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 1 of 5: Coordination numbers

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\text{Coordination numbers: } \text{Cu} = 2 \; (\text{linear}), \quad \text{O} = 4 \; (\text{tetrahedral})

Analysis

The stoichiometry is $\ce{Cu2O}$ , so the ratio of coordination numbers must be $CN(\ce{O}) : CN(\ce{Cu}) = 2 : 1$ . With oxygen tetrahedrally coordinated ( $CN = 4$ ), copper is linearly coordinated ( $CN = 2$ ).