Problem 18 - General Chemistry

Question

What is the coordination number of \(\mathrm{Cs}^{+}\) in \(\mathrm{CsCl}\) ? of \(\mathrm{Na}^{+}\) in \(\mathrm{NaCl}\) ? of \(\mathrm{Zn}^{2+}\) in \(\mathrm{ZnS}\) ?

Step-by-Step Solution

Answer

Coordination numbers are: CsCl: 8, NaCl: 6, ZnS: 4.

Step 1: Understand Coordination Number Definition

The coordination number refers to the number of nearest neighboring atoms or ions that surround a central atom in a crystal lattice. This depends on the specific crystal structure adopted by the compound.

Step 2: Determine CsCl Coordination Number

CsCl adopts a simple cubic crystal structure in which each Cs⁺ ion is surrounded by 8 Cl⁻ ions. Therefore, the coordination number of Cs⁺ in CsCl is 8.

Step 3: Determine NaCl Coordination Number

NaCl adopts a face-centered cubic (FCC) structure, also known as a rock salt structure. In this structure, each Na⁺ ion is surrounded by 6 Cl⁻ ions, giving it a coordination number of 6.

Step 4: Determine ZnS Coordination Number

ZnS typically adopts a zinc blende (sphalerite) structure in which each Zn²⁺ ion is tetrahedrally surrounded by 4 S²⁻ ions. Therefore, the coordination number of Zn²⁺ in ZnS is 4.

Key Concepts

CsCl structure

The cesium chloride (CsCl) structure is quite fascinating in the realm of crystal lattices. In this arrangement, cesium ions (Cs⁺) and chloride ions (Cl⁻) form a simple cubic structure. What makes it unique is that each Cs⁺ ion is surrounded by eight Cl⁻ ions, and each Cl⁻ ion is surrounded by eight Cs⁺ ions. Thus, both ions have a coordination number of 8. This symmetry highlights the equal contribution each ion makes toward stabilizing the crystal lattice. Additionally, this structure ensures that the large Cs⁺ ion fits comfortably in the cubic array formed by the smaller Cl⁻ ions.

NaCl crystal structure

The sodium chloride (NaCl) crystal structure, often referred to as the rock salt structure, is a staple example in studies of ionic compounds. In this configuration, the sodium ions (Na⁺) and chloride ions (Cl⁻) form a face-centered cubic (FCC) lattice. Each Na⁺ ion is surrounded by six Cl⁻ ions, and vice versa, giving both a coordination number of 6. This structure is efficient and results in a tightly packed arrangement. It's key to note that the interionic forces in NaCl are strong due to the high coordination number and the balance between the ionic sizes, contributing to its high melting and boiling points.

• Each corner of the cube contains a sodium ion.
• The face centers consist of chloride ions.

Together, this forms a repetitive and robust lattice.

ZnS zinc blende

The zinc sulfide (ZnS) zinc blende structure offers a different perspective on coordination in crystals. Here, zinc ions (Zn²⁺) are surrounded tetrahedrally by sulfur ions (S²⁻). This results in a coordination number of 4 for both ions. The tetrahedral arrangement provides a distinct advantage: it allows flexibility and prevents the overlapping of electron clouds more effectively than higher coordination arrangements might.

• ZnS crystals are often transparent and exhibit excellent optical properties.
• Tetrahedral coordination also contributes to its capability to conduct electricity under certain conditions.

This structure is common in many semiconductors and provides an intriguing comparison to other types of lattices in terms of stability and functionality.

Chemical bonding in crystals

Chemical bonding in crystals is a fundamental concept that explains how atoms or ions come together to form a solid. In crystals like CsCl, NaCl, and ZnS, these interactions are predominantly ionic. This means electrons are transferred between atoms, leading to the formation of charged ions that are held together by electrostatic forces.

Ionic Bonding

Ionic bonding is strong and directional, which results in stable structures. The strength of the ionic bond is influenced by factors such as:

• The charge on the ions: Higher charges generally equate to stronger bonds.
• The size of the ions: Smaller ions can get closer together, increasing bond strength.

Other Considerations

While ionic bonding is predominant, other forces like van der Waals interactions also play a role, particularly at lower temperatures or in complex crystals. Understanding these forces helps in predicting properties such as solubility, melting points, and hardness.