Problem 77 - Chemistry: An Atoms-Focused Approach

Question

Crystals of both \(\mathrm{LiCl}\) and $$\mathrm{KCl}$$ have the rock salt structure. In the unit cell of \(\mathrm{LiCl}\), adjacent $$\mathrm{Cl}^{-}$$ ions touch each other. In $$\mathrm{KCl}$$ they don't. Why?

Step-by-Step Solution

Answer

The chloride ions ($$\mathrm{Cl}^{-}$$) touch each other in the lithium chloride (LiCl) crystal structure but not in potassium chloride (KCl) due to the difference in the sizes of the cations ($$\mathrm{Li}^{+}$$ and $$\mathrm{K}^{+}$$). The smaller $$\mathrm{Li}^{+}$$ ions allow for more closely packed chloride ions in LiCl, resulting in adjacent $$\mathrm{Cl}^{-}$$ ions touching. However, the larger $$\mathrm{K}^{+}$$ ions in the KCl structure keep the chloride ions farther apart, preventing them from touching each other.

Step 1: Understanding the rock salt structure

The rock salt structure is a type of crystal structure commonly found in ionic compounds, such as LiCl and KCl. In this structure, anions and cations are arranged in a face-centered cubic (FCC) lattice, with each ion surrounded by 6 ions of the opposite charge.

Step 2: Knowing the cation sizes

The size of the cations plays an important role in determining the arrangement of the ions in the crystal. Specifically, the distance between the cations in the lattice determines the space available for chloride ions ($$\mathrm{Cl}^{-}$$) in the unit cell. The size of $$\mathrm{Li}^{+}$$ (76 pm) is smaller than $$\mathrm{K}^{+}$$ (138 pm), so there is less space between adjacent $$\mathrm{Li}^{+}$$ ions than $$\mathrm{K}^{+}$$ ions.

Step 3: Examining the distances between chloride ions

In the LiCl unit cell, the smaller size of the $$\mathrm{Li}^{+}$$ ions allows the chloride ions ($$\mathrm{Cl}^{-}$$) to be packed more closely together. As a result, the distance between the adjacent $$\mathrm{Cl}^{-}$$ ions is shorter, and they touch each other. On the other hand, in the KCl unit cell, the larger size of the $$\mathrm{K}^{+}$$ ions results in a greater distance between the adjacent $$\mathrm{Cl}^{-}$$ ions, so they don't touch each other.

Step 4: Conclusion

In summary, the reason why adjacent chloride ions ($$\mathrm{Cl}^{-}$$) touch each other in the crystal structure of LiCl but not in KCl is due to the difference in the sizes of the cations ($$\mathrm{Li}^{+}$$ and $$\mathrm{K}^{+}$$). The smaller $$\mathrm{Li}^{+}$$ ions in the LiCl structure allow for more closely packed chloride ions, resulting in the touching of adjacent $$\mathrm{Cl}^{-}$$ ions. However, the larger $$\mathrm{K}^{+}$$ ions in the KCl structure keep the chloride ions farther apart, preventing them from touching each other.

Key Concepts

Rock Salt Structure

The rock salt structure is a common crystalline arrangement seen in ionic compounds. It gets its name because the pattern resembles that of the mineral halite, or rock salt. This structure features ions organized in a face-centered cubic (FCC) configuration. Each unit cell consists of a repeating pattern where each type of ion is surrounded symmetrically by the opposite ion. This means that in compounds like \( \text{LiCl} \) and \( \text{KCl} \), both the anions and cations are arranged to optimize their ionic attractions.
In this lattice, each chloride ion \( \text{Cl}^- \) is surrounded by six cations \( \text{Li}^+ \) or \( \text{K}^+ \), forming an octahedral shape. Similarly, each cation is also surrounded by six anions. This high level of symmetry and close packing helps maximize the stability of the ionic crystal.

Cation Size

Cation size is crucial in determining how close ions can pack in a crystal. Smaller cations can fit into the spaces created by the anions more snugly than larger cations. The size of the cations \( \text{Li}^+ \) and \( \text{K}^+ \) dramatically affects their crystal structures. For instance:

• \( \text{Li}^+ \) ions are much smaller, measuring 76 pm in radius.
• \( \text{K}^+ \) ions are larger, with a radius of 138 pm.

These differences mean that the smaller \( \text{Li}^+ \) ions allow for a more compact arrangement of surrounding \( \text{Cl}^- \) ions compared to \( \text{K}^+ \) ions, impacting the distances between neighboring ions within the crystal lattice.

Crystal Lattice

A crystal lattice serves as a three-dimensional framework detailing how ions are spatially arranged. In the rock salt structure, this lattice is highly symmetrical, contributing to the stability and formation of the crystal. Each ion in the lattice is attracted to all surrounding ions of the opposite charge, which pulls them into a rigid and defined pattern.
In \( \text{LiCl} \), the small \( \text{Li}^+ \) ions result in closer and denser packing of \( \text{Cl}^- \) ions, while the larger \( \text{K}^+ \) ions in \( \text{KCl} \) lead to a less compact arrangement. Thus, the crystal lattice not only dictates how ions interact but also influences their overall separation within the formed crystal.

Face-Centered Cubic

The face-centered cubic (FCC) configuration is one of the most efficient ways to pack spheres, such as ions, in three-dimensional space. This structure is defined by having atoms at each of the corners and the centers of all the cube faces of the unit cell.
In the context of ionic compounds like \( \text{LiCl} \) and \( \text{KCl} \), the FCC arrangement means each cation is equidistantly surrounded by anions, and vice versa. This arrangement enhances the stability of the crystal by maximizing attraction forces between oppositely charged ions. The FCC layout is vital to understanding why ionic crystals tend to be so stable and hard.

Anion Arrangement

Anion arrangement in the rock salt structure refers to how negatively charged ions, such as \( \text{Cl}^- \), are spaced within the crystal lattice. This depends heavily on the size of the cations around which they are arranged. The smaller \( \text{Li}^+ \) ions allow \( \text{Cl}^- \) ions to be closer together, sometimes to the point of touching, as seen in \( \text{LiCl} \).
Conversely, in \( \text{KCl} \), larger \( \text{K}^+ \) ions push \( \text{Cl}^- \) ions further apart, preventing them from touching. Therefore, the specific arrangements of anions and their distances in the lattice have a direct correlation to the size of the neighboring cations, influencing the compound's physical properties.