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

[chucas11]

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.

 

[Kurdt]

This sounds like a homework question. Have you heard the tale of Archimedes and the gold crown?

 

[Mentz114]

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.

 

[tabchouri]

still, the volume of the crown is missing in the homework.
obviously impossible to tell without it

 

[Kurdt]

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.

 

[Mentz114]

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.