Use the Born–Haber cycle and data from Appendix IIB, Chapter 8 and this chapter to calculate the lattice energy of KCl. (ΔH_sub 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.

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.

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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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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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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Use the Born–Haber cycle and data from Appendix IIB and Table 9.3 to calculate the lattice energy of CaO. (ΔH_sub for calcium is 178 kJ/mol; IE₁ and IE₂ for calcium are 590 kJ/mol and 1145 kJ/mol, respectively; EA₁ and EA₂ for O are -141 kJ/mol and 744 kJ/mol, respectively.)

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Textbook Question

Write the Lewis structure for each molecule. a. PH₃ b. SCl₂ c. HI

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.)

Verified video answer for a similar problem:

Key Concepts

Born-Haber Cycle

Lattice Energy

Enthalpy Changes

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