Question

Tantalum crystallises in a cubic system, and the edge of the unit cell is 330pm. The density of Tantalum is 16.6 cm 3

g
​
. How many atoms of Ta are contained in one unit cell (n)? What type of unit cell does Ta form? (For Ta: MW=181 and N A
​
= 6.02×10 23
mol atoms ​
)(20 Pts.) Vanadium crystallises in a body - centered cubic system (n=2), and the edge of the unit cell is 305pm. What is the density of Vanadium? (For V: MW =51 and N A
​
= 6.02×10 23
mol
atoms ​
) (20 Pts.)

Answer 1

* Tantalum forms a face-centered cubic (fcc) unit cell with 4 atoms per unit cell.

* The density of vanadium is 5.97 g/cm^3.

The density of tantalum is 16.6 g/cm^3. The edge length of the unit cell is 330 pm. The molar mass of tantalum is 181 g/mol. The Avogadro constant is 6.022 * 10^23 mol^-1.

The density of a substance is defined as the mass per unit volume. So, the density of tantalum can be calculated as follows:

density = mass / volume

density = 1
`81 g / (6.022 * 10^23 mol) * (330 pm)^3 * (10^-12 cm^3 / pm^3)`

density = 16.6 g/cm^3

The number of atoms per unit cell can be calculated as follows:

number of atoms = density * volume / molar mass * Avogadro constant

number of atoms =
`16.6 g/cm^3 * (330 pm)^3 * (10^-24 cm^3 / pm^3) / 181 g/mol * 6.022 * 10^23 mol^-1`

number of atoms = 4

Therefore, tantalum forms a face-centered cubic (fcc) unit cell with 4 atoms per unit cell.

The density of vanadium can be calculated as follows:

density =
`51 g / (6.022 * 10^23 mol) * (305 pm)^3 * (10^-12 cm^3 / pm^3)`

density = 5.97 g/cm^3

Therefore, the density of vanadium is 5.97 g/cm^3.