Carbonic acid

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Carbonic acid
Image:Carbonic-acid-2D.png Image:Carbonic-acid-3D-vdW.png
Other names	Carbon dioxide solution
Molecular formula	H₂CO₃
SMILES	C(=O)(O)O
Molar mass	62.03 g/mol
CAS number	463-79-6
Density	1.0 g/cm³ (dilute solution)
Solubility (water)	exists only in solution
Acidity (pK_a)	6.36 (see text) 10.25
Disclaimer and references

Carbonic acid (ancient name acid of air or aerial acid) has the formula H₂CO₃. It is also a name sometimes given to solutions of carbon dioxide in water, which contain small amounts of H₂CO₃. The salts of carbonic acids are called bicarbonates (or hydrogencarbonates) and carbonates.

Carbon dioxide dissolved in water is in equilibrium with carbonic acid:

CO₂ + H₂O ⇌ H₂CO₃

The equilibrium constant at 25°C is K_h= 1.70×10⁻³: hence, the majority of the carbon dioxide is not converted into carbonic acid and stays 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 equilibrium between carbon dioxide and carbonic acid is very important for controlling the acidity of body fluids, and almost all living organisms have an enzyme, carbonic anhydrase, which catalyzes the conversion between the two compounds, increasing the reaction rate by a factor of nearly a billion.

1 Acidity of carbonic acid
- 1.1 pH and composition of a pure carbonic acid solution
2 Instability of carbonic acid
3 Carbonic acid and rain water
4 References
5 External links

[edit] Acidity of carbonic acid

Carbonic acid has two acidic hydrogens and so two dissociation constants:

H₂CO₃ ⇌ HCO₃⁻ + H⁺

K_a1 = 2.5×10⁻⁴ mol/L; pK_a1 = 3.60 at 25 °C.

HCO₃⁻ ⇌ CO₃²⁻ + H⁺

K_a2 = 5.61×10⁻¹¹ mol/L; pK_a2 = 10.25 at 25 °C.

Care must be taken when quoting and using the first dissociation constant of carbonic acid. The value quoted above is correct for the H₂CO₃ molecule, and shows that it is a stronger acid than acetic acid or formic acid: this might be expected from the influence of the electronegative oxygen substituent. However, carbonic acid only ever exists in solution in equilibrium with carbon dioxide, and so the concentration of H₂CO₃ is much lower than the concentration of CO₂, reducing the measured acidity. The equation may be rewritten as follows (c.f. sulfurous acid):

CO₂ + H₂O ⇌ HCO₃⁻ + H⁺

K_a = 4.30×10⁻⁷ mol/L; pK_a = 6.36.

This figure is often quoted as the dissociation constant of carbonic acid, although this is ambiguous: it might better be referred to as the acidity constant of carbon dioxide, as it is particularly useful for calculating the pH of CO₂ solutions.

[edit] pH and composition of a pure carbonic acid solution

At a given temperature, the composition of a pure carbonic acid solution (or of a pure CO₂ solution) is completely determined by the partial pressure <math>\scriptstyle p_{CO_2}</math> of carbon dioxide above the solution. To calculate this composition, account must be taken of the above equilibria between the three different carbonate forms (H₂CO₃, HCO₃⁻ and CO₃²⁻) as well as of the hydratation equilibrium between dissolved CO₂ and H₂CO₃ with constant <math>\scriptstyle K_h=\frac{[H_2CO_3]}{[CO_2]}</math> (see above) and of the following equilibrium between the dissolved CO₂ and the gaseous CO₂ above the solution:

CO₂(gas) ↔ CO₂(dissolved) with <math>\scriptstyle \frac{[CO_2]}{p_{CO_2}}=\frac{1}{k'_c}</math> where k'_c=29.76 atm/(mol/L) at 25°C (Henry constant)

The corresponding equilibrium equations together with the <math>\scriptstyle[H^+][OH^-]=10^{-14}</math> relation and the neutrality condition <math>\scriptstyle[H^+]=[OH^-]+[HCO_3^-]+2[CO_3^{2-}]</math> result in six equations for the six unknowns [CO₂], [H₂CO₃], [H⁺], [OH⁻], [HCO₃⁻] and [CO₃²⁻], showing that the composition of the solution is fully determined by <math>\scriptstyle p_{CO_2}</math>. The equation obtained for [H⁺] is a cubic whose numerical solution yields the following values for the pH and the different species concentrations:

<math>\scriptstyle p_{CO_2}</math> (atm)	pH	[CO₂] (mol/L)	[H₂CO₃] (mol/L)	[HCO₃⁻] (mol/L)	[CO₃²⁻] (mol/L)
10⁻⁸	7.00	3.36 x 10⁻¹⁰	5.71 x 10⁻¹³	1.42 x 10⁻⁹	7.90 x 10⁻¹³
10⁻⁶	6.81	3.36 x 10⁻⁸	5.71 x 10⁻¹¹	9.16 x 10⁻⁸	3.30 x 10⁻¹¹
10⁻⁴	5.92	3.36 x 10⁻⁶	5.71 x 10⁻⁹	1.19 x 10⁻⁶	5.57 x 10⁻¹¹
3.5 x 10⁻⁴	5.65	1.18 x 10⁻⁵	2.00 x 10⁻⁸	2.23 x 10⁻⁶	5.60 x 10⁻¹¹
10⁻³	5.42	3.36 x 10⁻⁵	5.71 x 10⁻⁸	3.78 x 10⁻⁶	5.61 x 10⁻¹¹
10⁻²	4.92	3.36 x 10⁻⁴	5.71 x 10⁻⁷	1.19 x 10⁻⁵	5.61 x 10⁻¹¹
10⁻¹	4.42	3.36 x 10⁻³	5.71 x 10⁻⁶	3.78 x 10⁻⁵	5.61 x 10⁻¹¹
1	3.92	3.36 x 10⁻²	5.71 x 10⁻⁵	1.20 x 10⁻⁴	5.61 x 10⁻¹¹
2.5	3.72	8.40 x 10⁻²	1.43 x 10⁻⁴	1.89 x 10⁻⁴	5.61 x 10⁻¹¹
10	3.42	0.336	5.71 x 10⁻⁴	3.78 x 10⁻⁴	5.61 x 10⁻¹¹

We see that in the total range of pressure, the pH is always largely lower than pKa₂ so that the CO₃²⁻ concentration is always negligible with respect to HCO₃⁻ concentration. In fact CO₃²⁻ play no quantative role in the present calculation (see remark below).

For vanishing <math>\scriptstyle p_{CO_2}</math>, the pH is close to the one of pure water (pH = 7) and the dissolved carbon is essentially in the HCO₃⁻ form.

For normal atmospherics conditions (<math>\scriptstyle p_{CO_2}=3.5\times 10^{-4}</math> atm), we get a slightly acid solution (pH = 5.7) and the dissolved carbon is now essentially in the CO₂ form. From this pressure on, [OH⁻] becomes also negligible so that the ionized part of the solution is now an equimolar mixture of H⁺ and HCO₃⁻.

For a CO₂ pressure typical of the one in soda drinks bottles (<math>\scriptstyle p_{CO_2}</math> ~ 2.5 atm), we get a relatively acid medium (pH = 3.7) with a high concentration of dissolved CO₂. These features are responsible for the sour and sparkling taste of these drinks.

Between 2.5 and 10 atm, the pH crosses the pKa₁ value (3.60) giving a dominant H₂CO₃ concentration (with respect to HCO₃⁻) at high pressures.

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

<math>\scriptstyle[H^+] \simeq \left( 10^{-14}+\frac {K_hK_{a1}}{k_c^\prime} p_{CO_2}\right)^{1/2}</math>

[edit] Instability of carbonic acid

It has long been recognized that it is impossible to obtain pure hydrogen bicarbonate at room temperatures (about 20 °C or about 70 °F). However, in 1991 scientists at NASA's Goddard Space Flight Center (USA) succeeded in making the first pure H₂CO₃ samples. They did so by exposing a frozen mixture of water and carbon dioxide to high-energy radiation, and then warming to remove the excess water. The carbonic acid that remained was characterized by infrared spectroscopy. The fact that the carbonic acid was prepared by irradiating a solid H₂O + CO₂ mixture has given rise to suggestions that H₂CO₃ might be found in outer space, where frozen ices of H₂O and CO₂ are common, as are cosmic rays and ultraviolet light, to help them react.

It has since been shown, by theoretical calculations, that the presence of even a single molecule of water causes carbonic acid to revert to carbon dioxide and water fairly quickly. Pure carbonic acid is predicted to be stable in the gas phase, in the absence of water, with a calculated half-life of 180,000 years.

There is a hypothetical acid orthocarbonic acid which is even more hydrated, being </sub>C(OH)₄.

[edit] Carbonic acid and rain water

A solution of carbon dioxide in water in equilibrium with the atmosphere (0.033% CO₂) has a pH of 5.6. Rain water is normally not quite saturated in CO₂, and has a pH of around 6 in the absence of atmospheric pollutants. This effect is separate from the phenomenon of acid rain, where industrial pollutants such as sulfur dioxide dissolve in rain water and lower its pH drastically. However, the acidity of rain water has important geological consequences for carbonate rocks such as chalk and limestone. An equilibrium is established between the calcium carbonate of the rock and calcium bicarbonate in solution:

CaCO₃ + CO₂ + H₂O ⇌ Ca(HCO₃)₂

This can erode underground caverns around fault lines which water runs down. As the calcium-rich water evaporates, the calcium carbonate precipitates, often as stalactites and stalagmites. Water drawn from chalk aquifers contains dissolved calcium carbonate, and is described as "hard".

[edit] References

Welch, M. J.; Lipton, J. F.; Seck, J. A. (1969). J. Phys. Chem. 73:3351.
Jolly, W. L. (1991). Modern Inorganic Chemistry (2nd Edn.). New York: MgGraw-Hill. ISBN 0-07-112651-1.
M. H. Moore and R. Khanna "Infrared and Mass Spectral Studies of Proton Irradiated H2O+CO2 Ice: Evidence for Carbonic Acid", Spectrochimica Acta, 47A, pp. 255-262 (1991)
T. Loerting, C. Tautermann, R.T. Kroemer, I. Kohl, E. Mayer, A. Hallbrucker, K. R. Leidl "On the Surprising Kinetic Stability of Carbonic Acid", Angew. Chem. Int. Ed., 39, pp. 891-895 (2001)