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The CO₂-Water Cluster

Hard water
Water softening
Magnetic descaling

Calcium carbonate equilibria

Carbon dioxide

Carbon dioxide hydration and equilibria

Carbon dioxide compared with carbon monoxide

CO₂ clathrate hydrates

Carbonic acid (H₂CO₃)

 

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

Carbon Dioxide

Carbon dioxide (CO₂) is a colorless, odorless gas. Liquid CO₂ only forms above 0.51 MPa, liquid density 1101 kg ˣ m⁻³, -37 °C; sublimation point, -78.5 °C, 0.10135 MPa, solid density 1562 kg ˣ m⁻³ increasing with decreasing temperature; triple point, 216.55 K, 518 kPa, gaseous density, 1.98 kg ˣ m⁻³ (at 0 °C, 100 kPa); critical temperature 31.1 °C, critical pressure 7.38 MPa, critical density 467.6 kg ˣ m⁻³, ¹³C content 1.1%. CO₂ is very soluble in water with 3.346 grams of CO₂ dissolving in water at 0 °C (1.713 L_{CO2 gas} ˣ L^{−1_{liquid water}} at 0.10135 MPa partial pressure CO₂). CO₂ is a linear molecule with the C=O bond length 0.114 nm and charges on the O and C atoms of -0.446 and + 0.892, respectively (using ab initio 6-311** calculation).

 

Massive deposits of solid CO₂ have been discovered at Mars's south pole and appear to be flowing like glaciers on Earth. It has zero dipole moment with low thermal and electrical conductivity. Adding dry ice to water causes a thick water fog to form from the liquid water. The common name for solid form of carbon dioxide is 'dry ice', first made commercially in 1925 by the DryIce Corporation of America.

CO₂ hydration and equilibria

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

 

The

pK_a1

 

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

The following equilibria occur (data at 25 °C, with all constants changing with temperature) with some debate over the exact values of the constants [1852, 2192]. Calcium carbonate equilibria are given on the water descaling page.

 

CO2 (g) + H2O CO2 (aq) (slow)		KH = 29 1 [IAPWS]
CO2 (aq) + H2O H2CO3 (slow)		KD = 590
HCO3− CO2 (aq) + H2O H2CO3 (fast)
H2CO3 + H2O H3O+ + HCO3− (fast)		K1 = 0.25 mM
		Ka1 = 0.45 µM (apparent) pKa1 = 6.35
HCO3− + H2O H3O+ + CO32− (fast)		Ka2 = 0.047 nM pKa2 = 10.33

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

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

 

H₂O + CO₂ H₂CO₃ catalyzed by HCO₃⁻ [3819] as given by ab initio 6-311** calculations.

Bicarbonate can similarly catalyze many hydrogen transfer reactions (e.g., keto-enol and imine-amine)

 

These equilibria are shifted in alkaline solution (pH > ~5) where OH⁻ ions remove the H₃O⁺ ions

 

H₃O⁺_(aq) + OH⁻_(aq)   2 H₂O_(aq)                      K_eq = 10¹⁴ ; 25 °C

 

Thus in alkaline solutions, the total concentration of carbonate carbon species ([H₂CO₃] + [HCO₃⁻ ] + [CO₃²⁻]) increases considerably (mouse over the figure below right). In addition to these equilibria, there should always be a balance of charges in solution (positive charges = negative charges), thus typically,

 

[H₃O⁺] + [Na⁺] + [K⁺] + 2 ˣ [Ca²⁺] + 2 ˣ [Mg²⁺] = [ Cl⁻] + 2 ˣ [S0₄²⁻] + [HCO₃⁻] + 2 ˣ [CO₃²⁻] + [OH⁻]

 

---

 

H₂O + CO₃^2- HCO₃⁻ + HO⁻ as given by ab initio 6-311** calculations

 

 

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⁻. Water in equilibrium with the atmosphere (0.04 %) has a concentration of about 15 µM CO₂ (aq) and a pH of about 5.6.

 

If CO₂-containing solutions are frozen, the excess CO₂ appears to hydrate to form H₂CO₃ dissociating to give bicarbonate anions upon thawing [3450].

 

Physiological acid-base balance may be described in different ways to the above to aid the understanding of complex acid-base clinical disorders [3364].

 

The variation of CO₂ solubility and pH has been modeled [4005]. Although CO₂ in solution under ambient conditions is mainly dissolved CO₂ (aq), under pressure in deep Earth conditions (at 11 GPa and 1000 K), it is found almost entirely as solvated carbonate CO₃²⁻(aq) and bicarbonate HCO₃⁻ (aq), where carbonic acid H₂CO₃(aq) is more abundant than CO₂(aq) [3764].

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Carbon dioxide compared with carbon monoxide

Carbon dioxide may be reduced to carbon monoxide [4351].

           CO₂ + e⁻   CO₂⁻       E°' = -1.85 V

      CO₂⁻ + H₂O   [CO₂H] + OH⁻

      [CO₂H] + e⁻   CO + OH⁻

 

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. The solubilities are explained by specific hydrogen-bonding between the oxygen atoms [166 ] in CO₂ and water molecules and the of vibrational energy [2192 ]. However, this explanation fails at low temperatures [2192 ], where the influence of the change in water structuring becomes critical; the solubility of CO₂ increasing dramatically in supercooled water.

 

CO is proposed as being less soluble as it only has a very small dipole (0.122 D) and a low charge on the oxygen weakens possible hydrogen bonding. Surprisingly, the 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, 3802].

 

O=C···H-O-H

 

CO₂(aq) has much weaker hydrogen bonding than the hydrogen bonds connecting H₂CO₃ to H₂O [2230]. The CO₂ may be considered hydrophobic. It forms either a hydration shell from the dodecahedral arrangement of 18 water molecules, where each CO2 oxygen atom is hydrogen-bonded to three water molecules, or a complete 20-molecule dodecahedral shell. Probably an oscillating combination of both. Such hydrogen bonding is likely to be weak, transient, and exchanging between a continuum of structures. Probaly an oscillating combination of both. 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. The weak hydrogen bonds formed between water and CO₂ may easily break (forming surrounding whole or partial dodecahedra) and exchange. Further, it may undergo temperature-dependent structural transformations at near-physiological temperatures [3675].

 

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

 

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. 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]. A similar distribution is given from the analysis of ab initio molecular dynamics simulations [4405].

 

Notably, the 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.

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CO₂ and CO clathrate hydrates

At high pressures (for example, >2 MPa) and low temperatures (for example, <4 °C) CO₂, forms crystalline clathrates (type CS-I clathrate, 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.

 

Compression of CO₂-clathrate hydrates gives rise to a range of products [3059], including solid H₂CO₃ and dry ice (solid CO₂). CO₂-filled ice is formed from the CS-I hydrate [3059c]. In contrast, CS-II gives a chiral structure [3059b], similar to ice-XVII, which is created with large open spiral channels containing the freely-moving CO₂ guest molecules (1:3.5 CO₂: H₂O, compared with 1:2 H₂: H₂O for the pre-ice-XVII structure). It has been suggested that ice XVII may be used as a cheap, practical, and environmentally friendly microporous material for the storage of CO₂.

 

Carbon dioxide clathrate formation has been proposed as a method of tackling global warming on its own (by removing CO₂from the atmosphere) or in combination with releasing methane clathrate (for energy production) from the seafloor. Liquid CO₂ quickly reacts with water under sufficient pressure (e.g., on the seafloor, at a depth of 2700 m - 4500 m) to form its clathrate hydrate (CO₂.5.75 H₂O), then would swell to many times its original size. This reaction is strongly exothermic [271 kJ ˣ kg⁻¹ of water). As the clathrates later dissolved, the use of this methodology for the permanent disposal of CO₂ on the seafloor was concluded as probably not realistic [3328].

 

Carbon monoxide also preferably forms S-I clathrate hydrate at low pressures but with S-II hydrate forming on storage at 10 MPa and 252 K for 12 weeks. The large cages of the CS-I carbon monoxide hydrate are able t0 absorb or release CO guest molecules with possible multiple occupancies of up to 1.39. In contrast, the small cages remain singly occupied [3327]. The stretching Raman bands of the encapsulated CO molecule differ depending on whether they are small (5¹²; slight Raman shift, cm⁻¹) or large (5¹²6²; greater Raman shift, cm⁻¹) clusters.

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Carbonic acid (H₂CO₃)

Carbonic acid in aqueous solution plays an essential role in living systems as part of the bicarbonate buffer system to maintain acid-base homeostasis (see above). It forms carbonates and bicarbonates. Although molecular H₂CO₃ exists in an aqueous solution, it decomposes to carbon dioxide and water on any isolation attempts. In contrast to the bisulfate ion, the bicarbonate ion is a base; i.e., it donates its proton only in alkaline solutions [4005].

 

However, both solid and gaseous carbonic acid has been prepared by other methods [3325]. The solid sublimes directly to the vapor state on warming up to -30 °C. Spectroscopic analysis showed that the carbonic acid vapor contained cis-cis and cis-trans monomers plus a hydrogen-bonded cyclic dimer (H₂CO₃)₂.

 

Carbonic acid forms complexes with halide ions (see left) in the gas phase, as characterized by negative ion photoelectron spectroscopy and ab initio calculations [4017].

 

A crystalline hydrate of H₂CO₃ (H₂CO₃.H₂O) is formed at high pressures and low temperatures (6.5 GPa, 140°C)) where the molecules lie co-planar in flat sheets [3326].

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This page was established in 2004 and last updated by Martin Chaplin on 12 January, 2022

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