If cupric oxide \((\mathrm{CuO})\) is exposed to reducing atmospheres at elevated temperatures, some of the \(\mathrm{Cu}^{2+}\) ions will become \(\mathrm{Cu}^{+}\) (a) Under these conditions, name one crystalline defect that you would expect to form in order to maintain charge neutrality. (b) How many \(\mathrm{Cu}^{+}\) ions are required for the creation of each defect? (c) How would you express the chemical formula for this nonstoichiometric material?

1. Identify the crystalline defect that forms under these conditions to maintain charge neutrality. - The Schottky defect forms when some Cu²⁺ ions are reduced to Cu⁺ ions, causing vacancies in the O²⁻ (oxygen) ions to maintain charge neutrality. 2. Determine the number of Cu⁺ ions required to create each defect. - There needs to be a vacancy in the O²⁻ ion for every two Cu⁺ ions created in the crystal lattice. 3. Provide an expression for the chemical formula of the resulting nonstoichiometric material. - The chemical formula can be expressed as: \(\mathrm{Cu}_{(1-x)}^{2+}\mathrm{Cu}_{x}^{+}\mathrm{O}_{(1-\frac{x}{2})}^0\) where "x" is the fraction of Cu²⁺ ions that are reduced to Cu⁺ ions in the crystal lattice (0 ≤ x ≤ 1).