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kumpel [21]
3 years ago
6

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weig

hed 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?
Mathematics
1 answer:
mr_godi [17]3 years ago
7 0

Answer:

  • 39.7%

Explanation:

<u />

<u>1. First find the density of your chain</u>

  • 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

<u />

<u>2. Second, write the denisty of the chain as the weighted average of the densities of the other metals:</u>

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%
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