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? A) 0.712 g/cm³ B) 2.98 g/cm³ C) 5.96 g/cm³ D) 8.77 g/cm³ E) 11.9 g/cm³

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula:

density = (mass of unit cell) / (volume of unit cell)

First, we need to calculate the mass of the unit cell. To do this, we need to know the atomic weight of vanadium, which is 50.9415 g/mol. A body-centered cubic unit cell of vanadium contains 2 atoms, so the mass of the unit cell is:

mass = 2 x atomic weight
mass = 2 x 50.9415 g/mol
mass = 101.883 g

Next, we need to calculate the volume of the unit cell. Since vanadium crystallizes in a body-centered cubic lattice, the volume of the unit cell can be calculated using the formula:

volume = a^3 x (4/3) x pi

where a is the length of the edge of the unit cell.

In this case, a = 305 pm = 305 x 10^-12 m. Plugging in the values, we get:

volume = (305 x 10^-12 m)^3 x (4/3) x pi 
volume = 1.423 x 10^-26 m^3

Now we can plug the mass and volume values into the density formula:

density = mass / volume 
density = 101.883 g / 1.423 x 10^-26 m^3 
density = 5.96 x 10^3 kg/m^3

To convert this to g/cm3, we divide by 1000:

density = 5.96 x 10^3 / 1000 g/cm3 
density = 5.96 g/cm3

Therefore, the answer is C (5.96 g/cm3).

Vanadium Crystallizes in a Body-Centered Cubic Lattice, and the Length