In a video, the water level was 15 milliliters in a graduated cylinder. After adding the gold chain, it turned to 20 millimeters.

Question

When I weighed the chain, its mass was 71.1 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?

 

Please explain and show work, thank you :)

Answer 1

71.1/5mL = 14.22 g/mL  this is the density of the gold chain.

 

x mL(9.7 g/mL) + y mL(19.3 g/mL) = 5mL(14.2 g/mL)

x + y = 5mL, y = 5 - x

xmL(9.7 g/mL) + (5mL-xmL)(19.3 g/mL) = 5mL(14.2 g/mL)

9.7x grams + 96.5grams - 19.3x grams = 71 grams

-9.6x grams = -25.5grams

x = 2.66 grams of silver/copper blend

y = 2.34 grams of gold

2.34/5  x 100 = 46.88 % = 46.8% gold