[Big-Daddy]

Normally due to H⁺ being the reference state in solution, all 'standard molar' state variables and 'standard value of formation' state variables are 0 for it. But H₂(g) has a standard enthalpy of formation = 0 and standard molar entropy of 115 Jmol^-1K^-1. Then shouldn't ΔG°(298) for the reaction

2H⁺(aq) + 2e^-  H₂(g)

be -34,720 J and K = 1 * 10⁶, E°=+0.1799? Yet elsewhere in chemistry E° is defined to equal 0 for this reaction?

[Rutherford]

Some energy change must still happen, it isn't 0 for the reaction. You can divide this reaction into two, whose enthalpies are known: affinity energy towards the electron of H⁺ and bond energy (H-H).

[Big-Daddy]

Some energy change must still happen, it isn't 0 for the reaction. You can divide this reaction into two, whose enthalpies are known: affinity energy towards the electron of H⁺ and bond energy (H-H).

Yes I see your point. It's unreasonably opportunistic to hope for these two to cancel out. Same goes for entropy. But then how is the conundrum in post 1 explained?

[Rutherford]

Forgot to mention the dissolution. These processes can be usefull:
H⁺(g)+e^- H·(g)  Ea
2H·(g) H₂(g) E_H-H
H⁺(g) H⁺(aq) ΔH_sol
If ε=0, ΔG=0, and then ΔH=TΔS. Find the required data, use Hess' law and check whether the previous relation is true.

[Big-Daddy]

Obviously it won't be true - the opening post explains why. H⁺ has 0 molar enthalpy or entropy and 0 entropy and enthalpy of formation but _H2 has non-0 for molar enthalpy and entropy (http://www.genchem.net/thermo/thermotbl.html). What's going on here??

[Rutherford]

This is a quote from the web:

The standard enthalpy change of formation is the energy change observed when 1 mole of a compound is formed from its base elements.H+ ion has a standard enthalpy of formation of zero because 1) it's not a compound and 2) it's formed from only 1 element - Hydrogen.
If you want to know the energy change associated with the formation of H+ you need to look up the First ionization enthalpy of Hydrogen.

Also, electrons participate in the reaction of H⁺ formation, so Δ_fH can't be properly used in this case. That's why I suggest using the data I wrote and not Δ_fH. Seems that Δ_fH of ions can be used if only ions participate in a reaction.

EDIT: Now I think that entropy change of the reaction could also be a problem, as zero entropy is differently defined for an ion and for a neutral molecule.

[Big-Daddy]

Also, electrons participate in the reaction of H⁺ formation, so Δ_fH can't be properly used in this case.

Are you are saying that standard formation values cannot be used in redox reactions? I've never heard of this, can you give some evidence please. I thought they could always be used.

EDIT: Now I think that entropy change of the reaction could also be a problem, as zero entropy is differently defined for an ion and for a neutral molecule.

I did some reading, now I think I understand. The scale used for species in solution is shifted from that used for everything else, and H⁺ is set as 0 - this is for entropy as well as enthalpy. This explains the problem in the OP: to calculate for this reaction, we need the true thermodynamic entropy and enthalpy values for H⁺, not the 0, which comes after scaling and is used only if all the reaction is in solution.

But how does this work in the first place? Wouldn't arbitrarily shifting some values of entropy majorly off-set ΔG° from the correct, true thermodynamic value?

Same question but asked a different way: how can zero entropy be defined differently, without causing the wrong values of ΔG° and thus K?

[Rutherford]

These values can't be easily measured, therefore referent values have to be taken, and all other adjusted to it. There shouldn't be any contradiction as in every calculation we use the difference of enthalpy and entropy between products and reactants, e.g. you can get 2 simply by summing 1 and 1, but also from -1 and 3. This is a half reaction, and there has to be some enthalpy change, as I said before, while the ΔfH calculations would give zero, so I think that ΔfH can't be used in half reactions. It's probably the same for entropy.