Confusing acid dilution calculations

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goldsilverpro

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I just got an email from a guy that bought 35% nitric and wanted to know how much it would take to dissolve a gram of silver. When I answered him, like most everyone else, I just assumed that 35% would be the same as diluting 70% with an equal amount of water. In thinking about this further, I find this to be in error. Actually, when diluting 70% nitric, 50/50, the result is close to 41%, not 35%.

http://www.handymath.com/cgi-bin/nitrictble2.cgi?submit=Entry

Using this chart, here is the math:

What happens when you dilute 70%, by weight, nitric 50/50? The specific gravity (g/ml or g/cc), at 20C, of 70% is 1.4134 (see chart). Therefore, a liter of 70% would weigh 1413.4 grams. Therefore, a liter of 70% would contain 1413.4 x .70 = 989.4 grams of nitric. By adding a liter of water, which weighs about 1000 grams, to a liter of 70% nitric (thereby diluting it 50/50), the total weight would be 1413.4 + 1000 = 2413.4 grams. Therefore, the final acid strength, by weight, of 50/50 70% nitric, would be 989.4/2413.4 = .41 or 41%.

Here again, by the chart, a liter of 41% nitric would contain 1252.7 x .41 = 513.6 grams of nitric. On the other hand, by the chart, a liter of 35% nitric would only contain 1214 x .35 = 424.9 grams of nitric. Therefore, the man I advised would require 513.6/424.9 = 1.209 times more 35% nitric than I told him. I told him to use 2.44 ml of 35%/gram of silver. It would actually take 2.44 x 1.209 = 2.95 ml of 35% nitric to dissolve one gram of silver.

As you can see, the math on this is not intuitive. You have to use a percentage/specific gravity chart like the one above in order to get the correct answer. There are other ways, but this is the easiest.

This works with all acids or any other solution that you can find a specific gravity chart on.

I did this math hurriedly. If anyone finds an error in my logic or my math, please let me know.

I might note that all this can vary slightly, depending on the actual temperatures involved. I used the specific gravities at 20C (68F) for all calculations.

Chris
 
Hi Chris

Thank you for crunching the numbers.
Though, somthing doesn't add up here. When I'll get home later I'll try and figure out what.
 
I'm a bit confused too.

1000 ml of 70% nitric has 700ml of pure nitric

1000ml of water added to the 1000ml of 70% nitric is a total of 2000ml of solution

700ml / 2000m = .35

right? :|
 
1000 ml of 70% nitric has 700ml of pure nitric

That's true, BY VOLUME, but it's 70% BY WEIGHT and 1000 ml of 70% weighs 1413.4 grams. Apples and oranges! The WEIGHT of nitric in a liter of 70% = 1413.4 x .70 = 989.4 grams.
My own Edit: That's NOT true, BY VOLUME. A liter of 70%, by weight, nitric contains 1413.4 - 989.4 = 424 grams or ml of water (it's 42.4%, by volume, water). Therefore, a 70%, by weight, nitric solution would be the same as a 100 - 42.4 = 57.6%, by volume, nitric solution.

1000ml of water added to the 1000ml of 70% nitric is a total of 2000ml of solution

That's true, but the 2000 ml weighs 1413.4 + 1000 = 2413.4 grams. BY WEIGHT, therefore, the nitric is 989.4/2413.4 = 41%

The problem is that you're combining 2 different materials, nitric and water, which have great differences in their specific gravities.
 
an international agreement for stating a concentration of acids is in percent w/w or percent v/v?because both calculations are correct.in only depends on apples and oranges...
 
Think I get it now. Adding a liter worth of say corn syrup to a liter of water is heavier than a liter of water to a liter of water. Same in volume different in weight.

So when we are cutting our 70% nitric we should use less nitric and more water... I think. I wanna say to use 6% less nitric EX. 94ml of nitric to every 100ml of water. But like GSP said, this math isn't very intuitive.
 
The purpose was to determine how much 35% nitric it would take to dissolve a gram of silver.

I can't see how this would have anything to to do with an international agreement. The concentrated acids we buy here in the US are all based on weight percentage, as far as I know. Hydrochloric is about 35-37%, Sulfuric is about 95-96%, and nitric is about 67-70%. All these percentages are by weight. I haven't carefully read an acid bottle label recently but, if I remember right, it just gives the percent and doesn't say whether it's by volume or by weight. It is assumed to be by weight. If it is different in other countries, I don't know. I would doubt it, though, unless it is designated on the label as being by volume.

So when we are cutting our 70% nitric we should use less nitric and more water... I think. I wanna say to use 6% less nitric EX. 94ml of nitric to every 100ml of water.

Not true because when we use the term 50/50, a by volume dilution, we are assuming you use 100 ml of 67-70% nitric and 100 ml of water.
 
You guys were starting to make me doubt. However, I just couldn't reconcile in my mind that a 70%, by weight, nitric solution was equal to a 70%, by volume, nitric solution (it isn't). I now know I was right on target all along. See my Edit above.

I told you this stuff was confusing.
 
goldsilverpro said:
You guys were starting to make me doubt. However, I just couldn't reconcile in my mind that a 70%, by weight, nitric solution was equal to a 70%, by volume, nitric solution (it isn't). I now know I was right on target all along. See my Edit above.

I told you this stuff was confusing.

Chris, you are my favorite math freak 8)
 
Interesting point GSP, I had always treated my acid concentrations as V/V.

Since this discussion was centered around nitric I read the label on mine. I use Mallinckrodt 68-70% ACS nitric. I will be darned if I can find anything that indicates if the concentration is V/V or W/W. Even where it is giving the trace contaminates in PPB it says “68-70% HNO3. The fomula weight on the container is no help as it is obviously just for the nitric not the mix as it is FW: 63.01 Even going to the manufacturers website I cannot find the answer.

At the end of the day without knowing if your concentration percentage starting point is V/V or W/W the math becomes meaningless.

This will bug me, thanks GSP!
 
i have asked my friends from inorganic department. it is w/w for all aquaeous solutions of acids
 
This calculator also shows 41% if you enter

1413.4 and 70 in the first section, and 1000 and 0 in the second one.

http://www.handymath.com/cgi-bin/chemcalcc.cgi?submit=Entry
 
Fournines said:
This calculator also shows 41% if you enter

1413.4 and 70 in the first section, and 1000 and 0 in the second one.

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

Great find, Matt! That's a calculator everyone should bookmark and use. Sure saves doing a lot of confusing math. Personally, though, I enjoy the math because it allows me to visualize what is really going on.
 
In general, if you combine 2 materials with different specific gravities (SG), the percentage, by volume, of the one with the higher SG, will be lower than it's percentage, by weight.

As a hypothetical thought experiment, to make this clearer, let's say you combined 1000 g of Au powder with 1000 g of Al powder. Then, let's say you could press all the air out, distort all the particles together, and make a solid cake. In this cake, the weight percentage of the gold is 50% but the volume percentage of the gold is only 14%. That is very easy to see how that would occur. In general, it's a similar situation when mixing 2 liquids of different SGs.
 
I just purchased 50% Nitric acid v/v & 50% Hydrochloric acid v/v both are in 500ml amber glass bottles. I am going to be refining gold but a very small amount as a test as I do not want to work with these chemicals in the first place. So there for I have some jewelry about 28 grams of 14k. What amounts of each acid do I use, did I purchase the correct chemicals? I also will be getting Nava granular pH Decreaser Granular Sodium Bi-sulfate to precipitate the gold from the solution which I believe is ok. Any help would be appreciated!
 
WiredOnSite, not bisulFATE, bisulFITE is what you'll need. You can find it @ beer & wine supplies stores or @ hardware stores as Stump Out by Bonide.
Do some more reading before starting your batch. You should inquart your 14k before running thru acids & many more steps before adding your SMB.

Take care!

Phil
 
I am really confused by these numbers. I would like to make real Aqua Regia (not HCl an Sodium Nitrate) and have seen a video which states "use 20 ml of Nitric acid and 60 ml of Hydrochloric acid". Everywhere that I have seen the formulation of Aqua Regia, it has been 1 part Nitric to 3 parts Hydrochloric. How is this affected if I use Nitric acid with a strength of 70%and Hydrochloric acid with a strength of 31% or 32%? I don't indulge in alcoholic beverages, but I'm almost ready to try. Do I use wine with 17.5% alcohol or whiskey at 50% alcohol? :roll:
 

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