Thank you! This is exactly what I was looking for. However I'm having trouble finding support for this in my Kaplan Gen Chem chapter on Redox reactions. If it's not too much trouble would you be able to link me to something more definitive? In any case, thanks!
Now I know what you're confused about. It's a matter of convention and signs. I can write out any electrochemical half reaction and have an E for that half-reaction.
But according to convention, we assign everything a standard reduction potential with the understanding that the reverse of that reaction, the oxidation, has the same magnitude potential but with opposite sign. Now when you calculate the E(cell), you're usually taught that it's E(cathode) - E(anode). This is misleading and is just a terrible way to teach it because many people forget that in this particular equation, E(cathode) and E(anode) specifically refer to standard reduction potentials. It emphasizes memorization too much and not the conceptual understanding of it. When you calculate E(cell), you're basically just calculating the
net potential of the cell. Therefore, an easier way to think of it is E(oxidation) + E(reduction) where E(oxidation) is the E of the oxidation reaction and E(reduction) is the E of the reduction reaction.
For example:
Say you have a Daniel cell. At the anode is the following reaction: Zn ---> Zn2+ + 2e-. At the cathode is the following reaction: Cu2+ + 2e- ---> Cu. Now calculate E(cell). If you do this the way you memorized it, you just have to look up the reduction potentials of Cu2+ and Zn2+ and subtract Zn2+ from Cu2+. But that obscures the concept. The concept is that you want the net potential of this cell. If I asked you to tell me how many steps I've taken forward when I took 2000 steps forward and 1000 steps backward, you would say 1000. You got that by adding 2000 and -1000. We're going to do the same thing.
You can look the following up in a table of standard reduction potentials:
Zn2+ + 2e- ---> Zn, E = -0.76 V
Cu2+ + 2e- ---> Cu, E = +0.34 V
How do you solve? Well, first you look at the half cell reactions I've written above. The half reaction occurring at the cathode is the exact same as the one you looked up, so you don't have to do anything to that. But the half reaction occurring at the anode is the reverse of the reaction you're given. So, as I noted above, all you have to do is flip the equation you're given, acknowledging that the E of that reaction simply reverses sign. This is because of conservation of energy. If this were not true, you could theoretically create infinite energy by reducing something and then oxidizing it again later. So now you have something like this:
Zn ---> Zn2+ + 2e-, E = +0.76 V
Cu2+ + 2e- ---> Cu, E = +0.34 V
You calculate the net potential and get 1.10 V. So let's go back to the reduction half-reaction of Zn2+ - you notice that it's negative. Specifically, it's negative
relative to the standard hydrogen electrode. So what does reduction potential measure? It measures something's
affinity for electrons relative to hydrogen. Negative means that the thing simply doesn't like electrons relative to hydrogen, i.e. it doesn't want to be reduced. This is the concept you
must know. Again, a positive reduction potential means something wants to be reduced. This is the convention.
Now, apply the same concept here but with oxidation potentials. Oxidation potential is simply the formal reverse of reduction potentials - therefore, something that has a high affinity for electrons won't want to be oxidized (it wants to keep its electrons) and the potential for the oxidation reaction is negative and vice versa. You have 2H+ + 2e- + NAD+ <---> NADH + H+. You're told explicitly that NADH is a key electron-donating molecule. Does that mean it has a high affinity for electrons or a low affinity for electrons? It has a low affinity for electrons because otherwise, it wouldn't want to donate those electrons. Therefore, it
wants to be oxidized. Why? Because you're taking electrons from something that doesn't want electrons to begin with. So NADH + H+ ---> 2H+ + 2e- + NAD+ must have a
positive E. Now, just as you flipped Zn2+ + 2e- ---> Zn above, you flip the previous equation and flip the sign of the E as you do so.