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))*(-log
10([HOCl])+(2.6/1.25-0.24*pH)*pH)
Oakton: 1399 - 1000*(ln(10)*8.314472*Temp(ºK)/(0.635*96485.3415))*(-log
10([HOCl])+0.24*pH)
Aquarius: 1709 - 1000*(ln(10)*8.314472*Temp(ºK)/(0.39*96485.3415))*(-log
10([HOCl])+0.164*pH)
Sensorex: 1308 - 1000*(ln(10)*8.314472*Temp(ºK)*(11.21-0.87*pH)/(96485.3415))*(-log
10([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):
E
red = E
0red - (RT/(zF)) * ln(a
red/a
ox)
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:
martino said:
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
- + H
2O ..... E
0 = +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))*( log
10([Cl
-] - log
10([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
