scan0013 - lattice enthalpy(AHlattice is the amount of heat...

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Unformatted text preview: lattice enthalpy (AHlattice) is the amount of heat at constant pressure necessary to separate the solid ionic crystal into its gaseous ions. The good news is that these two values are just about the same, though opposite in sign; lattice energy de- scribes a release in energy (Blame = “—”), whereas lattice enthalpy describes energy that is absorbed (AHIat-tjce = “+”). A Hattice g _ E lattice The magnitude of the lattice energies or lattice enthalpies increases as the charges on the ions increase, as shown in Table 8.3. In the series SCCl3, CaClz, and KCl, the charges decrease on the cation: (+3), (+2), and (+1), respectively, with a decrease in lattice enthalpies in the order ScC13 (4874 kl/mol), CaClz (2223 kI/mol), KCl (701 kI/mol). Coulomb’s law also indicates that as the distance between the ions decreases, the lattice enthalpies increase. Evidence of this is found by comparing LiBr (788 kI/mol), LiCl (834 kI/mol), and LiF (1030 kl/mol). The charges on the ions are the same in this series of compounds, but the size of the anion decreases from bromide to fluoride. Because the bromide ion (Br‘) is larger than Cl‘ or F7, LiBr has the smallest lattice enthalpy. In general, lattice enthalpies are greatest for ionic compounds that are made up of small, highly charged particles. Let’s revisit our section-opening question of why fluoride in our toothpaste is important. As we noted then, the replacement of a hydroxy group in the hydrox- yapatite, Ca5(PO4)3(OH), mineral that makes up our teeth gives rise to a new mineral called fluorapatite, Ca5(PO4)3(OH,F). Because F7 is smaller than OH‘, Coulomb’s law dictates that the force of attraction between the Ca2+ and the F’ Should be greater than that between Ca2+ and OH’ in this mineral. This is the case with, for example, nearly all binary ionic salts of fluoride compared to the metal hydroxide, so that the lattice enthalpy of, for example, silver fluoride (AgF), which is 953 kI/mol, is greater than the lattice enthalpy of silver hydroxide (AgOH), 918 kl/mol. It is therefore reasonable to consider that the lattice en— thalpy of fluorapatite is greater than that of hydroxyapatite. This is one of several reasons why fluorapatite is more stable than hydroxyapatite when bathed in our saliva—and more resistant to the formation of cavities. Fluorapatite formation is even more compelling when fluoride is present in our mouths from municipal water fluoridation or dental treatments; this is related to a concept called chemi— cal equilibrium, which we will consider in Chapters 16—18. EXERCISE 8.4 Predicting Lattice Enthalpies Use the relationship of ionic sizes to predict whether calcium fluoride (found in toothpaste) or calcium chloride (sidewalk salt) has the greater lattice enthalpy. Also predict whether aluminum chloride or sodium chloride has the greater lattice enthalpy. First Thoughts Comparing the lattice enthalpies of two ionic compounds can be accomplished by realizing that the magnitude of the lattice enthalpy is inversely proportional to the distance between the individual ions and directly proportional to the size of the nu— clear charge on the ions. The distance between the ions is directly related to the individual ionic radii. Solution Calcium fluoride (Can) and calcium chloride (CaClz) differ in the size of the anion bound to the calcium cation. From the discussion of atomic size, we noted that fluorine is smaller than chlorine. Moreover, the radius for both anions also follows this trend; fluoride is a smaller anion than chloride. Coulomb’s law says that Can 8.2 lonicBondingi 315 ...
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