this is a wiley plus problem and there is no reading lesson with this section so im not sure how to approach this question:

The element iridium has ccp packing with a face-centered cubic unit cell. The density of Ir is 22400 kg/m3. Calculate the volume (cm3) of the unit cell of iridium.

The molar mass of iridium is 192.22 g/mol

Thanks!

mass = volume x density; therefore,

volume = mass/density. You know the density; therefore, we need to determine the mass of a unit cell.
An atom of Ir has a mass of 192.22/6.022 x 10^23. There are 4 atoms/unit cell which makes the mass of a unit cell then
4 x 192.22/6.022 x 10^23. Substitute into the first equation above and calculate volume. If you want the volume in cc, you must have the density in g/cc. 22,400 kg/m^3 = 22.4 g/cc.

To calculate the volume of the unit cell of iridium in cm3, we need to know the density and the molar mass of iridium. Here's how you can approach this problem:

1. Convert the given density from kg/m3 to g/cm3. Since 1 kg equals 1000 g and 1 m3 equals 1,000,000 cm3, we can convert the density as follows:
Density (g/cm3) = Density (kg/m3) / 1000 / 1000000

In this case, Density (g/cm3) = 22400 / 1000 / 1000000 = 0.0224 g/cm3

2. Determine the number of iridium atoms in one unit cell. Since iridium has ccp (face-centered cubic) packing, each corner of the cubic unit cell contains 1/8th of an iridium atom, and each face center contains 1/2 of an iridium atom. Therefore, the total number of atoms in a unit cell is:
Number of atoms = (8 corners * 1/8) + (6 faces * 1/2) = 4

3. Calculate the mass of one unit cell. To do this, we need to find the mass of one iridium atom and multiply it by the number of atoms in the unit cell. The molar mass of iridium given is 192.22 g/mol. This means that the mass of one iridium atom is:
Mass of one atom = Molar mass / Avogadro's number

Avogadro's number (NA) = 6.022 x 10^23 atoms/mol

Mass of one atom = 192.22 g/mol / (6.022 x 10^23 atoms/mol) = 3.19281 x 10^-22 g

Mass of unit cell = Mass of one atom * Number of atoms = 3.19281 x 10^-22 g * 4 = 1.277124 x 10^-21 g

4. Calculate the volume of one unit cell using the formula:
Density = Mass / Volume

Rearrange the formula to solve for Volume:
Volume = Mass / Density

Volume of unit cell = 1.277124 x 10^-21 g / 0.0224 g/cm3 = 5.701 x 10^-20 cm3

Therefore, the volume of the unit cell of iridium is approximately 5.701 x 10^-20 cm3.

I hope this helps! Let me know if you have any further questions.