Unit Cell question? For 5(a) and 5(c), how are we determining that the answer is

Question

Unit Cell question?

For 5(a) and 5(c), how are we determining that the answer is K4CoS4? I keep counting it and getting K2CoS2. We know that the K and the S ratio must be 1:1, but how can we count the Cobalt?

5. 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. (6 pts) K4CoS4 2 pts each (b) Determine the oxidation state of the cobalt. (3 pts) +4 or 4 or IV (c) What is the coordination number of the cobalt (number of S nearest neighbors)? (3 pts)

Explanation / Answer

5 a) A fcc arrangement has both tetrahedral and octahedral holes.There are 8 tetrahedral holes and 4 octahedral holes in a fcc unit cell.

The face-centered cubic system has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell (18 × 8 from the corners plus 12 × 6 from the faces).

So an fcc has 4 S2-

It has 8 tetrahedral holes - half of which has K+ so 4 potassium

It has 4 octahedral holes - quarter of which has Co

So the formula is K4CoS4

Co is in an octahedral hole so it has 6 S2- around it.

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