Question

the current U.S. penny is only 2.5% copper the remaining portion is zinc. Given the density of copper as 8.94 g/cm and the density of zinc is 6.57 g/cm, calculate the density of a penny.

Answer 1

Frankly I don't think this problem is workable unless we make some assumptions which probably are not true. The penny has a mass of 2.50g
mass Cu = 2.50*0.025 = about 0.06 g
mass Zn = 2.50*0.975 = about 2.44 g

volume Cu = m/d = 0.06/8.94 = about 0.007 cc
volume Zn = m/d = 2.44/6.57 = about 0.371 cc
Total volume if we assume volumes are additive (they aren't) = 0.378
Then density penny = m/v = 2.50/0.378 = about 6.61 g/cc.
Volumes are not additive, especially in solid alloys but with such a low concn of Cu and a high concn of Zn, this number of 6.61 g/cc (almost the same as pure Zn) must be reasonably close. You could measure the density rather easily. Place exactly 15 mL water in a 25 mL graduated cylinder, add 10 weighed pennies and read the volume of water. The volume is the difference in the volume levels with and without pennies. Then I would divide the mass by 10 to find the mass of one penny, divide volume by 10 to find volume of one penny, then divide m/v to find density of one penny.