Convert to Eh and pe values

[aufdenkampe]

Presently the output is in mV relative to the silver chloride (Ag|AgCl 3M KCl) reference electrode.

We want to report the values relative to the Standard Hydrogen Electrode (SHE), which is by definition, the zero-point of chemical potentials. This will convert our mV readings into Eh (or E0 or e0) values (also in units of mV) and comparable to the output from other Oxidation Reduction Potential (ORP) electrodes.

From PaleoTerra, https://paleoterra.nl/measuring_redox_potential.html, we know that:

The potential of the common Ag|AgCl 3M KCl reference electrode at 20°C equals +213 mV versus the SHE. When the voltage measurement of a redox electrode against the Ag|AgCl 3M KCl reference reads +60 mV, the redox potential equals +273 mV vs. the SHE.

To convert to pE, or the negative log of the e- concentration, according to https://en.wikipedia.org/wiki/Reduction_potential:

we will have the relation pE=16.9 Eh at room temperature.

@fisherba, this may be useful for your work, especially for exploring Eh-pH diagrams, such as https://en.wikipedia.org/wiki/Pourbaix_diagram#/media/File:Pourbaix_Diagram_of_Iron.svg

[aufdenkampe]

In conversations with @fisherba, we just noticed that conversion from measured mV to Eh (or E0 or e0) is temperature dependent. As Sanders writes in Nov. 6, 2017 email:

The reference electrode potential is at a know chemical potential (e.g. 201 mV versus the Standard Hydrogen Electrode at 25 Celsius).
So a reading of 500 mV implicates the redox electrode is at 701 mV vs. SHE

... which is lower than the +213 mV given for 20°C on his website, https://paleoterra.nl/measuring_redox_potential.html, suggesting a negative temperature coefficient (i.e. potential decreases with increasing temperature). This negative relationship is also shown by tables in https://en.wikipedia.org/wiki/Silver_chloride_electrode, but that article also makes it clear that the temperature coefficient changes as a function of the KCl concentration, and also bromide impurities.

It looks like we might need to get the temperature coefficient from Sanders.

[aufdenkampe]

Several websites show the following equations for temperature dependence:

[ KCl ]	Potential vs. NHE, E in mV, T in °C
3.5M	E = 205 - 0.73 * (T - 25°C)
sat'd	E = 199 - 1.01 * (T - 25°C)

From the data in Table 5.3 of Sawyer, 2nd Ed.

However, fitting these values from Sanders, for KCl = 3.0M,

Temp	Potential vs. NHE
20°C	213 mV
25°C	201 mV

Gives this equation: E = 201 - 2.4 * (T - 25°C)