An element has ccp packing with a face-centered cubic unit cell. Its densiry is 2.70E3 kg/m3 and the unit cell volume is 6.64E-29 m3. Calculate the molar mass (g/mol) of the element to 3 significant figures.

Same as below.

the molar mass is 5.40g/mol

To calculate the molar mass of the element, we need to determine the number of atoms per unit cell and the mass of the unit cell.

1. Determine the number of atoms per unit cell:
In a face-centered cubic (FCC) unit cell, there are 4 atoms located at the corners of the unit cell and 8 atoms located at the face centers. The total number of atoms in the unit cell is therefore 4 + 1/2(8) = 4 + 4 = 8 atoms.

2. Calculate the mass of the unit cell:
The density of the element is given as 2.70E3 kg/m3, which means that for every cubic meter of the element there is a mass of 2.70E3 kg. The unit cell volume is given as 6.64E-29 m3. Therefore, the mass of the unit cell can be calculated using the formula: mass = density × volume.

mass = (2.70E3 kg/m3) × (6.64E-29 m3)
mass = (2.70E3 kg/m3) × (6.64E-29 m3) = 1.7896E-25 kg ≈ 1.79E-25 kg

3. Convert the mass of the unit cell to grams:
Since the molar mass is usually expressed in grams per mole (g/mol), we need to convert the mass from kilograms to grams. There are 1000 grams in a kilogram.

mass in grams = (1.79E-25 kg) × (1000 g/kg) = 1.79E-22 g

4. Determine the molar mass:
The molar mass of the element is equal to the mass of the unit cell multiplied by Avogadro's number (6.02214076 × 10^23 atoms/mole).

molar mass = (1.79E-22 g) / (6.02214076 × 10^23 atoms/mole) ≈ 2.98E-46 g/atom

Since we are asked to express the molar mass to 3 significant figures, the molar mass of the element is approximately 2.98E-46 g/mol.