Problem 108 - Chemistry: Atoms First

Question

Which of the following compounds requires the most energy to convert one mole of the solid into separate ions? (a) \(\mathrm{K}_{2} \mathrm{S}\) (b) \(\mathrm{K}_{2} \mathrm{O}\) (c) CaS (d) \(\mathrm{Cs}_{2} \mathrm{S}\) (e) CaO

Step-by-Step Solution

Answer

CaO (choice e) requires the most energy to convert one mole of the solid into separate ions.

Step 1: Understand Lattice Energy

Lattice energy is the energy required to separate one mole of an ionic compound into its constituent ions. It generally increases with the charge on the ions and decreases with the size of the ions. Thus, compounds with ions having higher charges and smaller sizes usually have higher lattice energies.

Step 2: Compare Ionic Charges

Looking at the options, compare the charges of cations and anions. Both \(\mathrm{K}_{2} \mathrm{S}\), \(\mathrm{K}_{2} \mathrm{O}\), and \(\mathrm{Cs}_{2} \mathrm{S}\) contain ions with a charge of +1 (K or Cs) and -2 (S or O), whereas CaS and CaO contain ions with a charge of +2 (Ca) and -2 (S or O). The compounds with ions that have a +2 and -2 charge will require more energy to dissociate compared to those with +1 and -2 charges.

Step 3: Compare Ionic Radii

For compounds with similarly charged ions, compare the ionic radii to determine lattice energy. Smaller ionic radii result in stronger attraction between ions and hence higher lattice energy. Among CaS and CaO, the ion O\(^{2-}\) is smaller than S\(^{2-}\), making the attraction stronger in CaO.

Step 4: Determine the Compound with Highest Lattice Energy

Based on the charges and sizes of the ions, CaO has ions with the highest charges (+2 and -2) and the smallest anion (O\(^{2-}\)). Therefore, CaO requires the most energy to convert one mole of solid into separate ions.

Key Concepts

Ionic Compounds

Ionic compounds are substances composed of positive and negative ions held together by strong electrostatic forces, known as ionic bonds. These compounds form when atoms of metallic elements give up electrons to atoms of non-metallic elements, creating ions with opposite charges that attract each other.

The structure of ionic compounds is typically a crystalline lattice where each ion is surrounded by ions of the opposite charge. This maximizes the attractive forces and minimizes repulsion between ions with the same charge, leading to the formation of a stable ionic solid.

Energetics of Ionic Solids

The energetics of ionic solids relates to the energy changes involved in forming or disrupting the ionic lattice. Lattice energy is a key concept here, defined as the energy required to completely separate one mole of a solid ionic compound into its gaseous ions.

Compounds with higher lattice energies are generally more stable and have higher melting points. To compare lattice energies, we look at the charges of the ions involved and their sizes. A greater charge magnifies the energy, while smaller ions, being closer together, also result in a stronger attraction and thus higher lattice energy.

Ionic Charges and Radii

The charge and size of ions play a pivotal role in the strength of the ionic bond. The charge on an ion affects how strongly it attracts or repels other ions. Ions with higher charges will exert stronger electrostatic forces, requiring more energy to overcome these forces when separating the ions.

Similarly, the ionic radii determine how close the ions can get to each other in the lattice. Smaller ions can pack more tightly together, increasing the overall attraction within the lattice. Therefore, a compound with smaller, highly charged ions will generally have a higher lattice energy than a compound with larger, less charged ions.

Chemical Bonds

Chemical bonds, such as ionic bonds, are the forces that hold atoms or ions together in a compound. Ionic bonds form between atoms with a large difference in electronegativity, typically between metals and non-metals. In these bonds, electrons are transferred from the less electronegative atom to the more electronegative one, resulting in the formation of positive and negative ions.

The strength of the ionic bond is a significant factor in the compound's properties, including its melting point, boiling point, and hardness. It's important to recognize that ionic bonds are just one type of chemical bond. Others include covalent bonds, where electrons are shared between atoms, and metallic bonds, found in pure metal structures.