A compound forms hexagonal close packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?

To determine the total number of voids in a compound that forms a hexagonal close-packed (HCP) structure, we first need to understand the arrangement of atoms and the types of voids present in this structure. In an HCP arrangement, atoms are closely packed, and there are two types of voids: tetrahedral and octahedral. Let's break this down step by step.

Understanding the HCP Structure

In a hexagonal close-packed structure, there are two layers of atoms that form a repeating pattern. Each unit cell contains a total of 6 atoms. The arrangement allows for the formation of both tetrahedral and octahedral voids:

• Tetrahedral voids: Each tetrahedral void is surrounded by four atoms. In an HCP structure, there are 8 tetrahedral voids per unit cell.
• Octahedral voids: Each octahedral void is surrounded by six atoms. There are 4 octahedral voids per unit cell in an HCP structure.

Calculating the Number of Voids

Now, let's calculate the total number of voids in 0.5 mol of the compound. First, we need to find out how many unit cells are present in 0.5 mol of the compound:

1 mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). Therefore, 0.5 mol contains:

0.5 mol × \(6.022 \times 10^{23}\) = \(3.011 \times 10^{23}\) atoms.

Since each unit cell of HCP contains 6 atoms, we can find the number of unit cells:

Number of unit cells = Total atoms / Atoms per unit cell = \(3.011 \times 10^{23} / 6 \approx 5.018 \times 10^{22}\) unit cells.

Finding the Total Number of Voids

Now that we know the number of unit cells, we can calculate the total number of voids:

Total voids per unit cell = Tetrahedral voids + Octahedral voids = 8 + 4 = 12 voids.

Total voids in 0.5 mol = Number of unit cells × Total voids per unit cell = \(5.018 \times 10^{22} \times 12 \approx 6.0216 \times 10^{23}\) voids.

Determining Tetrahedral Voids

Next, we need to find out how many of these voids are tetrahedral. Since there are 8 tetrahedral voids per unit cell, we can calculate the total number of tetrahedral voids:

Total tetrahedral voids in 0.5 mol = Number of unit cells × Tetrahedral voids per unit cell = \(5.018 \times 10^{22} \times 8 \approx 4.0144 \times 10^{23}\) tetrahedral voids.

Summary of Results

In summary, for 0.5 mol of a compound that forms a hexagonal close-packed structure:

• Total number of voids: approximately \(6.0216 \times 10^{23}\)
• Total number of tetrahedral voids: approximately \(4.0144 \times 10^{23}\)

This analysis shows how the arrangement of atoms in a close-packed structure leads to a specific number of voids, which are crucial for understanding the properties of materials, especially in solid-state chemistry and materials science.