Calcium fluoride is the well-known mineral fluorite. It is known that each unit cell contains four Ca2+ ions and eight F- ions and that the Ca2+ are arranged in a face-centered cubic lattice. The F- ions fill all the tetrahedral holes. The edge of the CaF2 unit cell is 5.46295 x 10^-8
cm in length. The density of the solid is 3.1805 g/cm^3. Use this information to calculate Avogadro's number.
I am completely lost on what to do. Here is what I have tried to do so far.
5.46295 x 10^-8 cm (taken to the third power)= 4.63035 x 10^-22 cm^3.
Then I utilized the density to convert to grams.
1.63035 cm^3 x 1g/3.1805 cm^3 = 5.1261 x10^-23 grams
Here is where I get lost. I tried using the molar mass of CaF2, but it's not equal to Avogadro's number.
Any pointers would be greatly appreciated!
Thank you,
Jay
Oh just kidding after much frustration and stepping away from the problem and coming back, I noticed that I messed up the density in my conversion. I had the right idea I just had to correct my mistake and then continue on with the molar mass of CaF2, then I divided 4 molecules by the calculated moles, to get Avogadro's number.
To calculate Avogadro's number, you need to follow these steps:
Step 1: Determine the mass of the unit cell.
The density (ρ) is given as 3.1805 g/cm^3, and you have already calculated the volume of the unit cell as 4.63035 x 10^-22 cm^3. So, you can multiply the density by the volume to get the mass:
Mass = density x volume = 3.1805 g/cm^3 x 4.63035 x 10^-22 cm^3 = 1.47219 x 10^-21 g
Step 2: Calculate the number of moles of CaF2 in the unit cell.
To find the number of moles, you need to divide the mass of CaF2 by its molar mass. The molar mass of CaF2 can be calculated as follows:
Molar mass of CaF2 = (molar mass of Ca) + 2 x (molar mass of F)
The molar mass of Ca is 40.08 g/mol, and the molar mass of F is 19.00 g/mol. Therefore,
Molar mass of CaF2 = 40.08 g/mol + 2 x 19.00 g/mol = 78.08 g/mol
Now, you can calculate the number of moles of CaF2:
Number of moles = mass / molar mass = (1.47219 x 10^-21 g) / (78.08 g/mol) = 1.88442 x 10^-23 mol
Step 3: Determine the total number of formula units in the unit cell.
You know that each unit cell contains 4 Ca2+ ions. Since each Ca2+ ion combines with 2 F- ions, the total number of CaF2 formula units can be calculated as follows:
Number of CaF2 formula units = 4 Ca2+ ions x (1 CaF2 formula unit / 2 Ca2+ ions) = 2 CaF2 formula units
Step 4: Calculate Avogadro's number (N).
Avogadro's number (N) represents the number of particles (atoms, molecules, or formula units) in one mole of that substance. It is known to be 6.022 x 10^23 particles/mol. To find Avogadro's number, you can use the equation:
N = (number of formula units) / (number of moles)
N = (2 CaF2 formula units) / (1.88442 x 10^-23 mol) ≈ 1.061 x 10^23 formula units/mol
Therefore, Avogadro's number is approximately 1.061 x 10^23 formula units/mol.