Specific Gravity of Alloyed Metals

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Hi,

I'd like to ask for some help regarding verifying the Specific Gravity of an alloyed metal, say a 22k gold chain, which gold content is supposed to be 91.6%. Pure Gold being 19.32 SG, a 91.6% pure item should be 91.6% of pure gold's SG, if I'm not mistaken. So a 22k gold item should be 17.70SG. Is this correct, or am I missing something?

Thank you.

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@Introspect,

Introspect wrote:

Is this correct, or am I missing something?

Not correct.

You also have to consider the contribution to specific gravity from the other metal besides gold that helps make up 22k gold.

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@Kolyo,

Ok, how would you calculate it then if it's 91.6% pure gold and the remainder is copper (SG of 8.96)?

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@Introspect,

22k gold is 91.6% gold by mass.
http://en.wikipedia.org/wiki/Carat_%28purity%29#Measure

Figure out what percentage by volume (P%) of the total metal that goes into the alloy is gold and what percentage (Q%) is copper.

Then take the weighted average of two specific gravities and that should give you the specific gravity of the alloy.

Your answer will be P% * 19.32 + Q% * 8.96

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@Kolyo,

So if Copper content is 8.4% and Gold 91.6%, it works as such?:

19.32 * 91.6% (Gold) = 17.69SG
8.96 * 8.4% (Copper) = 0.75SG

17.69 + 0.75 =18.44 total SG of the item?

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@Introspect,

No, the copper content by volume is a higher percentage, 16.3%. The gold content by volume is 83.7%.

Even though you have 11 times as many grams of gold as grams of copper, the gold is denser so it doesn't fill as much space as you would think.

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@Kolyo,

I still don't understand.

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@Introspect,

Do see the difference between "content by volume" and "content by mass"?

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@Kolyo,

If you have something that's very dense like gold, it's not going to fill as much space as the less dense substance.

Suppose I have 11g of pure gold, and suppose I have 1g of copper. (That's an acceptable combination to use in making "22-carat gold".) The gold has a density of 19.32 g/cm^3 so my gold fills 0.56936 cm^3 of space. The copper has a density of 8.96 g/cm^3 so my copper fills 0.11161 cm^3 of space. Together they fill 0.68097 cm^3 of space. So the gold fills 0.56936/0.68097 = 83.6% of the space. The content of the mixture by volume is 83.6% gold.

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@Kolyo,

Kolyo wrote:

If you have something that's very dense like gold, it's not going to fill as much space as the less dense substance.

Suppose I have 11g of pure gold, and suppose I have 1g of copper. (That's an acceptable combination to use in making "22-carat gold".) The gold has a density of 19.32 g/cm^3 so my gold fills 0.56936 cm^3 of space. The copper has a density of 8.96 g/cm^3 so my copper fills 0.11161 cm^3 of space. Together they fill 0.68097 cm^3 of space. So the gold fills 0.56936/0.68097 = 83.6% of the space. The content of the mixture by volume is 83.6% gold.

From this point you can get the density of the alloy by dividing the combined mass over the combine volume if you want. You don't have to use the weighted average formula I gave earlier.

density = (12g) / (0.68097 cm^3) = 17.622 g/cm^3

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One final word: the final density of the alloy will depend on whether you only use gold and copper or whether silver is included. If silver is included in 22k gold (as it appears to be) then the specific gravity will be higher, since silver is denser than copper.

Link:
http://asketc.com/7606/what-specific-gravity-does-a-22-carat-gold-coin-have

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@Kolyo,

Thank you. But this site says the SG of 22k Gold is 17.7, which is what I initially told you it should be, and you said I'm not correct. I got this by a very simple calculation. If 22k gold is 91.6% pure gold, then 91.6% of Pure Golds' SG should be taken to get the result.

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17.7 to 17.8 according that site.

The site also shows you how to calculate this value in a calculation similar to mine.

The reason they got an acceptable answer is because they factored in silver in their alloy. You told me the alloy would consist of just gold and copper. Apparently that was not correct. There is silver in the alloy.

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@Kolyo,

There is no silver in my item, I provided the specifics of this item. There can be various metals added to 22k gold, depending on the technique, so it's not all the same across the board. What is always the same is their claim of 22k, 18k, 14, etc. This claim is strictly regulated and defined in terms of % of gold in a given item. So knowing the % of Gold, we should also know how much % of this item is as dense as gold. Anyway, my method yielded the same answer as the complex equation, I must be on the right track then.

I also found this calculator on one of the links you sent, very useful!

http://www.handymath.com/cgi-bin/density.cgi?submit=Entry

And again, thank you for taking the time to help with this.

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@Introspect,

Introspect wrote:

There is no silver in my item, I provided the specifics of this item. There can be various metals added to 22k gold, depending on the technique, so it's not all the same across the board.

...which is why the specific gravity will not always be the same. The value depends on your choice of alloying metal(s).

Quote:

What is always the same is their claim of 22k, 18k, 14, etc. This claim is strictly regulated and defined in terms of % of gold in a given item. So knowing the % of Gold, we should also know how much % of this item is as dense as gold. Anyway, my method yielded the same answer as the complex equation, I must be on the right track then.

Sorry, but you just aren't. Try your method on 10k gold and see what happens.

According to this site, the possible specific gravities of 10k gold are between 11.03 and 11.59: http://www.hauserandmiller.com/reference/melting.html

10k-gold is 41.7% gold according to this site: http://www.goldpriceoz.com/gold-karat.html

What happens when you multiply 41.7% by 19.32?
(Hint: You don't a number over 10.)

Quote:

I also found this calculator on one of the links you sent, very useful!

http://www.handymath.com/cgi-bin/density.cgi?submit=Entry

Type this into the calculator:

91.6 [tab] 19.32 <-- indicating 91.6% gold
8.4 [tab] 8.96 <-- indicating 8.4% copper

What do you come up with?

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