“Dear Dr. Ron,
I see that you have developed software to calculate the density of an alloy if given the weight fractions of the constituent metals. Is it possible to find the weight fractions of the metals in an alloy given the alloy’s density? Thank you!”
Unfortunately, finding the weight fractions of the metals in an alloy from the alloy’s density can only be accomplished with a two metal alloy. First we must use the equation:
Where x is the weight fraction of metal A and the rhos are the associated densities. All that has to be done is to solve for x. The solution is worked out below in Figure 2, the final result is:Equation 2
As an example, let’s say you have a gold-copper alloy with a density of 18.42 g/cc. The density of gold (metal A) is 19.32 g/cc and that of copper (metal B) is 8.92 g/cc. Substituting these values into equation 2 gives the weight fraction of gold as 0.958. Hence the weight fraction of copper is 1-0.958 = 0.042.
I have developed an Excel-based software tool to perform these calculations. An image of it is shown in Figure 1. If you would like a copy of this tool send me a note.
Figure 1. A screen shot of the alloy metal weight fraction calculator.
Figure 2. The derivation of the weight fraction formula.