Editing Calcium carbonate (section)

=== With varying pH, temperature and salinity: {{chem2|CaCO3}} scaling in swimming pools ===
[[File:CaCO3-pH.gif|thumb|alt=Effects of salinity and pH on the maximum calcium ion level before scaling is anticipated at 25 °C and 1 mmol/L bicarbonate concentration (e.g. in swimming pools)]]
[[File:CaCO3-Temp.gif|thumb|alt=Effects of temperature and bicarbonate concentration on the maximum calcium ion level before scaling is anticipated at pH&nbsp;7 and 5,000&nbsp;ppm salinity (such as in swimming pools)]]
In contrast to the open equilibrium scenario above, many swimming pools are managed by addition of [[sodium bicarbonate]] ({{chem2|NaHCO3}}) to the concentration of about 2&nbsp;mmol/L as a buffer, then control of pH through use of HCl, {{chem2|NaHSO4}}, {{chem2|Na2CO3}}, NaOH or chlorine formulations that are acidic or basic. In this situation, dissolved inorganic carbon ([[total inorganic carbon]]) is far from equilibrium with atmospheric {{chem2|CO2}}. Progress towards equilibrium through outgassing of {{chem2|CO2}} is slowed by
{{ordered list
|the slow reaction
:{{chem2|[[Carbonic acid|H2CO3]] ⇌ CO2([[aqueous solution|aq]]) + H2O}};<ref>{{Cite journal | doi = 10.1021/jp909019u| pmid = 20039712| title = Comprehensive Study of the Hydration and Dehydration Reactions of Carbon Dioxide in Aqueous Solution| journal = The Journal of Physical Chemistry A| volume = 114| issue = 4| pages = 1734–40| year = 2010| last1 = Wang | first1 = X. | last2 = Conway | first2 = W. | last3 = Burns | first3 = R. | last4 = McCann | first4 = N. | last5 = Maeder | first5 = M. | bibcode = 2010JPCA..114.1734W}}</ref>
|limited aeration in a deep water column; and
|periodic replenishment of bicarbonate to maintain buffer capacity (often estimated through measurement of [[alkalinity|total alkalinity]]).}}

In this situation, the dissociation constants for the much faster reactions
:{{chem2|H2CO3 ⇌ H+ + HCO3− ⇌ 2 H+ + CO3(2−)}}
allow the prediction of concentrations of each dissolved inorganic carbon species in solution, from the added concentration of {{chem2|HCO3−}} (which constitutes more than 90% of [[Bjerrum plot]] species from pH&nbsp;7 to pH&nbsp;8 at 25&nbsp;°C in fresh water).<ref name="Mook 2000">{{cite book|last=Mook|first=W.|date=2000|url=http://www-naweb.iaea.org/napc/ih/documents/global_cycle/vol%20I/cht_i_09.pdf|contribution=Chemistry of carbonic acid in water|pages=143–165|title=Environmental Isotopes in the Hydrological Cycle: Principles and Applications|publisher=INEA/UNESCO|location=Paris|access-date=18 March 2014|archive-url=https://web.archive.org/web/20140318074927/http://www-naweb.iaea.org/napc/ih/documents/global_cycle/vol%20I/cht_i_09.pdf|archive-date=18 March 2014}}</ref> Addition of {{chem2|HCO3−}} will increase {{chem2|CO3(2−)}} concentration at any pH. Rearranging the equations given above, we can see that {{chem2|[Ca(2+)]}} = {{sfrac|''K''<sub>sp</sub>|[{{chem2|CO3(2−)}}]}}, and [{{chem2|CO3(2−)}}] = {{sfrac|''K''<sub>a2</sub> [{{chem2|HCO3−}}]|[{{chem2|H+}}]}}. Therefore, when {{chem2|HCO3−}} concentration is known, the maximum concentration of {{chem2|Ca(2+)}} ions before scaling through {{chem2|CaCO3}} precipitation can be predicted from the formula:

:[{{chem2|Ca(2+)}}]<sub>max</sub> = {{sfrac|''K''<sub>sp</sub>|''K''<sub>a2</sub>}} × {{sfrac|[{{chem2|H+}}]|[{{chem2|HCO3-}}]}}

The solubility product for {{chem2|CaCO3}} (''K''<sub>sp</sub>) and the dissociation constants for the dissolved inorganic carbon species (including ''K''<sub>a2</sub>) are all substantially affected by temperature and [[salinity]],<ref name="Mook 2000" /> with the overall effect that [{{chem2|Ca(2+)}}]<sub>max</sub> increases from freshwater to saltwater, and decreases with rising temperature, pH, or added bicarbonate level, as illustrated in the accompanying graphs.

The trends are illustrative for pool management, but whether scaling occurs also depends on other factors including interactions with {{chem2|[[magnesium|Mg]](2+)}}, [[Tetrahydroxyborate|{{chem2|[B(OH)4]−}}]] and other ions in the pool, as well as supersaturation effects.<ref>{{cite journal |last=Wojtowicz |first=J. A. |year=1998 |title=Factors affecting precipitation of calcium carbonate |journal=Journal of the Swimming Pool and Spa Industry |volume=3 |issue=1 |pages=18–23 |url=http://jspsi.poolhelp.com/ARTICLES/JSPSI_V3N1_pp18-23.pdf |access-date=18 March 2014 |archive-url=https://web.archive.org/web/20140318061934/http://jspsi.poolhelp.com/ARTICLES/JSPSI_V3N1_pp18-23.pdf |archive-date=18 March 2014}}</ref><ref>{{cite journal|last=Wojtowicz|first=J. A.|year=1998|title=Corrections, potential errors, and significance of the saturation index|journal=Journal of the Swimming Pool and Spa Industry|volume=3|issue=1|pages=37–40|url=http://jspsi.poolhelp.com/ARTICLES/JSPSI_V3N1_pp37-40.pdf|access-date=18 March 2014|archive-url=https://web.archive.org/web/20120824152654/http://jspsi.poolhelp.com/ARTICLES/JSPSI_V3N1_pp37-40.pdf|archive-date=24 August 2012}}</ref> Scaling is commonly observed in electrolytic chlorine generators, where there is a high pH near the cathode surface and scale deposition further increases temperature. This is one reason that some pool operators prefer borate over bicarbonate as the primary pH buffer, and avoid the use of pool chemicals containing calcium.<ref>{{cite web |last=Birch |first=R. G. |date=2013 |url=https://scithings.id.au/BABES.pdf |title=BABES: a better method than "BBB" for pools with a salt-water chlorine generator |website=scithings.id.au |access-date=11 October 2020 |archive-date=15 April 2021 |archive-url=https://web.archive.org/web/20210415065559/https://scithings.id.au/BABES.pdf |url-status=live}}</ref>