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Ch.9 - Chemical Bonding I: The Lewis Model
Tro - Chemistry: A Molecular Approach 4th Edition
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook
All textbooksTro 4th EditionCh.9 - Chemical Bonding I: The Lewis ModelProblem 47
Chapter 9, Problem 47

Use the Born–Haber cycle and data from Appendix IIB, Chapter 8 and this chapter to calculate the lattice energy of KCl. (ΔHsub for potassium is 89.0 kJ/mol.)

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Identify the steps involved in the Born–Haber cycle for KCl, which include sublimation of potassium, ionization of potassium, dissociation of chlorine, electron affinity of chlorine, and formation of KCl from gaseous ions.
Write the equation for the sublimation of potassium: \( \text{K(s)} \rightarrow \text{K(g)} \) with \( \Delta H_{\text{sub}} = 89.0 \text{ kJ/mol} \).
Write the equation for the ionization of gaseous potassium: \( \text{K(g)} \rightarrow \text{K}^+(g) + e^- \) and use the ionization energy from the appendix.
Write the equation for the dissociation of chlorine: \( \frac{1}{2} \text{Cl}_2(g) \rightarrow \text{Cl}(g) \) and use the bond dissociation energy from the appendix.
Write the equation for the electron affinity of chlorine: \( \text{Cl}(g) + e^- \rightarrow \text{Cl}^-(g) \) and use the electron affinity value from the appendix.

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Key Concepts

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

Born-Haber Cycle

The Born-Haber cycle is a thermodynamic cycle that relates the lattice energy of an ionic compound to other measurable quantities. It involves several steps, including the sublimation of the metal, ionization energy, electron affinity, and the formation of the ionic solid from gaseous ions. This cycle allows for the calculation of lattice energy by applying Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step.
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Lattice Energy

Lattice energy is the energy released when gaseous ions combine to form an ionic solid, or the energy required to separate one mole of an ionic solid into its gaseous ions. 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 in higher melting points and greater stability of the compound.
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Enthalpy Changes

Enthalpy changes refer to the heat content changes during a chemical reaction or phase change at constant pressure. In the context of the Born-Haber cycle, various enthalpy changes such as sublimation, ionization energy, and electron affinity are used to calculate the overall lattice energy. Understanding these individual enthalpy changes is crucial for accurately applying the Born-Haber cycle to determine the lattice energy of ionic compounds.
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