Overview Data Input Data Output DIC Charge Balance Physico-Chem Params Reactions Redox Mineral Phases

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 in two respects:

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

In both cases, as much CO₂ or O₂ is added to 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 pathways.

The Specific Feature of the Open-System Calculations

Open-system calculations differ from 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:

[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 K_H for gases and the solubility product K_sp 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). Then button Start.

A blue overview schema opens. In the overview schema, click on Details, that outputs the results: pH = 5.59 and DIC = 0.0161 mM (as shown on the right).

By click on button next (two times) you get the data that characterizes the carbonate system — among them the calculated pCO2 (which corresponds to the preset value 3.408).

Way 2. The calculation above tells us that 0.0161 mM DIC is required to attain the equilibrium state. This knowledge allows us to generate the same equilibrium solution by adding two reactants to pure water:

CaCl2	10 mM
CO2	0.0161 mM

Let us perform this calculation, but now without presetting of pCO2: button Reac, activate checkbox “two or more reactants” and enter the two reactants (don’t forget to uncheck the checkbox “Open CO2 System”).

Click on Start. As shown on the right, the same water composition is obtained: pH = 5.59 (and DIC = 0.0161 mM).

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 is achieved. Thus, way 2 is inefficient to obtain a solution that is in equilibrium with the CO₂ of the atmosphere.

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). 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”.

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

Footnotes