Q134-CP - Chemistry: Molecular Nature Of Matter And Change

Question

Question: Is it possible for a salt of formula AB₃ to have a face-centered cubic unit cell of anions with cations in all the eight available holes? Explain

Step-by-Step Solution

Answer

Answer

 

Yes, it is possible to form a face-centered cubic unit cell having formula AB₃ .

The cations and anions have eight available holes in which A has coordination number 6 and B has coordination number 2.

 

Step 1: Definition

The matter exists in three phases- solid, liquid, and gaseous. The solid-state molecules are arranged in a three-dimensional structure having a high force of attraction. The solid molecule can be arranged in two forms crystalline and amorphous solid.

 

Crystalline solid has the same structure throughout the molecule in a three-dimensional structure. The crystalline solid has a well-arranged structure.

 

Amorphous solids have a different arranged structure throughout the molecule in a three-dimensional structure. The amorphous has a weak force of attraction.

Step 2: Numerical Explanation

A cubic unit cell can be defined as a three-dimensional structure having the same length of sides. Here, a = b = c  .

The formula of the cubic unit cell is AB₃  .

The molecule is arranged in the face-centered cubic unit cell having the same length of the sides  a = b = c. 

Now, B is placed at the edge- the center of the cubic cell whereas A is placed at the face-center in the lattice. 

 

B is surrounded by two A-atoms, therefore, the coordination number of 2.

A is surrounded by six B-atoms, therefore, the coordination number is 6.

$$\begin{gathered} \mathrm{Total}\mathrm{Co}-\mathrm{ordination}=\mathrm{x}+\mathrm{y} \\ \mathrm{Total}\mathrm{Co}-\mathrm{ordination}=6+2 \\ \mathrm{Total}\mathrm{Co}-\mathrm{ordination}=8 \end{gathered}$$