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.
I have no idea, but I'm sure our chemistry guys will weigh in.
In the meantime, I find it hard to believe that you would be given such a question without having studied something like it already. How can you possibly have "no idea" where to start? Check your text or google face-centered lattices for ideas.
There was two slides over this, but they both involved one element.
To calculate the density of CaF2, you need to know the masses and volumes of the individual ions in the unit cell of the fluorite lattice.
Here's how you can start:
1. Determine the number of Ca2+ and F-1 ions in the unit cell:
- In a face-centered cubic lattice, there are 4 atoms located at the corners of the unit cell and 1 atom at the center of each face. This gives us a total of 5 atoms in the unit cell.
- In CaF2, there is one Ca2+ ion and two F-1 ions in the unit cell.
2. Calculate the total volume of the unit cell:
- The volume of a unit cell is determined by the formula: V = a^3, where 'a' is the edge length of the unit cell.
- In a face-centered cubic lattice, the edge length (a) can be calculated as a = 4 * r, where 'r' is the radius of the Ca2+ ion.
- Since r = 126 pm, a = 4 * 126 pm = 504 pm.
3. Calculate the volume occupied by each ion:
- Ca2+ ions occupy half of the cubic holes. Since there are 4 cubic holes in a unit cell, there are 2 Ca2+ ions in total.
- F-1 ions occupy all positions of the fluoride lattice, so there are 4 F-1 ions in total.
- The volume occupied by each Ca2+ ion is 1/2 of the volume of a single cubic hole.
- The volume occupied by each F-1 ion is equal to the volume of a single lattice position.
4. Calculate the mass of each ion:
- The mass of an individual Ca2+ ion is determined by multiplying its molar mass by the number of Ca2+ ions in the unit cell.
- The molar mass of calcium (Ca) is approximately 40.08 g/mol.
- Repeat this step for the F-1 ions, using the molar mass of fluorine (F), which is approximately 18.99 g/mol.
5. Calculate the total mass and density:
- Add the masses of all the ions in the unit cell to get the total mass.
- Divide the total mass by the total volume of the unit cell obtained in step 2 to calculate the density.
Remember to convert the given values from picometers (pm) to a consistent unit (e.g., angstroms or meters) before performing the calculations.
By following these steps, you should be able to determine the density of CaF2.