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New Contributor

## Question about reading NIST datasheets & Gibbs energy of reaction

I'm peeping the NIST thermo tables for H and H2, and I'm perplexed.

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

and

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?

Thank you!

4 Replies
Contributor III

## Re: Question about reading NIST datasheets & Gibbs energy of reaction

Dear Anton,

I'm not sure about rechecking all of your assumptions and calculations.  However, I did find this resource (Khan Academy) to provide a much clearer explanation of what Gibbs Energy is all about.  Maybe it will also give you some idea of what may be missing in your exercise.

https://www.khanacademy.org/science/ap-chemistry/thermodynamics-ap/gibbs-free-energy-tutorial-ap/a/g...

Best regards,

Steven

New Contributor II

## Re: Question about reading NIST datasheets & Gibbs energy of reaction

Anton--

Are you sure the entropy values are in kJ mol-1 K-1 rather than in J mol-1 K-1?

130.680 kJ K^-1 mol^-1 is a lot of entropy.

--David Shobe

Contributor

## Re: Question about reading NIST datasheets & Gibbs energy of reaction

David Shope has pointed out the answer. The units of heat capacity and entropy are J/(mol K).  Units matter!

Needless to say, the cleavage of H-H to 2H is endothermic by exactly the H-H bond energy: 2x 218.0 kJ/mol = 436.0 kJ/mol. The entropy effect is small at room temperature. This bond cleavage is endergonic by 2x 203.3 kJ/mol.

Alex Madonik

New Contributor

## Re: Question about reading NIST datasheets & Gibbs energy of reaction

Yes, that is definitely the problem!