Heads up for Spreadsheet Authors/Users

[ajdelange]

Sodium bicarbonate is often used to absorb protons where a grist contains a lot of high kilned (acidic) malts. The question addressed here is "How alkaline is bicarbonate from sodium bicarbonate?" (in other words, how much acid can it neutralize). Well the molecular weight of a bicarbonate ion is 61 mg/mmol and it carries a single negative charge so its equivalent weight must be 61 mEq/mg, no? No, unless the pH to which the mash is being adjusted is less than 4.38 (rule of thumb: pK - 2). Eighty-five mg (1 mmol containing 1 mmol of HCCO3-) of NaHCO3 does not absorb 1 mmol of protons above that pH. To absorb 1 mmol of protons requires the following amounts of bicarbonate ion depending on the target pH as shown:

pHz HCO3- required
5.3 66.6 mg
5.4 68.0
5.5 69.1
5.6 72.2

Thus these numbers represent the effective equivalent weight of the bicarbonate ion as a function of pHz. The sticky on carbonates and bicarbonates in this forum has the details on how to calculate these values.

So the reason for this post is that if you have created a spread sheet or calculator that assumes that each bicarbonate ion sucks up a proton at mash pH you will be in error. If you are using a spreadsheet that makes this assumption it is in error too. This same phenomenon occurs with acids (the normality of lactic and phosphoric acid depends on pHz) but the error incurred by assuming it constant is small because mash pH is pretty far from the closest acid pK. But with bicarbonate that distance is smaller (6.38 - 5.6 = 0.78; 6.38 - 5.3 = 1.08) and the error is, consequently larger.

I would assume that users of the popular spreadsheets will want reassurance that this is not a problem with the spreadsheets/calculators they use and I hope their authors will take a few minutes to check their programs and either correct them or let their users know that this is not a problem.

 

[FunkedOut]

Appreciate the heads up.
Does pickling lime suffer this same fate?

 

[ajdelange]

No. It's pKs are way above mash pH.

 

[ajdelange]

Rather than waiting for authors to weigh in you can check any calculator or spreadsheet you are using pretty easily. Feed it a DI mash with a pale malt such that some amount of acid is required to get a mash pH of 5.6. Specify a DI mash pH for the malt of 5.7 if the program allows that. If it doesn't lower the color or pick the lightest malt you can. Then specify acid until pH 5.6 is predicted. Use HCl if the program allows as this removes any problem with lactic acid's strength as a function of pH from consideration. Record the acid amount, call it A0, and then double it. Add sodium bicarbonate until the predicted mash pH is again 5.6. Record this. Zero the bicarb and reset the acid to A0. Increment it a little such that predicted pH is 5.3. Now add A0 to the incremented acid amount and again add bicarbonate until the predicted pH is 5.3. The amount of bicarbonate required in this second case (5.3) should be less than in the first case (5.6) by a noticeable amount.

I checked Brewer's Friend in this way and it is OK (I would have been surprised were it not). The process was quite tedious. I'll leave it to interested readers to check their own programs.

 

[ajdelange]

The spreadheet worry may turn out to be a tempest in a tea pot (I hope so). In any case the Brewing Science take away here is that, with respect to mash pH, phosphoric and lactic acids are strongish acids (meaning that they dump nearly 1 mEq of protons per mmole of the acid throughout the mash pH range). Lime is a strong base as are sodium hydroxide and potassium hydroxide but bicarbonate is a weak base. The number of protons it absorbs per mmol depends appreciably on the pH in the mash pH band.

 

[FunkedOut]

Bru'n Water 4.2 yields the same amount of bicarbonate in both cases.

 

[ajdelange]

A little surprised at that as he has the carbo equations in there elsewhere. But good to know.

 

[imasickboy]

Is this something you've only recently learned? Perhaps you can dumb it down and just tell us which spreadsheets/programs are subject to this issue? Or better yet, you probably should just privately tell the relevant authors that their software may have this issue. The way you delivered this topic makes it seem like you're being holier-than-thou, rather than helpful. I'm sure spreadsheet and software developers would much rather receive one email from you asking about this issue, rather than dozens, (or potentially more), from users.

 

[ajdelange]

Is this something you've only recently learned?

No, it's not something I have just learned. My programs have properly handled bicarbonate for years. In explaining how to compute mash pH estimates in another thread it occurred to me that maybe, given the way bicarbonate is often discussed, often being used as a proxy for alkalinity etc. that perhaps not all the dozens of people who have posted a spreadsheet/calculator or the thousands who have put one together for their own use have appreciated that they need to take the fact that bicarbonate is a weak base into account. I have certainly had plenty of indications that not everyone who publishes a spreadsheet fully understands the chemistry behind it. The only thing that is new to me here is that this is the first time I have explicitly calculated the effective equivalent weight of bicarbonate at mash pH and looked at the numbers. This is, of course, always implicitly done by a properly written program but as one would hardly have such a program report it, I was not aware of the magnitude of the effect.

Perhaps you can dumb it down and just tell us which spreadsheets/programs are subject to this issue?

In order to do that I'd have to test them all. If I find out the engine mounting bolts in the model car I drive are subject to cracking I'll tell that to the world but I won't follow every car of that brand I see to the drivers house and inspect his car. Having been warned, that's his job.

Or better yet, you probably should just privately tell the relevant authors that their software may have this issue.

In order to do that I'd have to know who all the authors are and I don't (though I certainly do know who some are) and test all their programs. Having been warned, that's their job.

The way you delivered this topic makes it seem like you're being holier-than-thou, rather than helpful.

It doesn't matter how it seems. What matters is that it is helpful. I have verified that one of the popular programs is OK in this regard and FunkedOut has determined that another isn't. He has been helped as has everyone who uses this program and so has the developer. I put a warning up about a potential problem with brewing software. It was for everyone - publishers, users, people who have done their own spreadsheets to help them on brew day, authors of smart phone apps etc. Should I have kept it secret so as not to seem holier than thou? That is at the core of PC = BS. In any event I have no problem with seeming holier than thou as long as people are helped.

I'm sure spreadsheet and software developers would much rather receive one email from you asking about this issue, rather than dozens, (or potentially more), from users.

Why would a user aware of this problem send an e-mail to the developer? To ask for his money back? No - these things are offered free of charge.

 

[mabrungard]

AJ, that pHz data set that you posted in the original post doesn't look right. Could you revisit that data? At a minimum, the value at 5.5 is odd.

You are correct that I had not employed this pH dependent response for sodium bicarb in Bru'n Water. I was unaware that that salt didn't contribute its full alkalinity in the typical wort pH range. That would explain why I often noticed that my observed wort pH seemed to be less than predicted when baking soda was used.

 

[FunkedOut]

I've only got a half dozen brews done while minding the water.
All of them using Bru'n Water as a guide.
I've always measured ph from 0.15 to 0.20 lower than predicted when not using baking soda.
0.15-0.25 lower than predicted when using baking soda (varying amounts).

I have not sought any assistance in this regard yet, as my ph meter is pure garbage. I don't trust the readings I am getting.
I have been seeking a decent deal on a quality meter instead.

 

[ajdelange]

AJ, that pHz data set that you posted in the original post doesn't look right. Could you revisit that data? At a minimum, the value at 5.5 is odd.

The way to calculate this is to use the charge on carbo concept that I came up with for John and which you've seen a thousand times. The code fragment

variable r1 = 10^(pH - 6.38)
variable r2 = 10^(pH - 10.38)
variable f0 = 1/(1 + r1 + r1*r2)
variable f1 = f0*r1
variable f2 = f1*r2
return -f1 - 2*f2

gives the charge on one mmol of carbo at pH. This what produced the curve in John's book (never understood why he would publish the curve but not the 5 lines of math behind it). Since a mmol of NaHCO3 has 100% of its carbo in the bicarbonate form the anion charge is -1 mEq when it hits the water. In shifting to pHz the charge will change from -1 to Q(pH) (which is a negative number of magnitude less than 1) so the number of protons absorbed is Q(pH) - (-1) = 1 + Q(pH) which is the mEq/mmol. The mmol/pH is the reciprocal of this and given the molecular weight of bicarbonate is 61 the effective equivalent weight at pHz is Weq = 61/(1 + Q(pHz)). That's where the numbers came from.

The numbers I posted this morning (computed by the code above) are only slightly different from the ones I posted this morning (which I did manually from my general use spreadsheet).

pHz HCO3- required
5.3 66.6 - 66.0738 mg
5.4 68.0 - 67.3876
5.5 69.1 - 69.0416
5.6 72.2 - 71.1238

The numbers after the - are the new numbers.
It's exactly the same as with acids but mirror image. Acids release allmost the protons they can when the final pH is at least 2 pH units higher than the highest pK. Bases absorb almost all the protons they can when the pH is at least 2 units less than the lowest pK (which is 6.38) for bicarbonate.

 

[mabrungard]

Thanks. When I plotted the previous data, it appeared that the 5.5 data point was not trending with the others. Your new data meets my expectations.