Sure.
First let's take a look at the only reaction that appears to be reasonably possible at the cathode (the negatively charged plate). The other reactions that can occur at this plate include the plating of metals (iron, copper) that are in the water. Also, the [EDIT] high (sorry about saying "low" at first -- I was "thinking" the right thing but "wrote" the wrong word) [END-EDIT] pH in the region of this plate make scaling of calcium carbonate much more likely.
2H+ + 2e- --> H2(g) ...................... Eo = 0V
In other words, this is the generation of hydrogen gas. It can also be written as coming from water to produce hydroxyl ion:
2H2O + 2e- --> H2(g) + 2OH- .......... Eo = -0.8277V
The different Eo readings reflect the fact that Eo is defined to be at standard conditions which means that each of the species dissolved in water have a concentration of 1 mole/liter and each gaseous component has a partial pressure of 1 atmosphere.
Now let's look at the two different competing reactions that appear to be reasonably possible at the anode (the positively charged plate):
2H2O --> O2(g) + 4H+ + 4e- ........... Eo = -1.229V
2Cl- --> Cl2(g) + 2e- ....................... Eo = -1.35827V
Cl2(g) + H2O --> HOCl + H+ + Cl-
----------------------------------------
Cl- + H2O --> HOCl + H+ + 2e- ......... Eo = -1.482V
The first reaction is where oxygen is produced from water. The other reactions are the production of chlorine where I show the additional reaction of chlorine dissolving in water to produce hypochlorous acid. You can see that the Eo value is more negative after chlorine gas dissolves in water to make hypochlorous acid and that would seem to imply that the reaction is not favored, but again this is only because the Eo is defined for standard conditions (which are theoretical and may not always be actually achievable) of 1 atmosphere pressure of chlorine gas with 1 mole/liter concentration of hypochlorous acid AND 1 mole/liter concentration of hydrogen ion (i.e. a pH of 0), AND 1 mole/liter concentration of chloride ion.
For the cathode, I listed the reduction potentials as oxidation potentials (i.e. with negative numbers) to indicate that a voltage needs to be applied to make the reaction occur. Note that it takes a lower (absolute) voltage to produce oxygen than chlorine. This represents a difference of about 25 kilojoule per mole in favor of oxygen formation over chlorine formation. HOWEVER, chemical reactions have what is known as an activation energy which is an energy barrier that must be overcome before the reaction can happen. In electrochemistry, this barrier is called overvoltage which represents the additional electrical potential needed to get an electrochemical reaction started. Oxygen has a very high overvoltage of 700 mV while chlorine has an overvoltage of only 50 mV.
So if we add the overvoltages to the standard potentials, we see that to produce oxygen it takes 1.229+0.7 = 1.929V while to produce chlorine it takes 1.35827+0.05 = 1.40827V. Or we can look at producing hypochlorous acid directly as 1.482+0.05 = 1.532V. Now these voltages do not account for the actual concentrations of the various species in pool water as I noted above.
If we want to really know about the true voltages required and which reactions are favored, we need to convert from standard conditions to actual concentrations. There is a formula for doing that called the Nernst equation as follows:
E = Eo - RT/nF * ln(K)
where "K" is the ratio of product concentrations (raised to powers corresponding to their stoichiometric quantity in the formula) to reactant concentrations. "R" is the gas constant, "T" is the temperature in Kelvin, "n" is the number of electrons in the equation and "F" is the Faraday constant. Sometimes this Nernst equation is written with a "+" and the "K" value is inverted to have reactants divided by products.
Anyway, if I assume reasonable initial conditions of a pH of 7.5 to get [H+] = 3.7x10^(-8), normal dissolved oxygen levels (based on 21% oxygen in the air and using Henry's Law) to get [O2] = 2.6x10^(-4) moles/liter and converting to 0.0065 atmospheres (partial pressure), using normal chlorine levels of 3 ppm with 30 ppm CYA to have [HOCl] = 5.8x10^(-7) moles/liter and chloride concentration of 3000 ppm to have [Cl-] = 0.052 then this adjusts the oxygen equation by (0.02585/4)*ln(0.0065*(3.7x10^(-8))^4) = -0.47V so E = -0.75V for oxygen. The chlorine equation is adjusted by (0.02585/2)*ln(5.8x10^(-7) * 3.7x10^(-8) / 0.052) = -0.37V so E = -1.11V for chlorine. I'm not certain on the handling of the oxygen quantity in terms of molarity vs. partial pressure, (I believe I did it correctly) but it turns out it doesn't matter much in this case so let's keep going.
Applying the overvoltages again gives is E = -1.45V for oxygen while we get E = -1.16V for chlorine. So at least initially, the production of chlorine is favored over the production of oxygen and if the voltage applied to the salt cell is set to be BETWEEN 1.16V and 1.45V, then only chlorine can be generated and oxygen cannot. [EDIT] I neglected to do the concentration adjustment calculation for the cathode for the production of hydrogen, but that would modify the overall voltage by the same amount regardless of whether oxygen or chlorine were produced at the anode so it's not that relevant to this discussion. [END-EDIT]
If higher voltages are used, then both chlorine and oxygen will be produced with chlorine favored over oxygen. If you have ever done the "home" experiment of taking two carbon cores from D-cell batteries and connecting them to a 6V transformer (as I have), then putting this into salt water produces both chlorine and oxygen (you can smell the chlorine and you can "pop" the gasses with a flame where the oxygen and hydrogen combine) and can somewhat vary the ratio of the two depending on the salt concentration. If you use sodium bicarbonate as the electrolyte, then you get only hydrogen and oxygen and not chlorine.
The salt cells appear to use voltages that are much higher than these minimum amounts that would ensure that only chlorine gets generated. I'm sure that this is partly due to the rather low chloride concentration in pool water (especially today, since early salt generators wanted 6000 ppm instead of 3000 ppm). Otherwise, you would need very large generating plates to get decent generation rates. So with voltages of 6-9 volts for some manufacturers and 22-30 volts for others, it would seem that both chlorine and oxygen could get produced. My guess is that the higher voltage units have a greater tendency to produce more oxygen proportionately than the lower voltage units, but that's just a guess.
Now what I do not know is whether the materials (coatings) used for the generating plates in a salt cell are designed to somehow inhibit the oxygen generation, but I suspect that is not the case. (If anyone knows about this, please let us know).
As the electrolysis proceeds, the product concentrations build up at the generating plates (though there is water flow to help keep them lower) and this slows down the generating reactions. Note that the reaction with oxygen produces hydrogen ion so is acidic and that the production of chlorine AND dissolving of that chlorine in water also produces hydrogen ion so is also acidic. However, the oxygen reaction produces one hydrogen for each electron while the chlorine reaction produces half a hydrogen for each electron. This means that as the pH gets lowered near the plate, the chlorine reaction will become more favored, assuming that the chlorine gas is able to dissolve in water rapidly. Having CYA in the water helps make this happen because it combines with the hypochlorous acid that is produced so that the reaction of chlorine dissolving in water can continue at a rapid pace. So the lower buildup of products in the chlorine reaction, due to CYA binding with the generated hypochlorous acid, means that this reaction becomes even more favored compared to the oxygen generation.
This can be netted out as follows:
2Cl- --> Cl2(g) + 2e-
Cl2(g) + H2O --> HOCl + H+ + Cl-
HOCl + CYA --> Cl-CYA + H2O
----------------------------------------
Cl- + CYA --> Cl-CYA + H+ + 2e-
Each succeeding reaction above moves the products into another form and that takes them away from being able to go "backwards" to create reactants again (or to inhibit or slow down the creation of more products). It is almost as if one turned up the water flow with respect to sweeping away chlorine gas, but that this is done chemically.
Richard
Bookmarks