Question

Consider the following: Li(s) \(+\frac{1}{2} \mathrm{I}_{2}(g) \rightarrow\) Liil(s) \(\Delta H=\) \(-292 \mathrm{kJ} . \mathrm{LiI}(s)\) has a lattice energy of \(-753 \mathrm{kJ} / \mathrm{mol} .\) The ionization energy of Li(g) is \(520 . \mathrm{kJ} / \mathrm{mol},\) the bond energy of \(\mathrm{I}_{2}(g)\) is 151 \(\mathrm{kJ} / \mathrm{mol}\) , and the electron affinity of \(\mathrm{I}(g)\) is \(-295 \mathrm{kJ} / \mathrm{mol}\) . Use these data to determine the heat of sublimation of Li(s).

Short answer

The heat of sublimation for Li(s) can be determined using the Born-Haber cycle and the given energy values. By applying Hess's law and substituting the given energy values into the equation, the heat of sublimation for Li(s) is calculated as 85 kJ/mol.

Step-by-step solution

Write down the Born-Haber cycle components

In the Born-Haber cycle, the formation of a solid ionic compound is represented as a combination of several steps. For LiI(s), the Born-Haber cycle includes the following steps: 1. Sublimation of solid lithium (Li(s) to Li(g)) - This step represents the unknown heat of sublimation that we want to determine. 2. Ionization of gaseous lithium (Li(g) to Li+(g) + e-) - This step involves the ionization energy of Li. 3. Bond dissociation of diatomic iodine (I2(g) to 2 I(g)) - This step includes the bond energy of I2. 4. Electron affinity of iodine (I(g) + e- to I-(g)) - This step represents the electron affinity of I. 5. Formation of the solid lithium iodide (Li+(g) + I-(g) to LiI(s)) - This step is associated with the lattice energy of LiI.

Determine the relationship between the given energy values and the heat of sublimation

According to the Hess's law, the overall energy change for the formation of LiI(s), which is the sum of the energy changes for all the steps mentioned above, should be equal to the enthalpy change for the given equation: Heat of sublimation (Li(s)) + Ionization energy (Li(g)) + Bond energy (I2(g)) + Electron affinity (I(g)) + Lattice energy (LiI(s)) = ∆H

Substitute the given energy values into the equation and solve for the heat of sublimation

Now plug in the given energy values into the equation: Heat of sublimation (Li(s)) + 520 kJ/mol + 151 kJ/mol + (-295 kJ/mol) + (-753 kJ/mol) = -292 kJ/mol Heat of sublimation (Li(s)) = -292 kJ/mol - 520 kJ/mol - 151 kJ/mol + 295 kJ/mol + 753 kJ/mol Heat of sublimation (Li(s)) = 85 kJ/mol So, the heat of sublimation for Li(s) is 85 kJ/mol.

Key concepts

Lattice Energy

Lattice energy is a crucial term when exploring ionic compounds. It refers to the energy released when ions are combined to form an ionic solid. In this context, lattice energy is paramount because it helps us understand the stability of the ionic lattice formed by the solid compound. For lithium iodide (LiI), the lattice energy is given as -753 kJ/mol.
This negative value indicates that energy is released when LiI forms from its gaseous ions, reflecting the strong attraction between oppositely charged ions.
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The magnitude of lattice energy is influenced by:

• The charge of the ions: Greater charges result in stronger attractions and higher lattice energies.
• The distance between the ions: Smaller ions have higher lattice energies due to closer proximity, leading to stronger electrostatic forces.

Lattice energy is essential for various applications such as predicting melting points, solubility, and overall compound stability.

Ionization Energy

Ionization energy is the energy required to remove the outermost electron from a gaseous atom, converting it into a cation. In our exercise involving lithium, the ionization energy for lithium in gaseous form is specified as 520 kJ/mol.
This step is integral in the Born-Haber cycle because forming a cation is necessary for establishing the ionic bond in LiI.
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Key points to remember about ionization energy include:

• It is always a positive value since energy must be supplied to overcome the attraction between the electron and the nucleus.
• Ionization energy increases across a period in the periodic table due to increasing nuclear charge, which holds electrons more tightly.
• Conversely, it decreases down a group due to increased distance from the nucleus and shielding effect.

Understanding ionization energy helps in assessing how easily an atom can form positive ions, a critical aspect of the Born-Haber cycle.

Electron Affinity

Electron affinity measures the energy change when an electron is added to a neutral atom, forming a negative ion. In the context of iodine, the electron affinity is given as -295 kJ/mol. This negative value means energy is released when iodine gains an electron, the process becoming energetically favorable.
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Factors affecting electron affinity include:

• The amount of nuclear charge: A higher nuclear charge may result in higher electron affinity.
• Atomic size: Smaller atoms tend to have higher electron affinities as the added electron is closer to the nucleus.
• Subshell configuration: Atoms with half-filled or fully filled subshells may have relatively lower electron affinities due to electron repulsion in the filled orbitals.

Electron affinity is vital in the Born-Haber cycle as it illustrates how readily an atom can form an anion, part of the essential steps in ionic compound formation.

Enthalpy Change

Enthalpy change, often denoted by \(\Delta H\), represents the total heat change during a reaction, encompassing both absorbed and released energies. In our example with LiI,the \(\Delta H\) of formation is noted as -292 kJ/mol. This value indicates that forming LiI from its constituent elements in their standard states releases energy, making it an exothermic process.
- - -Understanding enthalpy change is critical for:

• Determining the feasibility of a reaction: Exothermic reactions (\(\Delta H\) < 0) are thermodynamically favorable under constant pressure and may proceed spontaneously.
• Calculating energy requirements: It provides insights into how much energy is required or released during chemical transformations.
• Energy management in industrial processes: It is pivotal for designing systems where energy change needs to be controlled, such as in energy storage and thermal management systems.

Enthalpy change is a fundamental concept in thermodynamics and chemistry, essential for exploring and manipulating chemical reactions, especially in the formation of ionic compounds.