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Atoms combine to gain stability. They gain stability when they lose energy. In my book, it's given that the potential energy of the system is reduced during chemical combination. But I am eager to know: how is the potential energy of the system reduced?

I want the theoretical reason.

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    $\begingroup$ What do you mean by "How?" – quantitatively (e.g. how change in PE is calculated) or qualitatively (e.g. how PE changes according to mechanism)? As of now, the question seems to be too broad and unclear. $\endgroup$ – andselisk May 14 at 14:38
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    $\begingroup$ 'How PE changes according to mechanism' is what I meant. $\endgroup$ – Kaushik May 14 at 15:03
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The potential energy that changes during reactions is electrostatic energy (+/- attraction, +/+ or -/- repulsion) from the charged particles (electrons and protons) within the atoms. The theory is described by Coulomb's Law (involving the potential energy of charged particles): enter image description here http://guweb2.gonzaga.edu/faculty/cronk/CHEM101pub/energy.html

Generally, this comes from the attraction of electrons to nuclei and the repulsion between electrons and between nuclei. When atoms/molecules/the "system" becomes more stable, we will see either an increase in the attraction present (electrons are closer or less shielded from nuclei) or a decrease in repulsion (electrons or nuclei are further apart). enter image description here http://ch301.cm.utexas.edu/atomic/#bonding/bonding-all.php

More advanced theories will involve the changing of the allowed potential energy levels of the electrons either within atoms (atomic orbitals) or within molecules (molecular orbitals). Whichever theories are used, the net result is that there is more attraction and/or less repulsion in a more stable/lower potential energy state.

Interestingly, by the first law of thermodynamics, if the potential energy decreases, another type of energy must increase (so you don't end up with less energy than you started). It is normally thermal energy that increases and then is transferred as heat. This process ends up being one the most important ones in understanding why some processes happen and some do not.

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how is the potential energy of the system reduced?

To be honest, there is no specific mechanism to decrease in potential energy.

Potential energy is merely a mathematical function that scientists came up with to describe energy changes in physical systems after rigorous measurements and calculated through equations backed by experimental results. These equations, assume certain facts making up the postulates of the theories we apply to predict behaviour of atoms. Based on that we predict the behaviour of molecule, interaction with other molecules.

The postulate involved is that potential arises from the interaction between particles and at infinite distances, such interactions are negligible, so potential energy is zero. As the particles or atoms, whichever one we are dealing with come closer, the interactions get stronger producing positive or negative potential energy based on the nature of those interactions which are experimentally measured by energy absorbed by the system or energy released by the system respectively.

Take the simple example of hydrogen atoms combining to form a chemical bond. The change in energy is -218 kJ/mol and that is all. We have atomic theories, most accurate one being those of quantum mechanics but, in the end, there is no answer to that why. It is just the way the universe works.

PS I am not sure whether the term postulate is better or axiom.

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The mechanism is complicated by quantum chemistry aspects, but the principle can be tracked down to the low level classical electrostatic energy analysis, or even to the classical gravitational orbit energy analysis.

An object $O$ is on a circular orbit around a massive central object $C$. This $C$ puts the attractive force $F=A/r^2$ on the object $O$ (this is common for gravity and electrostatic force) .

The $O$ has:

  • potential energy $E_\mathrm{p}=-\frac Ar$
  • kinetic energy $E_\mathrm{k}=\frac A{2r}$
  • total energy $E=E_\mathrm{p} +E_\mathrm{p}=-\frac {A}{2r}$

If the object is orbiting along an elliptical orbit, the values of kinetic and potential energies are just the mean values, with the total energy as their sum being constant.

The potential energy is equal to the mechanical work to be done to free the object from the force field of the central force.

The quantum chemistry complicates it a lot, but with great simplification the following is valid:

Exothermic reactions releasing energy get the energy from energy of valence electrons. These electrons form during the reaction "lower orbits" ( molecular orbitals) with less energy. This less energy means more energy would be needed to release them as free electrons.

The above mentioned molecular orbital has 3 main meanings:

  • It is a wave function as a particular solution of electron wave equation

  • Determines probability of electron occurrence in particular location

  • Determines quantum state of the electroncluding, but not limited to, its energy.

The quantum aspects put specific limitations, mainly these:

  • Only particular values of electron energy and of some other quantities are allowed

  • Electrons do not have classical orbits, nor particular position nor velocity.

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