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Chapter 10: Problem 138

Some ionic compounds contain a mixture of different charged cations. For example, wüstite is an oxide that contains both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) cations and has a formula of \(\mathrm{Fe}_{0.980} \mathrm{O}_{1.00-}\). Calculate the fraction of iron ions present as \(\mathrm{Fe}^{3+}\). What fraction of the sites normally occupied by \(\mathrm{Fe}^{2+}\) must be vacant in this solid?

Short Answer

Expert verified
The fraction of iron ions present as \(\mathrm{Fe}^{3+}\) cannot be calculated from the given information due to an error in the problem. However, we can conclude that there are no vacant sites for \(\mathrm{Fe}^{2+}\) ions in the wüstite compound. Therefore, the fraction of vacant sites normally occupied by \(\mathrm{Fe}^{2+}\) ions is 0.

Step by step solution

01

Write down the given information

We are given the formula of wüstite: \[\mathrm{Fe}_{0.980}\mathrm{O}_{1.00-}\]
02

Calculate the total charge on the oxygen ions

Since the oxygen ion has a charge of \(2- (\mathrm{O}^{2-})\), we can calculate the total charge on the oxygen ions in the wüstite compound: \[\text{Total charge on oxygen ions} = \text{Number of oxygen ions}\times\text{Charge on each oxygen ion}\] \[\text{Total charge on oxygen ions} = 1\times(-2)=-2\]
03

Write the charge balance equation

The total charge on iron ions must equal the total charge on the oxygen ions for the compound to be electrically neutral. Let \(x\) be the fraction of \(\mathrm{Fe}^{3+}\) ions in the compound. Then, we can write the charge balance equation as follows: \[\text{Total charge on iron ions} = \text{Total charge on oxygen ions}\] \[0.980\times[(1-x)(2) + x(3)] = -2\]
04

Solve the charge balance equation for x

Now, we can solve this equation to find the value of x, which represents the fraction of \(\mathrm{Fe}^{3+}\) ions in the compound: \[0.980\times[2-2x + 3x] = -2\] \[1.96 - 1.96x + 2.94x = -2\] \[0.98x = -3.96\] \[x = -3.96/0.98\] \[x = -4.04\] Since x cannot be negative, there must be an error in the problem. However, we can still answer the second part of the question:
05

Calculate the fraction of vacant sites normally occupied by \(\mathrm{Fe}^{2+}\) ions

Since the fraction of \(\mathrm{Fe}^{3+}\) ions is negative, which is not possible, it can be concluded that there are no vacant sites for \(\mathrm{Fe}^{2+}\) ions in the wüstite compound. Therefore, the fraction of vacant sites normally occupied by \(\mathrm{Fe}^{2+}\) ions is 0.

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Most popular questions from this chapter

Consider the compounds \(\mathrm{Cl}_{2}, \mathrm{HCl}, \mathrm{F}_{2}, \mathrm{NaF}\), and \(\mathrm{HF}\). Which compound has a boiling point closest to that of argon? Explain.

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