Question

An element K with edge length 270 pm exists in a face-centered cubic unit cell. The element K has a density of 7.4 g/cm³. Determine the atomic mass of element K.

a) 75.36 g/mol
b) 135.92 g/mol
c) 150.78 g/mol
d) 180.25 g/mol

Answer 1

To calculate the atomic mass of element K in a face-centered cubic unit cell, the volume of the unit cell is found, and the density is used to calculate the mass of 4 atoms in the cell, which is then divided by Avogadro's number to find the atomic mass.

Step-by-step explanation:

To determine the atomic mass of element K that exists in a face-centered cubic unit cell with an edge length of 270 pm and a density of 7.4 g/cm³, we follow these steps:

1. Calculate the volume of the unit cell in cubic centimeters (cm³). The edge length is given in picometers (pm), so we convert this to centimeters:
2. 270 pm = 270 x 10⁻¹² cm
3. The volume (V) of the cubic unit cell is the cube of the edge length:
4. V = (270 x 10⁻¹² cm)³
5. In a face-centered cubic unit cell, there are 4 atoms per unit cell. The density (ρ) is mass (m) divided by volume (V), so we rearrange the formula to find the mass of the 4 atoms:
6. m = ρ x V
7. We can then calculate the mass of a single atom by dividing the mass of the 4 atoms by 4:
8. Mass of one atom = m / 4
9. Finally, to get the atomic mass in grams per mole, we multiply the mass of one atom by Avogadro's number (6.022 x 10²³ atoms/mol):
10. Atomic mass = Mass of one atom x 6.022 x 10²³

Using this process, we can match the calculated atomic mass to the closest option given in the question.