# Thread: ORP Modelling based on Nernst equation

1. ## ORP Modelling based on Nernst equation

Hi,

I was wondering can anyone help me find the relevant Oxidation and Reduction half reactions so I can incorporoate Nernst equation to model a feeback control. I have data on the following:

I would like to calculate /etimate Free available Chlorine within 20% accuracy.

I understand that NaOCl + H2O => NaOH and HOCl.
HOCl <> H+ OCl-

E = Eo -RT/NF 2.303 Log 10(Oxidants /reactants)

platinum ORP electrode and reference electrode of Ag/AgCl.

2. ## Re: ORP Modelling based on Nernst equation

It cannot be done in a pool environment because the ORP can be affected by many more variables that aren't electronically measurable other than FC.

3. ## Re: ORP Modelling based on Nernst equation

It is possible to come up with an equation that can be calibrated, ie given a starting ORP reading and a starting FC reading, calculate how much FC must have changed to correspond to a known ORP change, assuming all else remains the same. But it needs to be re-calibrated regularly, since all else does not remain the same.

4. ## Re: ORP Modelling based on Nernst equation

Welcome to TFP!

It's not just that the Nernst Equation can't be used in pools, but it doesn't even work in distilled water with chlorine in it as the ORP vs. FC from various manufacturers' probes varies not only in an absolute sense but in terms of the mV increase for every doubling of FC (with no CYA and at constant pH). I write about some of this in this post.

As Jason noted, you really have to measure the actual FC in your pool and see the associated ORP value. If you measure a mV for a doubling of FC, then that can give you are reasonable estimate of the slope, but pH will also be a factor. Normally, you just determine an FC goal and then set the ORP to the level that achieves that FC. ORP is useful for process control, but not for absolute measurements.

5. ## Re: ORP Modelling based on Nernst equation

Your opinions are appreciated, however the point has been missed somewhat.... What is the correct nernst equation for Hypochlorous acid with my the Ag/AgCl and platinum electrode.

That is exactly what im referring to , the calculation can be referred to as the theoretical ORP reading and you increase Pump speed on the Sodium Hypochlorite pump until the process variable (PV) mV reading meets the theoretical setpoint. However, can some one please provide the correct Nernst equation with appropriate electrode zero potential (Eo) value.

eagerly waiting.....

6. ## Re: ORP Modelling based on Nernst equation

As others have already pointed out, that is simply not possible. There is no official definition of what theoretical ORP values should be. ORP readings have always been defined in terms of what actual sensors do in the real world, which is not consistent between sensors (even of identical design).

Worse, using any kind of absolute theoretical model to drive process automation is a very bad idea. As we have also already pointed out, actual ORP readings fluctuate dramatically depending a quite a number of external variables. The only useful ORP measurement is the change in an ORP reading made with the same sensor at two different, reasonably close, times, thus the calibration procedure I mentioned earlier.

7. ## Re: ORP Modelling based on Nernst equation

Ok, if the conditions of microbiological control are in the post "break out" out period ...then residual FAC would mainly be influenced by sudden changes in a pool it may be nutrient loading from the number of people in the pool, in a spa by temperature , in a cooling tower would be most affected if there were oil leaks, changes in power being generated , time of day with relation to temperature.....

So it is difficult, yes. But a theoretical is quite possible. The purpose as already stated, is to model the theoretical ORP reading, because when you keep pH the same, then changes in Temperature and nutrient loading would be the factors in changing the FAC in post 'Break out' period.

It is easier to just dismiss a request, rather than trying to find out if, it is only the oxidation of hypochlorous acid. I am not asking or interested in 'Microbiological doctrine or theology', I am asking for some practical direction in confirming whether the reduction and oxidation reactions are correct. So if any feels that they me be able to contribute and direct me in this modelling of a , I would be appreciative.

Literature shows some of the following equations.....

HOCl + H => Cl- + H2O
E = 1,495 - 2.303*RT/nF) * log 10 ( [Cl-] / [H+] [HOCl] )

OCl + H2O + 2e- => Cl- + 2OH-
E = 0.849 - (2.303 RT/NF ) log 10( [Cl-] [OH]2 / [OCl] )

OCl + H2O + 2e- => HOCl- + OH-
E = 0.810 - 2.303(RT/NF ) log 10( [HOCl-] [OH] / [OCl] )

What about the other half reaction?
Do i use ORP electrode: Platinum?: Pt2+ + 2â€Šeâˆ’ Pt(s) E0 = +1.188

or how about the reference electrode: AgCl?: AgCl(s) + â€Šeâˆ’ Ag(s) + Clâˆ’ E0 = +0.22233

Some data points include the following:
1. pH = 7.39, Free Available Chlorine = 0.5 , T = 25 (Degrees celcius), ORP (Measured) = 716 mV
2. pH = 7.37, Free Available Chlorine = 5.32 , T = 26 (Degrees celcius), ORP (Measured) = 807 mV

At this stage of the model: I wont include the Amine based reactions that HOCl gets involved with......

8. ## Re: ORP Modelling based on Nernst equation

Sounds like your trying to create a product without doing any of your own research, good luck with that since what you are asking would be essentially proprietary information.

What you are asking for is not available freely, however the testing has been done to support what you are intending to do...it would be up to you to determine an equation to fit the model for various situations (PH, TDS, etc.). The reason why it hasn't been done to date is there is hundreds of variables to take into account and trying to find a single fit equation for all of them would essentially mean you would be a very rich man and sought after by 3M and other large corporations for it.

P.S. Not sure if you seen these graphs, they may assist you.
http://www.sbcontrol.com/orppaper.pdf

9. ## Re: ORP Modelling based on Nernst equation

In my Pool Equations spreadsheet around lines 381-384 I have approximate formulas based on the Nernst equation but modified to fit either tables of data from manufacturers or real-world measurements in pools (the latter for the Oakton sensor). The following are such formulas:

Chemtrol: 1308 - 1000*(ln(10)*8.314472*Temp(ºK)/((2.6-0.24*pH)*96485.3415))*(-log10([HOCl])+(2.6/1.25-0.24*pH)*pH)
Oakton: 1399 - 1000*(ln(10)*8.314472*Temp(ºK)/(0.635*96485.3415))*(-log10([HOCl])+0.24*pH)
Aquarius: 1709 - 1000*(ln(10)*8.314472*Temp(ºK)/(0.39*96485.3415))*(-log10([HOCl])+0.164*pH)
Sensorex: 1308 - 1000*(ln(10)*8.314472*Temp(ºK)*(11.21-0.87*pH)/(96485.3415))*(-log10([HOCl])-IF(pH>7.5, 2.99,2.99+0.13*(7.5-pH)))

You can see that all of the above have a resemblance to the classical Nernst equation which is not a coincidence since I started from that and then made adjustments to fit vs. pH and HOCl concentrations (there weren't measurements at significantly different temperatures so I couldn't independently fit for that):

Ered = E0red - (RT/(zF)) * ln(ared/aox)

However, the best-fit equations I listed all deviate significantly from the theoretical Nernst equation in several ways. The most obvious is the "slope" as a function of hypochlorous acid concentration. The mV increase from a doubling of [HOCl] should be equal to 1000*(RT/(zF))*ln(2) since C*ln(2x)-C*ln(x) = C*ln(2x/x) = C*ln(2). The half-reactions for hypochlorous acid have 2 electrons so at 86ºF we have 1000*(RT/(zF))*ln(2) = 1000*(8.314472*307.15/(2*96485.3415))*ln(2) = 9.17317 mV. The actual measured mV per doubling of chlorine are more than double that and vary significantly by manufacturer. At a pH near 7.5 and the 86ºF temperature we have the following:

Chemtrol: 22.7 mV
Oakton: 28.6 mV
Aquarius: 46.5 mV
Sensorex: 84.9 mV

As you can see from actual Oakton data measured in pools as shown in the second graph (the HOCl one, not the FC one) in this post and the curve fit, the implied number of electrons in the reaction is around 0.6 which of course doesn't make any sense. Notice also how two different sensors from different manufacturers measuring the same pool water can vary a lot with 23% of such pool measurements differing by more than 100 mV.

Based on the two points of data you provided:

Originally Posted by martino
Some data points include the following:
1. pH = 7.39, Free Available Chlorine = 0.5 , T = 25 (Degrees celcius), ORP (Measured) = 716 mV
2. pH = 7.37, Free Available Chlorine = 5.32 , T = 26 (Degrees celcius), ORP (Measured) = 807 mV
the implied slope of mV for every doubling of concentration is (807-716) / (ln(5.32/0.5)/ln(2)) = 91 / 3.411 = 26.7 which is roughly close to the Oakton sensor so your "n" factor is around 0.687 (compared to the Oakton 0.635). You don't have enough points at varying pH to determine the appropriate factor for, or dependence on, pH.

In addition to the slope and therefore number of electrons not making any sense, the standard reduction potential number also doesn't make any sense. The first two reactions you listed are equivalent -- the difference in standard reduction potentials is due to using hypochorous acid instead of hypochlorite ion and hydrogen ion instead of hydroxyl ion since "standard" reduction potentials have the solutes (chemical ions) in the equations at 1 molar concentration, gasses at 1 atm pressure. The third reaction you show is between hypochlorous acid and hypochlorite ion and is NOT an electron transfer half-reaction and is in fact at equilibrium so does not contribute to ORP. The first two reactions you showed are not charge balanced and are missing the electrons. My formulas above use hypochlorous acid concentrations so use the following half-reaction:

HOCl + H+ + 2e- ---> Cl- + H2O ..... E0 = +1.482V

As for the reference electrode, that depends on what you are using and the concentrations in that electrode. The theoretical Nernst equation for the above half-reaction in mV at 86ºF is:

E(mV) = 1482 - 1000*(8.314472*307.15/(2*96485.3415))*ln([Cl-]/([HOCl]*[H+])
E(mV) = 1482 - 1000*(8.314472*307.15/(2*96485.3415))*( ln([Cl-] - ln([HOCl]) - ln([H+]) )
E(mV) = 1482 - 1000*(ln(10)*8.314472*307.15/(2*96485.3415))*( log10([Cl-] - log10([HOCl]) + pH )

The equations I used for fitting don't have a chloride component because most manufacturers did not specify variations at different levels and one said there was no change with TDS (or salt levels) and as I noted above, these equations aren't even close to the above since the number of effective electrons factor is totally different. Also, note that varying chloride levels would change the standard potential, but should not affect the slope based on chlorine concentration when the chloride level was constant.

I don't understand what it is you are trying to do, but hopefully I have convinced you that simply using a Nernst equation to predict what will happen with your specific electrode is fruitless. You have to take actual measurements in controlled conditions and come up with a fitted equation. No one has adequately explained this huge discrepancy between theory and actual measurements and the manufacturers seem to be oblivious to this issue and their inconsistencies between models and manufacturers.

Also note that the presence of other oxidizers (such as potassium monopersulfate or ozone) will affect the ORP reading as will hydrogen gas bubbles from saltwater chlorine generators and have nothing to do with the hypochlorous acid concentration. Also note that the hypochlorous acid concentration is not the same as the Free Chlorine (FC) level and cannot be calculated using pH alone when Cyanuric Acid (CYA) is present. My spreadsheet will calculate the hypochlorous acid concentration given other water input parameters (mostly FC, CYA and pH), but this is not a simple formula when pH is also a factor. In my spreadsheet, I have the temperature dependence of the chlorinated isocyanurate equations turned off ("Use Temp. Dependent Cl-CYA" is set to FALSE in columns B and C around line 225) because such dependence is based on some activation energy numbers from Wojtowicz in JSPSI and not from a more thoroughly peer-reviewed scientific paper in a larger journal.

Richard

10. ## Re: ORP Modelling based on Nernst equation

Only God knows all the reactions affecting ORP in a swimming pool

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