The question asks for which half reaction would the electrode potential increase as the pH of the solution increases.
The explanation states that as the pH is increasing, the H+ is decreasing and OH- is increasing. However, the correct answer has OH- in the reactants rather than the products. I would think it would be the other way around. Can you please further explain?
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Exactly as you stated, when the pH goes up, that means [H+] is decreasing, and [OH-] is increasing (it is getting more basic). The question itself says: "For which of the following half-reactions should the electrode potential be expected to increase as the pH of the solution increases?"
What is this "electrode potential"? Think of it as a measure of how much the reaction wants to occur, similar to Gibbs free energy. Indeed, this is confirmed mathematically by the equation ΔG = -nFE, where E (the emf of the cell) is based off of the standard reduction potentials of the cathode and anode (essentially the same thing as electrode potentials). Note that if ΔG is negative (spontaneous), then E will be positive because of the sign in the equation. Therefore, a positive E will represent a more favorable reaction.
By that logic, what this question is really asking is when having additional OH- around will be "good" for the reaction - more favorable.
The reduction potentials in the passage are not written as equilibrium reactions (with double-headed arrows), but these reactions must be reversible. A Galvanic cell and an electrolytic cell with the same electrodes will be running reverse reactions (that is, if Mn is being oxidized in a Galvanic cell, it's being reduced in the electrolytic cell). Therefore, these reactions are reversible.
That (reversibility) should make you think about Le Châtelier's Principle. If having OH- is favorable, that must mean that OH- is a reactant -- it will push the reaction forward, encouraging it to occur. The only answer that shows that is D.
For answer choice C, having additional OH- around would actually encourage this reaction to reverse, and thus makes it (as written) less favorable.
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