Question

Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of each tantalum compound whose unit cell is depicted below:

a.

b.

Short answer

1. The formula of the compound is TaN.
2. The formula of the compound is TaC.

Step-by-step solution

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

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

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

Subpart (a) The formula of tantalum compound whose unit cell is been depicted as A.

In the cubic lattice,

The Ta-atom is present at the corner which is touched by the 8 atoms in the unit cell and at body centre one atom present at the centre of the unit cell.

$\begin{array}{c}\text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}Ta-atoms\hspace{0.17em}\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=(1×1)+(8×}\frac{\text{1}}{\text{8}}\text{)}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}Ta-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=1+1}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}Ta-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=2}\end{array}$

In this unit cell, one N atom inside the unit cell and 4 N-atom are present at$\frac{1}{4}$edge centre.

$\begin{array}{c}\text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}N-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=(1×1)+(4×}\frac{\text{1}}{\text{4}}\text{)}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}N-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=1+1}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}N-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=2}\end{array}$

In the compound, the Ta-atom is present at the corner and body-centre forming Ta-atom having co-ordination number 2 whereas the N-atom are present at edge centre having co-ordination number is 2.

Therefore, the formula of the compound is TaN.

Subpart (b) The formula of tantalum compound whose unit cell is been depicted as B.

In the cubic lattice,

The Ta-atom is present at edge-centre which is touched by the 4 atoms in the unit cell and at body centre one atom present at the centre of the unit cell.

$\begin{array}{c}\text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}Ta-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=(1×1)+(12×}\frac{\text{1}}{\text{4}}\text{)}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}Ta-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=1+3}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}Ta-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=4}\end{array}$

In this unit cell, one C-atom inside the unit cell and 8 C-atom are present at $\frac{1}{8}$corner and 6 C-atom present at $\frac{1}{2}$face-centre.

$\begin{array}{c}\text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}C-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=(8×}\frac{\text{1}}{\text{8}}\text{)+(6×}\frac{\text{1}}{\text{2}}\text{)}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}N-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=1+3}\\ \text{The\hspace{0.17em}number\hspace{0.17em}of\hspace{0.17em}N-atoms\hspace{0.17em}in\hspace{0.17em}the\hspace{0.17em}unit\hspace{0.17em}cell=4}\end{array}$

In compound, the Ta-atom are present body-centre and edge-centre forming Ta-atom having co-ordination number 2 whereas the N-atom are present at corner and face-centre having co-ordination number is 2.

Therefore, the formula of the compound is TaC.