Measuring Desity of Gold Chain

Question

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 66.7 grams.

I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.

Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?

Answer 1

You are given that the volume of the chain is 20-15 = 5 mL, and the mass is 66.7 grams. The density of the chain is therefore 66.7 grams/5 mL = 13.34 grams/mL

Assume you have x grams of gold in the chain. If you have x grams of gold, then you have (66.7 - x) grams of the other metal. Given these factors, then the volume of the chain can be calculated as

(x grams/19.3 g/mL) + [ (66.7 - x) grams/9.7 g/mL). This must equal the actual measured volume of 5 mL, so

(x grams/19.3 g/mL) + [ (66.7 - x) grams/9.7 g/mL) = 5 mL

(x/19.3) mL + [ (66.7-x)/9.7 ] mL = 5 mL

Multiply both sides by (19.3)*(9.7) to get

9.7x + (66.7 - x)*19.3 = 936.05

9.7x + 1287.31 - 19.3x = 936.05

Rearrange to get

351.26 = 9.6x

Divide by 9.6 to get x = 36.59 grams, which was defined as the number of grams of gold in the chain. Since the mass of the chain is 66.7 grams, the percent of gold in the chain is

(36.59/66.7) * 100% = 54.9% gold in the chain, given to one decimal place.

NOTE - The final answer is given to three significant figures, but the initial values in the problem are given to three (66.7 grams), two (15 mL) and one (20 mL) significant figure. In principle the final answer should be given to one significant figure.