Use the Born-Haber cycle outlined in Section 9.3 for LiF to...

Use the Born-Haber cycle outlined in Section $9.3$ for LiF to calculate the lattice energy of $\mathrm{NaCl}$. [The heat of sublimation of $\mathrm{Na}$ is $108 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta H_{\mathrm{f}}^{\circ}(\mathrm{NaCl})=-411 \mathrm{~kJ} / \mathrm{mol}$. Energy needed to dis- sociate $\frac{1}{2}$ mole of $\mathrm{Cl}_{2}$ into $\mathrm{Cl}$ atoms $=121.4 \mathrm{~kJ} .$ ]

Use the Born-Haber cycle outlined in Section $9.3$ for LiF to calculate the lattice energy of $\mathrm{NaCl}$. [The heat of sublimation of $\mathrm{Na}$ is $108 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta H_{\mathrm{f}}^{\circ}(\mathrm{NaCl})=-411 \mathrm{~kJ} / \mathrm{mol}$. Energy needed to dis-
sociate $\frac{1}{2}$ mole of $\mathrm{Cl}_{2}$ into $\mathrm{Cl}$ atoms $=121.4 \mathrm{~kJ} .$ ]

Key Concepts

Bond Dissociation Energy

Bond dissociation energy is the energy needed to break a chemical bond within a molecule so that it separates into individual atoms. In the Born-Haber cycle, it is used to account for the breaking of bonds in diatomic molecules, such as halogens, to form atomic species, which then participate in subsequent steps like electron gain.

Born-Haber Cycle

The Born-Haber cycle is a thermodynamic process that relates the lattice energy of an ionic solid to various energetic steps, such as sublimation, ionization, bond dissociation, and electron affinity. It uses Hess’s law to show that the sum of these individual energy changes equals the overall enthalpy change for the formation of the compound, making it an essential tool in solid state and inorganic chemistry for analyzing ionic bond strength.

Lattice Energy

Lattice energy is the energy released when gaseous ions combine to form an ionic crystal lattice. It is a measure of the strength of the ionic bonds within a solid, and high lattice energies typically indicate a more stable ionic compound. This concept is crucial in understanding the thermodynamic stability and properties of ionic solids.

Hess's Law

Hess’s law states that the total enthalpy change in a chemical reaction is independent of the pathway taken, provided the initial and final conditions are the same. This principle allows for the calculation of unknown enthalpy changes, such as lattice energy, by summing the enthalpic contributions from multiple steps in a reaction cycle like the Born-Haber cycle.

Sublimation Energy

Sublimation energy is the energy required to convert a substance from its solid phase directly into the gaseous phase. In the context of the Born-Haber cycle, this energy is used to produce gaseous atoms from a solid metal before they undergo ionization, which is an important step in forming ionic compounds.

Transcript

00:01 In this question we want to determine the lattice energy of certain fluoride and we're going to be looking into the bone harbour cycle that is illustrated in that question that we've been given.

00:11 So what we can do here is to look at the steps that are involved in that process.

00:16 We have an a solid that changes into n .a.

00:22 And the end of the change associated with this change under standard conditions, let's call this step number one.

00:28 This is going to be equal to 108 kilojoules per now the second step is we have our c l2 changing into c l so to balance this out we're going to have this is a curse this is also a gas so the end of the change associated with this change this is equal to 1 2 1 .4 and the units are in kilojol per more so the next step here is going to be sodium, the oxidation of sodium gas to form sodium glass and an electron and the end of the change associated with this step, this is going to be 495 .9.

01:19 And the units are also in kilojoules per more.

01:22 Now the next step is the oxidation or rather the reduction of chlorine, cl, that was formed in step number two.

01:32 That is add an electron to form c .l.

01:36 Minus gas and the end of the change associated with this step, this is equal to negative 3, 4, 9 kilojoules per.

01:46 Now the final step is going to be the reaction of the sodium glass that we formed in step 3 and the chloride ions that we formed in step 4 to produce the sodium chloride which is the solid.

02:03 And the end of the change, as a form to form in step 3...

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