must be greater than 2+. ScN, where the charge on Sc is 3+, has a lattice energy of 7547 kJ/mol. It is reasonable to conclude that the charge on M is 3+, and the M-X distance is greater than the Sc-N distance. 8.82 E = (1.14+1.26) 4(1.60 10⁻¹⁹ 10⁻¹⁰ = -3.836 10⁻¹⁸ = -3.84 10⁻¹⁸ J On a molar basis: (-3.836 J)(6.022 = -2.310 10⁶ J = -2310 kJ 215