The element strontium has ccp packing with a face-centered cubic unit cell. The volume of the unit cell is 2.25 x 10-25 L. Calculate the density (g/mL) of the element.
There are 4 atoms to the unit cell.
mass unit cell is
4*atomic mass Sr/6.022E23
volume = 2.25E-25L = 2.25E-22 cc.
density = mass/v = ?
To calculate the density of the element strontium, we need to know its molar mass and the number of atoms in the unit cell.
1. Determine the molar mass of strontium (Sr): The molar mass of Sr is 87.62 g/mol.
2. Determine the number of atoms in the face-centered cubic (FCC) unit cell: In an FCC structure, there are 4 atoms per unit cell. This can be determined by considering the positions of atoms within the unit cell.
3. Calculate the volume of one Sr atom:
- Since the unit cell is face-centered cubic, each atom is located at a corner (1/8 contribution) and in the center of each face (1/2 contribution).
- The volume contribution per atom = (1/8) + (1/2) = 5/8.
- Therefore, the volume of one Sr atom = (2.25 x 10^-25 L) * (5/8) = 1.40625 x 10^-25 L.
4. Calculate the volume occupied by all the atoms in the unit cell:
- Since there are 4 atoms in the unit cell, the total volume occupied by the atoms in the FCC unit cell = 4 * (1.40625 x 10^-25 L) = 5.625 x 10^-25 L.
5. Calculate the density:
- Density = (mass of the unit cell) / (volume of the unit cell).
- However, the mass is not given directly. We can use the molar mass since there are 4 atoms per unit cell.
- Mass of the unit cell = (molar mass of Sr) / (Avogadro's number) = (87.62 g/mol) / (6.022 x 10^23 mol^-1).
- Density = (87.62 g/mol) / (6.022 x 10^23 mol^-1) / (5.625 x 10^-25 L)
= (87.62 g) / (5.625 x 10^-25 L) / (6.022 x 10^23 mol^-1)
= 2.19 g/mL (approx.)
Thus, the density of strontium is approximately 2.19 g/mL.