Energy conservation is a universally important characteristic of matter that drives our cars, heats our homes, and powers our most destructive weapons. This article addresses what energy conservation means — and how it works — in the context of chemical reactions.
The Promise of Energy Conservation
The oxygen atoms in Earth’s atmosphere are almost always found in tightly bonded pairs rather than by themselves. This is because when two oxygen atoms share a pair of electrons, both can achieve the particularly stable arrangement of eight outer electrons.
But imagine that we have separated two individual oxygen atoms and placed them side-by-side in a vacuum, with no other particles nearby. Conservation of energy promises that if we allow these atoms to come together and form a bond, some equivalent amount of energy will be released into the surroundings. It is this corresponding release of energy that can be harnessed for useful work, e.g. by creating heat or driving an engine.
This seems a little fishy. What kind of energy will be released? Where will it go? What could absorb the energy since these atoms are sitting in empty space? And why must the energy go somewhere — why can’t the two atoms just come together and be happy without the world any the wiser?
To resolve this mystery we must slow down time and observe the interaction of the two oxygen atoms. Placed side-by-side, they immediately begin to move closer together because of the attractive electrical force between the positive nucleus of one and the negative electrons of the other (the dynamic electron clouds shift favorably for attraction via a “spontaneous” dipole).
There is an optimally stable separation distance between the nuclei of the two atoms, where the atoms feel neither an attractive nor a repulsive force. At this distance, they benefit from sharing electrons to form a full valence shell, yet they are not so jammed together that the nuclei repel each other. When separated by more than this distance, the atoms experience a net attractive force, and below this distance the internuclear repulsion dominates and they begin to push away from each other.
As the atoms approach this optimal point, they continue accelerating toward each other. When they arrive at this transition point, they are at the highest speed they have attained so far. What happens next?
The two atoms cannot suddenly dissipate their massive velocity upon realizing that they’ve reached the optimal bonding distance. The notion of bonding distance is meaningless to the atoms — they are just two objects hurtling toward each other according to Newton’s laws — and that means that they won’t stop until an opposing force turns them around.
At this transition point, the net force shifts to a slight repulsion because the positive nuclei are too close together. This begins to slow the approach of the atoms. As the distance between the nuclei approaches zero, the repulsive force keeps increasing toward infinity, slowing the atoms more and more. Eventually, the increasing repulsive force wears away all remaining velocity that the atoms have, and they come to a momentary stand-still, far too close together.
Of course, the atoms cannot remain at rest here. The strong repulsive force they experience at this distance sends them flying apart again. The net force turns attractive again at the optimal bonding distance, but they speed past this point too because of their built up kinetic energy.
Eventually the atoms run out of steam at the very position where they began, and the whole process repeats.
A convenient analogy for this process is a heavy ball swinging on a pendulum. Consider the position of the ball along the x-axis as it swings back and forth. The position at the lowest point in the swing corresponds to the optimal bonding distance in our oxygen story. If the pendulum could merely be placed at rest in this lowest energy position, it would happily stay there forever.
But if we drop the weight from a point on the right, it will swing past the bottom of the arc and come to rest at a point to the left symmetric to its starting positions, before beginning its swing back.
We can model this behavior mathematically in terms of kinetic energy based on the speed of the weight and potential energy based on its position. These quantities can be defined in such a way that their sum — the total energy of this system — is conserved at all points of the swing as a direct consequence of Newton’s basic laws of motion.
Because energy is conserved and we initially seeded the system with a positive amount of energy by pulling the ball up to the right, the pendulum in a vacuum will continue swinging back and forth forever. In the same way, the oxygen atoms in a vacuum will continue bouncing off one another indefinitely.
When Does it Ever End?
But the real world is not a vacuum, and we tend to find physical pendulums at rest with the weight at the bottom of the arc. Intuitively, we ascribe this to friction, or air resistance, but what does this really mean?
As the pendulum swings through the air, it collides constantly with tiny molecules in the air. On each collision, the pendulum imparts some of its momentum to the air molecules, which then bounce off at a higher velocity than before, and the pendulum is slowed down slightly. Although the air molecules are microscopic, the contribution of all of these collisions is non-negligible, and the pendulum is continually losing energy to the surrounding air. Eventually it will come to a complete stop.
The same phenomenon allows atoms to eventually bond together. If our two oxygen atoms are not in a vacuum, then it is possible for them to transfer sufficient energy to surrounding molecules to come to rest at a comfortable bonding distance. For example, if one of the oxygen atoms is suspended on the surface of a comparatively heavy dust particle, the dust can absorb the kinetic energy from the incoming oxygen atom and allow the two oxygen atoms to bond.
This is the mechanism we use to derive useful work from chemical reactions. For example, when wood is burned, carbon in the wood bonds with oxygen in the air to form the strong bonds in carbon dioxide. These carbon and oxygen are able to zap together and stick only because they pawn off all the excess energy formed by their attraction onto surrounding atoms, heating up the air.
Resolving the Mystery
We began with a claim stated in chemistry textbooks everywhere: when a chemical bond forms, an equivalent amount of energy is released into the environment. This phrasing begged the question: why? Why must a corresponding amount of energy be released?
Our new perspective makes the conservation of energy in this context obvious rather than mystical. It is not that whenever a bond forms, energy is magically released. Rather: the bond can never form unless the energy can be dumped off somewhere; otherwise the attractive force between the atoms would accelerate them past the bonding point and they would go on bouncing off of each other forever.