Open System: Exchange of CO2 and O2

The Thermodynamic System and its Environment

The aqueous solution (together with its mineral assembly) represents our ‘thermodynamic system’. Three types of coupling to the environment (e.g., the atmosphere) are distinguished:

  Exchange of Energy Exchange of Matter
Isolated system no no
Closed system yes no
Open system yes yes

In hydrochemistry, equilibrium calculations are usually performed for the closed system. Additionally, aqion allows calculations for the open system:

  •  CO2 exchange by presetting the CO2 partial pressure (or pCO2)
  •  O2 exchange by presetting the redox potential (or pe value)

In both cases just as much CO2 or O2 is added or removed from the water until the preset pCO2 or pe value is reached. The supply of CO2 and O2 in the environment is unlimited.

What is the aim of this procedure?

Using the ‘open CO2 system’ we are able to achieve chemical equilibrium of the aqueous solution with the CO2 in the atmosphere.1 Since CO2 is an acid (i.e. carbonic acid), the CO2 exchange controls the pH value.

On the other hand, by exchanging O2 – as the ultimate oxidizing agent – the initial water can be oxidized (pe ≥ 6) or reduced (pe < 0), i.e. we can change the redox potential of the aqueous solution (and trigger the precipitation of specific minerals).

Settings. The values of pCO2 and/or pe are set either in the input window or – in case of reactions (button Reac) – in the corresponding setup panel (button Setup). These are the options of the two principal calculation pathway.

The Specific Feature of the Open-System Calculations

Open-system calculations cannot be completely replaced by the reaction module which simply adds chemicals to the water. This is because the exchange of CO2 and/or O2 implies both addition and removal of chemicals:

CO2 and O2 in the open and closed system

[Remark: There is a striking similarity between gas exchange and mineral dissolution/precipitation. In both cases the amount that is added or removed from the water is determined by the chemical equilibrium constant: the Henry constant KH for gases and the solubility product Ksp for minerals.2]

Two examples should clarify the idea behind the open-system calculations.

Example 1: Equilibrium with Atmospheric CO2

Given a 10 mM CaCl2 solution we perform the calculations in two different ways: the first is based on pCO2, the second is based on the addition of the ‘reactant’ CO2.

Way 1. To generate the 10 mM CaCl2 solution: button H2O, button Reac, then enter 10 mmol/L CaCl2. To bring the water into CO2(gas) equilibrium click on Setup and activate the checkbox “Open CO2 System” (the default value pCO2 = 3.408 represents the partial pressure of CO2 in the atmosphere).

CaCl2 in equilibrium with CO2

Then button Start. In the overview schema click on Details, that outputs the results: pH = 5.59 and DIC = 0.0159 mM (as shown on the right-hand side).

By click on button next (two times) you get the data that characterizes the carbonate system – among them the calculated pCO2 value. Evidently, in this case pCO2 is 3.41.

Way 2. The calculation above tells us that 0.0159 mM DIC is required to attain the equilibrium state. This knowledge allows us to generate the equilibrium solution by adding two reactants to pure water:

CaCl2 10 mM
CO2 0.0159 mM

CaCl2 plus CO2

If you perform this reaction calculation using Reac (but now without pCO2), the same water composition is obtained: pH = 5.59 and DIC = 0.0159 mM (see right screenshot).

Note that we get the correct result because we know the dosage of CO2 beforehand. Otherwise you should trial and error until the desired pCO2 value of 3.41 (displayed in the carbonate-system output panel) is achieved. Thus, the second way is rather impractical.

Example 2: Redox Equilibrium at pe = 10 (Oxidation)

A solution of 10 mM FeCl2 has pH 5.88 and pe -1.8, which manifests a water in a reducing state. The aim is to enhance the pe value to 10 (oxidation). Again as in Example 1 we solve this problem in two ways.

Way 1. Button H2O, button Reac, then enter 10 mmol/L FeCl2. To set the pe value at 10 click on Setup and activate the checkbox “Open Redox System”.

FeCl2 in open O2 system

Run the calculation with button Start. The obtained oxidized water has pH = 3.67 and pe = 10.

Under these oxidizing conditions, the amorphous mineral Fe(OH)3 is supersaturated and precipitates (but this is not relevant for our further considerations).

In the subsequent output table you find in the raw “O2 exch” the amount of O2 added to the water: 0.145 mM. This information will be used in the second calculation below.

Way 2. We repeat the above calculation by adding two reactants to pure water:

FeCl2 10 mM
O2 0.145 mM

This calculation using Reac (but now without setting the pe value) produces exactly the same oxidized water with pH = 3.67 and pe = 10.

As mentioned in Example 1, this approach is impractical because it requires the knowledge of the amount of the O2-dosage beforehand.


  1. More about the CO2 exchange is presented as PowerPoint

  2. The similarity of gas exchange and mineral dissolution/precipitation is the reason why PhreeqC treats both gases and minerals by the same procedure called “EQUILIBRIUM_PHASES”. 

[last modified: 2018-04-30]