Question

Pick out the incorrect statement: (a) \(\mathrm{NaCl}\) has \(8: 8\) coordination, while \(\mathrm{CsCl}\) is with \(6: 6\) coordination (b) In \(\mathrm{Na}_{2} \mathrm{O}\) each oxide ion is coordinated by \(8 \mathrm{Na}^{+}\) ions and each \(\mathrm{Na}^{+}\)ion by 4 oxide ions (c) \(\mathrm{NaCl}\) structure transform to \(\mathrm{CsCl}\) structure on heating (d) In \(\mathrm{CaF}_{2}\) structure, each \(\mathrm{F}^{-}\)ion is coordinated by \(4 \mathrm{Ca}^{2}\) ions and each \(\mathrm{Ca}^{+}\)ion is coordinated by \(8 \mathrm{~F}\) ions

Short answer

Statements (a) and (c) are incorrect.

Step-by-step solution

Analyze Statement (a)

In statement (a), it's mentioned that \( \mathrm{NaCl} \) has \(8:8\) coordination and \( \mathrm{CsCl} \) is with \(6:6\) coordination. In reality, \( \mathrm{NaCl} \) has a \(6:6\) coordination number because each \( \mathrm{Na^+} \) ion is surrounded by 6 \( \mathrm{Cl^-} \) ions and vice versa. \( \mathrm{CsCl} \), on the other hand, has an \(8:8\) coordination due to each \( \mathrm{Cs^+} \) ion being surrounded by 8 \( \mathrm{Cl^-} \) ions. Thus, statement (a) is incorrect.

Analyze Statement (b)

Statement (b) asserts that in \( \mathrm{Na}_2 \mathrm{O} \), each oxide ion is coordinated by 8 \( \mathrm{Na}^+ \) ions and each \( \mathrm{Na}^+ \) ion by 4 oxide ions. In the anti-fluorite structure, typical for \( \mathrm{Na}_2 \mathrm{O} \), each \( \mathrm{O}^{2-} \) ion is indeed surrounded by 8 \( \mathrm{Na}^+ \) ions, and each \( \mathrm{Na}^+ \) is surrounded by 4 \( \mathrm{O}^{2-} \). Therefore, statement (b) is correct.

Analyze Statement (c)

In statement (c), it states that the \( \mathrm{NaCl} \) structure transforms to a \( \mathrm{CsCl} \) structure on heating. Normally, heating NaCl does not result in a structural transformation to the CsCl structure under typical conditions, as such transformations require specific pressures and temperatures not characteristic of simple heating. Therefore, statement (c) is incorrect under normal conditions.

Analyze Statement (d)

Statement (d) suggests that in the \( \mathrm{CaF}_2 \) structure, each \( \mathrm{F}^- \) ion is coordinated by 4 \( \mathrm{Ca}^{2+} \) ions, and each \( \mathrm{Ca}^{2+} \) ion is coordinated by 8 \( \mathrm{F}^- \) ions. This describes the fluorite structure of \( \mathrm{CaF}_2 \), where \( \mathrm{CaF}_2 \) indeed has such a coordination. So, statement (d) is correct.

Key concepts

Crystal Structures

Crystal structures are the regular geometric arrangements of atoms in a crystal. These structures significantly influence the properties of the material such as its strength, conductivity, and melting point.
Each atom in a crystal lattice, or each ion in ionic compounds, adopts a specific position, creating a repeating pattern that extends in three dimensions.
There are several different types of crystal structures; here are a few common ones:

• Face-centered cubic (fcc): Each atom in the cubic unit cell has 12 atoms as nearest neighbors, creating a compact structure. Examples include metals like copper and aluminum.
• Body-centered cubic (bcc): Each atom has 8 neighbors, less dense than fcc, found in metals like iron at room temperature.
• Hexagonal close-packed (hcp): Similar to fcc, with 12 neighbors but arranged differently, as seen in metals such as magnesium and zinc.

Understanding these structures helps in predicting the coordination number, or the number of nearest neighbors surrounding an atom or ion within the crystal.

NaCl Crystal Lattice

The NaCl crystal lattice, also known as the rock salt structure, is a classic example of an ionic compound's arrangement. This lattice is structured around the face-centered cubic (fcc) unit cell arrangement.
In NaCl, the coordination number is 6:6. Each sodium ion (\[\text{Na}^+ \]) is surrounded by six chloride ions (\[\text{Cl}^-\]), and vice versa. This symmetrical arrangement leads to high stability and results in its cubic shape.
The uniformity of the lattice ensures that each ion is completely surrounded by ions of opposite charge, cancelling out any net electronic interaction. This attribute makes NaCl soluble in water and gives it high melting and boiling points, characteristic of many ionic solids.

CsCl Crystal Lattice

The CsCl crystal lattice differs from NaCl in terms of structure and coordination numbers. CsCl adopts a simple cubic structure instead of the fcc of NaCl, leading to a different coordination number of 8:8.
Here, each cesium ion (\[\text{Cs}^+\]) is surrounded by eight chloride ions, and each chloride ion is similarly coordinated by eight cesium ions. The arrangement gives rise to a different crystal symmetry and density compared to NaCl.
The larger size of the cesium ion compared to the sodium ion allows the formation of this structure, which can also be influenced by the different ionic radii and lattice energy considerations. Understanding CsCl lattice structure helps explain its unique physical properties compared to NaCl.

CaF2 Fluorite Structure

The CaFeutrophil2fluorite structure is a type of cubic arrangement typical for calcium fluoride. This structure showcases an interesting arrangement, where each calcium ion (\[\text{Ca}^{2+}\]) is surrounded by eight fluoride ions (\[\text{F}^-\]). Conversely, each fluoride ion is coordinated by four calcium ions.
This 8:4 coordination is characteristic of the fluorite structure which provides it with distinct physical attributes, including high optical transparency and excellent chemical durability.
In the crystalline arrangement, the unit cell structure results in a high degree of symmetry, which is beneficial in applications requiring precision optics and robust material properties. The understanding of the fluorite structure can also be applied to other compounds that share similar packing and coordination numbers.