If molecular hydrogen is dissociated, or two hydrogen atoms in space collide, how much energy (in $\pu{eV}$, or perhaps $\pu{kJ/mol}$) does it take for an $\ce{H_2}$ molecule to form?

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    $\begingroup$ Zero. On the contrary, energy is released. $\endgroup$ Apr 8 at 7:58
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    $\begingroup$ I mean, it is a reaction just like any other, and I believe its activation energy is zero. $\endgroup$ Apr 8 at 8:04
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    $\begingroup$ Try to write H2 rather as \$\ce{H2}\$ ($\ce{H2}$) than as \$H_2\$ ($H_2$). The latter is typographically wrong. Element symbols should be upright. Furthermore, the MathJax extension mhchem), implemented in CH SE site, invoked by \ce{}, simplifies chemical formulas and equations a lot. $\endgroup$
    – Poutnik
    Apr 8 at 8:05
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    $\begingroup$ You can look up the H$_2$ dissociation energy, it is $D_0 = 432$ kJ/mol but if two H atoms collide they will not form H$_2$ (energy being conserved) as some energy has to be removed by a third body collision to stabilise the newly formed molecule. In total $ -432$ kJ/mol is released. $\endgroup$
    – porphyrin
    Apr 8 at 8:35

As porphyrin pointed out, two hydrogen atoms coming together from infinite distance will tend to bond, if the energy of the bond can be dissipated. This is unlike the situation where two magnets click together and stay together (because that interaction hits an absolute minimum, rather than a roller-coaster upswing as in the diagram. Ref 1). Two hydrogen atoms coming together from infinity would be attracted, gain kinetic energy from the potential energy of their separation, come too close, then repel each other - to infinity again. Over and over!

enter image description here

Perhaps instead of thinking of an activation energy, it is more relevant to consider a deactivation energy, which is all the energy that the bond needs to dissipate. You could ask whether it is possible for the two atoms to come together and emit a photon of the exact energy needed to quell the oscillation. Or even a lower energy photon, just to keep the molecule bonded, even if still in a high energy state. Alas! Selection rules seem to prevent this or at least minimize its likelihood, and recombination of hydrogen atoms is reported to occur thru three-body interactions. Ref 2

Can you do this any other way? Perhaps instead of observing them in free space, you could attach both atoms to a metal surface and let them find each other in small steps. Some metals, like zinc, evolve H$_2$ in acidic solution. Very very pure zinc reacts only very slowly with acids. Ref 3 My interpretation of that situation is that when the first evolution of hydrogen occurs, the hydrogen is in atomic form, and is attached (not strongly bonded) to the surface, whether that is actually metallic zinc or a nanothin layer of ZnO, perhaps as a ZnO - H moiety. A more stable state would be for two of these loosely attached hydrogen atoms to bind together to form H$_2$, but movement is inhibited (by a high activation energy). In less pure zinc, the presence of cathodic sites (like a little copper) provides a better site for H$_2$ evolution, lowers the activation energy and the process spreads over the rest of the zinc to allow rapid corrosion. Less pure zinc could be coated with a thin film of mercury to provide another surface for hydrogen atoms to be relatively immobilized on, and this also gives a high overpotential (a high activation energy)for hydrogen evolution. Ref 4

Some metals, noble metals which have no oxide layer, like Pt, Au and Pd, enable rapid migration of H$_2$ across their surface (thus not only a low, near zero activation energy, but also connection with a massive metal substrate that can accept some vibrational energy when two hydrogen atoms get together and dance for a while before settling down. They are good surfaces for evolving H$_2$.

A number of organic reactions were done with atomic hydrogen, using high activation energy to prevent formation of molecular hydrogen; this was classified as due to nascent hydrogen, a term now in disfavor. Ref 5

Ref 1. http://www1.biologie.uni-hamburg.de/b-online/library/newton/Chy251_253/Lectures/LewisStructures/Dihydrogen.html

Ref 2. I. Amdur, J. Am. Chem. Soc. 1938, 60, 10, 2347–2355

Ref 3. https://en.wikipedia.org/wiki/Zinc

Ref 4. https://en.wikipedia.org/wiki/Overpotential

Ref 5.https://en.wikipedia.org/wiki/Nascent_hydrogen

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    $\begingroup$ I wonder, what if both electrons happen to have the parallel spin, while $\ce{H2}$ needs them to be antiparallel ? Would not they repulse each other and refuse to approach close enough to react ? A photon or the 3rd object can carry away the spin to allow it to switch, but they first have to be willing to overlap. $\endgroup$
    – Poutnik
    Apr 8 at 14:36
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    $\begingroup$ @Poutnik: we think of the bond in H2 as between two s-orbitals. However there could be a bond between the s-orbital on one hydrogen and a p--orbital on the other. No spin problem, I think. Metastable for sure. Pretty diagrams of the excited states of H2 here: eso.org/~tstanke/thesis/fig6.html $\endgroup$ Apr 9 at 2:25

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