Density A brief History of the US (one-cent coin) Penny Composition Year Composition 1793 to 1837 100% Cu 1837 to 1857 Bronze (95% Cu, 5% Sn & Zn) 1857 to 1864 88% Cu & 12% Ni 1864 to 1942 Bronze (95% Cu, 5% Sn & Zn) 1943 Zinc-coated steel Brass (95% Cu & 5% Zn) 1944 to 1946 1946 to 1962 Bronze (95% Cu, 5% Sn & Zn) Brass (95% Cu & 5% Zn) 1962 to 1982 1983 to … 97.6% Zn & 2.4 % Cu Percent Composition of Zinc and Copper in US Pennies:    The current US penny is made of metallic copper (Cu) plated onto a zinc (Zn) core. In an object composed of multiple materials (like a penny), the density (d) is a weighted average of the densities of the pure substances that make up the object. Also assume that there is no change in volume when the pure metals are mixed. dpenny = (%𝐶𝑢 𝑏𝑦 𝑚𝑎𝑠𝑠)dCu + (%𝑍𝑛 𝑏𝑦 𝑚𝑎𝑠𝑠)dZn dpenny = (𝑝)dCu + (𝑞)dZn Where: %𝑝 + %𝑞 = 100 𝑞 = 1.00 − 𝑝 dpenny = (𝑝)dCu + (1.00 − 𝑝)dZn dpenny = (𝑝)dCu − (𝑝)dZn + 1.00𝑑𝑍𝑛 dpenny = (𝑝)[𝑑𝐶𝑢 − 𝑑𝑍𝑛 ] + 1.00𝑑𝑍𝑛 𝑝= 𝑑𝑝𝑒𝑛𝑛𝑦 − 1.00𝑑𝑍𝑛 = %𝐶𝑢 𝑏𝑦 𝑚𝑎𝑠𝑠 𝑑𝐶𝑢 − 𝑑𝑍𝑛   If we know the density of the penny (composite), we can use this equation to obtain the % copper (p) in the sample. The following measurements are needed to find the Percent Composition of Zinc and Copper in US Pennies: a) Density of a penny b) Density of pure copper. c) Density of pure zinc A Numerical Example (I): A piece of gold jewelry weighing 9.35 g. Its volume is measured 0.654 g/cm 3. Assume that the metal is an alloy of gold and silver, which have densities of 19.32 g/cm3 and 10.49 g/cm3, respectively. Calculate the percentage of gold (by mass) in the jewelry. Solution: dJewely = (𝑝)dAu + (𝑞)dAg 𝑑 9.35𝑔 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐽𝑒𝑤𝑒𝑙𝑟𝑦 𝑔 𝐽𝑒𝑤𝑒𝑙𝑟𝑦= = =14.3 ⁄ 3 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝐽𝑒𝑤𝑒𝑙𝑟𝑦 0.654𝑐𝑚3 𝑐𝑚 𝑝= 𝑝= 𝑑𝐽𝑒𝑤𝑒𝑙𝑟𝑦 − 1.00𝑑𝐴𝑔 = % 𝐺𝑜𝑙𝑑 𝑏𝑦 𝑚𝑎𝑠𝑠 𝑑𝐴𝑢 − 𝑑𝐴𝑔 14.3 − 10.49 = 0.431 = % 𝐺𝑜𝑙𝑑 𝑏𝑦 𝑚𝑎𝑠𝑠 19.32 − 10.49 Where p is the percent, p= 0.431. So 100 X 0.431 gives you 43.1, which is 43 percent gold. A Numerical Example (II): Using the values below, determine the composition (mass % Cu and mass % Zn) of a 1982 pennies. Density of copper= 8.96g/mL Density of zinc= 7.14g/mL Density of pre-1982 pennies= 8.10g/mL Solution: dpenny = (𝑝)dCu + (𝑞)dZn 𝑑𝑝𝑒𝑛𝑛𝑦 − 1.00𝑑𝑍𝑛 𝑝= = %𝐶𝑢 𝑏𝑦 𝑚𝑎𝑠𝑠 𝑑𝐶𝑢 − 𝑑𝑍𝑛 𝑔 𝑔 8.10 ⁄𝑚𝐿 − 7.14 ⁄𝑚𝐿 𝑝= = 0.527 %𝐶𝑢 𝑏𝑦 𝑚𝑎𝑠𝑠 𝑔 𝑔 8.96 ⁄𝑚𝐿 − 7.14 ⁄𝑚𝐿 𝑍𝑛 Where p is the percent, p= 0.527. So 100 X 0.527 gives you 52.7, which is 52.7 percent copper. Also, 100 – 52.7 = 47.3 gives the percent of zinc.

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