1. Borate Calculation

Moved to the Agree to Disagree forum by Divin Dave

I posted this at the end of the old thread on borate, but have no response.
Then I noticed the advice to start a new thread and not add to old ones, so...

The pool math calculator shows 495 ox of borax for 30 ppm in a 14,100 gal pool.
This calculates out to 250 ppm or about 130 ppm sodium borate, accounting for the decahydrate.
Can someone explain this apparent discrepancy?

Thanks

2. Re: Borate calculation

Borates are reported in units of boron.
Chlorine is reported in units of chlorine gas.
Alkalinity and calcium hardness are reported in units of calcium carbonate.
Salt, chlorine gas and cyanuric acid are the only chemicals reported in units that match what is actually added.

3. Re: Borate calculation

The "borate" referred to in Pool Math is on the basis of elemental boron concentration, [B]. There are 4 boron atoms per sodium tetraborate decahydrate (Na2B4O7 • 10 H2O)
and then you account for the ratio of the molar masses -

250ppm * (10.81/381.38) * 4 = 28.3ppm

My math may be a little off or your 250ppm calculation might be a bit off, but that is close to the 30ppm.

4. Re: Borate calculation

Originally Posted by JoyfulNoise
The "borate" referred to in Pool Math is on the basis of elemental boron concentration, [B]. There are 4 boron atoms per sodium tetraborate decahydrate (Na2B4O7 • 10 H2O)
and then you account for the ratio of the molar masses -

250ppm * (10.81/381.38) * 4 = 28.3ppm

My math may be a little off or your 250ppm calculation might be a bit off, but that is close to the 30ppm.
Thanks for the responses.

I used rounded figures, so the numbers are reasonably OK.
But if it is borate anion that we are interested in for its buffering and other properties, then the number should not be expressed based on boron atoms.
The true ppm of borate, not counting the sodium, is about 100, for the amount of borax the calculator gives.
Is this what is required? Or is the ppm given based on boron correct?
In other words do we really want 100 ppm borate anion. because that is what we get with 495 oz in my pool (14,100 gals)

Thanks again!

5. Re: Borate calculation

Chem Geek will be along soon with an answer that should warm your heart.

6. Re: Borate calculation

Chem Geek will be along soon with an answer that should warm your heart.
Can't wait! Looking forward to it.

7. Borate calculation

Originally Posted by Texaspops
Thanks for the responses.

I used rounded figures, so the numbers are reasonably OK.
But if it is borate anion that we are interested in for its buffering and other properties, then the number should not be expressed based on boron atoms.
The true ppm of borate, not counting the sodium, is about 100, for the amount of borax the calculator gives.
Is this what is required? Or is the ppm given based on boron correct?
In other words do we really want 100 ppm borate anion. because that is what we get with 495 oz in my pool (14,100 gals)

Thanks again!
Chemgeek can explain the choice of basis for Pool Math better than I can as he was integral in its development but I will go out on a limb with a possible explanation. Using elemental boron as the basis for the calculation is the most natural unit to work in. Once you know how many B-units you have, you can easily convert between borate anion or boric acid. At pool water pH, most of the boron is in the form of boric acid, not borate ion. When one measures boron by titration, one uses cis-diol complexation (mannitol) test. See this paper for details of the boron-mannitol complex. See this thread for how to perform a boron test using mannitol/bromothymol blue.

I would also add that in any studies done on environmental exposure or toxicology, all data is referenced in elemental boron units.

8. Re: Borate calculation

When working with chemistry, it's important to use an agreed upon standard reporting unit of equivalent weight. For borates, it's boron. Therefore, all measurements are calculated based on boron weight.

To some degree, the chosen equivalent is arbitrary.

9. Borate calculation

Originally Posted by Texaspops
Thanks for the responses.

I used rounded figures, so the numbers are reasonably OK.
But if it is borate anion that we are interested in for its buffering and other properties, then the number should not be expressed based on boron atoms.
The true ppm of borate, not counting the sodium, is about 100, for the amount of borax the calculator gives.
Is this what is required? Or is the ppm given based on boron correct?
In other words do we really want 100 ppm borate anion. because that is what we get with 495 oz in my pool (14,100 gals)

Thanks again!
I think to answer your question more clearly, the ppm value you enter into Pool Math is the elemental Boron basis and then Pool Math does the calculations to give you the correct amount of borax or boric acid needed to achieve that elemental boron concentration.

The recommended 50ppm upper value is based, in part, on boron toxicological limits which, as I referred to in my previous post, is how the EPA and other agencies report it - as, for example, ingested equivalent of elemental boron. The 50ppm value is not based on any particular buffering capacity calculation.

Pool Math, in its pH section, does take into account the buffering nature of boron in water by using the elemental boron concentration and then converting that into the amount of borate/boric acid present to modify the pH changes due to acid or base additions.

10. Re: Borate calculation

Originally Posted by JoyfulNoise
I think to answer your question more clearly, the ppm value you enter into Pool Math is the elemental Boron basis and then Pool Math does the calculations to give you the correct amount of borax or boric acid needed to achieve that elemental boron concentration.
I figured that this must be the case, but was mis-led by the use of borate in the wording. It is actually true that the ppm of borates/boric acid is really much higher than the values given based on just boron, and these species are present at those levels in the water. I understand that the equilibria chemistry of borates is very complex, with many different species present. Anyway I understand where the numbers come from now.

The 50ppm value is not based on any particular buffering capacity calculation.
But in the first post of the sticky on borates "Why and How" the first item under PROs is "more stable pH", aka buffering capacity.
So I took this to mean that buffering capacity is a key reason for use of borates in pool maintenance and expected that the ppm values would be
based on borate and not boron.

I like this forum and find it very useful and the writers knowledgeable and sensible. Also I appreciate the PoolMath section, thanks for setting it up.

11. Re: Borate calculation

Originally Posted by Texaspops
Thanks for the responses.

I used rounded figures, so the numbers are reasonably OK.
But if it is borate anion that we are interested in for its buffering and other properties, then the number should not be expressed based on boron atoms.
The true ppm of borate, not counting the sodium, is about 100, for the amount of borax the calculator gives.
Is this what is required? Or is the ppm given based on boron correct?
In other words do we really want 100 ppm borate anion. because that is what we get with 495 oz in my pool (14,100 gals)

Thanks again!
Doing some more reading has revealed that the true formula of borax is not Na2B4O7.10H2O but Na2B4O5(OH)4.8H2O.
This means that the anion is actually B4O5(OH)4(2-). Hence its level would be about 125 ppm. But in water it adds 5H20 and then becomes
4(H3BO3) with loss of 2(OH)-. This would then be 162 ppm of boric acid. Given that at pool pH most of it is as boric acid (due to the pK being somewhere around 9) this is the real ppm of the species involved.
Is there anything wrong with this analysis?

12. Re: Borate calculation

I would use boric acid pellets from Duda Diesel and forget the borax and MA mix.

13. Re: Borate calculation

Originally Posted by wjr75
I would use boric acid pellets from Duda Diesel and forget the borax and MA mix.
The end result is the same for the species in solution and their true ppm.
I haven't decided which route to go yet, but I agree that the boric acid method is easier.

14. Re: Borate calculation

You should base your decision on you CH level. If you have high CH and a pool with naturally rising pH, you'll find that borax raises the pH too much and often leads to temporary cloudiness. You start by lowering your pH but it's not as easy since the borax dissolves slowly and creates localized pockets of high pH water. Boric acid dissolves very rapidly and has only a small impact on pH. The cost difference between the two methods is minimal (a few dollars) even when you include shipping for a 55lbs bucket from Duda Energy.

As for your previous post, I get 171.6ppm boric acid for a 30ppm [B] concentration. But honestly, I'm not sure why that matters. PoolMath does all the conversions internally to calculate the weight of boric acid or borax needed based on the elemental boron concentration.

15. Re: Borate calculation

Originally Posted by JoyfulNoise
You should base your decision on you CH level. If you have high CH and a pool with naturally rising pH, you'll find that borax raises the pH too much and often leads to temporary cloudiness. You start by lowering your pH but it's not as easy since the borax dissolves slowly and creates localized pockets of high pH water. Boric acid dissolves very rapidly and has only a small impact on pH. The cost difference between the two methods is minimal (a few dollars) even when you include shipping for a 55lbs bucket from Duda Energy.
Boric acid it is then!

As for your previous post, I get 171.6ppm boric acid for a 30ppm [B] concentration. But honestly, I'm not sure why that matters. PoolMath does all the conversions internally to calculate the weight of boric acid or borax needed based on the elemental boron concentration.
Because I wanted to know the ppm of the actual species in solution. These are covalent species. It is not chemically correct to give the boron ppm as there is no free elemental boron (or free boron ions since boron does not ionize) in the water. I understand the basis of the calculation however, I just think it would be better to have a true representation. I also accept that the EPA and others use the elemental boron method, which is their main concern.

16. Borate calculation

Originally Posted by Texaspops
Because I wanted to know the ppm of the actual species in solution. These are covalent species. It is not chemically correct to give the boron ppm as there is no free elemental boron (or free boron ions since boron does not ionize) in the water. I understand the basis of the calculation however, I just think it would be better to have a true representation. I also accept that the EPA and others use the elemental boron method, which is their main concern.
This should probably be moved to the "Agree to Disagree" forum as the above statement is not quite correct but it is not totally incorrect either. It's a matter of proper convention and what is agreed upon usage.

It is precisely because boron forms covalently bonded, polyionic oxyanions that one must choose total elemental boron concentration as the basis for solution chemistry analysis. The same is true for dissolved inorganic carbon oxyanions. Only in the case of strong ionic compounds (e.g., NaCl) that do not exhibit strong pH dependence is it correct to talk in terms of a single species concentration.

Borates and carbonates in aqueous solutions exist as a range of ionic species that are pH dependent. In turns out that for boron oxyanions, the dominant species at typical pool water pH values is boric acid. However, there is no simple method of measuring boric acid concentration specifically. When one measures boron concentration, it is through boron complexation with cis-diol organic compounds (e.g., D-mannitol). And, in the case of boric acid and mannitol, the boric acid is losing its OH- groups through condensation. Thus the boron is directly reacting with the diol group. See this paper for a detailed description of boron-sugar interactions.

Carbonates are similar. In pool water, three distinct inorganic carbon oxyanions are present - carbonate (CO32-), bicarbonate (HCO3-) and aqueous carbon dioxide (CO2(aq)). The ratio of these species are pH dependent with the largest fraction being bicarbonate. When one measures dissolved inorganic carbon (DIC), it is usually through a total alkalinity test which is a strong acid titration and it is reported as milliequivalent per liter (mEq/L) or ppm of CaCO3. One can then use a series of six (6) simultaneous equations to solve for all the unknowns. Again, one rarely reports the concentration of a single carbon oxyanion species but rather the total equivalent concentration and then determines the equilibrium values of the constituents if they are needed for a particular purpose.

Another example is cyanuric acid. There are six (6) different chlorinated isocyanurate species as well as four (4) different cyanuric acid species. The relative proportions of these 10 different species depends on pH. The complete expression of the chemical equilibrium for all of these species and their interactions with chlorine require thirteen (13) simultaneous equations (ten of them are independent). However, when we measure and report CYA concentration, it is always measured and reported as total ppm's of cyanuric acid. That is because the test for CYA occurs at low pH (due to buffers in the R-0013 reagent) to make sure that most of the chlorinated isocyanurates are not present (converted to cyanuric acid) as the chlorinated isocyanurates only weakly react with melamine. Once again, a particular cyanurate species (chlorinated or not) is of little interest.

The last point to emphasize is this - PoolMath expects and uses the standard unit conventions when inputing concentration values and for doing calculations. Borates are reported as ppm boron, FC and CC as ppm Cl2, TA as ppm CaCO3, stabilizer as ppm CYA, salt as ppm chloride ion (Cl-), calcium hardness as mg/L (or ppm) CaCO3. Results of water tests should always be posted using the standard conventions.

17. Re: Borate calculation

Thank you for the detailed explanation. I appreciate the time and effort to do it.

I am not trying to be obstinate here, but part of your explanation is internally inconsistent.
You state that "It is precisely because boron forms covalently bonded, polyionic oxyanions that one must choose total elemental boron concentration as the basis for solution chemistry analysis. The same is true for dissolved inorganic carbon oxyanions."
But then you state that for CaCO3 that contains a carbon oxyanion, ppm is expressed as the entire molecule, not just based on elemental carbon.
But also state that for substances containing boron oxyanions, (ie Na2B4O5(OH)4.8H2O, borax) you have to use ppm for elemental boron.
Why then are the carbon oxyanions not given as ppm C?
To me it doesn't make good chemical consistency. But I can live with it for this purpose!

Furthermore, the reason for the boron situation being the mannitol titration method of analysis also seems spurious. After all it is boric acid/tetraborate that reacts with mannitol in a 1:! or 2:1 ratio, not boron.

But you are correct in that overall it doesn't matter for the vast majority of pool owners, who just want a nice pool and will do and follow
whatever is recommended and for whom the detailed chemistry is a mystery.
This is what the pool stores/companies have been getting away with for years, and I am glad to see that this site is devoted to
improving the situation and saving people money and headaches by pulling back the curtain to reveal what has been going on.

18. Re: Borate calculation

You are way overthinking this. The units of measurement when they are done by weight concentration as with mg/L or ppm (in water) are simply a CONVENTION as James stated. It is arbitrary and only needs to be consistent or understood in context. The 50 ppm is a concentration recommendation only when the units of measurement are in mg/L (or ppm) Boron. That is the convention everyone uses including the EPA when they set the 50 ppm limit.

Chlorine units are in ppm Cl2 so molecular chlorine regardless of the chemical that is added or the specific chemical chlorine species in the water, including that of chloramines that are typically also measured in those same weight concentration units. Ammonia units are usually mg/L N for atomic nitrogen but sometimes they are mg/L NH3 which of course is confusing unless explicitly stated.

CH and TA are both measured in ppm CaCO3 which for TA is particularly confusing since there's a factor of two difference that needs to be applied when trying to convert that to sodium bicarbonate amounts because carbonate can accept 2 hydrogen ions while bicarbonate can only accept one, so carbonate counts twice towards TA compared to bicarbonate.

For chemists, one usually measures concentrations in molar units (moles per liter) since that avoids most of this confusion. However, most standard water kit measurements are done as weight concentrations. If you look at a water quality report, you may even see a single measurement such as Calcium Hardness measured in different ways such as mg/L CaCO3 or mg/L Ca2+ or grains CaCO3 per gallon.

PoolMath uses the standard weight concentration conventions when doing its calculations for weight of actual products and of course lets you select from different products such as sodium tetraborate decahydrate found in 20 Mule Team Borax, sodium tetraborate pentahydrate found in some borate products (Proteam Supreme or BioGuard Optimize Plus), or boric acid.

19. Re: Borate calculation

Originally Posted by chem geek
You are way overthinking this. The units of measurement when they are done by weight concentration as with mg/L or ppm (in water) are simply a CONVENTION as James stated. It is arbitrary and only needs to be consistent or understood in context. The 50 ppm is a concentration recommendation only when the units of measurement are in mg/L (or ppm) Boron. That is the convention everyone uses including the EPA when they set the 50 ppm limit.

Chlorine units are in ppm Cl2 so molecular chlorine regardless of the chemical that is added or the specific chemical chlorine species in the water, including that of chloramines that are typically also measured in those same weight concentration units. Ammonia units are usually mg/L N for atomic nitrogen but sometimes they are mg/L NH3 which of course is confusing unless explicitly stated.

CH and TA are both measured in ppm CaCO3 which for TA is particularly confusing since there's a factor of two difference that needs to be applied when trying to convert that to sodium bicarbonate amounts because carbonate can accept 2 hydrogen ions while bicarbonate can only accept one, so carbonate counts twice towards TA compared to bicarbonate.

For chemists, one usually measures concentrations in molar units (moles per liter) since that avoids most of this confusion. However, most standard water kit measurements are done as weight concentrations. If you look at a water quality report, you may even see a single measurement such as Calcium Hardness measured in different ways such as mg/L CaCO3 or mg/L Ca2+ or grains CaCO3 per gallon.

PoolMath uses the standard weight concentration conventions when doing its calculations for weight of actual products and of course lets you select from different products such as sodium tetraborate decahydrate found in 20 Mule Team Borax, sodium tetraborate pentahydrate found in some borate products (Proteam Supreme or BioGuard Optimize Plus), or boric acid.
Thank you for the reply. I understand it all now!
Coming from a chemistry background, this entire subject area is weird to me, but as I mentioned in a previous post, i can see that it doesn't matter
to most pool owners, who just want quick ways to test their water and how much of various substances to add to it, as well as what not to use.

Not being familiar with the convention used for boron by EPA and others, I was amazed by the large amount of borax the PoolMath showed to be added for 30-40 ppm of "borate", because I had done my own calculation using borate, not boron as the actual species being added. Hence the original question.

I also find it odd that calculations in various posts, e.g for the molecular weights, are given to 0.1 or even 0.01 when there are not the abilities to weigh that precisely for adding materials nor to analyze to that level. For example by counting drops and multiplying by 10, will only give accuracy of 2 sig figs e.g either 120 or 130. Also the drops can be of different volumes, making the accuracy potentially worse.

Since you mentioned it, what exactly is the difference between CH and TA, if both are in ppm CaCO3 ?

20. Re: Borate calculation

Calcium is the concentration of calcium ions in the water. TA is all species that can accept a hydrogen ion as a sample is titrated down to a ph of 4.5.

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