 # Interest in Formula for Calculating Alloy Density Still Keen

Category:
• Indium Corporation

• Alistar writes

Dear Dr. Ron,

Can you send me the answer to your question of 14th Feb. 2005, which follows;

If the density of silver is 10.5 g/cc and the density of tin is 7.31 g/cc. What is the density of an alloy of 96% tin/4% silver.

Hint: The answer is not obtained by multiplying the densities by the percentages and adding together. This question requires thinking about the definition of density. Out of 150 people given this question on a certification test, only 2 got it right.

The correct answer is 7.40 g/cc (7.399927 exactly) Bob Jarrett was the first one with a correct answer. If anyone wants the technique explained or a copy of an Excel spreadsheet that perfroms these calculations send me an email (rlasky@indium.com)

Alistair

Dear Alistair,

An easy way to understand this (proposed by Bob Jarrett) is to consider the 96% tin, 4 % silver example.

Lets assume I have 1 g of this alloy, 0.96 g is tin and 0.04 g is silver.

The volume of the tin is 0.96 g/7.31g/cc = 0.131327cc

The volume of the silver is 0.04g/10.5g/cc = 0.00381cc

So 1 g of the alloy has a volume of 0.131327 + 0.00381 cc = 0.135137 cc

Hence it's density is 1g/0.135137cc = 7.39989g/cc

The general formula is:

1/Da = x/D1 + y/D2 + z/D3

Da = density of final alloy

D1 = density of metal 1, x = mass fraction of metal 1

same for metals 2 and 3

Formula continues for more than 3 metals.

I have developed an Excel spreadsheet (shown calculating the density of SAC 305) that calculates density automatically. If anyone wants a copy, send me an email at rlasky@indium.com.

Cheers

Dr Ron