Question

Calculate the average thickness of copper on the surface of a penny (produced after 1983) in units of a.) mm and b.) atoms of Cu. Show all calculations, including unit analysis.

Answer 1

Total weight of penny (produced after 1983) = 2.5 gm

Composition : Copper = 2.5 %, Zinc = 97.5 %

Diameter = 19.05 mm, Density of Copper = 7870 gm/l, Density of Zinc = 7140 gm/l, Molecular weight of copper = 63.5 gm/mol

Average Density of penny = (Density of Copper * Xcu) + (Density of Zinc * Xzn)

= (7870 * 0.025) + ( 0.7140 * 0.975) = 7158.25 gm/l

Total volume of penny = Total mass / Average density = (2.5 gm) / (7158.25 gm/l) = 3.5 * 10^-4 ltr

= 3.5 * 10^ -7 m3

Total Volume of penny = Area of penny * Total thickness

Total thickness = Total Volume of penny / ((pi/4)* D^2 ) m3/m2

= (3.5 * 10 ^-7)/ (0.7854 * (0.01905)^2)) m

= 1.22 * 10 ^-3 m

= 1.225 mm

Thickness of copper = Total thickness * Composition

= 1.225 * 0.025 mm

= 0.0306 mm

Now to calculate atoms of Copper,

Mass of copper = Total mass * composition of copper

= 2.5 gm * 0.025

= 0.0625 gm

moles of copper = Mass / Molecular weight gm / (gm / mol)

= 0.0625 / 63.5

= 9.84 * 10 ^ -4 mol

No. of atoms = moles * Avogadros number mol * ( atoms/mol)

= (9.84 * 10 ^ -4) * (6.023 * 10^23)

= 5.93 * 10^20 atoms of copper (or molecules of copper)