Did I Understand the 18-karat Gold Problem Wrong?

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SUMMARY

The discussion centers on the calculation of the overall density of an 18-karat gold alloy, which consists of 75% gold, 16% silver, and 9% copper. The user initially calculated the densities of each component based on their mass percentages but mistakenly interpreted these percentages as volume contributions. The correct approach requires calculating the total mass and volume of the alloy to determine the overall density accurately. The user concluded that their initial understanding was flawed due to this misinterpretation of mass versus volume.

PREREQUISITES
  • Understanding of alloy composition and karat measurement
  • Knowledge of density calculations and units (g/cm3)
  • Familiarity with mass versus volume concepts in material science
  • Basic arithmetic and algebra skills for calculations
NEXT STEPS
  • Study the principles of alloy density calculations
  • Learn about the differences between mass percentage and volume percentage
  • Explore the concept of specific gravity in materials
  • Practice with additional examples of density calculations for various alloys
USEFUL FOR

This discussion is beneficial for students in materials science, jewelers, and anyone interested in understanding the properties and calculations related to metal alloys, particularly in the context of gold and its applications.

PascalPanther
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I thought I understood this problem, but my answer is wrong.

"In a sample of 18-karat gold, 75 percent of the total mass is pure gold, while the rest is typically 16 percent silver and 9 percent copper. If the density of pure gold is 19.3 g/cm^3, while the densities of silver and copper are respectively 10.5 g/cm^3 and 8.90 g/cm^3, what is the overall density of this alloy of 18-karat gold?"

So I understand that 18-karat gold is 75% gold because it is 18 parts out of 24, with the other 6 parts made up of silver and copper, equaling 100%. So it made sense to me, to do this:
Gold: (0.75)(19.3 g/cm^3) = 14.475 g/cm^3
Silver: (0.16)(10.5 g/cm^3) = 1.68 g/cm^3
Copper: (0.09)(8.9 g/cm^3) = 0.801 g/cm^3
Then I added them: 16.96 = 17.0 g/cm^3

This is wrong, isn't that what it is asking for? Did I understand the question wrong?
 
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75% of the mass is gold, but you have been working with 75% of volume.
 

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