Yes, I can answer it exactly:
ORP and the Reef Aquarium - Reefkeeping.com
http://reefkeeping.com/issues/2003-12/rhf/feature/index.htm
The theoretical relationship between ORP and pH
One of the complications of ORP is that the measured value can sometimes depend on pH. Whether ORP does depend on pH or not, and to what extent, is determined by the exact redox reactions that are involved in controlling the ORP in that solution. There have been equations proposed that purport to "correct" ORP for changes in pH, giving a new parameter, sometimes called
rH. This parameter was proposed in the 1920's by W. M. Clark.7 One form of this correction is shown below:
rH = mV / 29 + (2 x pH)
and sometimes a correction for changes in oxygen concentration is thrown in:
rH = mV / 29 + (2 x pH) + [O2]
where [O2] is the concentration of O2 in ppm. The use of rH, however, presupposes a detailed understanding of the reactions involved, and is simply wrong for general use (as shown below). In a book8 that he published 40 years after his initial publication, Clark stated:
"
At this point the author must confess to the introduction of rH. He conceived that there might be occasions when it would be convenient to speak of relative oxidation-reduction intensity without having to specify both potential AND pH...
...Unfortunately both the original intent and the obvious limitations have been overlooked by many who have converted their potentials for SPECIFIC SYSTEMS to rH numbers...
...In brief, rH has become an unmitigated nuisance."
Nevertheless, many people still use rH. Since it is imbedded in many articles relating to aquarists, it is worth understanding where the pH dependence comes from, and why it is not always the same.
As an example of a solution where the redox is not pH dependent, take a solution of Fe++ and Fe+++ in water, with no other redox active species. In that case, the ORP is exactly determined by the relative concentration of the two iron species, and is unchanged with pH.
Fe+++ + e- <----> Fe++
Specifically, the
defining equation here is:
The main thing that is clear from this equation is that the ORP is independent of pH, and only depends on the relative concentrations of Fe++ and Fe+++.
The easiest way to think of the lack of pH dependence here is to recognize that neither H+ nor OH-participate in the reaction at all. So changing the pH has no direct impact on the reaction.
For many reactions where oxygen is an important participant, however, that is not the case:
O2 + 4H+ + 4e- <----> 2H2O
In this reaction, H+ does participate. Consequently, the oxidizing power is related to pH. As H+ is raised (by lowering pH), the reaction is driven to the right. One way to think of this is by LeChatlier's Principle where increasing the concentration of one species drives the reaction to the other side. In this case, lowering the pH increases the oxidizing power of the oxygen, and consequently raises the ORP. This result is the basis for the development of rH for many systems.
It is beyond the scope of this article to go into the detailed mathematics behind the pH dependence of ORP measurements, but Pankow does cover such issues in great detail in
Aquatic Chemistry Concepts.9 For our purposes, an important result is that the magnitude of the change in ORP with pH depends entirely on the number of H+ involved in the reaction per electron. In the case of the Fe+++/Fe++ situation, this value is zero. For the oxygen/water reaction, the value is 1.0. The standard definition of rH assumes that this ratio is exactly 1.0. Consequently, it may not apply to many redox reactions that take place in aquaria.
Shown below are some typical reactions that also take place in aquaria. First, the oxidation of acetic acid to carbon dioxide, again with one H+ per electron (this reaction typifies many reactions involving neutral organic materials):
2CO2 + 8H+ + 8e- <----> CH3COOH + 2H2O
but if the same reaction proceeds with acetate, the reaction is:
2CO2 + 7H+ + 8e- <----> CH3COO- + 2H2O
and the ratio of H+ to e- is no longer 1.0, but is now 0.875.
For the various reactions of the nitrogen cycle, we have ratios that vary from 1.0 to 1.33:
NO2- + 7H+ + 6e- <----> NH3 + 2H2O
NO2- + 8H+ + 6e- <----> NH4+ + 2H2O
NO3- + 2H+ 2e- <----> NO2- + H2O
N2 + 6H+ + 6e- <----> 2NH3
N2 + 8H+ + 6e- <----> 2NH4+
The iodide/iodate reaction fits the 1.0 ratio:
IO3- + 6H+ + 6e- <----> I- + 3 H2O
Some other redox reactions that have other ratios:
MnO2 + 4H+ + 2e- <----> Mn++ + 2H2O
SO4-- + 10H+ + 8e- <----> H2S + 4H2O
SO4-- + 9H+ + 8e- <----> HS- + 4H2O
So if one really wants to understand how ORP would change with pH, one would have to know what the species are in aquaria that control redox. If it is a mixture of species, then the end result will come back as a complex averaging of the different reactions involved. Unfortunately, the species involved have not been clearly defined for seawater. In aquaria, which vary considerably in the concentrations of many redox active species, the situation is even more complicated.
The empirical relationship between ORP and pH in aquaria
While understanding the details of the theoretical relationship between pH and ORP is complicated, measuring it for a single aquarium is fairly easy. Figure 1 shows simultaneous plots of pH and ORP values over the course of several days in the aquarium of Simon Huntington. Clearly, the measured ORP and the pH are on exactly opposite cycles, as one would expect from a system where reactions involving oxygen are important (and as is shown by rH).
Does the reaction exactly follow the one H+/e- rule? Maybe not exactly. Figure 2 shows a plot of rH as a function of time using Simon's data. If the effects of pH on ORP were exactly removed by calculating rH using:
rH = mV / 29 + (2xpH) + 6.67
then one might expect rH to not have a diurnal cycle. In this figure, the data suggest that there is still a diurnal dependence to rH, possibly due to pH effects. I have seen data from other aquaria as well, and in those cases the same holds: that rH largely compensates for ORP changes with pH, but not perfectly. Since things other than pH (such as O2) may change during the night and day in aquaria, this experiment may be confounded by these other variables.
Simon also ran an additional experiment on his aquarium. He took a water sample, and added either sulfuric acid or sodium hydroxide to it to adjust pH. In this experiment, the other factors that might cycle diurnally in an aquarium are constant. The results are shown in Figures 3 and 4. The fact that the ORP goes almost exactly back to where it was at the start, despite the pH excursions, suggests that the acids and bases are not altering the "base" ORP, but are only impacting ORP through pH.
The ORP moves inversely to pH, as expected (Figure 3). But, the fact that the rH is generally not flat as the pH is changed (Figure 4), but rather tracks with pH changes, suggests that the mathematical conversion used (rH = mV / 29 + (2xpH) + 6.67) is overcorrecting for pH changes. That result in turn implies that the pH dependence of ORP may be less than predicted by the H+/e- ratio of 1.0. Perhaps this result indicates that in Simon's aquarium, some reactions with an H+/e- ratio below one are important in controlling ORP.
Overall, my suggestion for aquarists using ORP measurement devices is to be aware of how pH can influence ORP measurements, but to not overly emphasize specific pH corrections.