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?

Whats the procedure?

Answer 1

Answer:

• 39.7%

Explanation:

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 denisty of the chain as the weighted average of the densities of the other metals:

Mass of gold × density of gold + mass of other metals × 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:

        $\dfrac{19.3\cdot x+9.7\cdot (66.7-x)}{66.7}=13.34$

       $19.3x+635.66-9.7x=889.778$

      $9.6x=254.118\\\\x=26.47$

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

• (26.47 / 66.7) × 100 = 39.7%