Calculating Phosphoric Acid Additions

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I'm having trouble coming up with the specific phosphoric acid additions I should be using for my pH adjustments. I've been using the approach specified in "Water" by Palmer and Kaminski, and the result of those calculations tells me that when using distilled water, a 1.4 gallon mash using 4.5lb Maris Otter w/ 3.1 mVal of Calcium (provided by 1 gram of gypsum and .3 grams of Calcium Chloride) would require about 24 mEq of acid to balance out at a pH of 5.4 I'm not exactly sure how to bridge the gap between 24 mEq of phosphoric acid and how many mL of my 85% Phosphoric acid solution I should be adding.

Another questions is assuming I am using distilled water, does the amount of acid needed change based on the volume of the mash? If I were to increase the volume to 2 gallons for some reason, I'm assuming the mEq of acid needed doesn't change because distilled water isn't introducing any new ions into the equation.

Also if I were to decide to treat my both my mash and sparge water volume all together, and then take from that the volume necessary for the mash, then I assume I would need more acid proportionate to the amount of sparge water I will be adding. If I had 1.4 gallons of sparge water it would require twice the acid since I will be splitting it up?

I've got myself so confused today, any help clarifying this would be immensely helpful to my sanity.
 
I'm having trouble coming up with the specific phosphoric acid additions I should be using for my pH adjustments. I've been using the approach specified in "Water" by Palmer and Kaminski, and the result of those calculations tells me that when using distilled water, a 1.4 gallon mash using 4.5lb Maris Otter w/ 3.1 mVal of Calcium (provided by 1 gram of gypsum and .3 grams of Calcium Chloride) would require about 24 mEq of acid to balance out at a pH of 5.4 I'm not exactly sure how to bridge the gap between 24 mEq of phosphoric acid and how many mL of my 85% Phosphoric acid solution I should be adding.
In transitioning from the bottle to pH 5.4 in the mash each mmol of phosphoric acid releases 1.02 mEQ of protons so you need 24/1.02 mmol. As the molecular weight of phosphoric acid is 98 mg/mmol that's 98*24/1.02 mg and as it's 85% acid a total of 98*24/(0.85*1.02) mg. Finally as the density of 85% phosphoric acid is 1685.6 mg/L we find we need 98*24/(0.85*1.02*1685.6) = 1.609 mL

Another questions is assuming I am using distilled water, does the amount of acid needed change based on the volume of the mash? If I were to increase the volume to 2 gallons for some reason, I'm assuming the mEq of acid needed doesn't change because distilled water isn't introducing any new ions into the equation.
Your reasoning is sound.


Also if I were to decide to treat my both my mash and sparge water volume all together, and then take from that the volume necessary for the mash, then I assume I would need more acid proportionate to the amount of sparge water I will be adding. If I had 1.4 gallons of sparge water it would require twice the acid since I will be splitting it up?
The mash water by itself must contain enough acid to neutralize all the malt akalinity so yes, if you use half the water for sparge and half for mashing the amount of acid in the total volume will be double what you would put in the mash water alone. But this leaves you with acidified sparge water and you don't need acid in sparge water that has no alkalinity so you will be adding extra acid to the wort and its pH will be lower than if you did not treat the sparge water. Wort seems to have buffering capacity about the same as that of the grains that went into making it so you can estimate the additional wort pH drop from the extra acid.
 
Thank you! I actually ended up pretty close in the end with my approach, I just didn't account for the density of the solution, which in the end still resulted in significantly more acid than necessary.

Also great point about not needing acid if sparging with distilled water. So it would only be necessary if sparging with water containing alkalinity, and the amount of acid needed for sparge is only based on the water profile and not considering any properties of the malt?

Does the fineness of the crush affect the pH of the mash? For BIAB if you use a really fine crush I can imagine that maybe more of the components of the malt that affect pH would be utilized and have a larger effect. I suppose one way to test would be to test the DI pH of a mash both finely and coursely crushed.

While mashing with Maris Otter I undershot my pH considerably and I don't know if it can all be accounted for by the additional acid. The crush from my local homebrew store was really course and seems to consistently be for Maris Otter. They mention it is a smaller grain size, but I'm not too sure about that. Wondering if that could be a factor as well.
 
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