# Finding Gold Purity using the water displacement method



## mary878 (Jul 5, 2016)

Hello to everyone. 

I recently visited Ghana and happened to meet a few gold buyers. I saw their method of buying gold and finding the purity as well. They used the water displacement method in determining the purity of the gold.

I have a question about the calculation.

Here is an example of the calculation:

Weight of Gold - 1002.29gms
Weight of Gold in Water - 55.53gms

Density = 1002.29 / 55.53 = 18.04

the next step - 18.04 - 10.51 x 52.838 / 18.04 = 22.05 Kt. 

I understood the step till finding density. But did not understand the next step. Can anyone tell me what does this value - 10.51 and 52.838 - stand for?

Thank you


----------



## upcyclist (Jul 5, 2016)

I'm not sure where that 52.838 comes from, but 10.51 is the density of silver. This method is assuming that the only other element in your alloy is silver (usually assumed for yellow golds). For red/rose golds, copper is assumed. 

As you probably can tell, this is not perfectly accurate, but it's close enough to not get ripped off. It's a field-expedient method, and is certainly better than nothing. Also, if your buyer is using the same method, in a way, it doesn't matter if it's not totally accurate, as long it's repeatable


----------



## goldsilverpro (Jul 5, 2016)

Something amiss here. The correct formula is: 
Density(D) = weight in air(Wa)/(weight in air(Wa) - weight in water(Ww) *OR*, D = Wa/(Wa-Ww)

Had you used your figures of Wa and Ww in the above formula, the density would calculate to be 1.059, which is obviously wrong.

In calculating this, I find the figure 55.53 is NOT the weight in water, as you stated. It IS the weight in air minus the weight in water, the denominator in the above formula. So, it was used properly by the buyer. I think you just misinterpreted what the numbers meant.

The actual weight in water had to be: 1002.29 - 55.53 = 946.76g
________________________________________________

I then tried a long, quite accurate formula that I normally use for calculating karat, and came up with 21.97K - pretty close to the buyer's number. To get this, I assumed that the only 2 metals involved are gold and silver, just like the buyer did. If desired, I can provide the formula I used, but it might take 1/4 page to explain it.

The math on all this is much more complex than you would think. It's not just a simple ratio and it's not that intuitive. It's also confusing math, much like the math relationship between the weight percentage and the volume percentage of various common acids and base solutions, that I have covered several times. 

The number, 52.838, is just a seemingly accurate factor the buyer came up with to make the calculations simpler. Without the factor, the calculation is much more laborious.

I might add that, although there are strict technical differences in the terms "density" and "specific gravity", they can be used to mean the same thing, at least for our purposes. You will see them used synonymously on the internet and in books.


----------



## GNL (Oct 6, 2019)

Hi, can you please provide the actual formulae, as i struggle to understand the 52.838 constant as well as the 10.51 number even though it looks like the density of silver.


----------



## GNL (Oct 8, 2019)

Sounds like 52.838 is a ratio of the specific gravity of Ag over that of Au, or the relative densities.

And the 10.51 would be density of Ag, however I believed Ag was 10.41 and Au was 19.32. Is there a valid reason to use different values in west africa? For instance the gravity constant in in Ouagadougou is 9.77 versus the widely assumed 9.81...

In any case, does anyone know the detailed formulae to get the calculation of 52.838 and confirm whether 9.51 is in fact a value for the density of silver ?

I believe this widely accepted formula used by buyers has an inherent margin in their favour, and i suspect it is build into these two “constants” that everyone accepts.

Can anyone help with this please?


----------



## butcher (Oct 8, 2019)

May not be related but 14K gold could actually be 13.5K and marked 14K legally...


----------



## AshesoftheUniverse (Oct 8, 2019)

For those who would delve further into this very ancient principle, I refer you to the following link:
https://en.wikipedia.org/wiki/Archimedes%27_principle


----------



## butcher (Oct 8, 2019)

Thanks for providing the link, this an ancient principle I use to get most of my gold while mining, Archimedes' principle is a law of physics fundamental to fluid mechanics, which is very useful in the mining industries as well as many other modern-day industries...


----------

