Ch.10 - Chemical Bonding I: The Lewis Model

Problem 47

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Chapter 10, Problem 47

The lattice energy of CsF is -744 kJ/mol, whereas that of BaO is -3029 kJ/mol. Explain this large difference in lattice energy.

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Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. It is influenced by the charges of the ions and the distance between them.

CsF consists of Cs^+ and F^- ions, while BaO consists of Ba^2+ and O^2- ions. The charges on the ions in BaO are higher than those in CsF.

According to Coulomb's Law, the lattice energy is directly proportional to the product of the charges of the ions. Therefore, the higher charges in BaO result in a greater lattice energy.

The size of the ions also affects lattice energy. Smaller ions can get closer together, increasing the lattice energy. Ba^2+ and O^2- are smaller than Cs^+ and F^-, contributing to the higher lattice energy of BaO.

In summary, the large difference in lattice energy between CsF and BaO is due to the higher ionic charges and smaller ionic radii in BaO, leading to stronger electrostatic attractions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Lattice Energy

Lattice energy is the amount of energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. Higher lattice energy indicates stronger ionic bonds, which typically results from greater charges on the ions and smaller ionic radii.

Ionic Charge

The charge of the ions significantly influences lattice energy. In the case of CsF, cesium (Cs) has a +1 charge and fluoride (F) has a -1 charge, resulting in a relatively lower lattice energy. In contrast, BaO consists of barium (Ba) with a +2 charge and oxide (O) with a -2 charge, leading to a stronger electrostatic attraction and thus a higher lattice energy.

Ionic Radius

The size of the ions, or ionic radius, also affects lattice energy. Smaller ions can pack more closely together, increasing the electrostatic attraction between them. In BaO, the smaller size of the oxide ion compared to the fluoride ion in CsF contributes to the larger lattice energy, as the closer proximity of the ions enhances the overall stability of the ionic lattice.

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Ionic Radius

Related Practice

Use Lewis symbols to determine the formula for the compound that forms between each pair of elements. a. Mg and S b. Sr and Br c. K and Se d. Al and S

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Use Lewis symbols to determine the formula for the compound that forms between each pair of elements. a. Sr and P b. Ba and S c. Sr and Se d. Rb and I

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Rubidium iodide has a lattice energy of -617 kJ/mol, while potassium bromide has a lattice energy of -671 kJ/mol. Why is the lattice energy of potassium bromide more exothermic than the lattice energy of rubidium iodide?

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Textbook Question

Arrange these compounds in order of increasing magnitude of lattice energy: CaO, NaBr, CsI, BaS.

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Textbook Question

Use the Born–Haber cycle and data from Appendix IIB, Chapter 9 and this chapter to calculate the lattice energy of LiBr. (ΔHsub for lithium is 138 kJ>mol.)

Textbook Question

Use the Born–Haber cycle and data from Appendix IIB and Table 10.3 to calculate the lattice energy of MgO. (ΔH_sub for magnesium is 137 kJ/mol; IE₁ and IE₂ for magnesium are 738 kJ/mol and 1450 kJ/mol, respectively; EA₁ and EA₂ for O are −141 kJ/mol and 744 kJ/mol, respectively.)