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Chapter 9: Problem 22

Explain how the lattice energy of an ionic compound such as \(\mathrm{KCl}\) can be determined using the Born-Haber cycle. On what law is this procedure based?

Short Answer

Expert verified
The lattice energy of KCl can be calculated using the Born-Haber cycle which involves the sum of the enthalpies for sublimation of potassium, ionization of potassium, dissociation of chlorine, electron affinity of chlorine, and formation of KCl. This process is based on Hess's Law.

Step by step solution

01

Understand the Born-Haber Cycle

The Born-Haber cycle is a hypothetical series of energy-conserving (enthalpy changing) steps that can be used to calculate the lattice energy of an ionic compound. The cycle applies Hess鈥檚 law, considering the enthalpy change of a sequence of reactions wherein the total change in energy is equal to the sum of energy changes for each steps.
02

Breaking Down The Components

For KCl, the Born-Haber cycle includes the following steps: 1) Sublimation of Potassium: Solid potassium is converted to gas. 2) Ionization of Potassium: Potassium gas is converted to \(K^{+}\) ion. 3) Dissociation of Chlorine: \(Cl_{2}\) is converted to 2Cl. 4) Electron Affinity of Chlorine: \(Cl\) gas gains an electron to become \(Cl^{-}\) ion. 5) Formation of KCl: \(K^{+}\) and \(Cl^{-}\) ions combine to form solid \(KCl\).
03

Calculation of Lattice Energy

The lattice energy can be determined by the algebraic sum of enthalpy changes of these steps, which should equal the enthalpy change of formation of \(KCl\). It is also the energy required to separate one mole of a solid ionic compound into gaseous constituent ions.
04

Underlying Law

The Born-Haber cycle is based on Hess's Law, which states that the total enthalpy change for the reaction is the sum of all changes regardless of the number of stages or steps.

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Most popular questions from this chapter

Most organic acids can be represented as \(\mathrm{RCOOH}\), in which \(\mathrm{COOH}\) is the carboxyl group and \(\mathrm{R}\) is the rest of the molecule. (For example, \(\mathrm{R}\) is \(\mathrm{CH}_{3}\) in acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\).) (a) Draw a Lewis structure of the carboxyl group. (b) Upon ionization, the carboxyl group is converted to the carboxylate group, \(\mathrm{COO}^{-}\). Draw resonance structures of the carboxylate group.

Write Lewis structures for \(\mathrm{SeF}_{4}\) and \(\mathrm{SeF}_{6}\). Is the octet rule satisfied for Se?

Because fluorine has seven valence electrons \(\left(2 s^{2} 2 p^{5}\right),\) seven covalent bonds in principle could form around the atom. Such a compound might be \(\mathrm{FH}_{7}\) or \(\mathrm{FCl}_{7}\). These compounds have never been prepared. Why?

Explain what an ionic bond is.

List these bonds in order of increasing ionic character: the lithium-to- fluorine bond in \(\mathrm{LiF},\) the potassium-to-oxygen bond in \(\mathrm{K}_{2} \mathrm{O},\) the nitrogen-tonitrogen bond in \(\mathrm{N}_{2}\), the sulfur-to-oxygen bond in \(\mathrm{SO}_{2}\), the chlorine-to-fluorine bond in \(\mathrm{ClF}_{3}\).
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