Calcium Fluoride, CaF2, adopts the fluorite lattice, which is described as a face-centered cubic array of Ca2+ ions with F-1 ions with Ca2+ ions in half of the cubic holes. The Radii of Ca2+ and F-1 are 126 and 117 pm, respectively. Calculate the density of CaF2 from these data. Please give me somewhere to start. I am completely lost on this question.
To calculate the density of CaF2, we need to know the formula weight and the volume of the crystal lattice. The formula weight can be calculated by adding the atomic masses of calcium (Ca) and fluorine (F) based on their molar ratio in CaF2.
Let's start by finding the formula weight of CaF2 using the atomic masses of Ca and F:
- Atomic mass of Ca = 40.08 g/mol
- Atomic mass of F = 18.998 g/mol
The molar ratio between Ca and F in CaF2 is 1:2. Therefore, the formula weight (FW) of CaF2 can be calculated as:
FW = (Atomic mass of Ca) + 2 * (Atomic mass of F)
Now, let's calculate the formula weight (FW) of CaF2:
FW = 40.08 + 2 * 18.998 g/mol
Next, we will use the formula weight and the crystal lattice structure to calculate the volume of the unit cell. The unit cell in a face-centered cubic lattice contains one formula unit:
- Number of Ca2+ ions = 1
- Number of F-1 ions = 4 (each face-centering F-1 ion contributes 1/8 to the unit cell volume)
The volume of the unit cell (V) can be calculated as:
V = (Number of Ca2+ ions) * (Volume of Ca2+) + (Number of F-1 ions) * (Volume of F-1)
The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * (Radius)^3
Now, let's calculate the volume of the unit cell:
- Volume of Ca2+ ion = (4/3) * π * (Radius of Ca2+)^3
- Volume of F-1 ion = (4/3) * π * (Radius of F-1)^3
Substituting the given radii values into the above equations, we can determine the volumes.
Lastly, to calculate the density (ρ) of CaF2, we divide the formula weight (FW) by the volume of the unit cell (V):
ρ = FW / V
Using these steps, you can now proceed with the calculations to determine the density of CaF2.