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Chapter 12 Solids and Modern Materials 241 12.37 Given: polonium, simple cubic structure d = 9.3 g/cm³; r = 167 pm; M = 209 g/mol Find: estimate NA Conceptual Plan: r and V(pm³) V(cm³) then d, V m then M, SC structure m = unit atom Solution: = 2r = 2 X 167 pm = 334 pm and V = = (334 X (10¹⁰ (1 cm)³ = 3.72597 X 10⁻²³ cm³ then d = Rearrange to solve for m. m = dV = 9.3 cm3 g X 3.72597 unit X cell 10⁻²³ = 3.46515 X 10⁻²² g unit cell then m = unit 1 atom cell X M Rearrange to solve for = unit 1 atom cell M = 1 atom X 209 1 mol X 3.46515 1 X 10⁻²² = 6.0 X 10²³ atoms mol Check: The units (atoms/mol) are correct. The magnitude (6 X 10²³ atoms/mol) is consistent with Avogadro's number. 12.39 (a) atomic because argon (Ar) is an atom (b) molecular because water (H₂O) is a molecule (c) ionic because potassium oxide (K₂O) is an ionic solid (d) atomic because iron (Fe) is an atom 12.41 LiCl has the highest melting point because it is the only ionic solid in the group. The other three solids are held together by intermolecular forces, while LiCl is held together by stronger coulombic interactions between the cations and anions of the crystal lattice. 12.43 (a) TiO₂ because it is an ionic solid (b) because it has a higher molar mass and therefore has stronger dispersion forces (c) Xe because it has a higher molar mass and therefore has stronger dispersion forces (d) CaO because the ions have greater charge and therefore stronger dipole-dipole interactions 12.45 The Ti atoms occupy the corner positions and the center of the unit cell: 8 corner atoms X (1/8 atom/unit cell) +1 atom in center = (1 + 1) Ti atoms/unit cell = 2 Ti atoms/unit cell. The atoms occupy four positions on the top and bottom faces and two positions inside the unit cell: 4 face-centered atoms X (1/2 atom/unit cell) +2 atoms in the interior = (2 + 2) atoms/unit cell = 40 atoms/unit cell. Therefore, there are 2 Ti atoms/unit cell and 40 atoms/unit cell; so the ratio Ti:O is 2:4, or 1:2. The formula for the compound is TiO₂. 12.47 In CsCl: The Cs atoms occupy the center of the unit cell: 1 atom in center = 1 Cs atom/unit cell. The Cl atoms occupy corner positions of the unit cell: 8 corner atoms X (1/8 atom/unit cell) = 1 atom/unit cell. Therefore, there are 1 atom/unit cell and 1 Cl atom/unit cell, so the ratio Cs:Cl is 1:1. The formula for the compound is CsCl, as expected. In BaCl₂: The Ba atoms occupy the corner positions and the face-centered positions of the unit cell: 8 corner atoms X (1/8 atom/unit cell) + 6 face-centered atoms X (1/2 atom/unit cell) = (1+3) Ba atoms/unit cell = 4 Ba atoms/unit cell. The Cl atoms occupy eight positions inside the unit cell: 8 Cl atoms/unit cell. Therefore, there are 4 Ba atoms/unit cell and 8 Cl atoms/unit cell, so the ratio Ba:Cl is 4:8, or 1:2. The formula for the compound is BaCl₂, as expected. 12.49 Cesium chloride does not have any of the listed crystal structures. Barium chloride has the fluorite crystal structure. 12.51 If all of the anions are removed, we have a face-centered cubic structure. Ceramics, Cement, and Glass 12.53 (a) B₄C is a component of a nonoxide ceramic. (b) Mg₂SiO₄ is a component of a silicate ceramic. (c) MoSi₂ is a component of a nonoxide ceramic. Copyright © 2017 Pearson Education, Inc.