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 67.2 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

The percentage of gold will be equal to 39.7%

What are percentages?

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

1. First find the density of your chain

Density = mass / volume

Volume = displaced water volume

                     = Volume of Final level of water - initial level of water

                     = 20 ml - 15 ml = 5 ml

Mass = 66.7 g

Density = 66.7g / 5 ml = 13.34 g/ml

2. Second, write the density of the chain as the weighted average of the densities of the other metals:

Mass of gold x density of gold + mass of other metals x density of other metals, all divided by the mass of the chain.

Calling x the amount of gold, then the amount of other metals is 66.7 - x:

[(19.3x+(9.7)(66.7-x)] / 66.7 = 13.34

19.3x + 635.66 - 9.7x = 889.778

9.6x = 254.118

x = 26.47

Then, there are 26.47 grams of gold in 66.7 grams of chain, which yields a percentage of:

(26.47 / 66.7) x 100 = 39.7%

Therefore the percentage of gold will be equal to 39.7%

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