Author Topic: Carbonate Hardness = Carbonate Alkalinity based on Source pH?  (Read 871 times)

Offline Big Monk

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After building my water for a long time, I am entertaining using my municipal water. I have reviewed the last 10 years of WQRs and the values are consistent based on the source, which in my case is 90% from Lake Ontario and 10% from Lake Otisco. I had the water tested a while back and it corresponded almost exactly with the WQR averages for a ten year period. So it's stable:

Ca = 33.9
Mg = 9.2
SO4 = 22.9
Cl = 27.7
Na = 8.9

My question relates to the phenomenon by which Carbonate Hardness = Carbonate Alkalinity for Water pH < 8.5.

Since the CO3 component of the alkalinity will generally be a small percentage of the HCO3 concentration when Water pH is < 8.5, is it fair to say that Carbonate Hardness = Carbonate Alkalinity in that scenario?

If so, it would seem that, for my water at least, HCO3 can be calculated as follows:

Hardness as CaCO3 = (2.497*33.9)+(4.164*9.2) = ~ 123

My local WQR quotes my Water pH as being between 7.1-8.5 (which i'll verify by measuring of course) so let's assume the median of 7.8. Assuming an Alkalinity value equal to the Hardness value:

CO3 = ((123*10^(7.8-10.33))/(1+2*10^(7.8-10.33)))*(60/50) = ~ 0.432

HCO3 = (123/(1+2*10^(7.8-10.33)))*(61/50) = ~ 149.13

CO3 < 0.5% of my water, so Hardness as CaCO3 = ~ Alkalinity as CaCO3, right? Did I make this clear as mud?

In general, my water seems well suited to brewing, with only a modest amount of acid required to neutralize the 149 ppm of HCO3.


« Last Edit: April 04, 2018, 12:36:41 PM by Big Monk »
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Offline hackrsackr

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #1 on: April 04, 2018, 02:46:09 PM »
Carbonate hardness will be zero at beer pH. It will all be bicarbonate. The h in hco3 becomes unbound to the co3 and binds to an OH to form a water molecule at 8.3 and above. Bicarbonate can only exist if there isn’t a bunch of hydroxide ions, which there aren’t any at beer pH. That’s part of the reason for using the caco3 equivalent and why lime softening works.

Kari summed it nicely a bunch of years ago.
http://braukaiser.com/wiki/index.php?title=Mash_pH_control


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Offline hackrsackr

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #2 on: April 04, 2018, 02:55:12 PM »
Why are you assuming hardness is equal to alkalinity? That’s only the case if Residual alkalinity is zero and rare for source water. If the pH is in the high 7 to low 8 range you provided, then your RA is a positive value, which means there is more alkalinity as CaCO3, then hardness as CaCO3.


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Offline Big Monk

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #3 on: April 04, 2018, 03:09:07 PM »
Why are you assuming hardness is equal to alkalinity? That’s only the case if Residual alkalinity is zero and rare for source water. If the pH is in the high 7 to low 8 range you provided, then your RA is a positive value, which means there is more alkalinity as CaCO3, then hardness as CaCO3.


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I’m trying to correlate the hardness as CaCO3 to Alkalinity as CaCO3 because my WQRs have stable Ca and Mg numbers but variable hardness and alkalinity. Over the last 10 years or so, the major brewing ions have not changed, but the WQRs quote ranges of 85-150 ppm as CaCO3 for alkalinity and 100-190 as CaCO3 for hardness. The alkalinity values I am calculating using the above equations seem to jive with the ranges in my WQR and I am just trying to get a sanity check.

I’m not trying to making any sweeping statement but rather just presenting my calculations for critique.

How do the calcs look to you?
« Last Edit: April 04, 2018, 03:16:31 PM by Big Monk »
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Offline hackrsackr

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #4 on: April 04, 2018, 04:37:03 PM »
Well I don’t have the formula in front of me, but isn’t hardness 7(Ca) + 3.5(Mg)?

I’m sorry I don’t really follow the rest... the hardness as CaCO3 is already correlated to alkalinity as CaCO3. That’s why they use the correlation.

The thing about hardness and alkalinity staying the same while calcium and magnesium fluctuate can’t be absolutely true as those minerals are the primary constituents of the hardness component.

So what I’m getting out of all this is that you’re trying to derive your bicarbonate value, but it’s not stated on your published water report (which is kinda unusual), and you haven’t had it lab tested. Is that correct?
If that’s the case; you can’t derive the alkalinity AFAIK. It must be measured. Hardness can be derived from Ca and MG. You can measure alkalinity at home pretty cheaply, with a total alkalinity kit. Which is usually bromocresol green/ methyl red, titrated with sulfuric n/50 (that’s from memory someone correct me if I’m wrong). I think it’s 25ml water couple drops of the indicator titrate from green to red. ML’s used multiplied by 20 will give you your total alkalinity as CaCO3. You could also send it out to ward labs, or call your water supplier, they’ll have the data. These are just snapshots in time though, measuring the water coming out of your tap on the day you use it is far more accurate. That goes for hardness as well. It’s easier to measure it, then go by averages. If this for your spreadsheet I’d suggest putting in an input device for the titrations for those who want to measure on the day. There really is no substitute for measuring those variables, if you want your pH model to be accurate, as fluctuations in those parameter assumptions will change the residual alkalinity. The model will then generate an incorrect output.


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Offline mabrungard

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #5 on: April 04, 2018, 05:22:12 PM »
Yes, that approach would work...if all the hardness was carbonate hardness (aka: temporary hardness). In the case of this water, a significant portion of the hardness is permanent hardness (aka: paired with SO4 and Cl ions).

So the bicarbonate ion content is not 149 ppm. Its more like 96 ppm.
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Offline kramerog

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #6 on: April 04, 2018, 05:31:12 PM »
What Martin Brungard said (not that Ive checked his calculations).  There is some confusion in this thread over the term carbonate hardness.  It is not the same as water hardness.  See https://en.wikipedia.org/wiki/Carbonate_hardness for more more info

Offline Big Monk

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #7 on: April 04, 2018, 05:40:37 PM »
Yes, that approach would work...if all the hardness was carbonate hardness (aka: temporary hardness). In the case of this water, a significant portion of the hardness is permanent hardness (aka: paired with SO4 and Cl ions).

So the bicarbonate ion content is not 149 ppm. Its more like 96 ppm.

Martin,

Can you expand on the 96 ppm result? i.e. how you arrive there?

I guess maybe part of the confusion is my fault. What I really want is to use the known values I have (Ca, Mg, SO4, Cl) to estimate, via calculation, my bicarbonate value in ppm.
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Offline kramerog

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #8 on: April 04, 2018, 06:55:48 PM »
Without delving into the actual calculations, assuming the water analysis analyzed for all the significant ions, there are equivalent amounts of anions (Ca++, Mg++, Na+) and cations (HCO3-, Cl-, SO4--).  Based on this equivalence it is possible to calculate the bicarbonate concentration, the alkalinity and the residual alkalinity. 

Just eyeballing the analysis, your water looks pretty versatile.

Offline mabrungard

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #9 on: April 04, 2018, 06:59:56 PM »
Roger said it. I assumed that the concentrations of other ions were correct and represented the vast majority of all dissolved content. I then solved to find the bicarbonate concentration that produces balanced cation/anion totals.
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Offline hackrsackr

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Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #10 on: April 04, 2018, 07:40:18 PM »
Roger said it. I assumed that the concentrations of other ions were correct and represented the vast majority of all dissolved content. I then solved to find the bicarbonate concentration that produces balanced cation/anion totals.
This is still just an estimate though, not an actual calculation, isn’t it? The other ions in the water will have an effect on this balance, and isn’t there a +\- .1 meq/l variance between the two typically seen? For the balance to be perfect, wouldn’t the pH have to be 7.00?
So using this method of determination would produce a range of probable results from 90-102ppm (ignoring the other ions in the water, and assuming the pH is 7.0), correct?


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« Last Edit: April 04, 2018, 07:59:03 PM by hackrsackr »

Offline Big Monk

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #11 on: April 05, 2018, 02:03:12 PM »
Without delving into the actual calculations, assuming the water analysis analyzed for all the significant ions, there are equivalent amounts of anions (Ca++, Mg++, Na+) and cations (HCO3-, Cl-, SO4--).  Based on this equivalence it is possible to calculate the bicarbonate concentration, the alkalinity and the residual alkalinity. 

Just eyeballing the analysis, your water looks pretty versatile.
Roger said it. I assumed that the concentrations of other ions were correct and represented the vast majority of all dissolved content. I then solved to find the bicarbonate concentration that produces balanced cation/anion totals.

Thanks gents. Just what I was looking for. I added in all the additional cations and anions from my full report to further shore it up.
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Offline Big Monk

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #12 on: April 05, 2018, 02:11:04 PM »
Roger said it. I assumed that the concentrations of other ions were correct and represented the vast majority of all dissolved content. I then solved to find the bicarbonate concentration that produces balanced cation/anion totals.
This is still just an estimate though, not an actual calculation, isn’t it? The other ions in the water will have an effect on this balance, and isn’t there a +\- .1 meq/l variance between the two typically seen? For the balance to be perfect, wouldn’t the pH have to be 7.00?
So using this method of determination would produce a range of probable results from 90-102ppm (ignoring the other ions in the water, and assuming the pH is 7.0), correct?


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The way I see it, from a practical standpoint is:

1.) I’ll be measuring water pH and estimating off that, so that goes away;

2.) I have all the other ions (K, F, NO3, NO2) to add in to make the estimation a little “sturdier”;

3.) The difference of 10-12 ppm HCO3 isn’t going to impact the estimated pH too dramatically, if at all.

So for me it’s a solid way to get a single value for HCO3 using the rest of the quoted ions, rather than trying to use the ranges for CaCO3 hardness and alkalinity quotes in my WQR.
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Offline hackrsackr

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #13 on: April 05, 2018, 08:05:11 PM »
Roger said it. I assumed that the concentrations of other ions were correct and represented the vast majority of all dissolved content. I then solved to find the bicarbonate concentration that produces balanced cation/anion totals.
This is still just an estimate though, not an actual calculation, isn’t it? The other ions in the water will have an effect on this balance, and isn’t there a +\- .1 meq/l variance between the two typically seen? For the balance to be perfect, wouldn’t the pH have to be 7.00?
So using this method of determination would produce a range of probable results from 90-102ppm (ignoring the other ions in the water, and assuming the pH is 7.0), correct?


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The way I see it, from a practical standpoint is:

1.) I’ll be measuring water pH and estimating off that, so that goes away;

2.) I have all the other ions (K, F, NO3, NO2) to add in to make the estimation a little “sturdier”;

3.) The difference of 10-12 ppm HCO3 isn’t going to impact the estimated pH too dramatically, if at all.

So for me it’s a solid way to get a single value for HCO3 using the rest of the quoted ions, rather than trying to use the ranges for CaCO3 hardness and alkalinity quotes in my WQR.
Good deal. 🤙🏻


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Offline hackrsackr

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Re: Carbonate Hardness = Carbonate Alkalinity based on Source pH?
« Reply #14 on: April 13, 2018, 12:40:37 AM »
Hey Martin,

With regards to HCO3 calculations and ionic balance; when I put 1 g of CaCO3 into 1 gallon distilled water, Bru’n Water gives me:

106 ppm Ca
322 ppm HCO3
5.3 mEq/l cations/5.3 mEq/l anions

Shouldn’t the ppm of HCO3 be way lower, yet anions still be 5.3 mEq/l? Something like:

106 ppm Ca
158 ppm HCO3
5.3 mEq/l cations/5.3 mEq/l anions