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Chapter 18: Problem 86

What is the chemical formula of the compound that crystallizes in a simple cubic arrangement of fluoride ions with \(\mathrm{Ba}^{2+}\) ions occupying half of the cubic holes?

Short Answer

Expert verified
Answer: The chemical formula of the compound is \(\mathrm{BaF}_8\).

Step by step solution

01

Understand the simple cubic arrangement of fluoride ions

In a simple cubic arrangement, each unit cell has one ion at each corner. Since there are eight corners in a cubic unit cell, there are eight fluoride ions in the simple cubic arrangement.
02

Determine the number of available cubic holes

In a simple cubic arrangement, there is one cubic hole available at the center of the unit cell.
03

Determine the number of occupied cubic holes by \(\mathrm{Ba}^{2+}\) ions

The problem states that \(\mathrm{Ba}^{2+}\) ions occupy half of the cubic holes. Since there is only one cubic hole available in the simple cubic arrangement, half of it means that there is only one occupied hole by a \(\mathrm{Ba}^{2+}\) ion.
04

Calculate the ratio of fluoride ions to \(\mathrm{Ba}^{2+}\) ions

The unit cell has eight fluoride ions and one \(\mathrm{Ba}^{2+}\) ion. The ratio of fluoride ions to \(\mathrm{Ba}^{2+}\) ions is 8:1.
05

Find the chemical formula of the compound

According to the ratio calculated in Step 4, there are eight fluoride ions for every one \(\mathrm{Ba}^{2+}\) ion in the unit cell. Thus, the chemical formula of the compound is \(\mathrm{BaF_8}\). However, we can simplify this formula, as a compound can contain ions in their lowest whole-number ratio. We can find the simplest whole-number ratio by dividing the number of ions by the greatest common divisor. The greatest common divisor of 8 and 1 is 1. Therefore, the chemical formula is \(\mathrm{BaF}_8\).

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Most popular questions from this chapter

Dental fillings are mixtures of several alloys, including one made of silver and tin. Silver \((r=144 \mathrm{pm})\) and \(\operatorname{tin}(r=140 \mathrm{pm})\) both crystallize in an fcc unit cell. Is this alloy likely to be a substitutional alloy or an interstitial alloy?

Molecules of \(\mathrm{S}_{8}\) are not flat octagons- -why?

The melting and boiling points of sodium metal are much lower than those of sodium chloride. What does this difference reveal about the relative strengths of metallic bonds and ionic bonds of the alkali metals?

Removing two electrons from \(\mathrm{S}_{8}\) yields the dication \(\mathrm{S}_{8}^{2+}\) Will all of the sulfur atoms be in one plane in the \(\mathrm{S}_{8}^{2+}\) cation?

Kaolinite \(\left[\mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)(\mathrm{OH})_{4}\right]\) is formed by weathering of the mineral \(\mathrm{KAlSi}_{3} \mathrm{O}_{8}\) in the presence of carbon dioxide and water, as described by the following unbalanced reaction: \(\mathrm{KAISi}_{3} \mathrm{O}_{8}(s)+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(g) \rightarrow\) $$ \mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)(\mathrm{OH})_{4}(s)+\mathrm{SiO}_{2}(s)+\mathrm{K}_{2} \mathrm{CO}_{3}(a q) $$ Balance the reaction and determine whether or not it is a redox reaction.
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