I assume that the words \"closest packed cubic arangement\" refer to a Face-Cent

Question

I assume that the words "closest packed cubic arangement" refer to a Face-Centered Unit cell (FCC), and I know how to count from a diagram the number of atoms in a unit cell (so center=1, face=1/2, edge=1/4, corner=1/8), but I am not sure how to determine the stoichiometry/count from this description of the holes. Nor do I know how to determine the coordination numbers here (parts c and d). I think I can do the oxidaiton state and magnetic moment, although descriptions of how those were determined would be very helpful too. Thank you.

A ternary compound contains potassium, sulfur and cobalt and its crystal structure is described as a closest packed cubic arrangement of sulfide anions with the potassium in half of the tetrahedral holes and the cobalt in a quarter of the octahedral holes. (a) From this description, determine the simplest whole-number stoichiometry of the compound. (b) Determine the oxidation state of the cobalt. (c) What is the coordination number of the cobalt (number of S nearest neighbors)? (d) What is the coordination number of the potassium (number of S nearest neighbors)? (e) Predict the magnetic moment of the compound. (Use the spin-only value).

Explanation / Answer

The face-centered cubic (fcc) has a coordination number of 12 and contains 4 atoms per unit cell.

K and the S ratio must be 1:1

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