A mineral that contains iron and sulfur has the cubic unit cell pictured below. What is the empirical formula for this mineral?
•Fe atoms are the smaller spheres; one on each corner and one on each face of the unit cell
•S atoms are the eight larger spheres; every S atom is entirely inside the unit cell
I was able to figure it out, just forgot to simplify in the end.
Good.
To determine the empirical formula of the mineral, we need to analyze the arrangement of atoms in the unit cell.
From the given information:
- Fe atoms are the smaller spheres, present on each corner and one on each face of the unit cell.
- S atoms are the eight larger spheres, with each S atom being entirely inside the unit cell.
Now, let's examine the number of atoms in the unit cell:
- Each corner of the cube contributes 1/8th of an Fe atom.
Since there are eight corners in a cube, the total contribution of Fe atoms from the corners is 8 * 1/8 = 1 Fe atom.
- Each face of the cube contributes 1 Fe atom.
Since there are six faces in a cube, the total contribution of Fe atoms from the faces is 6 * 1 = 6 Fe atoms.
- Each of the eight larger S atoms is entirely inside the unit cell, so the total number of S atoms is 8.
Therefore, the empirical formula for the mineral is Fe₁S₈.