Q12.128CP

Question

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

Step-by-Step Solution

Verified

Answer

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

1Step 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 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.

2Step 2: 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.

$\begin{matrix} The number of Ta-atoms in the unit cell =(1×1) + (8× \frac{1}{8}) \\ The number of Ta-atoms in the unit cell =1+1 \\ The number of Ta-atoms in the unit cell =2 \end{matrix}$

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

$\begin{matrix} The number of N-atoms in the unit cell = (1×1)+(4× \frac{1}{4}) \\ The number of N-atoms in the unit cell = 1+1 \\ The number of N-atoms in the unit cell = 2 \end{matrix}$

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.

3Step 3: 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.

$\begin{matrix} The number of Ta-atoms in the unit cell = (1×1)+(12× \frac{1}{4}) \\ The number of Ta-atoms in the unit cell = 1+3 \\ The number of Ta-atoms in the unit cell = 4 \end{matrix}$

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.

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

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.

Q12.127CP

Q12.129CP

Other exercises in this chapter

Q12.126CP

Polytetrafluoroethylene (Teflon) has a repeat unit with the formula F2C—CF2 . A sample of the polymer consists of fractions with the following distributio

View solution

Q12.127CP

A greenhouse contains 256m3 of air at a temperature of 26°C, and a humidifier in it vaporizes 4.20 L of water. (a) What is

View solution

Q12.129CP

Iron crystallizes in a body-centered cubic structure. The volume of one Fe atom is 8.38×10-24cm3, and the density of Fe is 7.874gcm-3 . Find an appro

View solution

Q12.130CP

Corn is a valuable source of industrial chemicals. For example, furfural is prepared from corncobs. It is an important solvent in synthetic rubber manufacturing

View solution