Question

What is the predicted density of a pure FCC iron lattice?

Options:
a) 7.87 g/cm³
b) 8.92 g/cm³
c) 6.89 g/cm³
d) 8.02 g/cm³

Answer 1

The predicted density of a pure FCC iron lattice is approximately 7.87 g/cm³.

Step-by-step explanation:

The predicted density of a pure FCC (face-centered cubic) iron lattice can be calculated using the formula density = mass/volume. The molar mass of iron is 55.845 g/mol, and the volume of a FCC unit cell can be calculated using the formula V = (4/3) * r^3, where r is the radius of the atom. For an FCC lattice, the atom is touching along the body diagonal of the unit cell, so the radius r is equal to half the length of the body diagonal. Given that the length of the side of the unit cell is a, the length of the body diagonal can be calculated using the formula d = sqrt(3) * a. Therefore, the volume of the unit cell is V = (4/3) * (r^3) = (4/3) * ((d/2)^3). The density is then calculated by dividing the molar mass of iron by the volume of the FCC unit cell.

Calculating the volume of the FCC unit cell:

1. Given that the length of the side of the unit cell is a, the length of the body diagonal d is calculated as d = sqrt(3) * a.
2. Using the length of the body diagonal d, calculate the volume of the unit cell: V = (4/3) * ((d/2)^3).

Calculating the density:

1. Use the molar mass of iron (55.845 g/mol) and the volume of the FCC unit cell to calculate the density using the formula density = mass/volume.

By performing these calculations, the predicted density of a pure FCC iron lattice is approximately 7.87 g/cm³.