Why does the concentration of hydrogen ions increase in the electrolysis of dilute sulphuric acid?

In the electrolysis of dilute sulphuric acid, I'm given these two half-equations:


anode: 4OH-(aq) -> 2H2O(l) + O2(g) + 4e-


cathode: 4H+(aq) + 4e- -> 2H2(g)


Why does the concentration of hydrogen ions increase?


Isn't the concentration of hydrogen ions decreasing here, rather than increasing as it is being discharged at the cathode?


*N.B: (This question originates from a past AQA GCSE Question: see question 2 part (d) [here](http://www.nusa.org.uk/data/homework/files/wal/c2_7.pdf).)*




Replace the anode equation with your new equation. Then find the overall equation for the reaction. You are correct that the net **number** of $\ce{H+}$ is not changing as a result of this process. However, something is being consumed. What is it? How does that change the concentrations of the other species present?


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The sulphuric acid does not take part in any reactions, and is only present to ensure that water conducts electricity.


Only the water self-ionises to form hydroxide (OH- and hydrogen (H+) ions, and its concentration decreases as it decomposes to form O2 and H2. 


Therefore, the concentration of hydrogen ions from sulphuric acid increases during the electrolysis of dilute sulfuric acid.


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There does seem to be 'resistance' to be accurate on the underlying mechanics of electrochemical reactions, likely due to complexity and the presence of radicals and associated short-lived intermediates (see, for example, this [discussion on the electrolysis](https://chemistry.stackexchange.com/questions/12315/electrolysis-of-water) of water presented on this forum).


In the case of dilute H2SO4 with H+ ions, expect the reaction:


$\ce{ H+ + e- -> .H }$


And, the kinetically possible self-reaction of the hydrogen atom radical:


$\ce{ .H + .H -> H2 (g) }$


So, the H+ ion is indeed being consumed and the dissociation of H2SO4 increases to re-balance the equilibrium:


$\ce{ H2SO4 <=> H+ + HSO4- }$


As support for my discussion I also note the electrolysis of dilute H2SO4 in organic reduction reactions ([see this ebook](https://books.google.com/books?id=vrITBZ-_jwEC&pg=PA321&lpg=PA321&dq=products+on+the+electrolysis+of+dilute+H2SO4+include+radicals&source=bl&ots=_TVEC_jJ-E&sig=ACfU3U2L21CuUhTnRPvhnFn3UQGMG-Kysg&hl=en&ppis=_c&sa=X&ved=2ahUKEwj8mJSImOjoAhUiT98KHUPEC7wQ6AEwC3oECAwQLA#v=onepage&q=products%20on%20the%20electrolysis%20of%20dilute%20H2SO4%20include%20radicals&f=false)).


To reiterate, electrolysis half-cell reactions do not relate to mechanics, more informative as to a possible reaction's likelihood only.


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