Question

List the individual steps used in constructing a Born-Haber cycle for the formation of \(\mathrm{BaI}_{2}\) from the elements. Which of the steps would you expect to be exothermic?

Short answer

To construct a Born-Haber cycle for the formation of \(\mathrm{BaI}_{2}\) from its elements, follow these steps: 1. Formation of gaseous atoms: Sublimate barium, and dissociate diatomic iodine gas. Both are endothermic processes. 2. Ionize barium: First, ionize gaseous barium twice, both steps are endothermic. 3. Ionize iodine: Add an electron to gaseous iodine to form an iodide ion. This electron affinity process is exothermic and must be performed twice (since there are two iodide ions in \(\mathrm{BaI}_{2}\)). 4. Formation of ionic lattice: Combine the gaseous ions to form an ionic solid. This lattice energy process is exothermic. The exothermic steps are the ionization of iodine (Step 3) and the formation of the ionic lattice (Step 4).

Step-by-step solution

Formation of gaseous atoms

In this step, we convert the elements, solid barium (Ba) and diatomic iodine gas (\(\mathrm{I}_{2}\)), into their gaseous atoms. For this process, we consider the sublimation of barium and the dissociation of iodine molecules: 1. Sublimation of barium: \(\mathrm{Ba (s) \rightarrow Ba (g)}\). This step requires the sublimation energy, which is always endothermic. 2. Dissociation of iodine: \(\frac{1}{2} \mathrm{I}_{2} (\mathrm{g}) \rightarrow \mathrm{I (g)}\). This step requires the bond dissociation energy of iodine, which is also endothermic as energy is needed to break the bond.

Ionization of barium

In this step, we ionize the gaseous barium atom to create a barium ion: \(\mathrm{Ba (g) \rightarrow Ba^{+} (g) + e^{-}}\). This is the first ionization energy of barium, and it is an endothermic process. \(\mathrm{Ba^{+} (g) \rightarrow Ba^{2+} (g) + e^{-}}\). This is the second ionization energy of barium and is also an endothermic process.

Ionization of iodine

In this step, an electron is added to the gaseous iodine atom to create an iodide ion: \(\mathrm{I (g) + e^{-} \rightarrow I^{-} (g)}\). This is the electron affinity of iodine and is an exothermic process as energy is released when the electron is added to the iodine atom. Since \(\mathrm{BaI}_{2}\) has two iodide ions, we'll need to perform this process twice.

Formation of the ionic lattice

In this step, the gaseous ions come together to form the ionic solid: \(\mathrm{Ba^{2+} (g) + 2 I^{-} (g) \rightarrow BaI (s)}\) This step corresponds to the lattice energy and is an exothermic process as energy is released when the ions are brought together to form the lattice. To summarize, we expect the exothermic steps to be the ionization of iodine (Step 3) and the formation of the ionic lattice (Step 4).

Key concepts

Lattice Energy

Lattice energy refers to the energy released when gaseous ions combine to form an ionic solid. It is an essential factor in the stability of ionic compounds. When BaI 2 (barium iodide) is formed from its gaseous ions, energy is released as the positively charged barium ions ( Ba 2+ ) and negatively charged iodide ions ( I - ) come together to form a structured lattice.
This process is exothermic, meaning it releases energy, which contributes positively to the stability of the ionic compound. Understanding lattice energy helps predict how tightly packed the ions in solid form are. Some points to remember about lattice energy:

• It is a measure of the bond strength in ionic compounds.
• The greater the lattice energy, the more stable the ionic compound.
• Lattice energy is affected by the size of the ions and their charges; smaller ions and higher charges typically lead to higher lattice energies.

Grasping this concept is key to understanding the energy changes involved in forming solid ionic compounds like barium iodide.

Sublimation Energy

Sublimation energy refers to the energy required to transform a substance from a solid to a gaseous state directly, without passing through the liquid state. It is an endothermic process, meaning energy is absorbed to overcome the forces holding the atoms in the solid structure. In the Born-Haber cycle for barium iodide ( BaI 2 ) formation, the sublimation of barium involves converting solid barium ( Ba (s) ) to gaseous barium ( Ba (g) ).
This step is crucial as it prepares the barium atoms for ionization.

• Sublimation is necessary for elements that naturally exist as solids, like barium, to proceed to the gaseous ion state.
• This absorbed energy is part of the energy input required in an initial step towards formation of an ionic compound.
• Understanding sublimation energy helps in calculating the total energy changes in processes like the Born-Haber cycle.

By acknowledging the role of sublimation energy, we get a comprehensive understanding of the energy dynamics in forming gaseous atoms from solid elements.

Ionization Energy

Ionization energy is the energy needed to remove an electron from an atom or ion in the gaseous state. For barium iodide ( BaI 2 ), ionization energy plays a pivotal role in converting gaseous barium atoms to barium ions. This process requires overcoming the attraction between the negatively charged electron and the positively charged nucleus, which is inherently endothermic as energy input is required.
For barium, multiple ionization energies are involved:

• The first ionization energy removes one electron ( Ba (g) → Ba + (g) + e - ).
• The second ionization energy removes another electron to form Ba 2+ .

Key points about ionization energy include:

• Higher ionization energies indicate a stronger hold on electrons by the nucleus.
• Ionization energy tends to increase across a period and decrease down a group in the periodic table.
• Understanding ionization energy helps explain the ease or difficulty of forming cations in ionic compounds.

By comprehending ionization energies, students can predict the energy changes involved in transforming atoms into ions in gaseous states.

Electron Affinity

Electron affinity refers to the energy change that occurs when an electron is added to a neutral atom to form a negative ion. In the case of forming barium iodide ( BaI 2 ), when converting gaseous iodine atoms ( I (g) ) into iodide ions ( I - (g) ), electron affinity describes the release of energy. Unlike ionization energy, electron affinity is exothermic, indicating that energy is released rather than required.
For iodine, adding an electron is favorable as it achieves a more stable electron configuration:

• Energy released helps counterbalance the energy absorbed in earlier steps like ionization and sublimation.
• It is an important concept in predicting the formation of anions.
• Higher electron affinities usually mean more stable negative ion formation.

Understanding electron affinity is crucial for grasping how elements gain electrons and form anions, contributing to the overall energy balance in chemical processes like those described in the Born-Haber cycle.