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I'm peeping the NIST thermo tables for $\text{H}$ and $\text{H}_2$, and I'm perplexed.

Seems to me that using

$$G=[\Delta H^\circ_f+H-H^\circ(T_r)]-T\cdot S^\circ$$ (well, actually correcting the entropy for partial pressures in a mixture of ideal gases) obtains some bewildering values for simple reactions.

Consider $\text{H}_2 \rightarrow 2\text{H}$ at standard pressure and standard temperature. If I'm calculating it correctly (which I am sure I am not), using the values at $298.15^\circ K$ in columns 2 ($S^\circ$), 4 ($H-H^\circ(T_r)$), and 5 ($\Delta H^\circ_f$) from the links above, I find that

$$G_{\text{H}_2}=0\frac{\text{kJ}}{\text{mol}}−298.15^\circ \text{K}\cdot130.680\frac{\text{kJ}}{^\circ \text{K}\;\text{mol}}\approx-38962\frac{\text{kJ}}{\text{mol}}$$

And

$$G_\text{H}=217.999\frac{\text{kJ}}{\text{mol}}−298.15^\circ \text{K}\cdot114.716\frac{\text{kJ}}{^\circ \text{K}\;\text{mol}}\approx-33984\frac{\text{kJ}}{\text{mol}}$$

Which is great, the reaction isn't spontaneous. Except... if I recall correctly,

$$G_\text{mixture} = \sum^\text{species}_j \mu_j n_j$$

Where $n_j$ is the number of mols of that species and for ideal gases at constant pressure & temperature,

$$\mu_j = H_j-TS_j = G_j$$

That would imply the mixture of one mol of $\text{H}_2$ has a total gibbs of the aformentioned $-38962\frac{\text{kJ}}{\text{mol}}$, but the mixture of two mols of $\text{H}$ (pressure neglected) would be $2\times(-33984\frac{\text{kJ}}{\text{mol}})=-67969\frac{\text{kJ}}{\text{mol}}$, 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?

Thank you!

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  • $\begingroup$ I've had experience doing calculations like this, but I have no idea what you are doing. Are you trying to determine the. equilibrium constant? $\endgroup$ – Chet Miller Oct 18 '20 at 15:59
  • $\begingroup$ See this thread, and get back to me with any questions you might have: chemistry.stackexchange.com/questions/141516/… $\endgroup$ – Chet Miller Oct 18 '20 at 16:11
  • $\begingroup$ @ChetMiller I'm writing a numerical solver to find the equilibrium composition of a mixture of species at a set T, P. The numerical solver constrains the system to preserve element quantities using the method of lagrange multipliers and then seeks a root for dG/dn_j by Newton's method. It does this all perfectly... it's the same method that Gordon & McBride use for NASA's CEA. The only problem is that it seems to want to disassociate species, and I think it's because I'm either pulling data from the NIST datasheets incorrectly or I am wrong about the basics--how to sum up system Gibbs. $\endgroup$ – neph Oct 18 '20 at 16:39
  • $\begingroup$ Perhaps I should reframe the problem. From NIST datasets, how would I calculate the Gibbs of 1 mol of H2 at 1 bar & 298.15 K? Then how would I calculate the Gibbs of 2 mols of H at 1 bar & 298.15 K? $\endgroup$ – neph Oct 18 '20 at 16:59
  • $\begingroup$ Your calculation for H doesn’t look right to me. The heat of formation should be 217999, not 217.999. $\endgroup$ – Chet Miller Oct 18 '20 at 19:13

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