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I'm not sure if this post is more appropriate here or in the physics section (it's about biophysics topics): if it's off-topic here, please excuse me and move it.

I was wondering if it's possible to calculate the enthalpy of formation of a gas molecule, in this example hydrogen chloride, in this way:

I calculate the energy required to form ions Cl- and H+ by summing the electron affinity of chlorine (-3.61 eV) and the energy of ionization of hydrogen (13.597 eV);

then I calculate the energy required to form the system of the two ions at distance a=127.4 pm (that is the distance between hydrogen and chlorine in the HCl molecule), considering zero the potential energy of the two ions at infinite distance:

(e is the electron charge)

[tex] U=\frac{e^{2}}{4\pi \varepsilon_{0} a } = -11.30\: eV [/tex]

If I sum all the energies I've found, I'd expect to find the enthalpy of formation of HCl gas,

but my value is different, (even if the order of magnitude seems to be correct):

my value is

13.597 - 3.61 - 11.30 = -1.313 eV

while the official value for enthalpy of formation of HCl gas (taken from wikipedia) is -0.95 eV.

Did I make some mistake or is this difference normal? Which factors I missed?

And I have another question: I noticed that if I calculate the self-energy (Born energy) of the two ions Cl- and H+ (using the atomic radius of each atom, and supposing to be in vacuum) the results are totally wrong and different from the values of the energy given by electron affinity and ionization energy (already at a first glance you may note that those results are both higher than zero!).

Cl- (a= 25 pm):

[tex] E =\frac{e^{2}}{8\pi \varepsilon_{0} a } = 7.19\: eV[/tex]

H+ (a=100 pm):

[tex] E =\frac{e^{2}}{8\pi \varepsilon_{0} a } = 28.79\: eV[/tex]

But isn't the purpose of the self-energy to approximate the energy of formation of ions? How can it be useful if its results are even wrong in sign? Naturally I know that I'm missing something, so please can you explain me? What are the limits of application of the self-energy?

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# Doubts about self-energy, enthalpy of formation and atomic radius

Can you offer guidance or do you also need help?

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