Question

A jeweler guarantees that a piece of jewelry is at least 95% gold, by mass. You consider buying a piece of gold jewelry that weighs 9.85g and has a volume of 0.675cm3. The jewelry contains only gold and silver. Suspicious of the jeweler, you look up the density of gold and silver, they are 19.3g/cm3 and 10.5g/cm3, and do a quick calculation to find out the % by mass of gold. Is the jeweler trying to cheat you?

Answer 1

The density of the sample is:
Density = mass / volume
Density = 9.85 / 0.675
Density = 14.6 g/cm³

If the sample has 95% gold, and 5% silver, its density should be:
0.95 x 19.3 + 0.05 x 10.5
Theoretical density = 18.9 g/cm³

The difference in theoretical and actual densities is very large, making it likely that the jeweler was not telling the truth.