Seems to me that using G=[ΔHf+H−H(Tr)]−T⋅S (well, actually correcting the entropy for partial pressures in a mixture of ideal gases) obtains some bewildering values for simple reactions. Consider H2→2H at standard pressure and standard temperature. If I'm calculating it correctly (which I am sure I am not), using the values at 298.15∘K in columns 2 (S), 4 (H−H(Tr)), and 5 (ΔHf) from the links above, I find that
G_H2= 0 kJ mol^-1 − 298.15 K⋅130.680 kJ K^-1 mol^-1 ≈ −38962 kJ mol^-1
G_H= 217.999 kJ mol^-1 − 298.15 K⋅114.716 kJ K^-1 mol^-1 ≈ −33984 kJ mol^-1
Which is great, the reaction isn't spontaneous. Except... if I recall correctly, G_mixture = ∑ μj nj, where nj is the number of mols of that species and for ideal gases at constant pressure & temperature, μj = Hj − Tsj = Gj.
That would imply the mixture of one mol of H2has a total gibbs of the aformentioned −38962 kJ/mol , but the mixture of two mols of H (pressure neglected) would be 2 × (−33984 kJ/mol)= −67969 kJ/mol, and now supposedly I've found that hydrogen gas spontaneously decomposes at standard temperature. That's clearly wrong.
(I've even done the calculations for a reaction considering pressure, and the doubling of mols of mixture post-reaction isn't enough to drive it into non-spontaneity except at absurdly high pressures)
So my question is: do I misunderstand how the Gibbs works for mixture of gases, how to read values off of the NIST themo tables, or both?