Chemistry extra credit ?

Question

Archimedes, a Greek mathematician and inventor of the second century B.C., was commissioned by the king of Syracuse to find out whether a crown that had been made for the king was fashioned from pure gold or from a mixture of gold and silver, a less expensive metal. Archimedes could not use chemical tests, for they would damage the crown, yet he was able to find the answer to the king's question. How did he carry out the king's request?

Answer 1

Well, if he could easily bend the crown, then it was pure gold.  If not, then the crown would be of the gold/silver mixture.

Or if Archimedes knew that Gold was more dense than silver, he could figure out the density of the crown and compare it to something that he knew to be pure gold or pure silver.  Supposing he had access to something that was pure gold, he could find the density (a little over 19 g/mL) and then compare that to the crown (which should be about the same if it were pure gold and less if it were the gold/silver mixture).

Answer 2

There is a legend that Archimedes shouted "Eureka"  (I have found it)  when he came up with the answer when sitting in his bathtub.

He realized that an object will displace water based on its volume.  So by immersing the item water and weighing the water displaced,  one can find the volume.   Then by weighing the item itself,  one can find the mass.   Gold and silver have a much greater density and specific gravity than base metals do so they would displace much less water for equal weight.

Answer 3

If you know mass of the crown, and it's volume, then you can determine its density.  Easy enough... step 1: Weigh the crown.  Step 2: find the volume by filling a bucket to the top with water and put the crown in the bucket.  Water will spill over the bucket, so you need a pan below the bucket to catch the water that spills over.  The volume of water that spills over is the same as the volume of the crown.

The density = mass / volume

If the density is the same as gold, then it's nearly pure.  If the density is somewhere between the density of gold and silver, then it is probably a mixture of the two metals.

While you may think it's more desirable to have a solid gold crown, this may not be true!  It would be harder on the neck to have such a heavy thing on your head, and also gold is very soft.  Most gold used in jewelery is not pure gold because it breaks to easily.  So if it is part silver, that's probably a better constructed crown.  But if all you care about is how much it's worth, then you want pure gold.

Take care,

David