U2.3 · Structure of Ionic SolidsPractice · 离子晶体的结构

All four have charges of +1 and −1; only the anion size changes. By Coulomb’s law, E ∝ q₁q₂/r: a larger anion means a larger separation r, weaker attraction, less energy to break up the lattice, and a lower melting point (lattice energies: NaF 923, NaI 704 kJ/mol). Ionic solids contain no molecules, so intermolecular forces don’t apply.

Compare q₁q₂/r using Coulomb’s law (r = sum of the ionic radii in pm; values × 1000): $\ce{LiF}$: 1 ÷ (76 + 133) = 4.78; $\ce{MgO}$: 4 ÷ (72 + 140) = 18.9; $\ce{BaO}$: 4 ÷ (135 + 140) = 14.5; $\ce{KCl}$: 1 ÷ (138 + 181) = 3.13. Charge first: MgO and BaO have a charge product of 4, far above 1 for LiF and KCl. Then size: $\ce{Mg^2+}$ is much smaller than $\ce{Ba^2+}$. So MgO is largest (measured 3791 kJ/mol).

In an ionic crystal, cations and anions alternate, so each ion is surrounded by oppositely charged ions. If a force shifts one layer by one position, cations line up with cations and anions with anions, and the strong repulsion cracks the crystal along that plane. In a metal the cations sit in an electron sea that still holds them after the layers slide, so the metal bends. Ionic bonds aren’t weak, and the electrons in an ionic solid aren’t delocalized.

CaO: q₁q₂/r = (2 × 2) ÷ (100 + 140) = 4 ÷ 240. KCl: (1 × 1) ÷ (138 + 181) = 1 ÷ 319. Ratio = (4 ÷ 240) ÷ (1 ÷ 319) = 4 × 319 ÷ 240 = 5.32. The charges contribute a factor of 4, and the smaller ions about 1.3 more.

All three have the same charges, and the anion radii are $\ce{Cl-}$ 181 pm < $\ce{Br-}$ 196 pm < $\ce{I-}$ 220 pm, so NaBr’s lattice energy should fall between NaI and NaCl (704–786 kJ/mol). The measured value is 747 kJ/mol. 820 is above NaCl and 680 is below NaI; 1500 kJ/mol is far beyond any sodium halide, whose ions carry only +1 and −1.

Equal x values mean equal distances between ions, so compare the y values there. Near x ≈ 4.2, the MX point is about 947 kJ/mol and the MO point about 3449 kJ/mol, about 4 times as large. Coulomb’s law, E ∝ q₊q₋/r, says that at the same distance only the charge product differs: (+2)(−2) for MO versus (+1)(−1) for MX. Ion size is already on the x axis, and an MO formula unit has only 2 ions.

From upper right to lower left the points are NaF, NaCl, NaBr, and NaI: the smaller the lattice energy, the less attraction there is to overcome on melting, and the lower the melting point. All four have the same charges (+1 and −1); only the anion size differs. I⁻ (220 pm) is the largest, so the ions are farthest apart and the Coulombic attraction is weakest. Every halide ion has a 1− charge, and I is the least electronegative halogen.