Final answer:
The metal vanadium crystallizes in a body-centered cubic lattice. To calculate the unit cell volume, we need to find the volume of the unit cell using the given density. Then, we can calculate the mass of the unit cell and determine the number of moles.
Step-by-step explanation:
The metal vanadium crystallizes in a body-centered cubic lattice. To determine the unit cell volume, we need to find the volume of the unit cell. In a body-centered cubic lattice, there is an atom at each of the eight corners of the cube and one atom in the center of the cube.
The volume of the unit cell can be calculated using the formula:
Volume of unit cell = (edge length)^3
Given the density of vanadium as 6.11 g/cm³, we can use the density formula to find the mass of the unit cell:
Mass of unit cell = density x volume of unit cell
Finally, we can use the atomic weight of vanadium to find the number of moles:
Number of moles = mass of unit cell / atomic weight of vanadium