I need to calculate the redox potential for the following:
1/2 O2 + 2H+ + 2e- <-> H2O
I'm using the formula
E = E'_0 + RT\nF ln ([electron acceptor]/[electron donor])
The electron acceptor is H+, so I can use the concentration of that which is indicated by the pH.
However, the electron donor seems to be H2O. The molarity of pure water is 55.346 M. Am I really supposed to use that? I have a suspicion that I'm not supposed to do that.
You are correct, using the molarity of pure water would not be appropriate in this case. The electron donor in this reaction is not H2O, but rather 1/2 O2.
To calculate the redox potential, you will need the standard reduction potential, E'_0, of the reaction. For the reaction you provided:
1/2 O2 + 2H+ + 2e- <-> H2O
The standard reduction potential E'_0 is typically given in tables or can be measured experimentally.
To calculate the redox potential, you can use the Nernst equation, which is a modified version of the equation you mentioned:
E = E'_0 + (RT/nF) ln ([electron acceptor]/[electron donor])
Where:
E = redox potential
E'_0 = standard reduction potential
R = gas constant (8.314 J/K·mol)
T = temperature in Kelvins
n = number of electrons transferred in the reaction
F = Faraday constant (96,485 C/mol)
[electron acceptor] = concentration of the electron acceptor (in this case, H+)
[electron donor] = concentration of the electron donor (in this case, 1/2 O2)
Remember that the concentrations should be in molar or activity units, rather than the molarity of pure water.
To calculate the redox potential using the Nernst equation, you are correct in using the formula:
E = E'_0 + (RT/F) * ln ([electron acceptor]/[electron donor])
In this case, the electron acceptor is H+ ions, which is related to the pH of the solution. The electron donor, on the other hand, is not H2O.
The reaction you provided is actually the reduction of oxygen (O2) to water (H2O), which means O2 is the electron acceptor and H2O is the electron donor.
To find the concentration of the electron donor (H2O), you typically use the concentration of its dissolved form, which is the concentration of water itself, not the molarity of pure water.
The molarity of pure water is indeed approximately 55.346 M, but in most cases, the concentration of water used in the Nernst equation is considered to be constant and essentially excluded from the equation. This is because the concentration of water remains relatively constant at around 55.5 M under normal conditions, and changes in its concentration have negligible effects on the overall redox potential.
Therefore, in this case, you can use a simplified version of the Nernst equation as follows:
E = E'_0 + (RT/F) * ln ([H+])
Where [H+] represents the concentration of H+ ions, which can be determined from the pH of the solution.
Note that E'_0 represents the standard electrode potential, R is the gas constant, T is the temperature in Kelvin, F is the Faraday constant, and ln denotes the natural logarithm.
By plugging in the appropriate values into this equation, you can calculate the redox potential for this reaction.