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Consider a simple chemical reaction, such as the association of two hydrogen atoms within the gas phase to form one hydrogen molecule. It is known that this reaction is related with energy release in the form of heat because the hydrogen molecule is more stable than the two hydrogen atoms.

Within a gas containing hydrogen atoms and hydrogen molecules, kinetic energy can be stored in several modes, including translation, vibration and rotation. If the energy of the reaction is to be released as heat, then directly after the reaction the temperature should slightly increase locally near the reaction. This local increase of temperature results in a transfer of energy to the "bath", and this transfer of energy is the heat.

Which one of the above mentioned modes of kinetic energy do you think is first activated directly after the reaction ? If I imagine two hydrogen atoms that decide to make a covalent bond at some "t", then directly after time "t" they feel a strong bonded radial force, and directly before they feel a weak "dipole force". So they should be pulled toward one another, possibly overshooting the equilibrium distance of the molecule, then relaxing back. So I guess the energy is dissipated in the vibration mode.

For my understanding, I would first like to focus on the case without radiation.

YoussefMabrouk
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2 Answers2

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The description of the mechanism by which a system reaches an equilibrium state is complex but once the equilibrium state has been reached one can use the equipartition of energy which is a "law of statistical mechanics stating that in a system in thermal equilibrium, on the average, an equal amount of energy will be associated with each degree of freedom. (A particle moving through space has three degrees of freedom because three coordinates are needed to describe its position.)".

Farcher
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Mechanisms of reactions
There may be different mechanisms of reaction, and how the energy is released depends on the specific mechanism. Besides transfer to the mechanical energy of the created molecules or the remaining gas, the energy can be released in a form of radiation (which is usually not considered when discussing an ideal gas, but which actually had to be taken into account in a realistic scenario - think about wood burning.)

Collision of atoms
Reaction between two atoms can be viewed as an inelastic collision (see, e.g., the discussion in How does an exothermic reaction release energy?) - the energy released either becomes the kinetic and rotational energy of the newly created molecule or is carried away by a photon (or a mix of both.) To speak meaningfully about the increase of temperature, many such reactions have to happen and the energy has to equilibrate between the molecules and atoms (via residual interactions responsible for establishing of the thermodynamic equilibrium - always mentioned in the introductory chapters of statistical mechanics textbooks, but not needed for the description of the equilibrium itself.)

Chemical potentials
Another way to view such a reaction is as a mixture of two ideal gases: a hydrogen atoms gas and a hydrogen molecules gas. We can then describe the reaction heat as a difference in the chemical potentials of the two species and apply Gibbs' phase rule (see, e.g., Why is the change in energy between products and reactants equal to the heat of reaction?.)

Chemical equilibrium
Finally, the inverse reaction may also happen - i.e., hydrogen molecules may absorb energy (via collisions or from photons) and dissociate into atoms. If we deal only with collisions, then eventually equilibrium is established between atoms and molecules, so that the rate of creation of new molecules equals to the rate of their dissociation. If the radiation is involved, then we need to consider the equilibrium between the atoms, molecules and the radiation (i.e., photon gas=black body radiation.) However, if the radiation is not confined (no resonator/mirrors), it will carry away some energy and the reaction would continue.

Roger V.
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