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The CO2-Water Cluster

V Carbon dioxide hydration

V Carbon dioxide compared with carbon monoxide


It is difficult to remove traces of carbon dioxide from aqueous solution and, once removed, aqueous solutions rapidly take up CO2 from any exposure to the atmosphere.

Carbonic acid, H2CO3


carbonic acid, H2CO3
CO2 hydration

 CO2 undergoes a slight hydration (~ 0.26 %) to H2CO3 (O=C(OH)2, see right) in solution with the resulting weakly acidic H2CO3 ionizing slightly.


pKa1 values along the saturation line


pKa1 values along the saturation line











The pKa1 varies with temperature ( [1862] see left) due to the higher CO2 solubility at low temperatures and as described elsewhere.


The following equilibria occur (data at 25 °C) with some debate over the exact values of the constants [1852, 2192].


CO2 (g) + H2O = CO2 (aq) (slow)

KH is the partial pressure of CO2 over the aqueous concentration of CO2

KH = 29 1 [IAPWS]
CO2 (aq) + H2O = H2CO3 (slow)

KD is the aqueous concentration of CO2 over the concentration of carbonic acid

KD = 590
H2CO3 + H2O = H3O+ + HCO3- (fast)

K1 is the hydrogen ion concentration times the bicarbonate concentration over the concentration of carbonic acid

K1 = 0.25 mM

Ka1 is the hydrogen ion concentration times the bicarbonate concentration over the sum of the concentration of carbonic acid and the concentration of dissolved CO2

Ka1 = 0.45 µM (apparent)
HCO3- + H2O= H3O+ + CO32- (fast)

Ka2 is the hydrogen ion concentration times the carbonate concentration over the concentration of bicarbonate

Ka2 = 0.047 nM

1 [CO2] is dissolved CO2, mol L-1 and, if determined from solubility also contains H2CO3, HCO3- and CO32-;

pCO2 is partial pressure of CO2 in the gas phase, atm.


Carbon dioxide (CO2) aqueous equilibria; mouse over


carbon dioxide (CO2) aqueous equilibria




There is some dispute over the reaction of CO2 (aq) with H2O [2185], with the possibility that the reactions are


CO2 (aq) +2 H2O =H3O+ + HCO3- (slow)

H3O+ + HCO3-=H2CO3 + H2O (fast)


The relative concentrations of the CO2 dissolution products are shown right [2317] with absolute concentrations corresponding to 0.032% atmospheric CO2 shown on mousing over the image.


As an example, water in equilibrium (25 °C) with pCO2 = 1 atm forms about 33.6 mM CO2 (aq) solution of pH 3.9, containing about 57 µM carbonic acid (H2CO3), 0.12 mM HCO3- and 0.056 nM CO32- .

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Carbon dioxide compared with carbon monoxide

Carbon dioxide (CO2) and carbon monoxide (CO) solubilities


CO2 and CO solubilities



Carbon dioxide (CO2) is more soluble than carbon monoxide (CO) in water [ IAPWS ], which is strange as it is both larger and without a dipole moment. This has been explained by specific hydrogen bonding between the oxygen atoms [ 166 ] in CO2 and water molecules plus effects from loss of vibration energy [ 2192 ]. This explanation, fails however at low temperatures [ 2192 ] where the influence of the change in water structuring becomes more important.


Charge on the CO and CO2 molecules as given by

ab initio 6-311** calculation

Charge on the CO and CO2 molecules as given by ab initio 6-311** calculation

CO is proposed as being less soluble as it only has a very small dipole (0.122 D), and low charge on the oxygen that weakens possible hydrogen bonding. Surprisingly, the global minimum energy for singly hydrated CO has the CO molecule lying in the water plane with the carbon atom pointing towards the H atom of the H2O molecule [3104].



CO2 in an 18-molecule water dodecahedral cluster


CO2 in an 18-molecule water dodecahedral cluster



CO2 has much weaker hydrogen bonding than H2CO3to H2O [2230]. The CO2 may form a hydration shell from a symmetrical dodecahedral arrangement of 18 water molecules where each CO2 oxygen atom is hydrogen-bonded to three water molecules. Such hydrogen bonding is likely to be weak, transient and exchanging between a continuum of structures. This allows some cooperation between the hydrogen bonding at both ends of the CO2 molecule.


Such a cluster can form the central part of an icosahedral water cluster (CO2(H2O)278) possessing just two defects (water molecules with only 3 rather than 4 hydrogen bonds). In this model, there are six water molecules closest to the CO2 in agreement with many studies [499].

Correlation functions for CO2 within an icosahedral water cluster


Carbon-oxygen and carbon-hydrogen pair correlation functions for carbon dioxide within an icosahedral water cluster.


The calculated carbon-oxygen pair correlation functions (PCF) are remarkably similar to those predicted by the icosahedral model. The dashed red lines [166] and solid blue lines [2332] are the calculated pair correlation functions, between the carbon atom in CO2 and the oxygen atoms of water, and the bars are the predictions from the icosahedral model. The solid bars were published 14 years before the solid blue line. Note that a similarly good fit is apparent if the central cluster is tetrakaidecahedral rather than dodecahedral. Such occupied 51262 inner-shell clusters are found to be more stable using theoretical modeling [876].


It is notable that calculated pair correlation functions between CO and water [166] are consistent with the CO molecules sitting centrally (clathrate-like) in expanded icosahedral water clusters; CO only forming extremely weak complexes to water (major, HOH---CO; minor H2O---OC).


For interactive Figures of the central dodecahedral cluster, see  Jmol.


At high pressures (for example, >2 MPa) and low temperatures (for example, <4 °C) CO2 forms crystalline clathrates (type-Iclathrate, 46 H2O:8 CO2 maximum), within a cubic arrangement of two dodecahedral (512) and six tetrakaidecahedral (51262) cages. In these structures there is no hydrogen bonding between the CO2 guest molecules and the water clathrate lattice and the CO2 molecules occupy both cages but prefer the tetrakaidecahedral cages.

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