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?

Question

Sullivan Nicholson

Chemistry

3 August, 08:49

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?

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Answers (1)

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Yasmin Abbott · 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.