Discovering the Composition of a Gold Crown: Mass, Density, and Ratios Explained

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In summary, the conversation is discussing a homework question about a gold crown and how to determine if it is made of pure gold or a gold and copper compound. The conversation mentions the tale of Archimedes and the concept of density. It is suggested to use the difference in mass when weighed in air and in water to determine the volume and density of the crown, and thus deduce the ratio of metals. The volume of the crown is missing in the homework, making it impossible to determine the ratio without it.
  • #1
chucas11
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Is it gold? Question, help needed :)

A gold crown hangs from a spring scale reading it's mass as 14.7 Kg. When the crown is submerged in water while still hanging from the spring scale, it's mass now reads 13.4 kg. Knowing that its either all gold, or a gold and copper compound, figure out which of the two it is. If it is a gold and copper compound, what are their ratios. Density of Au=19.32, Density of Cu=8.96.

I'm stuck, not really even sure where to start. :(. Any tips or help would be greatly appreciated.
 
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  • #2
This sounds like a homework question. Have you heard the tale of Archimedes and the gold crown?
 
  • #3
If the crown has a volume V, then the weight of the crown is its volume times its density. When the crown is weighed in water, the weight registered will be less by V times the density of water.

weight in air = density x volume - density of air x volume
weight in water = density x volume - density of water x volume

You can manipulate these to lose volume, and assume the density of air is zero.
 
  • #4
still, the volume of the crown is missing in the homework.
obviously impossible to tell without it
 
  • #5
tabchouri said:
still, the volume of the crown is missing in the homework.
obviously impossible to tell without it

You can work it out from the two masses. The difference in mass is the mass of the displaced water which you can work out the volume of since we know the density.
 
  • #6
tabchouri,

if you divide the two equations I've given, volume cancels out to give

weight in air/weight in water = (density - density of air )/(density - density of water)

and you can now work out density, which tells you the ratio of metals.
 
Last edited:

1. What are the characteristics of gold?

Gold is a chemical element with the symbol Au and atomic number 79. It is a dense, soft, and malleable metal with a bright yellow color. It is also highly ductile, meaning it can be drawn into thin wires, and it is an excellent conductor of electricity and heat.

2. How can I tell if something is made of real gold?

The most reliable way to determine if something is made of real gold is to have it tested by a professional using specialized equipment. However, you can also perform a few simple tests at home, such as the magnet test, density test, and acid test, to get an idea of the authenticity of the gold.

3. What is the difference between 24K, 18K, and 14K gold?

The difference between these different types of gold is their purity level. 24K gold is considered pure gold, meaning it is 99.9% gold. 18K gold is 75% gold and 25% other metals, while 14K gold is 58.3% gold and 41.7% other metals. The lower the karatage, the less pure the gold is.

4. Can gold be found in nature as nuggets?

Yes, gold can be found in its pure form as nuggets in nature. However, this is a rare occurrence, and most gold is found in small particles mixed with other minerals. Gold nuggets are typically found in river beds or areas where there has been a lot of geological activity.

5. What is the process for extracting gold from ore?

The process of extracting gold from ore involves crushing the rock containing the gold and using chemicals such as cyanide or mercury to dissolve the gold. The dissolved gold is then separated from the other materials and the pure gold is extracted through a series of refining processes.

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