Yhyjyk

In a question, Oxidation of metals/halogens by oxygen gas in acidic aqueous solution, there was a point made that reduction half-cells should not be reversed.

I was taught ($approx 1970$) in the following manner. Given the reduction half cells:

$$
beginalign
ceO2(g) + 4 H+(aq) + 4 e- &→ 2 H2O(l) &quad E^circ &= pu+1.23 V \
ceAg+ + e- &→ Ag(s) &quad E^circ &= pu+0.799 V \
ceBr2(l) + 2 e- &→ 2 Br-(aq) &quad E^circ &= pu+1.065 V
endalign
$$

To get the the standard oxidation potentials you reverse the products and reactants and you must also flip the sign of the reaction. So:

$$
beginalign
ceAg(s) &→ Ag+ + e- &quad E^circ &= pu-0.799 V \
ce2 Br-(aq) &→ Br2(l) + 2 e- &quad E^circ &= pu-1.065 V
endalign
$$

Now you can write a balanced chemical reaction as such:

$$
beginalign
ceO2(g) + 4 H+(aq) + 4 e- &→ 2 H2O(l) &quad E^circ &= pu+1.23 V \
ce4Ag(s) &→ 4Ag+ + 4e- &quad E^circ &= pu-0.799 V \
ceO2(g) + 4 H+(aq) + 4 Ag(s)&→ 4Ag+ + 2 H2O(l) &quad E_textTotal^circ &= pu+1.23 - 0.799 = +0.43 V
endalign
$$

and to get the cell potential the two half cells are added, one being positive and the other negative. If the EMF is positive the forward reaction is spontaneous, if negative the reverse reaction is spontaneous.

Is flipping the reduction reaction not the standard method taught these days to balance redox reactions?

I have a done significant amount of research over the past ten years to trace to origins of these electrochemical conventions and luckily got a chance to discuss these with some top electrochemists. I have been planning to write an article on this issue since it is a perpetual confusion. Basically, the origin of these "signs" issues originated in Germany and USA. The Ostwald school of thought, wrote the electrode potentials in accordance with the electrostatic sign of the electrode with reference to the standard hydrogen electrode. This was the so-called European convention. Keep in mind that electrostatic signs of the electrodes are invariant. It does not matter how you write them. A silver electrode in Ag+/Ag half-cell is always positively charged with respect to the hydrogen electrode under standard conditions.

The American school of thought, with its own influence such as Gibbs, Lewis and Randall, Ligane, Latimer, had a thermodynamic view of the signs relating electrode potentials to the Gibbs free energy. Latimer wrote a very famous book "Oxidation Potentials" which is available from Internet archives. Yes, under those conditions we can flip the signs back and forth while keeping Gibbs free energy in mind. The tug of war between European convention vs. American convention went on until the 50s-70s. Textbooks are usually 20 years behind current research...these issues lingered on.

Finally, electrochemists decided, including Allan J. Bard (from US who wrote a very influential electrochemistry book taught all over the world), that let us go back to the original notion- keep the electrostatic signs associated with the electrode potentials which are invariant with respect to the way we write them. This has "almost" terminated the sign convention issue of US vs. European signs of electrode potentials. The plus and minuses took almost a century to resolve. It is amazing to see the insight of those early scientists such as Ostwald, that world finally accepted their views.

I still teach switching the sign. I find it easier to remember adding up reduction potential and oxidation potential. The half reactions are written as reduction in a table of reduction potentials, so it makes sense that you have to treat the oxidation half reaction differently.

If the cell potential is calculated from reduction potential of the cathode half reaction minus that of the anode half reaction, there are more points of possible errors, including trouble with arithmetic.

You might argue that students learn more and gain deeper insight when given more opportunity to make mistakes, so maybe my approach is inferior. For example, students can use the approach I am using without knowing which electrode is the anode and which is the cathode.