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 \(\mathrm{Fe}_{0.950} \mathrm{O}_{1.00}\). 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?

In chemistry, particularly when dealing with ionic compounds such as wüstite, the concept of the charge balance equation is crucial. It states that the total positive charge in a compound must equal the total negative charge, maintaining electrical neutrality.

The charge balance equation is written by equating the sum of charges from all cations to the sum of charges from all anions. For instance, in wüstite, iron can be present as \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\), while oxygen is present as \(\mathrm{O}^{2-}\). If \(x\) is the fraction of \(\mathrm{Fe}^{3+}\) ions, the charge balance equation is set up by multiplying the fraction of each type of iron ion by its respective charge, and this sum should be equal to the charge from oxygen ions.

Understanding this equilibrium allows us to calculate the proportion of different ions in the compound. If an error is identified in the step-by-step solution provided, such as a wrong calculation or misinterpretation of the charge balance, correcting it would be crucial for identifying the correct composition of the ionic compound.

Ionic compounds can have a mixture of cations with different charges. When solving problems involving such cation mixtures, it's important to clearly define the variables representing the fraction of each cation type.

In the provided example of wüstite, which contains a mixture of \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\), we start by assigning a variable to the fraction of one cation to express the other cation's fraction in relation to it. This understanding of the cation mixture is essential for further steps, such as applying the charge balance equation or determining the stoichiometry of the compound.

Focusing on the step-by-step solution, ensure that the appropriate cation types and their fractions are accurately considered. Misunderstanding the cation mixture can lead to incorrect conclusions about the compound's structure or the calculation of vacant sites.

Stoichiometry is a branch of chemistry that involves calculating the amounts of reactants and products in chemical reactions. For ionic compounds, stoichiometry helps determine the proportions of each ion necessary to achieve neutrality.

The example given on wüstite's composition requires stoichiometric calculations to understand the ratio of iron to oxygen ions, and infer further details like the fraction of vacant sites. By understanding the ratio of ions and the overall formula of the compound, we can utilize stoichiometry to deduce not only the percentage of each type of cation but also the extent of vacancies or other defects within the crystal structure.

Be mindful of potential errors in solving stoichiometry problems, such as incorrect coefficients or misapplication of the mole concept. Aligning stoichiometry with the charge balance and recognizing the nature of the cation mixture ensures accurate and comprehensive solutions to such textbook exercises.