The "Back of the Napkin" math behind mash pH adjustments

[Silver_Is_Money]

The general back of the napkin formula is:

Delta_pH = mEq's/(BC x Kg)
Where:
BC = buffering capacity, in units of mEq/Kg_pH
Kg = Kilograms of grist being mashed
Delta_pH = pH_Initial - pH_Target
mEq's = the number of milliequivalents of acid or base required to move the pH to the target.

Some short cuts are in order here, since this is the back of the napkin, or down and dirty method, and foremost is a presumption that quite often BC ~= 35

The real trick is in determining a recipe grists initial pH condition, and Alkalinity, volume of mash water at said alkalinity, mineralization, and each grist components pHDI (pH in deionized water) all interact here, but we will skip the hard stuff and make more presumptions here. Lets presume that our aggregate grist is mashing in RO water, and therefore Alkalinity is near zip. Lets also presume low calcium and magnesium levels, whereby we can downplay (their generally overplayed) impact upon downward pH shift.

On to an example:

Givens for the example:
BC = 35
Kg_Grist = 5.25
Initial pre adjustment mash pH = 5.72
Target mash pH = 5.40
88% Lactic Acids relative strength at pH 5.40 = 11.451 mEq/mL

Lets go:
Delta_pH = mEq's/(BC x Kg)
(5.72-5.40) = mEq's/(35 x 5.25)
0.32 = mEq's/183.75
183.75 x 0.32 = mEq's
mEq's = 58.8
58.8 mEq/11.451 mEq/mL = 5.1 mL of 88% Lactic Acid

Answer = Add 5.1 mL of 88% Lactic Acid whereby to bring the pH of the mash to 5.40

 

[Silver_Is_Money]

The general presumption is that mEq's of calcium (as Ca++ ion) reduce mash pH only 1/3.5 times as effectively as mEq's of acid, and mEq's of magnesium (as Mg++ ion) reduce mash pH only 1/7 times as effectively as mEq's of acid.

Lets add to the above the presumptions of 20L mash water, and 85 ppm (mg/L) Ca++, and 10 ppm (mg/L) Mg++

MW of Ca++ = 40
EQW of Ca++ = 40/2 = 20

MW of Mg++ = 24.3
EQW of MG++ = 24.3/2 = 12.15

20L x 85 mg/L = 1,700 mg of Ca++ ions
20L x 10 mg/L = 200 mg of Mg++ ions

1,700/20 = 85 mEq of Ca++
85/3.5 = ~24.28 mEq's of acid equivalent

200/12.15 = 16.46 mEq's of Mg++
16.46/7 = ~2.35 mEq's of acid equivalent

From the above post we determined a need for 58.8 mEq's of acid.

But now we need only 58.8 - 24.28 - 2.35 = 32.17 mEq's of additional acid

So therefore: 32.17 mEq/11.451 mEq/mL = ~2.8 mL of 88% Lactic Acid

New Answer (thanks to 20L of RO water with 85 ppm Ca, and 10 ppm Mg) = add 2.8 mL of 88% Lactic Acid

NOTE: There is some recent/modern evidence that the real world impact of Ca and Mg is perhaps only about half (or in some cases even less) of what is exhibited above (within specifically the mash). Thus my mention of their impact perhaps being overplayed (or overstated, overemphasized)... The reason for this is that Paul Kolbach, the German brewing scientist who first quantified their impact many decades ago, measured their impact at "knockout", post boil, and not in the well upstream mash at all. But for years to decades people (including well respected brewing scientists) have mistakenly applied Kolbach's findings of ~3.5 and ~7 as the 'acid equivalent' mEq denominators (divisors) to the mash, instead of to knockout as intended and tested by Kolbach. And all mistakes in brewing literature and lore and practice and presumption and math, etc... eventually become firmly entrenched and radically unquestionable gospel truth if told or written over and over again sufficient times without question. For but one example of this, consider the entrenched fantasy that the IBU's of pellet hops are equal to those calculated for whole hops when multiplied by 1.1.

 

[Silver_Is_Money]

But what if there were also 75 mg/L (ppm) of Alkalinity (as CaCO3) in our 20L of mash water?

MW of CaCO3 = 100
EQW of CaCo3 = 100/2 = 50

I'll leave it for someone else to (hopefully) pick up this ball and run with it from here. Just remember that Alkalinity mEq's act in the opposite way as for acid or Ca or Mg mEq's. So they will add to 32.17 mEq's in our ongoing example.

 

[HighVoltageMan!]

But what if there were also 75 mg/L (ppm) of Alkalinity (as CaCO3) in our 20L of mash water?

I like your desire to be so precise. The problem comes in the way that there are so many assumptions and estimations in brewing. Dealing with organic agricultural products, estimating volumes, not to mention drinking beer while doing it. The pH meter is a brewers best friend, it allows for brewers to be brewers and not chemical engineers. I have watch experienced brewers do pH adjustments by the seat of their pants and nail it. It's the kind of thing a brewer gets from experience. The mash, boil and finish pH do not need to be precise. If a brewer can get the pitch pH to +.1 to -.2. ;that is really good. The yeast does the work in the fermenter and will drop the pH to a narrow window the yeast strain or style needs to be. So pH during brew day is like hand grenades, the closer the better, but sometimes it just needs to be close enough.

Theoretically, CaCO3 will raise pH. But in a more practical sense it has little effect on pH because it doesn't dissolve into solution, it just drops to the bottom of the vessel and sets there. It needs CO2 to be able to covert to the more soluble calcium bicarbonate, which will raise pH. There is a lot science in brewing, but I keep telling myself that it's a lot like cooking, a practical art of sorts.

 

[Silver_Is_Money]

I like your desire to be so precise. The problem comes in the way that there are so many assumptions and estimations in brewing. Dealing with organic agricultural products, estimating volumes, not to mention drinking beer while doing it. The pH meter is a brewers best friend, it allows for brewers to be brewers and not chemical engineers. I have watch experienced brewers do pH adjustments by the seat of their pants and nail it. It's the kind of thing a brewer gets from experience. The mash, boil and finish pH do not need to be precise. If a brewer can get the pitch pH to +.1 to -.2. ;that is really good. The yeast does the work in the fermenter and will drop the pH to a narrow window the yeast strain or style needs to be. So pH during brew day is like hand grenades, the closer the better, but sometimes it just needs to be close enough.

Theoretically, CaCO3 will raise pH. But in a more practical sense it has little effect on pH because it doesn't dissolve into solution, it just drops to the bottom of the vessel and sets there. It needs CO2 to be able to covert to the more soluble calcium bicarbonate, which will raise pH. There is a lot science in brewing, but I keep telling myself that it's a lot like cooking, a practical art of sorts.

We think alike. While you were typing this, I was typing this in a different forum thread:

https://www.brewersfriend.com/forum...m-s-to-water-profile.14556/page-3#post-135555

 

[Silver_Is_Money]

Fortunately for us, Alkalinity as a measure of CaCO3 is merely a theoretical construct, as an accepted 'universal' means whereby to gain a foothold and achieve a level playing field that is somewhat broader* than a strictly HCO3- (bicarbonate) in basis. Alkalinity itself is therefore merely a fantasy construct that just so happens to be a universally accepted fantasy. If waters alkalinity was factually a measure of waters CaCO3, and as stated above, CaCO3 mainly precipitates out and does not readily dissociate, then we wouldn't be able to functionally equate alkalinity to CaCO3. This is a somewhat unique case whereby accepting the fantasy is better than accepting the truth.

*Due to the universal acceptance of the CaCO3 fantasy, we can (for example) equate other anion species (such as OH-) to Alkalinity.

The real killer here is that, since Alkalinity as CaCO3 is a fantasy, and Kolbach's work has been perhaps grossly misconstrued and unjustly applied to the mash, RA (Residual Alkalinity) as currently popular (with respect to its application) must be a fantasy as well. This one seems to shake the RA faithful to their very core. Faith being strong, they may never accept it. But RA is merely a 'derivative' of a fantasy mixed with unsound assumptions... A fantasy thereby potentially twice removed from reality. RA is not fixed. It is a variable. And perhaps a highly variable variable.

Lastly, HCO3- (bicarbonate) can also be used/applied theoretically as a fantasy, albeit not generally a universally accepted one, and if I'm looking at it correctly, what is perhaps the most common spreadsheet based mash pH assistant software seems to do just this. No harm, no foul.... Will work just as well (with the big presumption here that the remaining math modeling is sound).

 

[Josh Hughes]

Thanks for making me feel stupid....

 

[Silver_Is_Money]

Thanks for making me feel stupid....

Does that mean you will not be the one filling in the blanks left behind in post #3 above?

 

[Josh Hughes]

Nope

 

[Minbari]

Thanks for making me feel stupid....

im with you man! lol

I just use EZwater calc. its usually close enough

 

[Josh Hughes]

im with you man! lol

I just use EZwater calc. its usually close enough

I use what is in the recipe builder. I do want to learn all of this. Summer reading maybe.

 

[Silver_Is_Money]

How many days should I wait for someone else to pick up this ball and run with it before eventually having to complete #3 myself?

Hint: The answer is straight forward, and pretty much all of it resides within another of my recent posts already.

 

[Craigerrr]

Sorry @Silver_Is_Money this makes my head hurt, I am glad that you are passionate about it though

 

[Donoroto]

I learn from each of your posts, but this is still a bit over my head.

I am guessing just under 3 ml of 88% Lactic acid would bring us back from 75 ppm of Alkalinity. ?

 

[Silver_Is_Money]

I learn from each of your posts, but this is still a bit over my head.

I am guessing just under 3 ml of 88% Lactic acid would bring us back from 75 ppm of Alkalinity. ?

75/50.04345 = 1.4987 mEq/L

20L x 1.4987 mEq/L = 29.974 mEq of Alkalinity

32.17 mEq + 29.974 mEq = 61.144 mEq of 88% Lactic Acid now required

61.144 mEq/11.451 mEq/mL = 5.34 mL of 88% Lactic Acid now required to move our hypothetical mash to 5.40 pH.

 

[Donoroto]

(Head explodes)

 

[Craigerrr]

E=mc2

 

[Megary]

@Silver_Is_Money

While, for me, all of this may not sink in, a lot of it does. (I’m actually surprised how much, honestly). I read every post and appreciate each one. In a funny way, despite the math and the equation thingies, water has become less of a dark alley than it was before. Maybe I don’t need to understand every little bit, but I definitely understand a lot more about pH, alkalinity, and water in general than before you started this exercise. I appreciate these posts...and I’m sure they will be a great reference for many who happen upon them.

Thanks.

 

[Josh Hughes]

@Silver_Is_Money

While, for me, all of this may not sink in, a lot of it does. (I’m actually surprised how much, honestly). I read every post and appreciate each one. In a funny way, despite the math and the equation thingies, water has become less of a dark alley than it was before. Maybe I don’t need to understand every little bit, but I definitely understand a lot more about pH, alkalinity, and water in general than before you started this exercise. I appreciate these posts...and I’m sure they will be a great reference for many who happen upon them.

Thanks.

I agree this is great stuff anything I pick up is great.

 

[Donoroto]

I am guessing just under 3 ml of 88% Lactic acid would bring us back from 75 ppm of Alkalinity. ?

I should clarify this statement. I forgot to "show my work"...

In Post 2 it is stated that 32.17 mEq needs 2.8 ml of 88% Lactic acid. Adding 75 PPM Alkalinity divided by a molecular weight of 50 is 1.5, and 20 liters then needs 30 mEq of acid. 30/11.45 = 2.62 ml of additional 88% LA for the batch. in my world, 2.62 is 'just under 3 ml'. The former response I did in my head, this one needed a calculator.

I rounded off here, since few of us have the ability to measure a tenth of a ml, much less a hundredth. And the napkin is getting crowded...