Equilibrio De Co2 En Agua

Carbon dioxide in water equilibrium


1. Introduction

Carbon dioxide does dissolve in water, however the system is somewhat complex[1].

First the CO2 dissolves according to:

(1) CO2 (g)  CO2 (l)

At room temperature, the solubility of carbon dioxide is about 90 cm3 of CO2 per 100 ml water (cl/cg = 0.8).

Any water-soluble gas becomes more soluble as the temperature decreases,due to the thermodynamics of the reaction: GAS (l)  GAS (g). The entropy change, S, of this reaction is positive because the gas molecules are less constrained than the gas molecules in solution. The change in Free energy of reaction with an increase in temperature is -S. This effect is particularly large for gases like CO2 that undergo specific reactions with water.

Equilibrium isestablished between the dissolved CO2 and H2CO3, carbonic acid.

(2) CO2 (l) + H2O (l)  H2CO3 (l)

This reaction is kinetically slow. At equilibrium, only a small fraction (ca. 0.2 - 1%) of the dissolved CO2 is actually converted to H2CO3. Most of the CO2 remains as solvated molecular CO2. As equation:

In fact, the pKa most reported for carbonic acid (pKa1 = 6.37) is not really the true pKa ofcarbonic acid. Rather, it is the pKa of the equilibrium mixture of CO2 (l) and carbonic acid. Carbonic acid is actually a much stronger acid than this, with a true pKa1 value of 3.58. However these values are also temperature dependent.

Carbonic acid is a weak acid that dissociates in two steps[2].

(3) H2CO3 + H2O  H3O+ + HCO3- pKa1 (25 °C) = 6.37

(4) HCO3- + H2O  H3O+ + CO32-pKa2 (25 °C) = 10.25

Note that these carbonate anions can interact with the cations present in the water to form insoluble carbonates. For instance, if Ca2+ is present limestone, CaCO3 is formed and if Mg2+ is present MgCO3 is formed. The formation of these deposits is an additional driving force that can pull the equilibrium more to the right resulting in acidification of the water[2].(5) Ca2+ + CO32-  CaCO3 S = 4.96 x 10-9 (S = solubility constant)

(6) Mg2+ + CO32-  MgCO3 S = 6.82 x 10-6

The above presented more schematically:

+ H2O + H2O + H2O + Ca2+
CO2(g)  CO2 (l)  H2CO3  HCO3-  CO32-  CaCO3 
+ H3O+ + H3O+

Note that the reverse is also true and that the scheme represents the solubility of CaCO3in an acidic solution resulting in the liberation of CO2 in the atmosphere.
2. Deriving [H2CO3]

If we assume CO2 is a simple gas we can apply Henry’s law that describes the equilibrium between vapor and liquid. Thus:

pCO2 = K . xCO2

where pCO2 is the partial pressure of the gas in the bulk atmosphere (Pa), K is a constant (Pa) and xCO2 is the equilibrium mole fraction of solute inliquid phase.

The solubility of CO2 is temperature dependent, as shown in Table 1: Solubility of CO2 at a partial pressure for CO2 of 1 bar abs[3].
Table 1: Solubility of CO2 at a partial pressure for CO2 of 1 bar abs[3].
Temperature (oC) 0 10 20 30 40 50 80 100
Solubility
(cm3 CO2/g water) 1.8 1.3 0.88 0.65 0.52 0.43 0.29 0.26

Furthermore, as stated above, CO2 reacts with the water ondissolution and therefore one would expect that Henry’s law has to be modified.

However, according to Carrol and Mather [4] a form of Henry’s law can be used for modeling the solubility of carbon dioxide in water for pressures up to about 100 MPa, as can be seen in Figure 1: Henry's Constant for Carbon Dioxide in Water - from Carroll et al. [4].


Figure 1: Henry's Constant for Carbon Dioxidein Water - from Carroll et al. [4]

They conclude that the Krichevsky-Kasarnovsky Equation, which can be derived from Henry’s Law, can be used to model the system CO2-H2O at temperatures below 100 oC.

Thus in the range of interest, 20-35 °C, the Henry coefficient for CO2 in water goes from 150 - 200 MPa/mole fraction

Applying the above to the conditions under investigation:
Temperature...