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Carbonate Species vs pH (Closed System)

Given is a 10^-3 molar carbonate solution (closed system with 1 mM DIC). What is the species distribution in the pH range between 1 and 13?

Preliminary Considerations

One of the most celebrated diagrams in hydrochemistry is undoubtedly the carbonate species distribution vs. pH (something as shown below). The carbonate speciation is the outcome of a set of equations for the pure CO₂-H₂O system.¹

However: For a given value of DIC, say 1 mM, the pH is fixed to 4.68 in a pure CO₂ solution at 25 and there is no chance to alter the pH unless the pure system is extended by an additional degree of freedom. This can be done by addition of NaOH (to increase pH) or HCl (to decrease pH):

To cover the desired pH range from 1 to 13, a series of options are available (even infinitely many). Here are only three:

Option 1. Start with the pure CO₂ solution and add successively HCl until pH 1 is reached. Then, take again the pure CO₂ solution and add successively NaOH until pH 13.

Option 2. Prepare an initial solution with pH 13 (by addition of 137.2 mM NaOH). Then add to this solution successively HCl until pH 1 is reached.

Option 3. Prepare an initial solution with pH 1 (by addition of 122.4 mM HCl). Then add to this solution successively NaOH until pH 13 is reached.

[Note: The titration curves for each option differ from another, at least slightly. This is caused by two things: (i) different ionic strengths and (ii) Na forms aqueous complexes such like NaHCO₃ and NaCO₃^-, whereas Cl does not.]

Titration Calculations for Option 1

There are two ways to perform the titration calculation for Option 1:²

Way 1. Choose the amount of HCl/NaOH and calculate the pH.

Start with pure water (button H2O) and use the reaction module (button Reac). Then enter two reactants:

• 1 mM CO2 (which is equivalent to 1 mM DIC)
• either HCl or NaOH (and repeat it with variable amount)

Way 2. Choose the pH and calculate the amount of HCl/NaOH.

Start with pure water (button H2O) and switch to molar units (checkbox mol). Enter 1 mM DIC, the desired pH value, say pH = 3, and set an arbitrary start value for chloride (to mimic HCl addition), say 1 mM Cl.

Click on Start and force charge-balance adjustment with parameter “Cl”. The program promptly outputs the correct amount of Cl (which is identical to the molar amount of HCl). The output tables (including table Ions) display the complete speciation. Some data are replicated in the table below.

For pH > 4.68, use Na instead of Cl (in order to simulate NaOH addition). In this way, you are able to calculate any titration point you wish. The table below gives you some idea.

What you finally achieve by Way 1 or Way 2 is something like this:³

Results and Discussion

Table. The table contains the amount of HCl or NaOH, the carbonate speciation, the ionic strength (I in mM), and the alkalinity (Alk in meq/L). Here, CO₂ stands for the composite carbonic acid.

The pure 1 mM CO₂ solution is marked by orange color.

Mass Conservation (Mole Balance). It’s easy to confirm that the sum of all carbonate species (in each table row) equals the total amount of dissolved inorganic carbon:

(1)

DIC  =  CO2 + HCO3- + CO3-2 + NaHCO3 + NaCO3-  =  1 mM

This equation can be rearranged into a sum of three terms

(2)

DIC  =  CO2 + [HCO3-]T + [CO3-2]T

where the sum of bicarbonates and the sum of carbonates are specified as separate entities:

(3a)		[HCO3-]T	=  HCO3- + NaHCO3
(3b)		[CO3-2]T	=  CO3-2 + NaCO3-

Diagrams 1. The top diagram displays the pH dependence of five carbonate species; the bottom diagram plots the pH dependence of CO₂, [HCO₃^-]_T, and [CO₃^-2]_T. Thereby, ion HCO₃^- is merged with NaHCO₃ to total bicarbonate, and ion CO₃^-2 is merged with NaCO₃^- to total carbonate.

The second diagram exhibits some kind of symmetry about pH = 8.2 which is known as the equivalence point of a pure NaHCO₃ solution. Hydrogen carbonate (blue curve) dominates the pH range between 6 and 10; this range almost coincides with the realm of natural waters (pH 6 to 8).

Diagrams 2. The plots can also be converted into a stacked-area chart. In this form it demonstrates the strict mass conservation in a closed system, where all carbonate species add up to 1  mM DIC — as demanded by Eq.(1):

Footnotes & Remarks