predicting potentials of cells from a cell diagram

[Kaylee Nezwek 1D]

hey! for textbook question 6N #3, it asks to predict the potential of each cell.
part a.) Pt (s) | H2 (g, 1 bar) | HCl (aq, 0.075 M) || HCl (aq, 1 M) | H2 (g, 1 bar) | Pt (s)

In the solutions manual, they used these half-rxns:
2 H+ (aq, 1 M) + 2 e- --> H2 (g, 1 atm) and E(cathode) = 0 V
H2 (g, 1 atm) --> 2 H+ (aq, 0.075 M) + 2 e- and E(anode) = 0 V
E(cell) = 0 V

I'm really confused on why these were used as the half-rxns? Why is HCl not used?Also, then in solving for E, the work shows: E = 0 V - (0.02569 V / 2) * ln([H+, 0.075 M]^2 P(H2) / [H+, 1 M]^2 P(H2)). I'm also confused on the values used within the ln expression...

Can anyone explain why these half-rxns were used and why the values in the ln expression were used? Maybe I just don't know how to solve these types of problems, but I was really confused on how to approach the problem and how to interpret the solutions manual. Thanks!

[Sara_Lim_2C]

I'm not entirely sure, but I think because HCl is a strong acid, it fully dissociates in water (and since it's aqueous we know it's in water). So HCl in that cell diagram would basically be H⁺, and that's why the 2H⁺ half reaction is used. That was my assumption, but I'm not sure if that's the exact reason. Could anyone else confirm?