An element has ccp packing with a face-centered cubic unit cell. Its density is 1540 kg/m3 and the unit cell volume is 1.73 x 10-22 cm3. Calculate the molar mass (g/mol) of the element to three significant figures.

CCP: cubic close pack

You have the density (1.54 g/cc) and the volume of the unit cell (1.73 x 10^-22 cc). From mass = volume x density you can calculate mass of atoms in one unit cell. Then you know [(4 atoms/unit cell x molar mass)/6.02 x 10^23] = mass atoms. You may want to check Avogadro's number to three s.f.

Determine molar mass from this.

The 4 atoms.unit cell is where I got confused. How do you know that? And how does it change for hexagonal close pack and body centered cubic?

To calculate the molar mass of the element, we need to use the given density and unit cell volume.

First, we need to convert the unit cell volume from cm^3 to m^3. We know that 1 m = 100 cm, so 1 m^3 = (100 cm)^3. Therefore, 1 m^3 = 1,000,000 cm^3.

Given unit cell volume = 1.73 x 10^(-22) cm^3
Converting to m^3: 1.73 x 10^(-22) cm^3 x (1 m^3/1,000,000 cm^3) = 1.73 x 10^(-28) m^3

Next, we can calculate the number of unit cells in 1 m^3 using the face-centered cubic (FCC) arrangement. In a face-centered cubic unit cell, there are 4 atoms per unit cell. Therefore, the number of unit cells in 1 m^3 is given by:

Number of unit cells = (1 m^3) / (unit cell volume) = (1 m^3) / (1.73 x 10^(-28) m^3)

Now, we divide this by 4 (since there are 4 atoms per unit cell) to obtain the number of atoms in 1 m^3.

Number of atoms per m^3 = Number of unit cells / 4

Next, we need to calculate the mass of the element in 1 m^3. This can be done using the density.

Mass of the element in 1 m^3 = density x volume = 1540 kg/m^3 x 1 m^3 = 1540 kg

Finally, to find the molar mass in g/mol, we need to find the mass of one mole of atoms. Since we calculated the mass in 1 m^3, we divide by the number of atoms in 1 m^3 to get the molar mass.

Molar mass = Mass of the element in 1 m^3 / Number of atoms per m^3

I will now carry out the calculations:

Number of unit cells = (1 m^3) / (1.73 x 10^(-28) m^3) = 5.78 x 10^27 unit cells

Number of atoms per m^3 = Number of unit cells / 4 = (5.78 x 10^27 unit cells) / 4 = 1.45 x 10^27 atoms/m^3

Mass of the element in 1 m^3 = 1540 kg

Molar mass = (Mass of the element in 1 m^3) / (Number of atoms per m^3) = (1540 kg) / (1.45 x 10^27 atoms/m^3)

Calculating this, we obtain the molar mass of the element.