Question

Vanadium crystallizes in a body-centered cubic lattice, and the length of the edge of a unit cell is 305 pm. What is the density of V

Answer 1

Answer:

5.96 g/cm^3

Explanation:

Corner atom = 1/8

Atoms in center = 1

Atoms in face of the cube= 1/2  

Molar mass of V = 50.94 g/mol (from period table)

1 mole = 6.02x10^23

In BCC unit cell:

(8 x 1/8)+ 1=2 per 1 unit cell

Mass: 2(50.94g)/6.02x10^23 = 1.69x10^-22 g/unit cell

305pm=(305x10^-12m÷10^-2m) x (1mL÷1cm^3)

           = 2.837 x 10^-23 mL

1pm=10^-12m

1cm=10^-2m

1mL=1cm^3

density=mass/volume

density of V = 1.69x10^-22g÷2.837x10^-23mL

                    =5.957g/mL

                    =5.96g/cm^3