Question

Compare and contrast the structures of the following solids. a. \(\mathrm{CO}_{2}(s)\) versus \(\mathrm{H}_{2} \mathrm{O}(s)\) b. \(\mathrm{NaCl}(s)\) versus \(\mathrm{CsCl}(s)\) ; see Exercise 71 for the structures.

Short answer

Both \(\mathrm{CO}_{2}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(s)\) have covalent bonding within their molecules but differ in their crystal structures and intermolecular forces. Solid \(\mathrm{CO}_2\) has a molecular solid structure with weak van der Waals forces, while solid water has a hexagonal lattice structure with strong hydrogen bonding. On the other hand, both \(\mathrm{NaCl}(s)\) and \(\mathrm{CsCl}(s)\) have ionic bonding but differ in their crystal structures. Sodium chloride forms a face-centered cubic (FCC) crystal structure, while cesium chloride forms a simple cubic crystal structure, leading to variations in coordination numbers.

Step-by-step solution

Identify the bonding type in each compound

First, we will identify the type of bonding present in each compound. This will help us understand their crystal structures more effectively. a. \(\mathrm{CO}_{2}(s)\): Carbon dioxide has covalent bonding between the carbon and oxygen atoms, forming a linear molecule. \(\mathrm{H}_{2} \mathrm{O}(s)\): Water has covalent bonding between the oxygen and hydrogen atoms, forming a bent molecule due to the presence of two lone pairs on the oxygen atom. b. \(\mathrm{NaCl}(s)\): Sodium chloride consists of ionic bonding between positively charged sodium ions (\(\mathrm{Na}^+\)) and negatively charged chloride ions (\(\mathrm{Cl}^-\)). \(\mathrm{CsCl}(s)\): Cesium chloride also consists of ionic bonding, between positively charged cesium ions (\(\mathrm{Cs}^+\)) and negatively charged chloride ions (\(\mathrm{Cl}^-\)).

Discuss the crystal structures of each compound

Now that we know the bonding types present in these compounds, we can discuss their crystal structures in more detail. a. \(\mathrm{CO}_{2}(s)\): Solid carbon dioxide, also known as dry ice, has a molecular solid structure held together by weak van der Waals forces. The repeating structural unit is a single \(\mathrm{CO}_2\) molecule. Due to the weak intermolecular forces, dry ice sublimes directly into gas at low pressures, without passing through a liquid phase. \(\mathrm{H}_{2} \mathrm{O}(s)\): Solid water, or ice, forms a hexagonal lattice structure held together by strong hydrogen bonding between adjacent water molecules. This lattice structure causes ice to be less dense than liquid water, resulting in ice floating on water. b. \(\mathrm{NaCl}(s)\): Sodium chloride forms a face-centered cubic (FCC) crystal structure, with alternating \(\mathrm{Na}^+\) and \(\mathrm{Cl}^-\) ions in a 1:1 ratio. Each ion is surrounded by six neighbors of the opposite charge, creating a three-dimensional lattice structure. \(\mathrm{CsCl}(s)\): Cesium chloride forms a simple cubic crystal structure, with one \(\mathrm{Cs}^+\) ion in the center and eight \(\mathrm{Cl}^-\) ions at the corners of the cubic unit cell. Each ion is surrounded by eight neighbors of the opposite charge, creating a 1:1 ratio in the three-dimensional lattice structure.

Compare and contrast the structures in each pair

Finally, we will compare the structures within each pair. a. \(\mathrm{CO}_{2}(s)\) vs. \(\mathrm{H}_{2} \mathrm{O}(s)\): Both have covalent bonding within their respective molecules but differ in their crystal structures and intermolecular forces. Solid \(\mathrm{CO}_2\) has a molecular solid structure with weak van der Waals forces holding it together, while solid water has a hexagonal lattice structure with strong hydrogen bonding. This results in vastly differing physical properties, such as the lower density of ice compared to water and the sublimation of dry ice at low pressures. b. \(\mathrm{NaCl}(s)\) vs. \(\mathrm{CsCl}(s)\): Both structures have ionic bonding and a 1:1 ratio of cations and anions, but have different arrangements of their ions. Sodium chloride forms a face-centered cubic (FCC) crystal structure, while cesium chloride forms a simple cubic crystal structure. This difference in arrangement leads to variations in coordination numbers, with each ion in \(\mathrm{NaCl}\) being surrounded by six neighbors of the opposite charge, while in \(\mathrm{CsCl}\), each ion is surrounded by eight neighbors of the opposite charge.

Key concepts

Covalent Bonding

Covalent bonding is a fundamental concept in chemistry that involves the sharing of electron pairs between atoms. This type of bonding occurs primarily between non-metals and allows them to achieve a stable electron configuration, resembling that of noble gases.
For example, in a water molecule (\(\mathrm{H}_{2}\mathrm{O}\)), the oxygen atom shares electrons with two hydrogen atoms. Due to the presence of lone pairs of electrons on oxygen, the molecule adopts a bent shape, which is crucial for the hydrogen bonding that occurs in ice. Similarly, in carbon dioxide (\(\mathrm{CO}_2\)), carbon forms two double bonds with oxygen, resulting in a linear molecular structure.

Covalent bonding often involves the formation of molecular orbitals, and the strength of the bond depends on the overlap between these orbitals. Strong covalent bonds lead to stable molecules, which exhibit specific physical properties like shape, polarity, and reactivity.

Ionic Bonding

Ionic bonding involves the electrostatic attraction between oppositely charged ions and is one of the primary types of chemical bonding. It occurs when one atom donates electrons to another, resulting in the formation of ions which are then attracted to each other due to their opposite charges.

For instance, in sodium chloride (\(\mathrm{NaCl}\)), a sodium atom donates an electron to a chlorine atom. This results in the formation of a positive sodium ion (\(\mathrm{Na}^+\)) and a negative chloride ion (\(\mathrm{Cl}^-\)), which create a strong ionic bond. These ions are arranged in a face-centered cubic (FCC) lattice structure, where each ion is surrounded by six ions of the opposite charge.

Ionic compounds generally have high melting and boiling points, and they conduct electricity when dissolved in water or melted, due to the movement of ions.

Hydrogen Bonding

Hydrogen bonding is a special type of dipole-dipole interaction that occurs when a hydrogen atom, covalently bonded to a highly electronegative atom like oxygen, nitrogen, or fluorine, experiences an attraction to a lone pair of electrons on another electronegative atom.

In the case of ice, the hydrogen bonds between water molecules lead to a hexagonal lattice structure. Each oxygen atom can form hydrogen bonds with up to four other water molecules, creating a rigid network that is less dense than liquid water.

Hydrogen bonds are weaker than covalent bonds but stronger than van der Waals forces. They are crucial in determining the properties of water, such as its high boiling point, surface tension, and the solid state being less dense than the liquid state.

van der Waals Forces

Van der Waals forces are weak intermolecular forces that arise from transient induced dipoles in molecules. These forces play a significant role in the formation of molecular solids.

In solid carbon dioxide, or dry ice, these weak forces are responsible for holding the \(\mathrm{CO}_{2}\) molecules together. Since these forces are much weaker than other types of molecular interactions like hydrogen bonds, dry ice sublimates easily, turning directly from a solid to a gas at room temperature without passing through a liquid phase.

These forces include van der Waals dispersion forces (London forces) and van der Waals dipole-dipole interactions. Despite their weakness, they are crucial in determining the physical properties of molecular substances, such as boiling and melting points, solubility, and the ability to sublimate.