# What is the significance of charge balancing when analysing system speciation (carbonate system given as an example)?

Following on from my previous question and accepted answer, How do I quantify the carbonate system and its pH speciation?, I also calculated a charge balance ($$CB$$) on the system where $$z$$ is the species' ionic charge:

$$CB = \sum{z\times[\textrm{positive ions}]}=\sum{z\times [\textrm{negative ions}]}$$

The CB is thus;

$$\ce{ [H+] = [OH-] + [HCO3-(aq)] + 2[CO_{3}^{2-}(aq)]}$$

Usually, I'd assume this number to equal zero for complete balance which makes sense. The system indeed shows this when looking at this balance (which I've done by getting the difference in negative and positive ionic charge) I see that the charge balance becomes unbalanced (i.e. >0) at around pH = 12.5 signifying a net negative charge as seen in the graph below: Here are my main questions concerning this:

1. (For a better personal understanding) What is the practical significance of including these charge balance equations?

2. As the charge balance is not in integer values (I.e. it can’t be [z] or the quantised [e-]), what is the units of the charge balance?

3. What are the practical differences in doing the same calculations with activities instead of concentrations (I.e. not assuming infinite dilution)? I have read in other questions that the standard pH model is not the best to use at extreme pH values and activity is the better model.

4. What does the charge balance impact on for the chemical species? Is it to infer species' reactivity? Does this infer that around pH= 12.5 the system becomes unstable, highly reactive and thus more likely to form an unwanted precipitate?

(For context, I am trying to better understand this behaviour of extreme alkaline systems because I want to keep track of the pH of other solutions I'm making by mixing highly alkaline solutions with sodium silicate systems. Sometimes these systems form precipitates when they've mixed, other times they don't. I thought understanding the pH and charge balancing of everything is a good place to start, hence why I'm here.)

• My comments have been deleted, relevant have been moved to my answer. Aug 25, 2022 at 6:44

(For a better personal understanding) What is the practical significance of including these charge balance equations?

• There are variables for concentration of $$\ce{H+}$$, $$\ce{Na+}$$, $$\ce{CO2(CO2+H2CO3)}$$, $$\ce{HCO3-}$$, $$\ce{CO3^2-}$$, $$\ce{OH-}$$, i.e. 6 variables.
• There are 3 equations for equilibrium (2 for CO2, 1 for H2O).
• There is 1 equation for charge balance. $$[\ce{H+(aq)}] + [\ce{Na+(aq)}] = [\ce{OH-(aq)}] + [\ce{HCO3-(aq)}] + 2[\ce{CO3^2-(aq)}]$$
• There are 2 equations for the molar amount inventory ( 1 for Na+, 1 for total CO2 )
• So 6 equations for 6 variables, therefore solvable. Without CB equation, there would be infinite number of solutions, having still 1 degree of freedom. You could deliberately ( within a range) choose a value of 1 of 6 variables and still being able to solve the equations set for values of remaining 5 variables.
• You have omitted in your analysis the essential presence of other cations, like of alkali metals. You cannot have $$\mathrm{pH}>7$$ (at $$\pu{25^{\circ}C}$$) and to have $$\ce{H+(aq)}$$ as the only cation, as then $$[\ce{H+(aq)}] \lt [\ce{OH-(aq)}]$$. If the system consists just of $$\ce{H2O}$$ and $$\ce{CO2}$$ in any of its dissolved forms, without addition of a base like e.g. $$\ce{NaOH}$$, $$\ce{Na2CO3}$$ or $$\ce{NaHCO3}$$, so having truly just $$\ce{H+(aq)}$$ cations, then your chart should end at $$\mathrm{pH}=7$$, as you would not be able to reach alkalic $$\mathrm{pH}$$.

As the charge balance is not in integer values (I.e. it can’t be [z] or the quantised [e-]), what is the units of the charge balance?

The unit of the charge balance is the molar density of elementary charges - $$\pu{1 mol/L}$$, equivalent $$\approx \pu{96490 C/L}$$

What are the practical differences in doing the same calculations with activities instead of concentrations (I.e. not assuming infinite dilution)? I have read in other questions that the standard pH model is not the best to use at extreme pH values and activity is the better model.

Involving activities instead of concentrations is kind of opening of a can of worms or even the Pandora's box. It has several aspects:

• Increasing ionic strength $$I = \sum_i{c_iz_i^2}$$ leads to decreasing of activity coefficients and decreasing activities, what leads to higher equilibrium concentration of respective ions.
• Addressing solutions with significant ionic solutions. For Ionic Strength $$I \le \pu{0.1 M}$$ is applicable Debye–Hückel equation, for more concentrated solutions Pitzer equations
• Addressing solutions with extreme pH values and related extreme ionic concentrations. For these ighly concentrated solutions, you can safely throw all pH calculations out of the window.

What does the charge balance impact on for the chemical species? Is it to infer species' reactivity? Does this infer that around pH= 12.5 the system becomes unstable, highly reactive and thus more likely to form an unwanted precipitate?

Having 1 mol of extra ions out of charge balance would blow solution from the vessel, yourself from the room, many things from the house and possibly making house to spread out like a big firework. As nearly 100000 Coulombs is like 1000 times bigger charge than the longest 10 km long CG+ lightnings with potential difference up to a billion Volts.

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• I see, thanks for the great reply! To follow up then, the non-zero charge balance occurring when $pH \geq 13$ is explainable in this scenario (as you suggest) due to the inapplicability of my conventional pH calculations from this point onwards as it becomes a highly concentrated solution? Aug 24, 2022 at 15:02
• I have moved comments to the answer. Aug 25, 2022 at 6:41
• Great answer! The feedstock I usually use is sodium silicate mixed with sodium hydroxide. I was thinking that only the speciation of the silicates was important but you correctly point out that I need to also focus on the Na cation. I have never looked into sodium speciation but it seems I will have to in order to get to the bottom of this. Thanks for the insight! :) Aug 25, 2022 at 11:02

[OP] I am trying to better understand this behavior of extreme alkaline systems because I want to keep track of the pH of other solutions I'm making by mixing highly alkaline solutions with sodium silicate systems.

You are missing sodium ions in your model. To get alkaline at all, you need some carbonate or bicarbonate salt. To get past ph 13 or so, you need to add hydroxide directly, e.g. in the form of NaOH. So there will be substantial concentration of sodium, fixing your charge balance.

[OP] What is the practical significance of including these charge balance equations?

Typically, your system will be underdetermined if you leave it out. In your case, you probably set the pH to a certain value, but in reality, a mixture has a pH and there is no dial (other than adding stuff) to change it.

• Great answer thank you! I was thinking that only the speciation of the silicates was important but you correctly point out that I need to also focus on the Na cation. I have never looked into sodium speciation but it seems I will have to in order to get to the bottom of this. Thanks for the insight and please let me know if you have any info on this, cheers! :) Aug 25, 2022 at 11:03