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Chapter 12: Problem 33

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?

Short Answer

Expert verified
#Answer# (a) Oxygen vacancies (b) 2 Cu+ ions (c) Cu₁₊ₓO₁₋ₓ

Step by step solution

01

(a) Identifying a crystalline defect for cupric oxide in a reducing atmosphere

Since the reducing atmosphere results in the reduction of \(\mathrm{Cu}^{2+}\) ions to \(\mathrm{Cu}^{+}\) ions in cupric oxide, a possible crystalline defect that can form to maintain charge neutrality in the system is the formation of oxygen vacancies.
02

(b) Number of Cu+ ions needed for the creation of each defect

To maintain charge neutrality in the system, the positive charge of the Cu+ ions must be equal to the negative charge of the oxygen vacancies. For every two \(\mathrm{Cu}^{+}\) ions formed by reducing Cu2+ ions, one oxygen vacancy (two negative charges) is required to maintain charge neutrality: \(2\times(\mathrm{Cu}^{+})=\)1 \times (-2e) from the oxygen vacancy Thus, 2 Cu+ ions are needed for the creation of each oxygen vacancy.
03

(c) Expressing the chemical formula for the nonstoichiometric material

Since CuO is the stoichiometric compound and some of the Cu2+ ions are reduced to Cu+ ions, we can express the chemical formula for the nonstoichiometric material as: \(\mathrm{Cu}_{1+x}\mathrm{O}_{1-x}\) Where x represents the fraction of \(\mathrm{Cu}^{2+}\) ions that are reduced to \(\mathrm{Cu}^{+}\) ions, and (1-x) represents the fraction of oxygen vacancies that are formed.

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Most popular questions from this chapter

A three-point bending test is performed on a glass specimen having a rectangular cross section of height \(d=5 \mathrm{~mm}(0.2\) in.) and width \(b=10 \mathrm{~mm}(0.4\) in.); the distance between support points is \(45 \mathrm{~mm}\) (1.75 in.). (a) Compute the flexural strength if the load at fracture is \(290 \mathrm{~N}\left(65 \mathrm{lb}_{\mathrm{f}}\right)\). (b) The point of maximum deflection \(\Delta y\) occurs at the center of the specimen and is described by $$ \Delta y=\frac{F L^{3}}{48 E I} $$ where \(E\) is the modulus of elasticity and \(I\) is the cross-sectional moment of inertia. Compute \(\Delta y\) at a load of \(266 \mathrm{~N}\left(60 \mathrm{lb}_{\mathrm{f}}\right)\).

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