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The dissociation energy of one mole of sodium chloride is therefore

D = ( 7.88 eV ion pair ) ( 23.052 kcal 1 mol 1 eV ion pair ) = 182 kcal / mol = 760 kJ / mol .

Significance

This theoretical value of the dissociation energy of 766 kJ/mol is close to the accepted experimental value of 787 kJ/mol. Notice that for larger density, the equilibrium separation distance between ion pairs is smaller, as expected. This small separation distance drives up the force between ions and therefore the dissociation energy. The conversion at the end of the equation took advantage of the conversion factor 1 kJ = 0.239 kcal .

Check Your Understanding If the dissociation energy were larger, would that make it easier or more difficult to break the solid apart?

more difficult

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Covalent bonding in solids

Crystals can also be formed by covalent bonding. For example, covalent bonds are responsible for holding carbon atoms together in diamond crystals. The electron configuration of the carbon atom is 1 s 2 2 s 2 2 p 2 —a He core plus four valence electrons. This electron configuration is four electrons short of a full shell, so by sharing these four electrons with other carbon atoms in a covalent bond, the shells of all carbon atoms are filled. Diamond has a more complicated structure than most ionic crystals ( [link] ). Each carbon atom is the center of a regular tetrahedron, and the angle between the bonds is 110 ° . This angle is a direct consequence of the directionality of the p orbitals of carbon atoms.

Figure a shows a crystal lattice. A cube formed by dotted lines marks an area in the lattice. There are four light blue spheres, one on each diagonally opposite corner of the cube. There is a dark blue sphere in the center of the cube. All spheres are connected to each other by lines of the same length. This length is 0.154 nm. Figure b is the photograph of a diamond.
Structure of the diamond crystal. (a) The single carbon atom represented by the dark blue sphere is covalently bonded to the four carbon atoms represented by the light blue spheres. (b) Gem-quality diamonds can be cleaved along smooth planes, which gives a large number of angles that cause total internal reflection of incident light, and thus gives diamonds their prized brilliance.

Covalently bonded crystals are not as uniform as ionic crystals but are reasonably hard, difficult to melt, and are insoluble in water. For example, diamond has an extremely high melting temperature (4000 K) and is transparent to visible light. In comparison, covalently bonded tin (also known as alpha-tin, which is nonmetallic) is relatively soft, melts at 600 K, and reflects visible light. Two other important examples of covalently bonded crystals are silicon and germanium. Both of these solids are used extensively in the manufacture of diodes, transistors, and integrated circuits. We will return to these materials later in our discussion of semiconductors.

Metallic bonding in solids

As the name implies, metallic bonding is responsible for the formation of metallic crystals. The valence electrons are essentially free of the atoms and are able to move relatively easily throughout the metallic crystal. Bonding is due to the attractive forces between the positive ions and the conduction electrons. Metallic bonds are weaker than ionic or covalent bonds, with dissociation energies in the range 1 3 eV .

Summary

  • Packing structures of common ionic salts include FCC and BCC.
  • The density of a crystal is inversely related to the equilibrium constant.
  • The dissociation energy of a salt is large when the equilibrium separation distance is small.
  • The densities and equilibrium radii for common salts (FCC) are nearly the same.

Conceptual questions

Why is the equilibrium separation distance between K + and Cl different for a diatomic molecule than for solid KCl?

Each ion is in the field of multiple ions of the other opposite charge.

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Describe the difference between a face-centered cubic structure (FCC) and a body-centered cubic structure (BCC).

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In sodium chloride, how many Cl atoms are “nearest neighbors” of Na + ? How many Na + atoms are “nearest neighbors” of Cl ?

6, 6

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In cesium iodide, how many Cl atoms are “nearest neighbors” of Cs + ? How many Cs + atoms are “nearest neighbors” of Cl ?

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The NaCl crystal structure is FCC. The equilibrium spacing is r 0 = 0.282 nm . If each ion occupies a cubic volume of r 0 3 , estimate the distance between “nearest neighbor” Na + ions (center-to-center)?

0.399 nm

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Problems

The CsI crystal structure is BCC. The equilibrium spacing is approximately r 0 = 0.46 nm . If Cs + ion occupies a cubic volume of r 0 3 , what is the distance of this ion to its “nearest neighbor” I + ion?

0.65 nm

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The potential energy of a crystal is 8.10 eV /ion pair. Find the dissociation energy for four moles of the crystal.

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The measured density of a NaF crystal is 2.558 g/cm 3 . What is the equilibrium separate distance of Na + and Fl ions?

r 0 = 0.240 nm

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What value of the repulsion constant, n , gives the measured dissociation energy of 221 kcal/mole for NaF?

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Determine the dissociation energy of 12 moles of sodium chloride (NaCl). ( Hint: the repulsion constant n is approximately 8.)

2196 kcal

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The measured density of a KCl crystal is 1.984 g/cm 3 . What is the equilibrium separation distance of K + and Cl ions?

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What value of the repulsion constant, n , gives the measured dissociation energy of 171 kcal/mol for KCl?

11.5

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The measured density of a CsCl crystal is 3.988 g/cm 3 . What is the equilibrium separate distance of Cs + and Cl ions?

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Practice Key Terms 5

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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