CdO is cubic with a lattice constant a=4.695 A˚ and a density ρ of 8.15 g/cm3. Determine the crystal structure of CdO.
Simple Cubic
Face Centered Cubic
Body Centered Cubic
Face Centered Cubic
To determine the crystal structure of CdO, we can start by calculating the number of atoms per unit cell using the given information.
For a Simple Cubic (SC) structure, there is only one atom per unit cell. The coordination number is 6, and the packing efficiency is 52.4%.
For a Face Centered Cubic (FCC) structure, there are 4 atoms per unit cell. Each corner atom is shared between 8 neighboring unit cells, and each face-centered atom is shared between 2 neighboring unit cells. The coordination number is 12, and the packing efficiency is 74%.
For a Body Centered Cubic (BCC) structure, there are 2 atoms per unit cell. Each corner atom is shared between 8 neighboring unit cells, and the body-centered atom is located at the center of the unit cell and is not shared. The coordination number is 8, and the packing efficiency is 68%.
Now, let's calculate the number of atoms per unit cell for CdO using the given lattice constant a and density ρ:
1. Calculate the volume of the unit cell:
Volume of unit cell = a³ = (4.695 A)³ = 104.87 A³
2. Convert the unit cell volume to cm³:
1 cm³ = 10⁻²⁴ A³ (conversion factor)
Volume of unit cell (cm³) = 104.87 A³ * (1 cm³ / 10⁻²⁴ A³) = 104.87 * 10²⁴ cm³ = 1.05 * 10²⁶ cm³
3. Calculate the mass of the unit cell:
Mass of unit cell = density * volume of unit cell
Mass of unit cell = 8.15 g/cm³ * 1.05 * 10²⁶ cm³ = 8.55 * 10²⁶ g
4. Calculate the molar mass of CdO:
Molar mass of CdO = atomic mass of Cd + atomic mass of O
Molar mass of CdO = 112.4 g/mol + 16.0 g/mol = 128.4 g/mol
5. Calculate the number of moles of CdO in the unit cell:
Number of moles = mass of unit cell / molar mass of CdO
Number of moles = (8.55 * 10²⁶ g) / (128.4 g/mol) = 6.66 * 10²⁴ mol
Now, we can determine the crystal structure based on the number of atoms per unit cell:
- Since the number of moles of CdO in the unit cell is 6.66 * 10²⁴ mol, which is not a whole number, we can conclude that CdO does not have a simple cubic structure.
- Since the number of atoms per unit cell (4 atoms) is a whole number, we can conclude that CdO has a Face Centered Cubic (FCC) crystal structure.
Therefore, the crystal structure of CdO is Face Centered Cubic (FCC).