[Diamonds]

Hello,

The half-reaction at the cathode for the electrolysis of sulfuric acid was always given to me as:

2H⁺ + 2e^-  H₂

However, now I am seeing it as:

2H₂O + 2e^-    2OH^- + H₂.

Aren't these the same things?
Adding two protons to each side makes two waters on the right, which cancels with the two waters already present on the right. Giving the two protons combining with two electrons to form hydrogen gas.

Writing either of these when a test says "Write the balanced equation for the cathode half-equation" is fine right?

Thanks in advance!

[Borek]

Both are correct, although in the solution with low pH I would prefer the first one, while in the solution with high pH I would prefer the latter.

[Diamonds]

So if a question were to ask me about the pH in the cathode after it is done with electrolysis, I would need to use the second one with the hydroxide, and then just do pOH and convert to pH?

Thanks for your response!

[Borek]

Please elaborate, I am not sure I understand what you are asking about.

Before electrolysis you have a solution of sulfuric acid, after electrolysis you have a solution of sulfuric acid (just a little bit more concentrated). In both cases pH can be calculated in the same way.

[Diamonds]

Oh I'm sorry, I meant a solution of sodium sulfate, Na₂SO₄. Basically the question says it's being electrolyzed for a certain time with a certain current, then it says what is the pH in the cathode after it's done being electrolyzed. So for that I would need the cathode half-reaction that has a hydroxide in it, right?

[Borek]

Think harder. What is the TOTAL electrolysis reaction (anode and cathode included)?

[Diamonds]

The total reaction is 2H₂O    2H₂ + O₂.

But the question asked only for the cathode pH, so why would I be considering the total galvanic cell reaction?

[Borek]

OK, sorry, slight miscommunication.

Question is a little bit ambiguous. If there is efficient mixing and no separation of anode and cathode spaces, solution stays neutral. But if they are separated then yes, removing hydrogen at cathode means locally increasing concentration of OH^-.