How to make 10% Phosphoric Acid if starting from 85%, 75%, or 30% Phosphoric Acid

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Larry Sayre, Developer of 'Mash Made Easy'
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(Molarity x Volume) = (Molarity x Volume)

The Molarity of 85% Phosphoric Acid is 14.6502
The Molarity of 75% Phosphoric Acid is 12.0848
The Molarity of 30% Phosphoric Acid is 3.6140
The Molarity of 10% Phosphoric Acid is 1.0745

Example: To make 500 mL of 10% Phosphoric Acid from 85% Phosphoric Acid:

14.6502/1.0745 = 13.634435
500/13.634435 = 36.67185
The answer is to add 36.67185 mL of 85% Phosphoric Acid to ~250 mL of distilled water, and then slowly and carefully make up to a final volume of 500 mL by adding additional distilled water.

Checking our work by plugging into the above listed formula:

(14.6502 x 36.67185) = (500 x 1.0745) = (TRUE or FALSE)
537.25 = 537.25 = TRUE

It may prove easier to use weight vs. volume.

The Density of 85% Phosphoric Acid is 1.689 g/CC
The Density of 75% Phosphoric Acid is 1.579 g/CC
The Density of 30% Phosphoric Acid is 1.181 g/CC
The Density of 10% Phosphoric Acid is 1.053 g/CC

For the above example:

36.67185 mL x 1.689 g/mL = 61.94 grams of 85% Phosphoric Acid to be added to ~250 mL of distilled water, and then slowly and carefully made up to a final volume of 500 mL by adding additional distilled water.

The process seen above would be the same for the 75% and 30% strengths, only using their respective values of Molarity and Density.

WARNING: Use all possible caution and safety, and be sure to wear appropriate protective equipment.

Warning #2: Never add water to acid. Always add acid to water, and be sure that it is an adequate amount of water.

Warning #3: Someone please check my work and let us all know if I have listed any of the properties of the various acid concentrations incorrectly above, or if this simple method is in any way flawed, or if I have my warnings listed incorrectly.
 
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NOTE: A correction has been made to the above. If you copied it earlier, get an updated copy please.
 
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Larry Sayre, Developer of 'Mash Made Easy'
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A bit of trivia. Presuming up front that I've calculated it correctly, If you take a full 950 mL bottle of 85% Phosphoric Acid (such as for the Duda Diesel brand) and make it up to 1.00 US Gallons, its concentration will be 30.43%.

1.00 US Gallon of 30.00% Phosphoric Acid requires 934.14 mL of 85% Phosphoric Acid. Call it 934 mL.
 
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An alternative valid dilution formula that does not directly involve molarity or normality:

Vol1 x Density1 x Conc%1 = Vol2 x Density2 x Conc%2
 

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I'm not a chemist - I deal with ones and zeroes - so why doesn't V1C1 = V2C2 work?

Cheers!
 
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I'm not a chemist - I deal with ones and zeroes - so why doesn't V1C1 = V2C2 work?

Cheers!

It only works if fluid densities remain constant and unchanging in conjunction with dilution. They don't. And the differences in outcome are dramatic as a consequence.
 
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Another way to look at this is that if a certain gram weight of 100% pure Phosphoric Acid is present within the pre-dilution volume, then assuredly the very same gram weight of 100% pure Phosphoric Acid must be present within the post dilution volume.

Grams = Density x Percent_Concentration x Volume
 
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For converting 85% to 10% and ending up with 1 liter:

The case for 85% is:
1.689 g/mL x 0.85 x 73.3466 mL = 105.300 grams of pure 100% Phosphoric Acid initial

The case for ending up with 1 Liter of 10% Phosphoric Acid when diluting 73.3466 mL of 85% is:
1.053 g/mL x 0.10 x 1,000 mL = 105.300 grams of pure 100% Phosphoric Acid final

105.300 grams initial = 105.300 grams final
 
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day_trippr

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Could you give me a case for 85% ending up as 200ml of 25%?

Cheers! (and thanks in advance :))
 
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It looks like if you ignore the critical density changes you wind up making roughly a 34.7% concentration while believing (in error) that you have made a 25% concentration. That's a substantial error.
 
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Thanks for that then. Appreciate it...

Cheers!

If your entire history of pH adjustment, and your choice as to the best fit software has been strongly influenced by such a large mistake, then a total re-evaluation of all of said history and your conclusions derived from it is likely in order. Software previously considered to be way off due to calling for seemingly insanely more acid may now seem to be more appropriate.
 
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I've been giving some thought with regard to a potentially ideal concentration percent target by which to dilute 85% (or 75%) Phosphoric Acid, and I've settled upon 30%. At the 30% concentration level Phosphoric Acid has sufficiently close enough to the same acid strength (within the range of typical mash and wort pH's) as for AMS/CRS, such that pH reduction data for AMS/CRS can be used directly for 30% Phosphoric Acid.

And while I'm assuredly not an expert in this, so thereby this part of my thought process must be taken with due suspicion and a proverbial "grain of salt", my first assumption would be that the relative danger level for 30% Phosphoric Acid must likewise be relatively similar overall to that for AMS/CRS.
 

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Thanks for making this post. I have been mixing this up wrong since I bought the gallon jug a few years back, I originally proved out the Mash Made Easy sheet with LHBS bought 10% and stopped checking the ph after it was correct a few times.

I have been mixing this up using V1*C1=V2*C2. So 1 liter of final mixture would get 117 ml acid, measured by volume and 883 ml of RO water measured by weight.

Rather than dumping the batch I have I calculated the concentration using Vol1 x Density1 x Conc%1 = Vol2 x Density2 x Conc%2. 117 x 1.689 x 0.85 = 1000 x V x C. I then solved it a few times using the densities posted above. 1.0824 g/ml and 15% concentration is the most correct solution, I'm thinking I'll just plug 15% into Mash Made Easy and run with it.

Does my math and logic work out?
 
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I calculate that 113.1 mL of 85% Phosphoric Acid made up to 1,000 mL with distilled water = 15% final acid concentration
 

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Thank you kindly @IslandLizard! Glad to hear that it has been of use. I don't often receive thanks for my efforts. Well appreciated!!!
YVW! It's sad you don't get more noticeable appreciation for all you do here. But I'm quite sure those in the know, and understand the value of your contributions, appreciate your hard work and time it takes to post it here.

I wanted to post a thank you right after you posted the thread, as I bookmarked it. Then came back to it, a year or so later to actually use it. It's darn handy.
 

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I too wish to add my grateful thanks for this and many other helpful subjects Larry has initiated. I'm British, and while we might have a great many differences of opinion on beer, the chemistry and science is true for all.
 
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