{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T15:14:11Z","timestamp":1783955651131,"version":"3.55.0"},"reference-count":12,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2014NextGenerationEU","award":["GRINS PE00000018\u2014CUP D13C22002160001"],"award-info":[{"award-number":["GRINS PE00000018\u2014CUP D13C22002160001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Molecules"],"abstract":"<jats:p>Calculating the pH values of carbonic acid solutions is an important task in studies of chemical equilibria in freshwater systems, with applications to environmental chemistry, geology, and hydrology. These pH values are also highly relevant in the context of climate change, since increasing atmospheric CO2 affects the concentration of dissolved carbon dioxide and carbonic acid, collectively denoted as [H2CO3*] = [H2CO3(aq)] + [CO2(aq)]. Solving equilibrium systems to obtain analytical functions is particularly useful when such functions are required, for example, in data fitting. We show here that, although exact or near-exact solutions typically result in third- to fourth-order equations that must be solved numerically, reasonable approximations can be derived that lead to analytical second-order equations. In this framework, the chosen approximations need to meet the boundary conditions of the systems, particularly for cT \u2192 0 and for high cT values (where cT = [H2CO3*] + [HCO3\u2212] + [CO32\u2212]). Finally, we provide exact solutions for a closed system containing both H2CO3* and alkalinity, which enables the description of virtually any aquatic environment without assuming equilibrium with atmospheric CO2. Implications for pH calculations in natural waters are also briefly discussed.<\/jats:p>","DOI":"10.3390\/molecules31020292","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T09:03:10Z","timestamp":1768381390000},"page":"292","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Calculation of the pH Values of Aqueous Systems Containing Carbonic Acid and Significance for Natural Waters, Following (Near-)Exact and Approximated Solutions: The Importance of the Boundary Conditions"],"prefix":"10.3390","volume":"31","author":[{"given":"Arianna","family":"Rosso","sequence":"first","affiliation":[{"name":"Dipartimento di Chimica, Universit\u00e0 degli Studi di Torino, Via Pietro Giuria 5, 10125 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2841-5721","authenticated-orcid":false,"given":"Davide","family":"Vione","sequence":"additional","affiliation":[{"name":"Dipartimento di Chimica, Universit\u00e0 degli Studi di Torino, Via Pietro Giuria 5, 10125 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"16788","DOI":"10.1007\/s11356-018-1679-x","article-title":"Long-term trends in Swiss rivers sampled continuously over 39 years reflect changes in geochemical processes and pollution","volume":"25","author":"Zobrist","year":"2018","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1767","DOI":"10.5194\/bg-13-1767-2016","article-title":"Reviews and Syntheses: Ocean acidification and its potential impacts on marine ecosystems","volume":"13","author":"Mostofa","year":"2016","journal-title":"Biogeosciences"},{"key":"ref_3","unstructured":"Gustafsson, J. (Visual MINTEQ, 2000). Visual MINTEQ, version 3.1."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Robbins, L.L., Hansen, M.E., Kleypas, J.A., and Meylan, S.C. (2010). CO2calc: A User-Friendly Seawater Carbon Calculator for Windows, Mac OS X, and iOS (iPhone), U.S. Geological Survey.","DOI":"10.3133\/ofr20101280"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Castellino, L., Alladio, E., Bertinetti, S., Lando, G., De Stefano, C., Blasco, S., Garc\u00eda-Espa\u00f1a, E., Gama, S., Berto, S., and Milea, D. (2023). PyES\u2013an open-source software for the computation of solution and precipitation equilibria. Chemom. Intell. Lab. Syst., 239.","DOI":"10.1016\/j.chemolab.2023.104860"},{"key":"ref_6","first-page":"285","article-title":"Quantifying the possible short- and long-term impacts of superoxide redox chemistry on seawater pH","volume":"3","author":"Mostofa","year":"2015","journal-title":"Can. Chem. Trans."},{"key":"ref_7","unstructured":"Christian, G.D., Dasgupta, P.K., and Schug, K.A. (2020). Analytical Chemistry, Wiley. [7th ed.]."},{"key":"ref_8","unstructured":"(2025, September 01). Python. Available online: https:\/\/www.python.org."},{"key":"ref_9","unstructured":"Skoog, D.A., West, D.M., Holler, F.J., and Crouch, S.E. (2000). Analytical Chemistry: An Introduction, Brooks\/Cole Pub Co."},{"key":"ref_10","unstructured":"National Institute of Standards and Technology (2025, October 01). NIST Chemistry WebBook, Available online: https:\/\/webbook.nist.gov."},{"key":"ref_11","unstructured":"(2025, October 01). Solution of Cubic Equations with the Python Code. Available online: https:\/\/docs.scipy.org\/doc\/scipy\/reference\/optimize.html."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1038\/s41467-022-28711-z","article-title":"Aragonite dissolution protects calcite at the seafloor","volume":"13","author":"Sulpis","year":"2022","journal-title":"Nat. Commun."}],"container-title":["Molecules"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1420-3049\/31\/2\/292\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T09:03:32Z","timestamp":1768381412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1420-3049\/31\/2\/292"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":12,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["molecules31020292"],"URL":"https:\/\/doi.org\/10.3390\/molecules31020292","relation":{},"ISSN":["1420-3049"],"issn-type":[{"value":"1420-3049","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,14]]}}}