Carbonic acid

When carbon dioxide dissolves in water, it exists in chemical equilibrium with carbonic acid:[4]

${\displaystyle {\ce {CO2 + H2O <=> H2CO3}}}$

The hydration equilibrium constant at 25 °C is called K_h, which in the case of carbonic acid is [H₂CO₃]/[CO₂] ≈ 1.7×10⁻³ in pure water[5] and ≈ 1.2×10⁻³ in seawater.[6] Hence, the majority of the carbon dioxide is not converted into carbonic acid, remaining as CO₂ molecules. In the absence of a catalyst, the equilibrium is reached quite slowly. The rate constants are 0.039 s⁻¹ for the forward reaction (CO₂ + H₂O → H₂CO₃) and 23 s⁻¹ for the reverse reaction (H₂CO₃ → CO₂ + H₂O). The addition of two molecules of water to CO₂ would give orthocarbonic acid, C(OH)₄, which exists only in minute amounts in aqueous solution.

Addition of base to an excess of carbonic acid gives bicarbonate (hydrogen carbonate). With excess base, carbonic acid reacts to give carbonate salts.

Bicarbonate is an intermediate in the transport of CO₂ out of the body by respiratory gas exchange. The hydration reaction of CO₂ is generally very slow in the absence of a catalyst, but red blood cells contain carbonic anhydrase, which increases the reaction rate, producing bicarbonate (HCO₃⁻) dissolved in the blood plasma. This catalysed reaction is reversed in the lungs, where it converts the bicarbonate back into CO₂ and allows it to be expelled. The equilibration plays an important role as a buffer in mammalian blood.[7] A 2016 theoretical report suggests that carbonic acid may play a pivotal role in protonating various nitrogen bases in blood serum.[8]

The oceans of the world have absorbed almost half of the CO₂ emitted by humans from the burning of fossil fuels.[9]  It has been estimated that the extra dissolved carbon dioxide has caused the ocean's average surface pH to shift by about −0.1 unit from pre-industrial levels. This is known as ocean acidification, even though the ocean remains basic.[10]

Carbonic acid is a carboxylic acid with a hydroxyl group as the substituent. It is also a polyprotic acid: it is specifically diprotic and so has two protons that may dissociate from the parent molecule. Thus, there are two dissociation constants, the first of which is for the dissociation into the bicarbonate (also called hydrogen carbonate) ion HCO₃⁻:

${\displaystyle {\ce {H2CO3 <=> HCO3^- + H+}}}$

K_a1 = 2.5×10⁻⁴;[4] pK_a1 = 3.6 at 25 °C.

Care must be taken when the first dissociation constant of carbonic acid is quoted and used. In aqueous solutions, carbonic acid exists in equilibrium with carbon dioxide, and the concentration of H₂CO₃ is much lower than the concentration of CO₂. In many analyses, H₂CO₃ includes dissolved CO₂ (referred to as CO₂(aq)), H₂CO₃* is used to represent the two species when writing the aqueous chemical equilibrium equation. The equation may be rewritten as follows:[4]

H₂CO₃* ⇌ HCO₃⁻ + H⁺

K_a(app) = 4.47×10⁻⁷; pK(app) = 6.35 at 25 °C and ionic strength = 0.0.

Whereas the apparent pK_a is quoted as the dissociation constant of carbonic acid, it is ambiguous, and it might better be referred to as the acidity constant of dissolved carbon dioxide, as it is particularly useful for calculating the pH of CO₂-containing solutions. A similar situation applies to sulfurous acid (H₂SO₃), which exists in equilibrium with substantial amounts of unhydrated sulfur dioxide.

The second constant is for the dissociation of the bicarbonate ion into the carbonate ion CO₃²⁻:

${\displaystyle {\ce {HCO3^- <=> CO3^{2-}{}+ H+}}}$

K_a2 = 4.69×10⁻¹¹; pK_a2 = 10.329 at 25 °C and ionic strength = 0.0.

The three acidity constants are defined as follows:

${\displaystyle K_{a1}={\frac {[{\text{H}}^{+}][{\text{HCO}}_{3}^{-}]}{[{\text{H}}_{2}{\text{CO}}_{3}]}},}$

${\displaystyle K_{a}{\text{(app)}}={\frac {[{\text{H}}^{+}][{\text{HCO}}_{3}^{-}]}{[{\text{H}}_{2}{\text{CO}}_{3}]+[{\text{CO}}_{2}{\text{(aq)}}]}},}$

${\displaystyle K_{a2}={\frac {[{\text{H}}^{+}][{\text{CO}}_{3}^{2-}]}{[{\text{HCO}}_{3}^{-}]}}.}$

pH and composition of carbonic acid solutions

The composition of a carbonic acid solution is fully determined by the partial pressure ${\displaystyle p_{{\text{CO}}_{2}}}$ of carbon dioxide above the solution. To calculate the composition, account must be taken of

• the following equilibrium between the dissolved CO₂ and the gaseous CO₂ above the solution:

CO₂(gas) ⇌ CO₂(dissolved) with ${\displaystyle \textstyle {\frac {[{\text{CO}}_{2}]_{aq}}{p_{{\text{CO}}_{2}}}}={\frac {1}{k_{\text{H}}}},}$ where k_H = 29.76 atm/(mol/L) (Henry constant) at 25 °C

${\displaystyle \Leftrightarrow [{\text{CO}}_{2}]_{aq}=p_{{\text{CO}}_{2}}/k_{\text{H}}}$

• the hydration equilibrium between dissolved CO₂ and H₂CO₃ with constant ${\displaystyle K_{h}={\tfrac {[{\text{H}}_{2}{\text{CO}}_{3}]_{aq}}{[{\text{CO}}_{2}]_{aq}}}}$ (see above)

${\displaystyle \Leftrightarrow [{\text{H}}_{2}{\text{CO}}_{3}]_{aq}=K_{h}[{\text{CO}}_{2}]_{aq}={\frac {K_{h}}{k_{\text{H}}}}p_{{\text{CO}}_{2}}}$

• the first dissociation equilibrium of carbonic acid (see K_a1 above)

${\displaystyle \Leftrightarrow [{\text{H}}^{+}][{\text{HCO}}_{3}^{-}]=K_{a1}[{\text{H}}_{2}{\text{CO}}_{3}]={\frac {K_{h}K_{a1}}{k_{\text{H}}}}p_{{\text{CO}}_{2}}}$

• the second dissociation equilibrium of carbonic acid (see K_a2 above)
• the dissociation equilibrium of water: ${\displaystyle [{\text{H}}^{+}][{\text{OH}}^{-}]=10^{-14}}$
• the charge neutrality condition ${\displaystyle [{\text{H}}^{+}]=[{\text{OH}}^{-}]+[{\text{HCO}}_{3}^{-}]+2[{\text{CO}}_{3}^{2-}]}$

When isolating [HCO₃⁻] in the first dissociation equilibrium, [HCO₃²⁻] in the second dissociation equilibrium and [OH⁻] in the dissociation equilibrium of water, then substituting all three in the charge neutrality condition, a cubic equation in [H⁺] is obtained, whose numerical solution yields the values for the pH and the concentrations of the different species in the following table. (the second dissociation equilibrium can be neglected for this particular problem, reducing the cubic equation to a simple square root; see remarks below the table.)

${\displaystyle p_{{\text{CO}}_{2}}}$ (atm)	pH	[CO2] (mol/L)	[H2CO3] (mol/L)	[HCO3−] (mol/L)	[CO32−] (mol/L)
1.0 × 10−8	7.00	3.36 × 10−10	5.71 × 10−13	1.42 × 10−09	7.90 × 10−13
1.0 × 10−7	6.94	3.36 × 10−09	5.71 × 10−12	5.90 × 10−09	1.90 × 10−12
1.0 × 10−6	6.81	3.36 × 10−08	5.71 × 10−11	9.16 × 10−08	3.30 × 10−11
1.0 × 10−5	6.42	3.36 × 10−07	5.71 × 10−10	3.78 × 10−07	4.53 × 10−11
1.0 × 10−4	5.92	3.36 × 10−06	5.71 × 10−09	1.19 × 10−06	5.57 × 10−11
3.5 × 10−4	5.65	1.18 × 10−05	2.00 × 10−08	2.23 × 10−06	5.60 × 10−11
1.0 × 10−3	5.42	3.36 × 10−05	5.71 × 10−08	3.78 × 10−06	5.61 × 10−11
1.0 × 10−2	4.92	3.36 × 10−04	5.71 × 10−07	1.19 × 10−05	5.61 × 10−11
1.0 × 10−1	4.42	3.36 × 10−03	5.71 × 10−06	3.78 × 10−05	5.61 × 10−11
1.0 × 10+0	3.92	3.36 × 10−02	5.71 × 10−05	1.20 × 10−04	5.61 × 10−11
2.5 × 10+0	3.72	8.40 × 10−02	1.43 × 10−04	1.89 × 10−04	5.61 × 10−11
1.0 × 10+1	3.42	3.36 × 10−01	5.71 × 10−04	3.78 × 10−04	5.61 × 10−11

• In the total range of pressure, the pH is always much lower than pK_a2 (= 10.3) so that the CO₃²⁻ concentration is always negligible with respect to HCO₃⁻ concentration. In fact, CO₃²⁻ plays no quantitative role in the present calculation (see remark below).
• For vanishing ${\displaystyle p_{{\text{CO}}_{2}}}$, the pH is close to the one of pure water (pH = 7), and the dissolved carbon is essentially in the HCO₃⁻ form.
• For normal atmospheric conditions (${\displaystyle p_{{\text{CO}}_{2}}=3.5\times 10^{-4}}$ atm), we get a slightly acidic solution (pH = 5.7), and the dissolved carbon is now essentially in the CO₂ and HCO₃⁻ forms.
• For a CO₂ pressure typical for bottled carbonated drinks (${\displaystyle p_{{\text{CO}}_{2}}}$ ~ 2.5 atm), we get a relatively acidic medium (pH = 3.7) with a high concentration of dissolved CO₂. These features contribute to the sour and sparkling taste of these drinks.
• Between 2.5 and 10 atm, the pH crosses the pK_a1 value (3.60), giving [H₂CO₃] > [HCO₃⁻] at high pressures.
• A plot of the equilibrium concentrations of these different forms of dissolved inorganic carbon (and which species is dominant) as a function of the pH of the solution is known as a Bjerrum plot.

Remark

As noted above, [CO₃²⁻] may be neglected for this specific problem, resulting in the following very precise analytical expression for [H⁺]:

${\displaystyle [{\text{H}}^{+}]\simeq {\sqrt {10^{-14}+{\frac {K_{h}K_{a1}}{k_{\text{H}}}}p_{{\text{CO}}_{2}}}}}$

Carbonic acid forms as a by-product of CO₂/H₂O irradiation, in addition to carbon monoxide and radical species (HCO and CO₃).[3] Another route to form carbonic acid is protonation of bicarbonates (HCO₃^-) with aqueous HCl or HBr. This has to be done at cryogenic conditions to avoid immediate decomposition of H₂CO₃ to CO₂ and H₂O.[11]. Amorphous H₂CO₃ forms above 120 K, and crystallization takes place above 200 K to give "β-H₂CO₃", as determined by infrared spectroscopy. The spectrum of β-H₂CO₃ agrees very well with the by-product after CO₂/H₂O irradiation.[3] β-H₂CO₃ sublimes at 230 - 260 K largely without decomposition. Matrix-isolation infared spectroscopy allows for the recording of single molecules of H₂CO₃.[12]

The fact that the carbonic acid may form by irradiating a solid H₂O + CO₂ mixture or even by proton-implantation of dry ice alone[13] has given rise to suggestions that H₂CO₃ might be found in outer space or on Mars, where frozen ices of H₂O and CO₂ are found, as well as cosmic rays.[14][15] The surprising stability of sublimed H₂CO₃ up to rather high-temperatures of 260 K even allows for gas-phase H₂CO₃, e.g., above the pole caps of Mars.[12] Ab initio calculations showed that a single molecule of water catalyzes the decomposition of a gas-phase carbonic acid molecule to carbon dioxide and water. In the absence of water, the dissociation of gaseous carbonic acid is predicted to be very slow, with a half-life in the gas-phase of 180,000 years at 300 K.[14] This only applies if the molecules are few and far apart, because it has also been predicted that gas-phase carbonic acid will catalyze its own decomposition by forming dimers, which then break apart into two molecules each of water and carbon dioxide.[16]

Solid "α-carbonic acid" was claimed to be generated by a cryogenic reaction of potassium bicarbonate and a solution of HCl in methanol.[17][18] This claim was disputed in a PhD thesis submitted in January 2014.[19] Instead, isotope labeling experiments point to the involvement of carbonic acid monomethyl ester (CAME). Furthermore, the sublimed solid was suggested to contain CAME monomers and dimers, not H₂CO₃ monomers and dimers as previously claimed.[20] Subsequent matrix-isolation infrared spectra confirmed that CAME rather than carbonic acid is found in the gas-phase above "α-carbonic acid".[21]The assignment as CAME is further corroborated by matrix-isolation of the substance prepared in gas-phase by pyrolysis.[15]

Despite its complicated history, carbonic acid may still appear as distinct polymorphs. Carbonic acid forms upon oxidization of CO with OH-radicals.[22] It is not clear whether carbonic acid prepared in this way needs to be considered as γ-H₂CO₃. The structures of β-H₂CO₃ and γ-H₂CO₃ have not been characterized crystallographically.

• Dihydroxymethylidene (carbonous acid)
• Nonvolatile acid
• Ocean acidification

•  "Climate and Carbonic Acid" in Popular Science Monthly Volume 59, July 1901
• Welch, M. J.; Lifton, J. F.; Seck, J. A. (1969). "Tracer studies with radioactive oxygen-15. Exchange between carbon dioxide and water". J. Phys. Chem. 73 (335): 3351. doi:10.1021/j100844a033.
• Jolly, W. L. (1991). Modern Inorganic Chemistry (2nd Edn.). New York: McGraw-Hill. ISBN 978-0-07-112651-9.
• Moore, M. H.; Khanna, R. (1991). "Infrared and Mass Spectral Studies of Proton Irradiated H2O+Co2 Ice: Evidence for Carbonic Acid Ice: Evidence for Carbonic Acid". Spectrochimica Acta. 47A (2): 255–262. Bibcode:1991AcSpA..47..255M. doi:10.1016/0584-8539(91)80097-3.
• W. Hage, K. R. Liedl; Liedl, E.; Hallbrucker, A; Mayer, E (1998). "Carbonic Acid in the Gas Phase and Its Astrophysical Relevance". Science. 279 (5355): 1332–1335. Bibcode:1998Sci...279.1332H. doi:10.1126/science.279.5355.1332. PMID 9478889.
• Hage, W.; Hallbrucker, A.; Mayer, E. (1995). "A Polymorph of Carbonic Acid and Its Possible Astrophysical Relevance". J. Chem. Soc. Faraday Trans. 91 (17): 2823–2826. Bibcode:1995JCSFT..91.2823H. doi:10.1039/ft9959102823.

• Ask a Scientist: Carbonic Acid Decomposition (archive)
• Why was the existence of carbonic acid unfairly doubted for so long?
• Carbonic acid/bicarbonate/carbonate equilibrium in water: pH of solutions, buffer capacity, titration and species distribution vs. pH computed with a free spreadsheet
• How to calculate concentration of Carbonic Acid in Water