CHEM1002 2012-N-4 November 2012
• The diagram below shows the structure of an alloy of copper and gold with a gold
atom at each of the corners and a copper atom in the centre of each of the faces. The
length of the side of the cubic unit cell is 0.36 nm.
= Au = Cu
What is the chemical formula of the alloy?
Marks
6
There are 8 Au atoms and each is on a corner so contributes 1/8 to the unit cell:
total number of Au atoms = 8 × 1/8 = 1
There are 6 Cu atoms and each is on a face so contributes 1/2 to the unit cell.
total number of Cu atoms = 6 × 1/2 = 3
Answer: AuCu3 or Cu3Au
Pure gold is 24 carat, whilst gold alloys consisting of 75 % gold by weight are termed
18 carat gold. What carat gold is this alloy?
The molar mass of Cu3Au is:
molar mass = (3 × 63.55 (Cu) + 196.97 (Au)) g mol-1 = 387.62 g mol-1
The percentage gold is therefore:
percentage gold = 196.97 / 387.82 ×100% = 50%
As 100% gold is 24 carat and 75% gold is 18 carat, this corresponds to 12 carat.
Answer: 12 carat
What is the volume (in cm3) of the unit cell?
The length of the side of the unit cell is 0.36 nm. This corresponds to 0.36 × 10-9
m or 0.36 × 10-7 cm. As the unit cell is cubic, its volume, V, is given by:
V = (0.36 × 10-7)3 cm3 = 4.7 × 10–23 cm3
Answer: 4.7 × 10–23 cm3
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