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27.03.2014

The energy released during the formation of a solid ionic compound from its constituent gaseous ions.
Lattice energy mainly depends upon the charge of ions and inter ionic distance in a crystal lattice.
It’s not possible to calculate the lattice energy directly from formation reaction of ionic solid or from their decomposition. Lattice energy of calcium oxide can be calculated by using Born-Heber cycle based on Hess’s Law. Like calcium oxide the lattice energy of potassium chloride can also be calculated by using Born-Haber cycle. This is a€?Lattice Energies in Ionic Solidsa€?, section 8.3 from the book Principles of General Chemistry (v. This content was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book. PDF copies of this book were generated using Prince, a great tool for making PDFs out of HTML and CSS. For more information on the source of this book, or why it is available for free, please see the project's home page. DonorsChoose.org helps people like you help teachers fund their classroom projects, from art supplies to books to calculators.
To understand the relationship between the lattice energy and physical properties of an ionic compound. Recall from Chapter 2 "Molecules, Ions, and Chemical Formulas" that the reaction of a metal with a nonmetal usually produces an ionic compound; that is, electrons are transferred from the metal (the reductant) to the nonmetal (the oxidant). U, which is always a positive number, represents the amount of energy required to dissociate 1 mol of an ionic solid into the gaseous ions. Because the lattice energy depends on the product of the charges of the ions, a salt having a metal cation with a +2 charge (M2+) and a nonmetal anion with a a?’2 charge (X2a?’) will have a lattice energy four times greater than one with M+ and Xa?’, assuming the ions are of comparable size (and have similar internuclear distances). Because lattice energy is inversely related to the internuclear distance, it is also inversely proportional to the size of the ions. Using Equation 8.4, predict the order of the lattice energies based on the charges on the ions.
The magnitude of the forces that hold an ionic substance together has a dramatic effect on many of its properties. The melting points follow the same trend as the magnitude of the lattice energies in Figure 8.2 "A Plot of Lattice Energy versus the Identity of the Halide for the Lithium, Sodium, and Potassium Halides". In addition to determining melting point and hardness, lattice energies affect the solubilities of ionic substances in water. In principle, lattice energies could be measured by combining gaseous cations and anions to form an ionic solid and then measuring the heat evolved. Because enthalpy is a state function, the overall I”H for a series of reactions is the sum of the values of I”H for the individual reactions. The Borna€“Haber cycle for calculating the lattice energy of cesium fluoride is shown in Figure 8.4 "The Borna€“Haber Cycle Illustrating the Enthalpy Changes Involved in the Formation of Solid Cesium Fluoride from Its Elements". This equation describes the sublimationThe conversion of a solid directly to a gas (without an intervening liquid phase). This equation describes the ionization of cesium, so the enthalpy change is the first ionization energy of cesium. This equation describes the dissociation of fluorine molecules into fluorine atoms, where D is the energy required for dissociation to occur (Table 8.3 "Selected Bond Dissociation Enthalpies at 298 K").
This equation describes the formation of a gaseous fluoride ion from a fluorine atom; the enthalpy change is the electron affinity of fluorine.
Equation 8.7 may be used as a tool for predicting which ionic compounds are likely to form from particular elements. The lattice energy of BaO, with a dipositive cation and a dinegative anion, dominates the Borna€“Haber cycle. Remember from Equation 8.4 that lattice energies are directly proportional to the product of the charges on the ions and inversely proportional to the internuclear distance.
If the formation of ionic lattices containing multiply charged ions is so energetically favorable, why does CsF contain Cs+ and Fa?’ ions rather than Cs2+ and F2a?’ ions?

Lattice energy is usually the most important energy factor in determining the stability of an ionic compound. A Write a series of stepwise reactions for forming MgH2 from its elements via the gaseous ions.
B Use Hessa€™s law and data from the specified figures and tables to calculate the lattice energy. A Hessa€™s law allows us to use a thermochemical cycle (the Borna€“Haber cycle) to calculate the lattice energy for a given compound. The ionic solid shows unique properties which are quite different from its constituent elements. In other words the energy used to decompose the ionic solid into its constituent cation and anion is called lattice energy. Therefore there must be some indirect way to determine the lattice energy and generally use Hess’s cycle for that purpose.
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Ionic compounds are usually rigid, brittle, crystalline substances with flat surfaces that intersect at characteristic angles.
In such an arrangement each cation in the lattice is surrounded by more than one anion (typically four, six, or eight) and vice versa, so it is more stable than a system consisting of separate pairs of ions, in which there is only one cationa€“anion interaction in each pair. We see from Equation 8.4 that lattice energy is directly related to the product of the ion charges and inversely related to the internuclear distance. This effect is illustrated in Figure 8.2 "A Plot of Lattice Energy versus the Identity of the Halide for the Lithium, Sodium, and Potassium Halides", which shows that lattice energy decreases for the series LiX, NaX, and KX as the radius of Xa?’ increases. Conversely, for a given alkali metal ion, the fluoride salt always has the highest lattice energy and the iodide salt the lowest. For compounds with ions with the same charge, use the relative sizes of the ions to make this prediction. We know from Equation 8.4 that lattice energy is directly proportional to the product of the ionic charges. The melting pointThe temperature at which the individual ions in a lattice or the individual molecules in a covalent compound have enough kinetic energy to overcome the attractive forces that hold them together in the solid., for example, is the temperature at which the individual ions have enough kinetic energy to overcome the attractive forces that hold them in place. Unfortunately, measurable quantities of gaseous ions have never been obtained under conditions where heat flow can be measured. CsF is a nearly ideal ionic compound because Cs is the least electronegative element that is not radioactive and F is the most electronegative element. Recall from Chapter 7 "The Periodic Table and Periodic Trends" that energy is needed to ionize any neutral atom.
Recall from Chapter 7 "The Periodic Table and Periodic Trends" that electron affinities can be positive, negative, or zero.
Because Reaction 5 is the reverse of the equation used to define lattice energy and U is defined to be a positive number, I”H5 is always negative, as it should be in a step that forms bonds.
The process we have used to arrive at this value is summarized in Table 8.4 "Summary of Reactions in the Borna€“Haber Cycle for the Formation of CsF(s)". The extra energy released when BaO forms from its ions more than compensates for the additional energy required to form Ba2+(g) and O2a?’(g) ions from Ba(s) and 12O2(g). Charge on ionsAs the charge on oppositely charged ions increases, the electrostatic force of attraction increases between them which results in high lattice energy.
Hess’s cycle which is used to determine the lattice energy is also known as Born-Haber cycle. You may also download a PDF copy of this book (147 MB) or just this chapter (5 MB), suitable for printing or most e-readers, or a .zip file containing this book's HTML files (for use in a web browser offline). The value of the constant ka€? depends on the specific arrangement of ions in the solid lattice and their valence electron configurations, topics that will be discussed in more detail in Chapter 12 "Solids". Consequently, we expect RbCl, with a (a?’1)(+1) term in the numerator, to have the lowest lattice energy, and GaP, with a (+3)(a?’3) term, the highest. Hardness is directly related to how tightly the ions are held together electrostatically, which, as we saw, is also reflected in the lattice energy.

Instead, lattice energies are found using the experimentally determined enthalpy changes for other chemical processes, Hessa€™s law, and a thermochemical cycle called the Borna€“Haber cycleA thermochemical cycle that decribes the process in which an ionic solid is conceptually formed from its component elements in a stepwise manner., similar to those introduced in Chapter 5 "Energy Changes in Chemical Reactions". The accompanying enthalpy change is called the enthalpy of sublimation(I”Hsub)The enthalpy change that accompanies the conversion of a solid directly to a gas. Hence, regardless of the compound, the enthalpy change for this portion of the Borna€“Haber cycle is always positive. The I”H for this reaction, too, is always positive because energy is required to dissociate any stable diatomic molecule into the component atoms. In this case, I”H is negative because of the highly negative electron affinity of fluorine. The same amount of energy will be used in the decomposition of this ionic solid into its constituent ions. Therefore an ionic solid with divalent ions have much larger lattice energies compare to solids with monovalent ions. A similar effect is seen when the anion becomes larger in a series of compounds with the same cation.
To decide whether BaS or CaO has the greater lattice energy, we need to consider the relative sizes of the ions because both compounds contain a +2 metal ion and a a?’2 chalcogenide ion. Thus melting points vary with lattice energies for ionic substances that have similar structures.
Developed by Max Born and Fritz Haber in 1919, the Borna€“Haber cycle describes a process in which an ionic solid is conceptually formed from its component elements in a stepwise manner.
Thus the first three terms in Equation 8.7 make the formation of an ionic substance energetically unfavorable, and the fourth term contributes little either way. Furthermore, forming an F2a?’ ion is expected to be even more energetically unfavorable than forming an O2a?’ ion. When both are bonded together to form sodium chloride, the whole process involves various steps. According to Hess's law, for a reaction which can complete in more than two ways, the overall energy change remains same in all ways. These properties result from the regular arrangement of the ions in the crystalline lattice and from the strong electrostatic attractive forces between ions with opposite charges. Not only is an electron being added to an already negatively charged ion, but because the Fa?’ ion has a filled 2p subshell, the added electron would have to occupy an empty high-energy 3s orbital.
Sodium chloride is an ionic solid which consists of ions formed by the transfer of electrons. Radius or size of ionAs the ionic radius decreases, ions get closer to each other increasing the strength of the attractions as wellas the lattice energy of ionic solid. This means that lattice energy is the most important factor in determining the stability of an ionic compound. Cesium fluoride, therefore, is not Cs2+F2a?’ because the energy cost of forming the doubly charged ions would be greater than the additional lattice energy that would be gained. The similar trend can be observed in alkali halide.Overall as we go down in a group, ionic radius increases and lattice energy decrease.
In fact, because of its high melting point, MgO is used as an electrical insulator in heating elements for electric stoves. In a crystal of sodium chloride, these ions are stacked up alternatively into the cube-shaped arrangement. Overall all ionic compounds make a crystal shape where ions are held together into a crystal lattice which is an arrangement of alternating ions held together by opposite charges.
The high magnitude of lattice energy for magnesium oxide contributes to high charge and small size of ions. As the lattice energy increases, the strength and stability of the crystal lattice increases.

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