Problem 95 - Chemistry The Molecular Science

Question

Determine the lattice energy for L.iCl(s) given these data: Sublimation enthalpy of \(\mathrm{Li}, 161 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{IF}_{1}\) for \(\mathrm{Li}\), \(520 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{BE}\) of \(\mathrm{Cl}_{2}(\mathrm{~g}), 242 \mathrm{~kJ} / \mathrm{mol} ;\) electron affinity of \(\mathrm{Cl},-349 \mathrm{~kJ} / \mathrm{mol} ;\) formation enthalpy of \(\mathrm{LiCl}(\mathrm{s})\) \(-408.7 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

The lattice energy of LiCl(s) is -861.7 kJ/mol.

Step 1: Understanding the Born-Haber Cycle

The Born-Haber cycle is used to calculate the lattice energy of an ionic compound. It involves several steps: sublimation of the metal, ionization of the metal, dissociation of the non-metal molecule, electron affinity of the non-metal, and enthalpy of formation for the ionic compound.

Step 2: List Known Values

We are given the following:- Sublimation enthalpy of Li: \(161 \text{ kJ/mol}\)- Ionization energy of Li: \(520 \text{ kJ/mol}\)- Bond dissociation energy (BE) of \(\text{Cl}_2(\text{g})\): \(242 \text{ kJ/mol}\)- Electron affinity of Cl: \(-349 \text{ kJ/mol}\)- Enthalpy of formation for \(\text{LiCl(\text{s})}\): \(-408.7 \text{ kJ/mol}\)

Step 3: Determine the Dissociation Energy for Cl Atom

The bond dissociation energy given refers to the Cl-Cl bond. Since \(\text{Cl}_2\) needs to split into 2 Cl atoms for the process, the energy for one mole of Cl atoms is half the BE:\[ \text{Dissociation energy for Cl atom} = \frac{242}{2} = 121 \text{ kJ/mol} \]

Step 4: Calculate the Lattice Energy using the Born-Haber Cycle

The lattice energy can be calculated using the Born-Haber equation:\[\Delta H_{\text{lattice}} = \Delta H_{\text{formation}} - (\Delta H_{\text{sublimation}} + IE + \frac{1}{2}BE + EA)\]Substitute the known values:\[\Delta H_{\text{lattice}} = -408.7 - (161 + 520 + 121 - 349)\]\[\Delta H_{\text{lattice}} = -408.7 - 453 = -861.7 \text{ kJ/mol}\]

Step 5: Interpretation of the Answer

The calculated lattice energy is \(-861.7 \text{ kJ/mol}\). This is the energy released when one mole of LiCl solid is formed from gaseous Li+ and Cl- ions.

Key Concepts

Born-Haber Cycle

The Born-Haber Cycle is a step-by-step thermodynamic process used to calculate the lattice energy of an ionic compound. Imagine it as an energy roadmap indicating the energy changes during the formation of an ionic crystal.
This process considers several crucial thermochemical steps:

• Sublimation of the metal: The conversion of a solid metal to its gaseous atoms.
• Ionization of the metal: Removing an electron from the gaseous metal atoms to form cations.
• Dissociation of the non-metal molecule: Separating a diatomic gas molecule into individual atoms.
• Electron affinity: Adding an electron to the gaseous non-metal atoms to form anions.
• Enthalpy of formation: Forming the ionic solid from its gaseous ions.

By combining these steps, the Born-Haber Cycle helps chemists determine the required lattice energy, a crucial parameter indicating the stability of ionic compounds.

Ionization Energy

Ionization energy is the amount of energy required to remove an electron from a gaseous atom or ion. It is a critical concept in understanding the formation of cations.
In the context of the Born-Haber Cycle, this energy is crucial when considering metals like Lithium (\(\text{Li}\)) which lose electrons to form positive ions. With a given ionization energy of 520 kJ/mol for \(\text{Li}\), this process requires energy input. The higher the ionization energy, the more difficult it is to remove the electron and the more energy is needed.
This step is vital because it dictates how much energy is required to create the cations necessary for forming ionic compounds. Every ionization involves intricate electronic interactions within an atom, and understanding them highlights why some elements form ions more readily than others.

Sublimation Enthalpy

Sublimation enthalpy refers to the energy required to convert one mole of a substance from a solid to a gaseous state, bypassing the liquid phase entirely. For metals like Lithium (\(\text{Li}\)), this is a key step in the Born-Haber Cycle.
The sublimation enthalpy of \(\text{Li}\) is given as 161 kJ/mol, indicating the energy needed for this phase change. This process ensures the metal atoms are in a gaseous state, ready for further chemical transformations in the ionization step.
This concept underscores the importance of energy transformations in physical changes and their impact on chemical formation. Obtaining the gaseous phase of the metal is crucial to facilitate the interactions required for ionic bond formation.

Electron Affinity

Electron affinity is the energy change that occurs when an electron is added to a gaseous atom, resulting in a negative ion. It is an exothermic process, meaning it typically releases energy.
In the Born-Haber Cycle, electron affinity is crucial when considering non-metals, such as Chlorine (\(\text{Cl}\)), which gain electrons to form anions. Chlorine's electron affinity is -349 kJ/mol, indicating energy release upon gaining an electron.
This energy change reflects the attraction between the added electron and the nucleus of the atom. Additionally, it reveals the tendency of non-metals to acquire electrons during bond formation. The negative value signifies that the process is energetically favorable and suggests the stability of the resulting ions.