Hello everyone,

I need some help regarding the correct formula for determining the density of an alloy.

For this example I'll use cartridge brass (C260) which is 70 % copper and 30 % zinc, by weight.

The density of copper is

8.96 g/cm3 and that of zinc is

7.14 g/cm3 (cm3 or cc).

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The first formula, a popular one so it seems but which is incorrect, assumes volume fractions:

(70 cc * 8.96 g/cc + 30 cc * 7.14 g/cc) / 100 cc = (627.2 g + 214.2 g) / 100 cc = 841.4 g / 100 cc = 8.414 g/cc

I say it's incorrect because alloys are not made like that, but by using mass fractions.

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The second formula, which I had relied upon until now, assumes mass fractions:

100 g / (70 g / 8.96 g/cc + 30 g / 7.14 g/cc) = 100 g / (7.8125 cc + 4.2017 cc) = 100 g / 12.0142 cc = 8.323 g/cc

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And a third formula which uses the molar mass for each of the constituents.

The standard atomic weight (and corresponding molar mass) for copper is 63.546 and for zinc is 65.38.

70 g / 63.546 g/mol = 1.1016 mol

30 g / 65.38 g/mol = 0.4589 mol

1.106 mol + 0.4589 mol = 1.5605 mol for the whole alloy

Now for the mole fractions:

1.1016 mol / 1.5605 mol = 0.706

0.4589 mol / 1.5605 mol = 0.294

Then I use the density:

0.706 * 8.96 g/cc + 0.294 * 7.14 g/cc = 6.326 g/cc + 2.099 g/cc = 8.425 g/cc

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I need the formula for accurately calculating the mass of some metal parts that I design using a CAD program.

Until now I had relied upon the second formula but after some research a few days ago I came upon the third one which gave me some doubts.

The thing is that across the internet various manufacturers of different alloys give the density in the data sheet, and that value is way off of what I get using either formula, even the first incorrect one.

http://www.farmerscopper.com/cartridge-brass-260-c260-c26000.htmlhttps://www.ajoster.com/sites/default/files/downloads/C-26000_B36_CARTRIDGE-BRASS_AJ-OSTER.pdfhttps://www.diehl.com/cms/files/Diehl_Metall_Strip_MB30_V3_M-SM.pdfhttps://www.wisetool.com/density.htmNo matter what I use, I don't get the results that are given on sites like these. And I could go on to list more examples than the one given above.

What am I missing?