Calculating Bicarbonate and Carbonate

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ajdelange

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This is for the guys (like me) that ask why, in these days of multiple cores in multiple processors doing everything in 64 bits, we are using approximate bicarbonate and carbonate calculations suitable for slide rules from the 1950's. It's not hard to calculate bicarbonate and carbonate quite accurately from pH and alkalinity.

But before launching off into that let's ask why we care about bicarbonate and carbonate content in our brewing water. In fact we don't really other than because we are nerdy sorts. When we are finished making beer all the carbonate and nearly all the bicarbonate have been converted to gas (CO2) and driven off. There is more bicarbonate in finished beer from the CO2 we apply to carbonate it than there is from the water we brewed it with. What we are concerned with is how much acid we must add to get the pH low enough to convert all the carbo (bicarbonate and carbonate) to to carbonic (CO2) and the alkalinity measurement tells us that. Alkalinity is, arguably, the most important parameter in describing water intended for brewing. In other contexts carbonate and bicarbonate content are of little import as well. This is why one rarely finds them listed in water reports.

Alkalinity is simply the number of milliequivalents of acid that are required to decrease the pH of a liter of a water sample from whatever pH it has when it is given to you to a standard reference pH. This varies from 4.5 in the ISO method to 4.4 in Ward Labs tests to whatever you like as long as you report it per Standard Methods for the Analysis of Water and Waste Water. Because it is true that if 100 mg of calcium carbonate is placed in a liter of water and if that calcium carbonate is dissolved by bubbling CO2 through the water until its pH reaches 8.3 that it will take approximately 2 mEq of acid to reduce the pH of that mix from 8.3 to around pH 4.3 water chemists in North America often multiply the acid mEq by 50 and represent alkalinity as 50*mEq 'ppm as CaCO3' on the basis that the water we just described got its alkalinity from 100 mg/L calcium carbonate. The number of milliequivalents of EDTA required to chelate the calcium in this liter is also 2 and so, multiplying that number by 50 we get 100 'ppm as CaCO3' hardness as well. Very handy, when talking about natural waters. If we have alkalinity of around 70 and hardness about the same we know that mother nature has dissolved about 70 mg of limestone into each liter of water.

There are a couple of problems with this. First is that if we are not talking about natural waters the system is thrown off. If we put 100 mg of limestone is a beaker, add a liter of water and then add enough hydrochloric acid to dissolve it and bring the pH to 8.3 the alkalinity of that water is 1 mEq/L or 50 ppm as CaCO3 though the hardness is still 100. This is not really a problem for us as home brewers. What is really a problem is that people not familiar with the system get horribly confused. How often have I seen "Here's my water report, sodium 23 mg/L, Calcium Carbonate 75..." The guy doesn't have any calcium carbonate. He has 'alkalinity as Calcium Carbonate'.

What's worse is that the confusion is not limited to neophytes. This post was really motivated by 3 recent discoveries:
1. Ward Labs has been computing carbonate and bicarbonate incorrectly for years (status: they have been made aware of this but I haven't verified that they have fixed it)
2. LaMotte was instructing users to compute bicarbonate using a multiplier that was off by a factor of 2. (status: the instructions have been fixed).
3. Bru'n water takes the 'as CaCO3' thing a step further and reports alkalinity 'as Bicarbonate' except that they don't call it 'alkalinity as bicarbonate' they call it 'bicarbonate'. Thus we find a fellow that adds lime (which contains no bicarbonate) to DI water (which contains no bicarbonate) now has mix which has appreciable bicarbonate it it.

All this would have been avoided had people stuck with specifying alkalinity in mEq/L.
LaMotte has fixed the problem. Ward Labs is aware of the problem and either has, or, presuming they research it further, will fix the problem. Martin may yet be convinced but 'ppm as CaCO3' in the US isn't going away. It's been standard practice for too long. So if you see 'as CaCO3' just divide by 50, preferably without even thinking about it, and go ahead. When measuring alkalinity, unless you are using a drop count kit, you will be measuring out mEq/L anyway. Mutiply by 50 and write that down but try to think in terms of the mEq/L.

If you still want to know bicarbonate and carbonate ion concentrations after all that you can calculate them accurately as follows:

You must know:
1. The pH of the sample, pHs
2. The end point pH of the titration used to determine the alkalinity (usually around 4.4 - that's what Ward Labs uses), pHe
3. The alkalinity in mEq/L (divide ppm as CaCO3 by 50), alk

Most will obtain the alkalinity number from a lab or water authority report many of whom do not calculate bicarbonate and carbonate (because they really aren't that important). If they do they don't always do it right and you can use this method to check. Others will measure alkalinity themselves. For instructions and further insight check http://wetnewf.org/pdfs/measuring-alkalinity.html.

Here's what you do:

1. Subtract 1000*(10^-pHe - 10^-pHs) from the alkalinity
2. Subtract 1000*( 10^(pHs-14) - 10^(pHe - 14) ) from the adjusted alkalinity from Step 1.
3. Compute r1 = 10^(pHs - 6.38)
4. Compute r2 = 10^(pHs - 10.38)
5. Compute f0 = 1/(1 + r1 + r1*r2)
6. Compute f1 = f0*r1
7. Compute f2 = f1*r2
8. Compute Q(pHs) = -f1 -2*f2
9. Repeat steps 3 - 8 for pHe to compute Q(pHe). Obviously you only need to do this the first time assuming that you always process data with the same pHe.
10. Compute C = alk/( Q(pHe) - Q(pHs) ) using the adjusted alkalinity from Step 2.
11. Bicarbonate = 61*f1*C mg/L; Carbonate = 60*f2*C mg/L using the f's calculated for pHs

I won't get into the why's here. That can be done in discussion if there is interest. I will point out that phosphate, borate, and silicate are possible sources of error (as they are for the approximate calculation too) but we can correct for them using this method. See below for phosphate correction.

In the approximate method, two titrations are done. The first to 8.3 and the second to 4.4. The first gives the P alkalinity and the second the M. Carbonate is taken to be 60*2*P and Bicarbonate to be 61*(M - 2*P) where both M and P are in mEq/L. To quote Standard Methods for the Examination of Water and Wastewater: "...ion concentrations in the strictest sense are not represented in the results,..." Problems arise when P is measured as bigger than it should be. P=0 for any pH < 8.38 but some water reports show finite carbonate content when the pH is less than this. This leads to under reporting of bicarbonate.

All this is sort of moot because you don't really need to know bicarbonate and carbonate. It is sufficient to know C (the total carbon content) of the water and the f's (which are a function of pH). The only thing bicarbonate and carbonate are needed for is computation of sample ion balance. The anion charge contribution of bicarbonate and carbonate is simply -C*(f1 + 2*f2).

Correction for Phosphate (Added 5/6/14)

The same symbols, r's, f's and Q's are used here as above but these are for this separate calculation. They do not replace any of the r's, f's or Q's used above.

1a. Compute r1 = 10^(pHs - 2.12)
2a. Compute r2 = 10^(pHs - 7.21)
3a. Compute r3 = 10^(pHs - 12.44)
4a. Compute f0 = 1/(1 + r1 + r1*r2 + r1*r2*r3)
5a. Compute f1 = f0*r1
6a. Compute f2 = f1*r2
7a. Compute f3 = f2*r3
8a. Compute Q(pHs) = -f1 -2*f2 - 3*f3
9a. Repeat steps 1 - 8 for pHe to compute Q(pHe). Obviously you only need to do this the first time assuming that you always process data with the same pHe.
10a. Compute P*( Q(pHe) - Q(pHs) ) where P is the total moles of Phosphorous or Phosphate from your water report. Divide mg/L phosphorous by 30.974. Divide mg/L phosphate by 95.
11a. Subtract this from the alkalinity before doing any of the other steps in the carbonate/bicarbonate calculation.

Similar corrections can be calculated for borate and silicate but they are too small to be bothered with.
 
Much appreciated, thanks for your time and effort.

As for the slide rule (retro math) thing, I taught my granddaughter how to use one last year. She thought
it was cool and took it to school and ended up teaching her very young teacher how to use it. Now, if I could
convince her mother she should learn how to brew beer. It's all about independence and self-reliance.
 
Much appreciated, thanks for your time and effort.

Not a problem. I'm trying to get Ward Labs to pick up on this (to remove inconsistencies in their reports for samples with pH > 8) and hope the spreadsheet and calculator authors will too.

As for the slide rule (retro math) thing, I taught my granddaughter how to use one last year. She thought
it was cool and took it to school and ended up teaching her very young teacher how to use it.

I used to visit a company out in the Bay Area. The president had his slide rule framed and hanging on the wall with a sign that said "In case of power failure break glass".
 
AJ,

Here's one of my Ward lab reports, click to enlarge:


For alk, I should use "Total Alkalinity, CaCO3" or "Total Hardness, CaCO3)?

In step 11, for Bicarbonate, use the f1 from pHs step 6 and for Carbonate, use f2 from pHe step 6?

I ran it through excel and didn't get the same number for carbonate you posted in another thread for Flipadelphia. I did get the correct numbers you posted for mtnagel though.

Nate
 
For alk, I should use "Total Alkalinity, CaCO3" or "Total Hardness, CaCO3)?

The alkalinity. For your example alkalinity of 54 ppm as CaCO3 alk = 54/50 = 1.08 mEq/L

In step 11, for Bicarbonate, use the f1 from pHs step 6 and for Carbonate, use f2 from pHe step 6?

No, the pHs values in both cases. You have pointed out that this isn't clear so I edited to make it more so.

I ran it through excel and didn't get the same number for carbonate you posted in another thread for Flipadelphia. I did get the correct numbers you posted for mtnagel though.

Try it again with f1(pHs) and f2(pHs). Also bear in mind that I may have used non - ideal chemistry for some of the example numbers I've thrown out (in another thread). For your water, using ideal chemistry, bicarb would be 63.58 and carbonate 0.26. The numbers you calculate should be close to that.

There will be slight differences because in the algorithm I've just given 6.38 and 10.38 for the pKs but the spreadsheet I use calculates the pKs from a formula based on temperture. At 20 °C it comes up with 6.3817 for pK1 and 10.3756 for pK2.
 
Hello, I don't think I've ever posted before, and if I did it was years ago. Anyway, I used to be fanatical all-grain brewer for 5 or so years in the 90's, then other interests took precedence, but now I find that I'm hankering to brew again. So looking around the forum I ran across this extremely valuable thread. My career for the last 28 years has been as a geochemist, more specifically a hydrogeochemist, so I spend my days looking at water analysis and more typically using industry standard software to model what happens when various human-caused incidents impact water quality. So, I live in New Mexico, east of Albuquerque, where all of tap water comes from a deep groundwater source and as a result has an extremely high carbonate alkalinity. As a newbee all-grain brewer I quickly discovered how sparging with hard water can leach tannins from the grain husks resulting in a nasty mouth-puckering final product. I visited our water coop and picked up an analysis of our water and plugged it into the public domain software, PHREEQC, from the USGS. It's a very powerful and relatively easy tool to use, and it can handle any form alkalinity that your lab provides for you. In addition you can do things like model your water chemistry after heating it to boiling, which drives out CO2(g) and precipitates CaCO3(s) (calcite) and it will give you the resulting water composition. And also do things like figuring out acid additions, it's a very powerful tool. You can download the package here:

https://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc/index.html

If anyone has a use for this, I'd be happy to assist.

Paul
 
We do appreciate the offer. I had a look at the manual and I'm afraid it appears rather as if you are offering to furnish Stradavarii to an inner city youth orchestra! Wasn't the Obama administration planning to do that?
 
I got:
HCO3 = 100 ppm
CaCO3 = 0.3 ppm
with:
pHs = 7.8
pHe = 5.4
alk = 91/1.22/50=1.49 (it was reported as HCO3)

In Bru'n using 91/1.22 with pH 7.8 I get:
HCO3 = 90.5 ppm
CaCO3 = 0.3 ppm

So which formula is Bru'n using? Is the same but with another pHe?
 
I believe he uses the same formulas as in No. 1 but probably with a pHe of 4.4 as that is what is used by Ward Labs who does most of the testing for HBT readers or 4.5 which is the ISO standard. It would be great if some lab used pHe = 5.4 as that is a good mash pH and the reported alkalinity would then be exactly the amount of acid needed to treat the water for brewing but no lab that I know of tests to that end point. Of course if you are doing the testing yourself you can stop at 5.4 (or whatever mash pH you are planning to use) and note the alkalinity there saving yourself calculation required to use the ISO alkalinity. You would probably, however, then want to go on to add the approximately 10% additional acid required to reach the ISO pHe.
 
The water report from my municipal water supplier actually use 5.4. They use this standard https://www.sis.se/api/document/preview/18780/ if you are interested.

What do you mean by:
It would be great if some lab used pHe = 5.4 as that is a good mash pH and the reported alkalinity would then be exactly the amount of acid needed to treat the water for brewing...

By the way, I am right to assume that "alkalinity as CaCO3"=1.22*"alkalinity as HCO3"?
 
The system really botched my post so I am essentially re-doing the whole thing this morning.

I was not only interested in the second part of the ISO standard but fascinated by it. Why would anyone want to measure alkalinity with an end point as high as 5.4? The reason is that the the end point should be on a flat part of the titration curve (with mEq/L on the vertical axis and pH on the horizontal which is the opposite of the way titration curves are usually presented). The flat parts are the parts which are more than a couple of pH units from the acid system's pKs which for carbonic acid are at 6.38 an 10.38. pH 4.5 (which I believe is pHe for part 1 of the ISO standard) meet this requirement. If, however, there is another acid system such as humic with its pKs near 4 then the curve will turn vertical near 4 and thus 4 is not a good pHe. So your water must contain a fair amount of humic acid.

It is really immaterial what the pHe is as long as a couple of places along the titration curve can be found that are fairly distant from the pKs of any acids other than carbonic unless you can back out the contributions from the other acids. In drinking water usually sufate and phosphate are the only things that have contribute any alkalinity and their contributions are usually so tiny that they can be ignored. Humic acid is clearly a consideration in some cases to the extent that ISO has a separate standard for it. I was totally unaware of this.

The real question for you concerns how you take alkalinity with respect to a pHe of 5.4 and turn it into something you can use with one of the popular brewing spreadsheet/calculator programs. The approach you have taken of using the formulas in No. 1 with pHe of 5.4 to calculate the bicarbonate and entering the bicarbonate into the program is probably appropriate. The alternate approach would be to take the alkalinity for pHe 5.4, use the formulas to calculate the alkalinity for pHe = 4.5, multiply that by 61 and enter that as the bicarbonate number. Which is more appropriate for a particular spreadsheet I couldn't say as I have never been able to figure out in detail how those programs handle alkalinity. They ask you to enter bicarbonate and if you don't have bicarbonate to estimate it from the alkalinity by dividing the alkalinity in ppm as CaCO3 by 50 and then multiply by 61 or by multiplying alkalinity in mEq/L by 61.



By the way, I am right to assume that "alkalinity as CaCO3"=1.22*"alkalinity as HCO3"?
One mEq of proton absorbing power comes (at low pH) from 61 mg HCO3- ion or 50 mg of CaCO3 (when it has been dissolved by carbonic acid). Thus the ratio is 61/50 = 1.22
 
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Thank you for taking the time to answer :)

I think there are two reasons for using 5.4. One is, as you said (which also it is stated in the standard), to minimize the effect of humic acids but also phosphates, ammonia etc. The other reason is that the indicator they use, which is a mix of methyl orange and bromocresol green, change color at pH 5.4.

To me it seems that they really wanted a standard that can be used with either a pH meter or an indicator to determine when they reach the end point pH, and for some reason they found 5.4 to be the best compromise. I do wonder how it affects the repeatability though, because if a pH meter is used instead of the indicator (which they actually recommend), it would not require much error in sample preparation to swing the alkalinity in either direction would 5.4 fall on a steep part of the titration curve. Probably this is why the alkalinity in the water report has an error of +/- 4.6

Anyway, here is the complete water report: https://image.ibb.co/he3xD8/water_rep.png (it's in Swedish, but the chemical formulae for many of the species are also written.)
 
I think there are two reasons for using 5.4. One is, as you said (which also it is stated in the standard), to minimize the effect of humic acids but also phosphates, ammonia etc.



The plot below shows titration curves for water with 1 mmol/L carbo (solid red) and for water with 1 mmol/l carbo and 0.5 mmol/L humic assuming humic to have pKa = 4.0 (dashed blue). Noting that the humic acid molecules are huge this is way more than would be found in any potable water. The large concentration is there to emphasize the effect humic acid can have on the titration curve.

Humic.jpg


As noted in my previous post 4.5 is in a flattish region of the carbonic curve between the first pk of carbonic acid and where the alkalinity of the water turns the curve upwards again. Note also that at pHe = 4.5 one mmol of carbo gives an alkalinity reading of one mEq/L. Handy. Now when the humic acid is present it absorbs protons too so that the acid required to get to pH 4.5 is greater and the carbo alkalinity estimate is too high unless the humic acid is accounted for. But it takes a lot of humic acid to cause a significant error. Humic acid at half the molar level of the carbo acid only increases the carbo alkalinity by 12% and, by the reasoning above, you are never going to see a humic acid molar level anywhere near that high. Note that your COD is < 1mg which is 0.06 mmol which can burn 0.12 mmol of carbon. It is clear from this that your humic acid levels are in the micro or nanomole regions.

Now at pHe = 5.4 the curves show that the effect of humic acid, if it is present, is much smaller then at 4.5 but as the levels are so low there is no point, that I can see, in using pH 5.4 for an endpoint. As the curves clearly show, and as I mentioned in my earlier post, the chosen pHe is arbitrary as long as it is far away from the pKs of other weak acids in the sample. Just take the reading at whatever pHe and follow the red curve up to whatever pH you are interested in.

The pKa of ammonium ion is 9.25, for phosphate we have 2.1, 7.2 and 12.4, for sulfuric 1.92. Of these the only one of concern would be phosphate. pHe = 4.5 is 1.4 units from the first pH and 2.7 from the second. OTOH pH 5.4 is 2.3 units from the first pK and 1.6 from the second so neither of the two choices is terribly appealing from consideration of phosphate. Fortunately, in this regard at least, phosphate levels in potable water are usually quite low. 5.4 is a better choice WRT sulfate but a worse one WRT ammonium though these would not result in large errors in either case.


The other reason is that the indicator they use, which is a mix of methyl orange and bromocresol green, change color at pH 5.4.
By blending indicators you can get indicators that produce a continuum of colors and then publish a chart or just descriptions of the colors for any of several pH's. Hach does this in one of their kits and advises choosing and end point pH (and color) which depends on the expected alkalinity. All this sounds interesting but as I am color blind it is meaningless. I measure alkalinity with a pH meter.

To me it seems that they really wanted a standard that can be used with either a pH meter or an indicator to determine when they reach the end point pH, and for some reason they found 5.4 to be the best compromise. I do wonder how it affects the repeatability though, because if a pH meter is used instead of the indicator (which they actually recommend), it would not require much error in sample preparation to swing the alkalinity in either direction would 5.4 fall on a steep part of the titration curve.
The curve is twice as steep at 5.4 as it is at 4.5.


Probably this is why the alkalinity in the water report has an error of +/- 4.6

One of the big problems with accuracy (assuming a pH meter is used) is that may samples are not in equilibrium with the air WRT CO2 and start to shed it as soon as the sample is out of the plumbing.


Anyway, here is the complete water report: https://image.ibb.co/he3xD8/water_rep.png (it's in Swedish, but the chemical formulae for many of the species are also written.)

Close enough to German for me to figure out.
 
I am trying to build a water profile in beersmith 3, based off a recent water report, and was wondering if anyone can help me figure out what to put for my Calcium and for the Bicarbonate.

The report says:
Alkalinity as CACO3 (ppm) is 89-114
Hardness as CACO3 (ppm) is 80-104

But I dont understand how to break that down into calcium and bicarbonate for the mineral profile. I am attaching the report to the thread....I am in the "FENA" colomn of the report
 

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~Bicarbonate = 61/50 x Alkalinity

~Total Hardness = (2.5 x Ca++ ) + (4.12 x Mg++)

Mg is often in the ballpark range of 20% of Ca. (But this is just a loose generalization)

Guess: Ca++ ~= 27.5 ppm, Mg++ ~= 5.5 ppm, Alkalinity ~= 102 ppm, Bicarb ~= 124.4 ppm (But this is just a guess)
 
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I am trying to build a water profile in beersmith 3, based off a recent water report, and was wondering if anyone can help me figure out what to put for my Calcium and for the Bicarbonate.

The report says:
Alkalinity as CACO3 (ppm) is 89-114
Hardness as CACO3 (ppm) is 80-104

But I dont understand how to break that down into calcium and bicarbonate for the mineral profile. I am attaching the report to the thread....I am in the "FENA" colomn of the report

You post this to a Sticky thread entitled Calculating Bicarbonate and Carbonate?

Calculating bicarbonate and carbonate from alkalinity and pH is the subject of the first post. And while the post doesn't specifically go into it the only reason we are concerned with alkalinity is that we want to be able to calculate the amount of acid required to set the pH of the water at our desired mash pH. You do not need to know the bicarbonate or carbonate levels to do this. You need to know the alkalinity and pH. This is why water reports usually don't list bicarbonate and carbonate. Where they do they are calculated from alkalinity and pH as described in No. 1 which also points out that sometimes they are not calculated correctly.

For best results avoid calculators that ask for bicarbonate and particularly avoid them if they only accept bicarbonate and not pH. Try to use one like Brewers Friend which accepts alkalinity and pH and which manages the carbonates in water properly. Otherwise you are limited to programs that use the approximation in No. 18 which is good enough for many cases which fall in the pH range which includes yours.Taking your reported alkalinity at 114 and pH at 7.99 the approximation would give you bicarbonate at 139.1 mg/L. Calculating it by the method of No.1 it is 137.45 mg/L.

While bicarbonate and carbonate levels are really immaterial to brewers calcium and magnesium numbers are not. Where only a hardness number is given there is really no way to get calcium and magnesium numbers other than to note that neither can be greater than the value taken if we assume all the hardness is calcium or all magnesium. Divide the hardness by 50 to convert it to mEq/L. Thus your hardness range is 1.6 - 2.08 mEq/L. Calcium has an equivalent weight of 20 so if all the hardness were attributed to calcium the calcium level would be between 32 and 41.6 mg/L. For magnesium the equivalent weight is 12.15 mg/mEq so if all magnesium (most unlikely) the concentration would be between 19.5 and 25.3 mg/L. Splitting down the middle (assuming calcium and magnesium to be eqiequivalent i.e. half the hardness attributable to each) you would have calcium 16-20.8 mg/L and magnesium 9.9 - 12.6 mg/L. But you don't really have the right to assume it is half and half any more than that is 100% calcium. I suppose the conservative approach would be to assume all the hardness is from calcium as calcium has a larger effect on mash pH. Calcium at any of these levels is not going to have much effect on pH
 
I didn't realize this was a sticky thread actually, I posted this in another category, and someone mentioned posting it in the brewing science and soon as I opened the forum, I saw the title of the exact same thing I was trying to figure out, so my apologies.

Not being very good in chemistry is of course a weakness of mine, I am just trying to wrap my head around how all of the chemistry works using the report I posted to use in Beersmith 3 and in Bru'n Water, but I am learning that there are some variances between the 2 programs (as seen in another thread about lactic acid issues I posted)

Basically I just want to build a good water profile for my area to use in my recipes on beer smith. The recipe design, and entire brewing process is very simple and easy for me, and I make very good beer already (to include quite a few localized competitive wins) but I want to take my beer to the next level and make it "Great" beer and be able to compete on a much broader scope, and I feel like to do that, I need to learn a lot more of the chemistry aspect to learn what subtle differences in salt uses and acid uses can make, and really dial in the "details" behind the scenes.
 
No apology necessary. I just sometimes wonder if people read before they post.

I applaud your desire to understand how the chemistry works. Most people just want a tool they can plug numbers into without understanding what they mean. It is for the very few who want to understand that I rave on.
 
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So if you see 'as CaCO3' just divide by 50, preferably without even thinking about it, and go ahead. When measuring alkalinity, unless you are using a drop count kit, you will be measuring out mEq/L anyway. Mutiply by 50 and write that down but try to think in terms of the mEq/L.

So based on this, in my report it says Alkalinity as CaCO3 (PPM) is 89-114, and lets say I used a medium of 101.5, then dividing that by 50, it gives me 2.03, so that is the number I would put into Brewers friend under the alkalinity section, got it.

the only reason we are concerned with alkalinity is that we want to be able to calculate the amount of acid required to set the pH of the water at our desired mash pH.

The report says 7.22-7.99, so again using a medium of 7.61 as my PH number, these are what I should base my acid contributions off of to bring the mash PH down to what I want (5.2-5.5)?
 
So based on this, in my report it says Alkalinity as CaCO3 (PPM) is 89-114, and lets say I used a medium of 101.5, then dividing that by 50, it gives me 2.03, so that is the number I would put into Brewers friend under the alkalinity section, got it.
Yes, you can do it that way but be sure the units pull-down menu to the right of the alkalinity entry field is set for mEq/L. By default it is set to ppm as CaCO3.

The report says 7.22-7.99, so again using a medium of 7.61 as my PH number, these are what I should base my acid contributions off of to bring the mash PH down to what I want (5.2-5.5)?
Yes but taking care of the water's alkalinity is only half the problem. You will need to take care of the grains' alkalinities too.

You don't need a calculator to figure the water's acid requirement. Just acidify the water to your target pH and then tell your calculator that you are using 0 alkalinity water. It will then calculate the acid needed for the malts. The other advantage of this is that it is exact whatever the actual alkalinity and pH of your water at the time you drew it. You can calculate the approximate amount of acid you will need as 90% of the alkalinity in mEq/L
 
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