An element has ccp packing with a face-centered cubic unit cell. Its density is 8.92 g/cm3 and the unit cell volume is 4.72 x 10-26 L. Calculate the molar mass (g/mol) of the element to three significant figures.
Are you sure the units of the unit cell volume are not milliliters? Compute the mass of a unit cell and divide by the number of atoms assignable to each cell. (That number is four for this crystal structure) The mass per atom multiplied Avogadro's number will tell you the molar mass.
Except for what I believe to be incorrect units for the unit cell volume, I conclude that the element is copper.
To calculate the molar mass of the element, we need to use the given density and the volume of one unit cell.
The density is given as 8.92 g/cm³, which means that in one cubic centimeter of the element, there is a mass of 8.92 grams. Since we are given the volume of the unit cell in liters, we need to convert the density from g/cm³ to g/L.
1 cm³ is equal to 1 mL, and since there are 1000 mL in 1 L, we can convert the density:
Density = 8.92 g/cm³ = 8.92 g/mL = 8.92 g/L
Now, let's calculate the number of unit cells present in 1 L of the element. The given unit cell volume is 4.72 x 10⁻²⁶ L.
Number of unit cells in 1 L = 1 L / (4.72 x 10⁻²⁶ L) = (1 / 4.72 x 10⁻²⁶) unit cells
Since the unit cell of a face-centered cubic (FCC) structure consists of 4 atoms, the number of atoms present in 1 L of the element is 4 times the number of unit cells:
Number of atoms in 1 L = 4 x (1 / 4.72 x 10⁻²⁶) atoms
To calculate the molar mass, we need to know the number of atoms in one mole. The Avogadro's number tells us that there are 6.022 x 10²³ entities (atoms, molecules, etc.) in one mole. Therefore, we can calculate the molar mass:
Molar mass = (4 x (1 / 4.72 x 10⁻²⁶)) x (6.022 x 10²³) g/mol
Calculating this expression will give us the molar mass of the element to three significant figures.