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 \(\mathrm{O}\). (d) The enthalpy of formation of \(\mathrm{CaO}\) is small. (e) \(\mathrm{CaO}\) is stable to atmospheric conditions.

Short answer

The best explanation for the stability of CaO relative to the free elements is (a) The lattice energy of CaO is large enough to overcome these processes, as a large lattice energy indicates a strong ionic bond that can overcome the energy required to remove electrons from Ca and add electrons to O.

Step-by-step solution

Analyze the given statements

The exercise provides the following statements: (a) The lattice energy of CaO is large enough to overcome these processes. (b) 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 CaO is small. (e) CaO is stable to atmospheric conditions. Step 2: Analyze Statement (a)

Check for lattice energy as explanation

Lattice energy is the energy required to separate a solid ionic compound into gaseous ions. If the lattice energy of CaO is large, it means the substance has a strong ionic bond and can overcome the energy required to remove two electrons from Ca and to add two electrons to O. This explanation seems reasonable, but let's check the other statements. Step 3: Analyze Statement (b)

Check for covalent bonding as explanation

CaO is an ionic compound, not a covalent compound. Therefore, statement (b) is irrelevant and incorrect. Step 4: Analyze Statement (c)

Check for molar mass as explanation

The molar mass of a compound does not directly affect its stability or the energy required to remove or add electrons. So, statement (c) is not a good explanation. Step 5: Analyze Statement (d)

Check for enthalpy of formation as explanation

A small enthalpy of formation would indicate that the formation of CaO is not very exothermic, meaning less energy would be released during its formation. While this may be true, it does not explain the stability of CaO relative to the free elements. This explanation is not sufficient on its own. Step 6: Analyze Statement (e)

Check for stability to atmospheric conditions as explanation

The stability of CaO to atmospheric conditions might be a contributing factor to its overall stability, but it does not explain why the compound is stable relative to the free elements. This explanation is not sufficient, either. Step 7: Choose the best explanation

Determine the best explanation

Based on the analysis of the given statements, the best explanation for the stability of CaO relative to the free elements is (a) The lattice energy of CaO is large enough to overcome these processes. This is because a large lattice energy indicates a strong ionic bond, which can overcome the energy required to remove electrons from Ca and add electrons to O.

Key concepts

Lattice Energy

Lattice energy plays a critical role in the formation and stability of ionic compounds like calcium oxide (CaO). This energy is the measure of the strength of the forces holding the ions together in an ionic solid. It is defined as the amount of energy released when oppositely charged gaseous ions combine to form an ionic solid.

Here are some key points to remember about lattice energy:

• A large lattice energy indicates strong attractive forces between ions, resulting in higher stability of the ionic compound.
• It compensates for the energy required to remove electrons from metal atoms and add them to non-metal atoms, making the overall reaction favorable.
• Lattice energy is influenced by the charge and the size of the ions involved. Higher charges and smaller ionic radii typically result in greater lattice energies.

In the case of CaO, the large lattice energy helps overcome the energy hurdles involved in the electron transfer processes, thus contributing significantly to the compound's stability.

Enthalpy of Formation

The enthalpy of formation provides insight into the energy changes taking place during the formation of a compound from its elements in their standard states. Essentially, it's the heat change associated with the formation of one mole of a compound from its elemental forms.

Understanding enthalpy of formation involves the following aspects:

• If the enthalpy of formation is negative, it indicates that energy is released in the process, making it exothermic and usually favorable.
• A small or less negative enthalpy of formation would mean less energy is released, which might not be as favorable for a compound's formation.
• For compounds like CaO, the enthalpy of formation can suggest stability but doesn't solely explain it without considering the lattice energy.

While a large lattice energy can balance the enthalpy of formation, in cases where the enthalpy is not significantly negative, both these factors together cater to the formation and stability of ionic compounds.

Ionic Compound Stability

Ionic compound stability refers to how favorable it is for a compound to exist in its ionic form compared to its individual elements. Several factors contribute to this stability, ensuring that compounds like CaO remain intact under normal conditions.

The following factors influence ionic compound stability:

• The lattice energy, as discussed, influences stability by promoting strong ionic bonds.
• Enthalpy of formation, when favorable, supports the idea that the compound releases energy and is stable.
• Ionic bonding itself, resulting from the electrostatic attraction between ions, creates a crystalline structure that further stabilizes the compound.
• Environmental conditions such as temperature and pressure can also affect the stability, but compounds like CaO are generally stable under normal atmospheric conditions.

In conclusion, the combined effects of high lattice energy, a favorable enthalpy of formation, and inherent strong ionic bonding lead to the overall stability of ionic compounds. This synergy explains why CaO remains a stable substance despite the energy changes involved in its formation.