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 mass and the volume of the substance. From the information given, we can start by determining the volume of CaF2.
First, let's find the unit cell volume of CaF2. In the fluorite lattice, Ca2+ ions are located at the corners of the cube, while F-1 ions occupy the face centers. This means that there are 4 Ca2+ ions in each unit cell and 8 F-1 ions.
The unit cell volume can be calculated using the formula:
Unit cell volume = (Number of atoms in the unit cell) x (Volume of one atom)
The volume of one atom can be approximated using the formula for the volume of a sphere:
Volume of one atom = (4/3) x π x (Atomic radius)^3
Using the given radii:
Ca2+ ion radius (r_Ca) = 126 pm = 126 x 10^-12 cm
F-1 ion radius (r_F) = 117 pm = 117 x 10^-12 cm
Now we can calculate the volumes of the Ca2+ and F-1 ions:
Volume of one Ca2+ ion = (4/3) x π x (r_Ca)^3
Volume of one F-1 ion = (4/3) x π x (r_F)^3
Next, determine the unit cell volume:
Unit cell volume = (4 x Volume of one Ca2+ ion) + (8 x Volume of one F-1 ion)
Now that we have the volume of the unit cell, we need to find the mass of the unit cell. The molecular weight of CaF2 can be calculated using the atomic masses of Ca and F. The molar mass of Ca is 40.08 g/mol, and the molar mass of F is 18.99 g/mol.
The molecular weight of CaF2 = (Molar mass of Ca) + (2 x Molar mass of F)
Finally, we can calculate the density of the CaF2 crystal:
Density = (Mass of unit cell) / (Unit cell volume)
Now that we have the calculation steps, you can plug in the values for the radii of Ca2+ and F-1 ions, the atomic masses of Ca and F, and follow the formulae to calculate the density of CaF2.