Problem 2

Copper(I) oxide

\ce{Cu2O}

is a semiconductor used in solid-state electronics and solar cells. The cubic unit cell has lattice constant

a = 427.0

pm, with oxygen atoms (A) forming a body-centered cubic sub-lattice and copper atoms (B) occupying positions forming a face-centered cubic sub-lattice. (a) What are the coordination numbers of Cu and O? (b) Calculate the shortest

\ce{O-O}

\ce{Cu-O}

, and

\ce{Cu-Cu}

distances. (c) Calculate the theoretical density of stoichiometric

\ce{Cu2O}

in g cm

^{-3}

. (d) A non-stoichiometric sample has

0.2\%

of all Cu atoms oxidized to

\ce{Cu^2+}

. What percentage of Cu sites are vacant, and what is

x

\ce{Cu_{2-x}O}

? (e) Write balanced equations for the reaction of

\ce{Cu2O}

with: (1) atmospheric

\ce{O2}

in humid air; (2) dilute sulfuric acid; (3) hot concentrated sulfuric acid.

Step 3 of 5: Theoretical density

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\rho = \dfrac{Z \cdot M(\ce{Cu2O})}{N_A \cdot a^3} = \dfrac{2 \times 143.09}{6.022\times10^{23} \times (427.0\times10^{-10})^3} = 6.106\ \text{g cm}^{-3}

Analysis

Each unit cell contains 2 oxygen atoms and 4 copper atoms, corresponding to $Z = 2$ formula units of $\ce{Cu2O}$ . With cell volume $V = a^3 = 7.791\times10^{-23}$ cm $^3$ , $\rho = (2\times 143.09) / (6.022\times10^{23} \times 7.791\times10^{-23}) = 6.106$ g cm $^{-3}$ .