There have been some ridiculous practices in swimming pool water chemistry over the past couple of years,, and one of the worst offenders is in the pseudoscience of allowing pH to seek its level. Often attempting to back up this tomfoolery with references to Henry’s Law, a principle that describes the relationship between a concentration of a gas in a liquid and the pressure of that same gas above the liquid, it seems as though the goal is to baffle the reader with bullshit rather than dazzle with brilliance. The ‘law,’ named for the English chemist William Henry who first proposed it in 1803, is especially important in chemistry, and is used to understand the behavior of gases in solution. However, claims that it can apply to swimming pool water chemistry are far-fetched. The truth of the matter is Henry’s Law fails with pool pH.
Bad Chemistry
According to Henry’s Law, the concentration of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. In other words, as the pressure of the gas increases, the gas concentration in the liquid also increases. This is not being disputed and mathematically can be expressed as:
C = kP
Here C represents the concentration of the gas in the liquid, P is the partial pressure of the gas above the liquid, and k is a constant of proportionality known as Henry’s law constant.
The problem is this relationship between concentration and pressure does not hold true for all gases in all solutions. In fact, it is known that when the gas in question also reacts with the solution it is in Henry’s law does not apply. This is the scenario we experience with swimming pool water where carbon dioxide (CO2) reacts with water (H2O), forming carbonic acid (H2CO3). So, the practice of allowing pH to seek its own level is nothing short of bad chemistry.
When CO2 dissolves in water, it reacts with the water molecules to form carbonic acid (H2CO3). This equilibrium reaction can be expressed as:
CO2 + H2O ⇌ H2CO3
With additional side reactions as H2CO3 dissociates to H+ and HCO–3
Gas reactions
The formation of carbonic acid affects the concentration of CO2 in the water and, therefore, violates Henry’s Law. This is because the concentration of carbon dioxide in the water is no longer solely determined by the partial pressure of carbon dioxide above the water. Instead, it is also affected by the concentration of carbonic acid in the water.
As a result, the relationship between the concentration of CO2 in water and the partial pressure of carbon dioxide above the water is no longer linear, as predicted by Henry’s Law. Instead, it becomes more complex, and the equilibrium between the gas (carbon dioxide) and carbonic acid must be considered.
Limitations of Henry’s Law: This law is only applicable when the molecules of the system are in a state of equilibrium. Henry’s law does not hold true when gases are placed under extremely high pressure. The law is not applicable when the gas and the solution participate in chemical reactions with each other.
In addition to affecting the concentration of CO2 in water, the formation of carbonic acid also affects the pH and TA (Total Alkalinity) of the water. Carbonic acid is a weak acid that can donate a proton to water molecules to form bicarbonate ions (HCO–3) and hydrogen ions (H+). The hydrogen ions contribute to the measurement of hydrogen ion activity in the solution lowering the pH, whereas the bicarbonate ions contribute to the Total Alkalinity. It is important to understand the complex interplay between CO2, carbonic acid, pH , and TA in order to comprehend why the principle does not apply.
The theory of the ‘pH ceiling’ in swimming pools is flawed.
Applicability of Henry’s Law: Henry’s law only works if the molecules are at equilibrium. Henry’s law does not work for gases at high pressures… Henry’s law does not work if there is a chemical reaction between the solute and solvent…
The pH level of water plays a crucial role in aspects beyond LSI and water balance. It has a significant impact on the growth of algae, the efficacy of chlorine as a disinfectant, chlorine loss, and the potential for chemical reactions that can alter the overall chemistry of the water.
High pH promotes algae growth
We know alga prefers a more alkaline environment with a pH on the higher side of the acceptable range. This is because the nutrients that algae need to grow, such as phosphorus and nitrogen, are more readily available at those pH levels above 7.6. The higher the pH of the water the more ideal ideaitions for algae to growth and colonization.
It is also understood that the effectiveness of chlorine is pH dependent. The higher the level, the lower the concentration of hypochlorous acid which is the form of chlorine that is most effective at killing bacteria and other microorganisms in water.
High pH promotes chlorine loss
The lower the concentration of hypochlorous acid, the more significant the concentration of hypochlorite ions. That’s a problem. Hypochlorite ions do not share hypochlorous acid’s attraction to CyA (cyanuric acid). The higher pH has left the lion’s share of chlorine in the water subject to solar degradation. As a result, the amount of chlorine necessary to maintain even a minimal level will increase exponentially.
Remember that the saturation index only pertains to the protection of the vessel, whether the water is corrosive or scale-forming. The pool service pro needs to consider the big picture and every way a target pH can affect the water quality. The same holds true for CH (calcium hardness) which can easily be an entire article on its own.
While much of what was written in this blog post is correct, some is incorrect or misinterpreted.
The quotes about Henry’s Law “The law is not applicable when the gas and the solution participate in chemical reactions with each other” and “Henry’s law does not work if there is a chemical reaction between the solute and solvent…” are only true with regard to consumptive reactions or where one does not account for equilibrium values of dissolves/aqueous carbon dioxide (or H2CO3* that combines carbonic acid and carbon dioxide since most Henry Law constants refer to that combination of species that are proportionally related to each other).
So long as one CALCULATES the CO2/H2CO3 (i.e. H2CO3*) which means accounting for the pH-dependent equilibrium you show between that and bicarbonate ion and carbonate ion, then Henry’s Law most definitely applies and can be used. The reason is that the equilibrium reactions are VERY fast while the outgassing of carbon dioxide is slow. So one can see how out-of-equilibrium one is with respect to carbon dioxide in water vs. in air. And it also means that there will be a slowdown in carbon dioxide outgassing as one gets closer to the Henry’s Law equilibrium and that such NET outgassing stops at a higher pH where the ratio of carbon dioxide concentrations in water and air (or H2CO3*/CO2(g)) match Henry’s Law constant.
As for the dependence of algae growth on pH, this is complicated because it depends on algae species but as noted in https://algaeresearchsupply.com/pages/algae-culture-and-ph, marine algae tend to prefer higher pH while freshwater algae as normally found in pools tend to prefer lower pH. But anyone who has seen algae in pools knows that with sufficient nutrients (particularly phosphates) and sunlight (again, depends on algae type for whether they prefer direct vs, indirect sunlight) then algae can grow rather quickly doubling every 3-8 hours depending on species.
It is true that higher pH has more hypochlorite ion and that this breaks down from the UV in sunlight more quickly than hypochlorous acid.
The main reason why one may want to target one or both of a lower TA (really adjusted TA aka carbonate alkalinity) and a higher pH is to reduce the rate of carbon dioxide outgassing that leads to a rise in pH in pools not having other pH influences such as acidity from a Trichlor chlorine source. This will reduce the amount of acid that needs to be added to the pool so saves cost there though as you point out more chlorine will be used at higher pH so there is a tradeoff. And, of course, to balance the saturation index one needs a higher Calcium Hardness (CH). Use of this principle on Trouble Free Pool, particularly in pools with saltwater chlorine generators and in spas using bleach (after Dichlor or otherwise initially adding CYA) results in much greater pH stability and much lower acid usage. It is a great example of applied science.
Rudy,
.
The Krichevsky-Kasarnovsky Equation modifies Henry’s Law to account for the effects of HIGH PRESSURE on the solubilities of slightly soluble gases. See Yuming Yu, Lili Li, and Loren G. Hepler, “Partial molar volumes of acidic gases in physical solvents and prediction of solubilities at high pressures”, Can. J. Chem. 70, 55, (1992). The “Carbon in Lakes” document you are quoting states “the conditions under investigation:” of “80 – 90 bar” which is 78.9 to 88.8 atm so HIGH PRESSURE that is not the condition air (with carbon dioxide) over pool water.
.
So let’s look inside the Carroll and Mather paper “The system carbon dioxide-water and the Krichevsky-Kasarnovsky equation” (which costs $39.95 to buy online). Quoting from that paper “To obtain Henry’s constants from solubility data, especially at high pressure, the method of Krichevsky is often used.” In this paper, Table I shows various sources of experimental data for the system carbon dioxide-water, but they are ALL looking only at high pressure (the lowest was a range from 3 to 80 atm but others were even higher ranges).
.
So let’s use the Krichevsky-Kasarnovsky equation for carbon dioxide in air at 1 atm to see what sort of correction is needed to the Henry’s Law constant. From the Xu/Li/Hepler paper, the Krichevsky-Kasarnovsky is the following where I use the meanings instead of symbols for clarity since this comment can’t use equation sub/superscripting.
.
ln(adjusted Henry’s Law constant) = ln(original Henry’s Law constant) + [(low concentration partial molar volume of dissolved gas)*(total pressure – equilibrium vapor pressure of solvent)]/RT
.
The Henry’s Law constant in the above equation is a ratio of mole fractions (fugacity of gas to mole fraction of dissolved gas in liquid phase). The low concentration partial molar volume of dissolved gas for carbon dioxide in water is 33.9 cm^3/mol = 0.0339 liters (see Joseph C. Moore, et al., “Partial Molar Volumes of “Gases” at Infinite Dilution in Water at 298.15 K”, J. Chem. Eng., 1982, 27, 22-24). The total pressure is 1 atm and the equilibrium vapor pressure of water at 25°C is 0.0313 atm. The temperature is in Kelvin so is 273.15 + 25 = 298.15K and the gas constant R is 0.08206 L•atm/(mol•K). So we have an adjustment of 0.0339*(1-0.0313)/(0.08296*298.15) = 0.00133
.
So the factor that the Henry’s Law constant needs to be increased is exp(0.00133) = 1.0013 or only 0.13% which is negligible. When the pressures are higher, such as at 10 atm with a 1.3% factor or 50 atm with a 14% factor, then this becomes important, but not at normal atmospheric pressures.
.
So the bottom line is that at normal atmospheric pressures, Henry’s Law can be used.
.
Thanks,
Richard
You’ll have to forgive me. The concept is intriguing, and of course do value your input, always. However, the application in offering Henry’s Law as a justification for swimming pools to SEEK what a ‘ceiling’ that works as the ideal operating pH of a specific pool has far too many variables. Aside from the abundance of research stating that the formation of carbonic acid will skew the results, there is still surface area, temperature, decreases in atmospheric pressure with increases in elevation, and increasing psi at varying levels of depth of water. As well, thermal stratification and psi of water at increasing depths, although not significant, Henry’s law appears to have a focus on surface waters and does not account for the 0.43 increase in psi per foot depth increase.
On top of this the fact that Henry’s Law was not designed for solutions where chemicals would be added that also affect the levels of CO2 in that body of water (ie HCl, sodium carbonate, sodium bicarbonate, etc. All this and then still the fact (as I do heavily dispute the article on algae you share earlier as a reference) the algae species we typically see in swimming pools prefer a ph of > 7.6, which is based on an abundance of available research and the species of Navicula sp., Nostoc sp., Oscillatoria, Microcystis, and Leptolyngbya in my personal collection of living algae in my four-year stint in the practice of algaculture. In all, the practice of allowing pH to seek it’s own levels, whether I agree on the application of Henry’s law in swimming pools or not, is still bad chemistry and an awful practice for professionals in the field.
Richard Falk April 19, 2023
P.S.
When one uses a lower TA level to have less carbonates, and carbon dioxide, in the pool or spa, one can use other chemicals to provide additional pH buffering, if desired. In pools, CYA is also a pH buffer so ones with higher CYA levels sometimes have enough buffering. Some people add borates to the pool for the additional buffering and this was not only used at Trouble Free Pool but was also later promoted by Bob Lowry. For spas, while borates are an option, there are also other pH lock products some of which use phosphate buffers which is OK in covered spas since the lack of sunlight doesn’t make the risk of algae growth too high even if active chlorine levels get too low.
I am well aware of this, but manipulating Total Alkalinity or any facet of water chemistry to achieve a desired pH is not Henry’s Law, correct? This, and the chemicals added to manipulate Total Alkalinity, will also control pH to one extent or another, which is not in line with the theory. Beyond this, encouraging (not you) individuals to allow the pH of their pool water to ‘seek its level’ in hopes that the pool owner will balance the water to LSI is an extensive reach and careless as it is not sharing the other concerns in maintaining a high pH beyond the damage of improper water balance.
Richard Falk April 21, 2023
Rudy,
Ernest (“Chip”) Blatchley, III is a Purdue University professor who has done a lot of research on disinfection by-products in swimming pools, particularly regarding air quality and volatile compounds. There are numerous papers where Henry’s Law is specifically applied. Here is one of the most recent ones:
Real-Time Measurements of Gas-Phase Trichloramine (NCl3) in an Indoor Aquatic Center
Tianren Wu, Tomas Földes, Lester T. Lee, Danielle N. Wagner, Jinglin Jiang, Antonios Tasoglou, Brandon E. Boor, and Ernest R. Blatchley III
Environmental Science & Technology 2021 55 (12), 8097-8107
“Two-film theory suggests that the transfer of compounds
from the liquid to gas phase is strongly influenced by their
respective Henry’s law constants (H).”
Real swimming pools. Real application of science to studying outgassing of disinfection by-products like nitrogen trichloride, and real correlations between disinfection by-product concentrations and carbon dioxide gas concentrations. Increased swimmer activity led to greater water-to-gas transfer of volatile compounds, including that of carbon dioxide.
For some specific formulas using Henry’s Law in real swimming pools see the following:
Dynamic behavior of gas-phase NCl3 and CO2 in indoor pool facilities,
Lester T. Lee, Tianren Wu, Brandon E. Boor, Ernest R. Blatchley,
Building and Environment, Volume 233, 2023, 110088, ISSN 0360-1323
At steady-state, with no people in the
pool, equation (7) will reduce to equation (13).
Qg(Cg,ss – Cg,in) = Kl A (Cl,ss – Cl*) (13)
Where,
Cg,ss (mg/m3) = steady-state concentration of CO2 in the gas phase
(concentration when no people were present in the pool facility).
Cg,in (mg/L) = concentration of CO2 in the air that is brought into the
pool facility.
Cl,ss (mg/L) = steady-state concentration of CO2 in the liquid-phase
(concentration when no people were present in the pool facility).
Cl∗ (mg/L) = equilibrium concentration of CO2 in the liquid-phase
(concentration when no people were present in the pool facility)
calculated by application of Henry’s law to measured values of CO2
concentration in air above the pool.
The bottom line is that the relatively fast equilibrium of CO2 in the water with carbonates (carbonic acid, bicarbonate ion, carbonate ion) and the relatively slow outgassing of CO2 from liquid to gas phases allows for Henry’s Law to be used in a two-film model. One can absolutely, positively, use Henry’s Law as a guide for how far out-of-equilibrium swimming pools are (i.e. how over-carbonated they are) relative to equilibrium with air and as a result how much concentration gradient influence there is on the rate of carbon dioxide outgassing and the resulting rise in pH.
Thanks,
Richard
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Rudy,
While much of what was written in this blog post is correct, some is incorrect or misinterpreted.
The quotes about Henry’s Law “The law is not applicable when the gas and the solution participate in chemical reactions with each other” and “Henry’s law does not work if there is a chemical reaction between the solute and solvent…” are only true with regard to consumptive reactions or where one does not account for equilibrium values of dissolves/aqueous carbon dioxide (or H2CO3* that combines carbonic acid and carbon dioxide since most Henry Law constants refer to that combination of species that are proportionally related to each other).
So long as one CALCULATES the CO2/H2CO3 (i.e. H2CO3*) which means accounting for the pH-dependent equilibrium you show between that and bicarbonate ion and carbonate ion, then Henry’s Law most definitely applies and can be used. The reason is that the equilibrium reactions are VERY fast while the outgassing of carbon dioxide is slow. So one can see how out-of-equilibrium one is with respect to carbon dioxide in water vs. in air. And it also means that there will be a slowdown in carbon dioxide outgassing as one gets closer to the Henry’s Law equilibrium and that such NET outgassing stops at a higher pH where the ratio of carbon dioxide concentrations in water and air (or H2CO3*/CO2(g)) match Henry’s Law constant.
As for the dependence of algae growth on pH, this is complicated because it depends on algae species but as noted in https://algaeresearchsupply.com/pages/algae-culture-and-ph, marine algae tend to prefer higher pH while freshwater algae as normally found in pools tend to prefer lower pH. But anyone who has seen algae in pools knows that with sufficient nutrients (particularly phosphates) and sunlight (again, depends on algae type for whether they prefer direct vs, indirect sunlight) then algae can grow rather quickly doubling every 3-8 hours depending on species.
It is true that higher pH has more hypochlorite ion and that this breaks down from the UV in sunlight more quickly than hypochlorous acid.
The main reason why one may want to target one or both of a lower TA (really adjusted TA aka carbonate alkalinity) and a higher pH is to reduce the rate of carbon dioxide outgassing that leads to a rise in pH in pools not having other pH influences such as acidity from a Trichlor chlorine source. This will reduce the amount of acid that needs to be added to the pool so saves cost there though as you point out more chlorine will be used at higher pH so there is a tradeoff. And, of course, to balance the saturation index one needs a higher Calcium Hardness (CH). Use of this principle on Trouble Free Pool, particularly in pools with saltwater chlorine generators and in spas using bleach (after Dichlor or otherwise initially adding CYA) results in much greater pH stability and much lower acid usage. It is a great example of applied science.
Thanks,
Richard Falk (aka “chem geek”)
Richard! Hello, my friend. I agree that Henry’s law can be forced to somewhat work by changing the Henry coefficient for CO2 per the Krichevsky-Kasarnovsky Equation, but the change in coefficient is necessary because Henry’s law is not applicable in situations where the gas reacts with the solute or where other chemicals are added that affect the equilibrium. John J. Carroll and Alan E. Mather, “The System Carbon Dioxide-Water and the Krichevsky-Kasarnovsky Equation,” Journal of Solution Chemistry, vol. 21, pp. 607-621, 1992. https://link.springer.com/article/10.1007/BF00650756
https://view.officeapps.live.com/op/view.aspx?src=http%3A%2F%2Fwww2.hawaii.edu%2F~kinzie%2Fdocuments%2F470%2FCO2solubility.doc&wdOrigin=BROWSELINK
As far as the pH needed for optimum algae growth, my statement regarding pH requirement is based upon specific genera found identified in U.S. swimming pools, research pertaining to such (see references in my post), and my own research from those ‘swimming pool’ genera I grow in my lab. Here’s another https://www.frontiersin.org/articles/10.3389/fmicb.2022.1044464/full#:~:text=To%20investigate%20the%20morphological%20and%20physiological%20effects%20high,2019%29%2C%20as%20described%20previously%20%28Zepernick%20et%20al.%2C%202021%29.
Best, Rudy
Rudy,
.
The Krichevsky-Kasarnovsky Equation modifies Henry’s Law to account for the effects of HIGH PRESSURE on the solubilities of slightly soluble gases. See Yuming Yu, Lili Li, and Loren G. Hepler, “Partial molar volumes of acidic gases in physical solvents and prediction of solubilities at high pressures”, Can. J. Chem. 70, 55, (1992). The “Carbon in Lakes” document you are quoting states “the conditions under investigation:” of “80 – 90 bar” which is 78.9 to 88.8 atm so HIGH PRESSURE that is not the condition air (with carbon dioxide) over pool water.
.
So let’s look inside the Carroll and Mather paper “The system carbon dioxide-water and the Krichevsky-Kasarnovsky equation” (which costs $39.95 to buy online). Quoting from that paper “To obtain Henry’s constants from solubility data, especially at high pressure, the method of Krichevsky is often used.” In this paper, Table I shows various sources of experimental data for the system carbon dioxide-water, but they are ALL looking only at high pressure (the lowest was a range from 3 to 80 atm but others were even higher ranges).
.
So let’s use the Krichevsky-Kasarnovsky equation for carbon dioxide in air at 1 atm to see what sort of correction is needed to the Henry’s Law constant. From the Xu/Li/Hepler paper, the Krichevsky-Kasarnovsky is the following where I use the meanings instead of symbols for clarity since this comment can’t use equation sub/superscripting.
.
ln(adjusted Henry’s Law constant) = ln(original Henry’s Law constant) + [(low concentration partial molar volume of dissolved gas)*(total pressure – equilibrium vapor pressure of solvent)]/RT
.
The Henry’s Law constant in the above equation is a ratio of mole fractions (fugacity of gas to mole fraction of dissolved gas in liquid phase). The low concentration partial molar volume of dissolved gas for carbon dioxide in water is 33.9 cm^3/mol = 0.0339 liters (see Joseph C. Moore, et al., “Partial Molar Volumes of “Gases” at Infinite Dilution in Water at 298.15 K”, J. Chem. Eng., 1982, 27, 22-24). The total pressure is 1 atm and the equilibrium vapor pressure of water at 25°C is 0.0313 atm. The temperature is in Kelvin so is 273.15 + 25 = 298.15K and the gas constant R is 0.08206 L•atm/(mol•K). So we have an adjustment of 0.0339*(1-0.0313)/(0.08296*298.15) = 0.00133
.
So the factor that the Henry’s Law constant needs to be increased is exp(0.00133) = 1.0013 or only 0.13% which is negligible. When the pressures are higher, such as at 10 atm with a 1.3% factor or 50 atm with a 14% factor, then this becomes important, but not at normal atmospheric pressures.
.
So the bottom line is that at normal atmospheric pressures, Henry’s Law can be used.
.
Thanks,
Richard
You’ll have to forgive me. The concept is intriguing, and of course do value your input, always. However, the application in offering Henry’s Law as a justification for swimming pools to SEEK what a ‘ceiling’ that works as the ideal operating pH of a specific pool has far too many variables. Aside from the abundance of research stating that the formation of carbonic acid will skew the results, there is still surface area, temperature, decreases in atmospheric pressure with increases in elevation, and increasing psi at varying levels of depth of water. As well, thermal stratification and psi of water at increasing depths, although not significant, Henry’s law appears to have a focus on surface waters and does not account for the 0.43 increase in psi per foot depth increase.
On top of this the fact that Henry’s Law was not designed for solutions where chemicals would be added that also affect the levels of CO2 in that body of water (ie HCl, sodium carbonate, sodium bicarbonate, etc. All this and then still the fact (as I do heavily dispute the article on algae you share earlier as a reference) the algae species we typically see in swimming pools prefer a ph of > 7.6, which is based on an abundance of available research and the species of Navicula sp., Nostoc sp., Oscillatoria, Microcystis, and Leptolyngbya in my personal collection of living algae in my four-year stint in the practice of algaculture. In all, the practice of allowing pH to seek it’s own levels, whether I agree on the application of Henry’s law in swimming pools or not, is still bad chemistry and an awful practice for professionals in the field.
P.S.
When one uses a lower TA level to have less carbonates, and carbon dioxide, in the pool or spa, one can use other chemicals to provide additional pH buffering, if desired. In pools, CYA is also a pH buffer so ones with higher CYA levels sometimes have enough buffering. Some people add borates to the pool for the additional buffering and this was not only used at Trouble Free Pool but was also later promoted by Bob Lowry. For spas, while borates are an option, there are also other pH lock products some of which use phosphate buffers which is OK in covered spas since the lack of sunlight doesn’t make the risk of algae growth too high even if active chlorine levels get too low.
I am well aware of this, but manipulating Total Alkalinity or any facet of water chemistry to achieve a desired pH is not Henry’s Law, correct? This, and the chemicals added to manipulate Total Alkalinity, will also control pH to one extent or another, which is not in line with the theory. Beyond this, encouraging (not you) individuals to allow the pH of their pool water to ‘seek its level’ in hopes that the pool owner will balance the water to LSI is an extensive reach and careless as it is not sharing the other concerns in maintaining a high pH beyond the damage of improper water balance.
Rudy,
Ernest (“Chip”) Blatchley, III is a Purdue University professor who has done a lot of research on disinfection by-products in swimming pools, particularly regarding air quality and volatile compounds. There are numerous papers where Henry’s Law is specifically applied. Here is one of the most recent ones:
Real-Time Measurements of Gas-Phase Trichloramine (NCl3) in an Indoor Aquatic Center
Tianren Wu, Tomas Földes, Lester T. Lee, Danielle N. Wagner, Jinglin Jiang, Antonios Tasoglou, Brandon E. Boor, and Ernest R. Blatchley III
Environmental Science & Technology 2021 55 (12), 8097-8107
“Two-film theory suggests that the transfer of compounds
from the liquid to gas phase is strongly influenced by their
respective Henry’s law constants (H).”
Real swimming pools. Real application of science to studying outgassing of disinfection by-products like nitrogen trichloride, and real correlations between disinfection by-product concentrations and carbon dioxide gas concentrations. Increased swimmer activity led to greater water-to-gas transfer of volatile compounds, including that of carbon dioxide.
For some specific formulas using Henry’s Law in real swimming pools see the following:
Dynamic behavior of gas-phase NCl3 and CO2 in indoor pool facilities,
Lester T. Lee, Tianren Wu, Brandon E. Boor, Ernest R. Blatchley,
Building and Environment, Volume 233, 2023, 110088, ISSN 0360-1323
At steady-state, with no people in the
pool, equation (7) will reduce to equation (13).
Qg(Cg,ss – Cg,in) = Kl A (Cl,ss – Cl*) (13)
Where,
Cg,ss (mg/m3) = steady-state concentration of CO2 in the gas phase
(concentration when no people were present in the pool facility).
Cg,in (mg/L) = concentration of CO2 in the air that is brought into the
pool facility.
Cl,ss (mg/L) = steady-state concentration of CO2 in the liquid-phase
(concentration when no people were present in the pool facility).
Cl∗ (mg/L) = equilibrium concentration of CO2 in the liquid-phase
(concentration when no people were present in the pool facility)
calculated by application of Henry’s law to measured values of CO2
concentration in air above the pool.
The bottom line is that the relatively fast equilibrium of CO2 in the water with carbonates (carbonic acid, bicarbonate ion, carbonate ion) and the relatively slow outgassing of CO2 from liquid to gas phases allows for Henry’s Law to be used in a two-film model. One can absolutely, positively, use Henry’s Law as a guide for how far out-of-equilibrium swimming pools are (i.e. how over-carbonated they are) relative to equilibrium with air and as a result how much concentration gradient influence there is on the rate of carbon dioxide outgassing and the resulting rise in pH.
Thanks,
Richard