Recently, I posted a derivation of the equations to determine the mass fractions of two metals in a binary alloy. I thought it may be helpful to develop an Excel software tool to perform these calculations.
To use the tool, you enter the densities of the two metals and the density of the alloy in the blue cells as seen in Figure 1 below. The calculated mass fraction of each metal is shown in the gray cells.
Figure 1. The data entry for the mass fraction calulator. The densities are entered into the blue cells and the mass fractions are calculated and shown in the gray cells.
As an example, let’s assume you purchase some 14 karat gold. Unfortunately, to your eye it looks more like 10 karat gold, so you want to check it out. As a reminder, when gold is expressed in karats, the alloying metal is copper. First you need to measure the density of the gold alloy. An easy way to do this is the wet gold technique as discussed in a past blog post. From using this technique, you determine that the density of the alloy is 11.53 g/cc. The density of gold is 19.3 g/cc and that of copper is 8.96 g/cc. You will recall that 14 karat gold is (14/24) gold or a mass fraction of 0.5833.
The weight fraction of gold is shown to be 0.4167 or 10/24, as shown in Figure 1, indicating that the gold is 10 karat, not 14 karat.
Time to complain to the seller!