Question

Cobalt fluoride crystallizes in a closest packed array of fluoride ions with the cobalt ions filling one-half of the octahedral holes. What is the formula of this compound?

Short answer

The formula of cobalt fluoride is CoF2, as fluoride ions form a closest packed array and cobalt ions fill one-half of the octahedral holes. The ratio between fluoride and cobalt ions is 2:1, meaning there is one cobalt ion for every two fluoride ions in the crystal structure.

Step-by-step solution

Identify the ions and their arrangement in the crystal

In cobalt fluoride, cobalt ions are present in one-half of the octahedral holes, and the fluoride ions form a closest packed array.

Understand the octahedral holes in a closest packed array

In a closest-packed array of anions (in this case, fluoride ions), there is one octahedral hole per anion. So, if there are 'x' fluoride ions in the closest packed array, there would be 'x' octahedral holes.

Determine the number of cobalt ions

Since one-half of the octahedral holes are filled with cobalt ions, there will be \(\cfrac{x}{2}\) cobalt ions present in the crystal, where 'x' represents the number of fluoride ions.

Calculate the ratio between fluoride and cobalt ions

In the crystal, the ratio between fluoride ions and cobalt ions will be: \(x: \cfrac{x}{2}\), where 'x' represents the number of fluoride ions and \(\cfrac{x}{2}\) represents the number of cobalt ions. To simplify the ratio, we can multiply both parts by 2: \(2x:x\), which results in the ratio: \(2:1\)

Determine the formula of the compound

Based on the ratio obtained in step 4 (2:1), the formula for the compound will be CoF2 (Cobalt fluoride), with one cobalt ion for every two fluoride ions in the crystal structure.