Problem 27 - Chemistry The Central Science In Si Units

Question

Energy is required to remove two electrons from Ca to form \(\mathrm{Ca}^{2+},\) and energy is required to add two electrons to \(\mathrm{O}\) to form \(\mathrm{O}^{2-}\). Yet \(\mathrm{CaO}\) is stable relative to the free elements. Which statement is the best explanation? (a) The lattice energy of \(\mathrm{CaO}\) is large enough to overcome these processes. (b) \(\mathrm{CaO}\) is a covalent compound, and these processes are irrelevant. (c) CaO has a higher molar mass than either Ca or O. (d) The enthalpy of formation of \(\mathrm{CaO}\) is small. \((\mathbf{e}) \mathrm{CaO}\) is stable to atmospheric conditions.

Step-by-Step Solution

Answer

Option (a): The lattice energy of CaO is large enough to overcome these processes.

Step 1: Understanding the Question

We need to determine why the compound CaO is stable relative to its free elements, Ca and O, despite the energy required to ionize Ca and add electrons to O.

Step 2: Analyze Given Options

We analyze the options: - Option (a): Suggests large lattice energy outweighs energy costs. - Option (b): Suggests covalent nature, making energy details irrelevant. - Option (c): Mentions molar mass, unrelated to stability. - Option (d): Mentions small enthalpy of formation, not directly addressing stability. - Option (e): States stability to atmospheric conditions, not explaining why.

Step 3: Consider Lattice Energy

Lattice energy is the energy released when gaseous ions form an ionic solid. The large lattice energy of an ionic compound like CaO can offset the ionization energy of Ca and electron affinity of O, contributing to its stability.

Step 4: Eliminate Irrelevant and Incorrect Options

- Eliminate (b) as CaO is ionic, not covalent. - Eliminate (c) as molar mass does not affect stability. - Eliminate (d) since stability is not about small enthalpy. - Eliminate (e) as it does not justify relative stability to free elements.

Step 5: Conclusion

From the discussed reasoning, option (a) is the best explanation because the large lattice energy compensates for the energy expenditures associated with forming CaO from its elements.

Key Concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons to achieve full outer electron shells, resulting in positive and negative ions. These opposite charges attract each other, leading to the formation of a solid lattice structure. The strength of this attraction relies on the lattice energy, which is the energy released when the ionic solid is formed from its gaseous ions.
The lattice energy is crucial for the stability and formation of ionic compounds. For example, in calcium oxide (CaO), calcium (\(Ca^{2+}\)) loses two electrons to form a cation, while oxygen (\(O^{2-}\)) gains two electrons to form an anion. The strong electrostatic attraction between these ions releases a significant amount of lattice energy, making the compound stable.
Lattice energy is affected by:

• Magnitude of the charges: Higher charges lead to stronger attractions.
• Size of the ions: Smaller ions result in greater lattice energy.

The substantial lattice energy in ionic compounds like CaO is what makes them energetically favorable, outweighing the initial energy input required for ion formation.

Ionization Energy

Ionization energy refers to the energy required to remove an electron from an atom or ion in its gaseous state. It is a key factor in the formation of ionic compounds as it determines how readily an atom can form a positive ion or cation.
For calcium (\(Ca\)), the ionization energy is needed to remove electrons and form calcium ions (\(Ca^{2+}\)). This process requires substantial energy, as removing electrons involves overcoming the attraction between the negatively charged electrons and the positively charged nucleus.
Despite this energy requirement, ionic compounds like CaO are still considered stable because the lattice energy compensates for the ionization energy. This means the energy released when ions form an ionic solid usually exceeds the energy needed to separate electrons from an atom in the gaseous state.Important aspects of ionization energy include:

• Energy input: Required for electron removal to form cations.
• Multiple ionization energies: Sequential ion removals need different amounts of energy.

Understanding ionization energy helps explain why calcium readily forms \(Ca^{2+}\) ions in ionic compounds.

Electron Affinity

Electron affinity is the energy change that occurs when an electron is added to a neutral atom in its gaseous state. It reflects how much an atom "wants" an additional electron, playing a crucial role in forming anions like oxygen in ionic compounds.
When oxygen (\(O\)) gains electrons to become \(O^{2-}\), energy is released, which is signified by its negative electron affinity value. This energy release contributes to the overall energy balance necessary for forming stable ionic compounds like CaO.
Key aspects of electron affinity include:

• Energy release: Indicates attraction strength toward gaining electrons.
• Variability among elements: Different atoms have varied electron affinities based on electron configurations.

In the context of lattice energy, electron affinity helps explain how anions are stabilized when they gain electrons, resulting in energy that counteracts the cost of ionization energy.

Stability of Compounds

The stability of a compound refers to its energy state relative to its individual elements. A compound is considered stable if it is energetically favorable, meaning the total energy released during formation outweighs the energy required for its construction.
In the case of calcium oxide (\(CaO\)), despite the significant energy needed to form ions (ionization energy for \(Ca\) and electron affinity for \(O\)), the stability is achieved because the lattice energy compensates for these energy expenditures.
Stability is influenced by:

• Lattice energy: High lattice energy leads to strong ionic bonds that stabilize the compound.
• Enthalpy changes: The overall energy changes when forming the compound versus breaking it down.
• Resistance to decomposition: Stable compounds resist breaking down under normal conditions.

Understanding these factors helps explain why some compounds, such as CaO, are more stable than their individual elements, leading to their persistent formation and presence in nature.