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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

Which of the following properties are associated with ceramics and which are associated with metals? (a) ductile; (b) thermal insulator; (c) electrically conductive; (d) malleable

What is the formula of the silicate mineral talc, obtained by replacing \(\mathrm{Al}^{3+}\) ions in pyrophyllite \(\left[\mathrm{Al}_{4} \mathrm{Si}_{8} \mathrm{O}_{20}(\mathrm{OH})_{4}\right]\) with \(\mathrm{Mg}^{2+}\) ions?

Substitutional alloys may form when the difference in atomic radii between the alloying elements is less than \(15 \%\) a. Predict which of the following alloys has the greatest mismatch in atomic radii: AuZn, AgZn, or CuZn. b. Find the atomic radii of \(\mathrm{Cu}, \mathrm{Ag}, \mathrm{Au},\) and \(\mathrm{Zn}\) in Appendix 3, and calculate the percent difference in their atomic radii. Are all three alloys expected to form substitutional alloys? c. If gold is alloyed with silver in a 1: 1 ratio, do the atoms still touch along the face diagonal of a face-centered cubic unit cell?

Explain why an alloy that is \(28 \%\) Cu and \(72 \%\) Ag melts at a lower temperature than the melting points of either Cu or \(\mathrm{Ag}\)

Why does an amorphous solid not produce an XRD scan with sharp peaks?
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