I suspect that you mean H2O not HO2? The latter is not a chemical compound that exists.

Atomic H and atomic O only exist under plasma conditions.

The formation of NO can use either reaction or both depending on the reactants available as the starting points.

Do you mean HO2-radical? What is the reaction?

 H + O2 = HO2(.) ?

DeltaG of the latter reaction must be known. Check NIST database. 

Dear Jeffrey J Weimer

I must disagree, HO2 can be stabilized by third body collisions in combustions. It is the most important molecule in all combustion.

I attach a figure from my paper. According to the figure you can see that the HO2 H + O2 channel is more favorable than the OH+O channel.

 There are about 30 kJ/mol difference between them. But this is the raw energy difference on the potential energy surface of the reaction. If you need I can give the zero-point energies and harmonic frequencies for the HO2 and for the O2 and you can estimate the free energy and also the dissociation constant. I think it is enough if you consider only the H + O2 channel. The contribution of the other channel will be not negligible only at high temperatures, but the H+O2 will be always the dominant.

(For high temperatures you can estimate the equilibrium branching ratio of the two channel)

@P Szabo: Strictly speaking, HO2 is the designation for a neutral chemical compound in some ambiguous phase state. Such a species per se does not exist, let alone existing in existing in a gas, liquid, or solid state. The systems you propose are with gas phase free radicals, not atomic species. The IUPAC designation for a free radical is specific ...

https://goldbook.iupac.org/html/R/R05066.html

Finally, proper conventions in thermodynamic expressions always demand that state indications for the species must be given in order to perform the calculations without ambiguity.

With all of this, the COMPLETE (i.e. correct, adequate, and proper) formulation for the chemical reaction under question is *H(g) + O2(g) *HO2(g). Using this approach, we will have no disputes or ambiguities, only the fundamental questions of the original posting.

Your question is confusing. Are you asking about a peroxide radical/ion?

To. actually answer your question. In an equilibrium reaction calculation all products that can be formed should be considered O2+H HO2 O + OH. Of course there are other reactions that also occur (H and O can react with lots of other things).You have to consider all reactions unless you can show conclusively that one of them is insignificant compared to the or is not fast enough to have a chance to approach equilibrium. There is also the possibility that the product from one of these mechanisms will continue to react with something else so quickly that a true equilibium cannot be achieved but a steady state composition of intermediates will probably still occur

Thank you all for your interest to my question. To be more specific, my question is about determination of dissociation reaction of HO2 which is of very great importance in combustion according to the paper "The Journal of Chemical Physics 103, 9947 (1995); doi: 10.1063/1.469884".

However, when I consider HO2 among the products in my equilibrium model using the dissociation reaction O2+0.5H2 HO2, I get 8.805e-7 to get its mole fraction for stochiometric combustion of methane whereas I get 5.62e-7 in GASEQ and NASA CEA. For all other species, (N2, O2, OH, H, H2, O, N, CO2, CO, Ar, NO2, H2O and NO) I get exact the same equilibrium mole fractions that of GASEQ and CEA.

Additionally, as seen in the attachment which I presented the reactions considered in four different studies, the dissociation reactions of NO differs. Authors either used H2O+0.5N2-->H2+NO or 0.5N2+0.5O2-->NO. Among many studies I investigated, I did not come across both of these are used to obtain the equilibrium NO mole fraction. I wonder how to decide which dissociation reaction to be used for a specific species.

I appreciate any help and comments on this problem.

There are a few possible explanations why the equilibrium information from 2 sources are different such as:.

* You have extrapolated one or more of the relationships beyond the temperature range where it is accurate.

* You have misinterpreted the information fro one or both of the sites. 

* One or both of the site has wrong information

If you can you should rrad the original publications to check that the data was reported and interpreted  correctly.

I actually had a similar experience a little over 15 years ago with publish and accepted information about what should be a very well understood system C6 paraffin Isomeration.  Two well respected simulators (Petrofine  and Process) gave very different answers.  Fortunately I knew which one was correct because I had a lot of commercial data.  I was able to find the original articles and  found there were two publications with lab data on C6 isomerization information each used by different simulators the one Process used accidentally reported liquid phase equilibrium data as if it was vapor phase equilibrium.  After correcting for VLE the two different sources agree very well. I hope the problem with your data sources is as easy to sort out as my problem was. 

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I have carefully read many original books and papers including the ones I have cited. I can not decide which one of the given reactions is true for NO formation and I want to learn its scientific reasoning. Then I expect that I will be able to determine which reaction to regard for H2O equilibrium. Thank you.

Don't let the words deceive you.  Look carefully at the raw data and the description of how that data was gathered.  If you are conviced both experiments were performed and reported correctly the next logical conclusion is that the reprocibility of the data is poor and you should average all of the data and include 95% condience limits for your work.

From the thermodynamic point of view, both reactions are valid. They are not independent to each other. In a system of N chemical species made by Na atoms, You need N-Na reactions. This is called a minimal reaction set. You can add other reactions to the set, but this introduces equations linearly dependent on the other. N2+O2=2NO and 0.5N2+0.5O2=NO are the same, with the difference that the equilibrium constant of the first reaction is the square of the second reaction. You should look to a thermodynamic books as https://www.researchgate.net/publication/235419279_Fundamental_Aspects_of_Plasma_Chemical_Physics_Thermodynamics

or the book by Smith and Missen  https://www.researchgate.net/publication/44409741_Chemical_reaction_equilibrium_analysis_theory_and_algorithms_William_R_Smith_Ronald_W_Miseen

Form the point of view of kinetics, thinks are very different, and in gas phase none of those reactions play a fundamental role, but the main channels of NO productions are the well known Zeldovich reactions N2+O=NO+N and O2+N=NO+O

Book Fundamental Aspects of Plasma Chemical Physics: Thermodynamics

Book Chemical reaction equilibrium analysis : theory and algorith...

If you use chemical equilibrium constants, you only consider linearly independent reactions. If you use a method based on minimizing Gibbs thermodynamic potential, you forget about chemical reactions and you take all reagents into account.

Regards,

If you use equilibrium constants you only consider the reaction pathway defined by those reaction constants and there is a danger that you may have left out a viable reaction pathway. On the other hand if you use Gibbs free energy minimization there is the danger that you assume all reaction pathways are viable even though some actually are not viable.

I used to and I was/am aware of the advantages and disadvantages of both methods. First - stoichiometric constraints, second - unnecessary reagents as wel as local minima.

Regards,