Where does the energy in coal bonds come from?


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> I have been told that when the plants intake carbon dioxide they break carbon and oxygen apart and the carbon is utilised in making the plant's body. This process is driven by the sun's energy so when they decompose and form coal the bonds of coal have the sun's energy stored in it.
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The above statement makes absolutely no sense to me.


When the sun's energy was utilised to separate carbon and oxygen how can the coal bonds store it?


If the coal bonds don't store the sun's energy where does the energy released on burning them come from?




Indeed it's in some way counterintuitive to say that the sun's energy is 'stored' in the coal bonds. Energy never comes from *breaking* bonds, it is released when *forming* bonds.


In the case at hand, the sun's energy is used to break carbon-oxygen bonds through photosynthesis. You get that energy back when carbon-oxygen bonds are formed by $\ce{C}$ and $\ce{O2}$ reacting to $\ce{CO2}$: that's where the energy of burning coal comes from.


The details can be quite delicate, since in most chemical reactions new bonds are formed at the same time as old bonds are broken. It then boils down to the relative energies of those bonds. In the case of burning coal, it costs less energy to break the $\ce{C-C}$ bonds of coal than what the formation of $\ce{C=O}$ bonds yield, so the reaction is exothermic.


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As has been pointed out the energy comes in the form of visible light from the sun. The reaction written in summary or overview is


$$\displaystyle \ce{2H2O \overset{light}\to O2 + 4H^+ + 4e^-}$$
$$\displaystyle \ce{CO2 +4H^+ + 4e^-\to (CH2O) + H2O}$$


where in the first step, the oxidation of water, the light does not react directly with water. In the second step, $\ce{CH2O}$ represents carbohydrate and the electrons are carried by proteins.


The overall reactions occur in proteins in the cell membrane of chloroplasts (in green plants) and the first step is absorption of a red photon typically of $700$ nm. This causes an electron to be transferred from a chlorophyll dimer, (the special pair) down an electron transfer chain involving cytochromes and other proteins that eventually reduces the carbon dioxide, the second reaction above.


As the special pair is now short of an electron it recovers this via a metalloprotein grabbing an electron from water. Using X-ray diffraction all these protein structure are now known and ultrafast spectroscopy has measured most if not all the rates of these primary processes.


In energy terms, the couple: CO2-glucose has a redox potential $\Delta V=-0.43$ eV and for $\ce{H2O - O2}$ is $+0.82$ eV so the total redox span is $1.25$ eV and as $4$ electrons are involved this is makes $5$ eV in total. A visible photon at $700$ nm has an energy of $1.77$ eV and as one electron is released /photon absorbed then the total energy supplied is $7.1$ eV, which is more than enough for this reaction.


However, there are losses in the process, and the efficiency rarely exceeds $0.36$ which makes the useable energy available $0.63$ eV/photon which is not enough thus we need $5/0.63\to 8$ photons in total. This suggest that two photosystems (see Z-scheme) are needed in green plants and this is indeed the case.


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**Photosynthesis is a little like the reverse of burning**


The idea that chemicals or their bonds *store* energy needs some clarification. The storage is always *relative* to some other reachable arrangement of bonds that can be achieved by some actual chemical reaction. So, if we say a specific compound "stores" energy we need to specify *relative to what*.


If we say coal *stores* energy what we usually mean is that we can burn coal (crudely, impure carbon) in air in a reaction that creates carbon dioxide and a large amount of heat. This is a simple widely observed and widely used reaction that we know releases energy.


But why? The energy is released because the total amount of energy tied up in the bonds of carbon dioxide is less than the energy tied up in the oxygen molecules and the solid carbon of the coal. When we burn coal that energy appears as light and heat we can use to warm our homes. We could, under different circumstances, react coal with other chemicals and get different outcomes (i'm sure coal will also burn in fluorine). But since the air around us has ~20% oxygen, burning coal is a very convenient way for us to produce heat.


The reason we say coal "stores" solar energy is because photosynthesis allows plants to drive the reaction in the opposite direction. Crudely (photosynthesis involves some very complex details) plants use the energy from sunlight to allow them to make a range of complicated carbohydrates by taking carbon dioxide from the air and water from the ground. (note photosynthesis also releases oxygen which is the main reason there is any in the atmosphere). The bonds in those more complicated molecules have higher net energy compared to the carbon dioxide and water they are made from and also compared to the products they would create if we burned them in air (wood burns too).


Coal is basically old plants that have been transformed by geological processes to impure carbon. So the ultimate reason we can burn it and release energy is because ancient plants captured energy from the sun to make more complicated molecules necessary for their growth. Burning is like the opposite of photosynthesis.


Coal "stores" energy because the arrangement of bonds in carbon and oxygen have higher energy than the arrangement in carbon dioxide and, in an atmosphere containing oxygen, we can release that difference as heat by burning the coal. But the ultimate reason the coal is the way it is is because plants made other complicated, higher energy, molecules by capturing solar energy to build them. Hence it is not unreasonable to say that coal "stores" energy from the sun (though it is oversimplifying a lot).


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Electrons around the nuclei of atoms exist in various energy states due to quantum mechanical principles. Due to these principles, they are confined to certain configurations (shells and orbitals). Chemical bonds occur when an electron of one atom can simultaneously take up a vacant position of another atom.


For example, a neutral atom of carbon has six electrons which balance the charge of its six protons; two in a complete inner shell and four in its outer shell. The outer shell of carbon can hold up to eight electrons. A neutral atom of oxygen has eight protons and eight electrons; two in the inner shell and six in the outer shell (which can also hold up to eight electrons). So, an atom of carbon can bond with two atoms of oxygen as follows: two of the carbon atom's outer electrons are shared with one oxygen atom, allowing the oxygen atom to "complete" its outer shell, and the other two of the carbon atom's outer electrons are similarly shared with another oxygen atom.


When a carbon atom and two oxygen atoms are bonded like this, the electrons are in a lower energy state than if each of the atoms existed in an independent, neutral state. Different configurations, such as two oxygen atoms bonded to each other, or a cluster of carbon atoms bonded to each other also each have different energy states (of their outer electrons). Plants have complex arrangements of special molecules which allow them to use energy received from sunlight to break the bonds of carbon dioxide and water molecules to build sugars and release molecular oxygen. Breaking the carbon dioxide and water bonds is all about elevating electrons in those atoms to higher energy states. This is how/where the energy is stored. When carbon and oxygen combine to form carbon dioxide, the electrons drop to lower energy states, which means energy is released.


As plants decay into substances like coal, bonds are reformed and some energy is released - that's what drives the decay process, but the bonds between carbon atoms in coal and in molecular oxygen are still at a higher energy state than in carbon dioxide.


There is one other notion here about activation potential. The resulting oxygen and sugar molecules are stable (they don't immediately react and go back to carbon dioxide and water) because it takes some amount of energy to initiate the transition. It's like a hill with a small dip at the top, you can roll a ball up the hill over a lip and into the dip and it won't roll back down again unless you first lift it back over the lip.


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> When the sun's energy was utilised to separate carbon and oxygen how can the coal bonds store it?
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You use the word 'utilised' as if this means the energy is used; it no longer exists. But energy never disappears, it just changes form. When you take a rubber band and pull the ends apart, you consume (or better: move) energy, which is stored in the rubber band. If you now release one end of the rubber band it will snap together, the energy is released. Imagine there is a rubber band between the oxygen and the carbon atoms\*, by separating the two, you add energy to the system. By combining the two, you release that energy again.


\*The analogy does not hold for very long, moving the atoms further apart will not increase the energy stored in the system.


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[Here's](https://www.sciencedirect.com/topics/earth-and-planetary-sciences/coal-structure) a nicely simplified description of the structure of coal:



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> V.D Macromolecular Nature of Coals
> Coals are believed to be three-dimensionally cross-linked macromolecular
> networks containing dissolved organic material that can be removed by extraction.
> This model offers the most detailed and complete explanation of the chemical and
> mechanical behavior of coals. It is a relatively recent model and is somewhat
> controversial at this writing. The insoluble portion of the coal comprises the
> cross-linked network, one extraordinarily large molecule linked in a three-
> dimensional array. This network is held together by covalent bonds and hydrogen
> bonds, the weak interactions that play such a large role in the association of
> biological molecules. The extractable portion of the coal is simply dissolved in
> this solid, insoluble framework.
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That was taken from a 2003 article in an encyclopedia about coal structure.


The plant matter the coal came from was somewhat similar in nature in that it also contained a lot of cross-linked organic molecules. The above can be read to imply that each lump of coal is a single solid molecule plus dissolved liquids and gasses but that's probably taking it a bit too far.


Lots of chemical reactions happen under heat and pressure including increased cross-linking of organic molecules. The heat and pressure can be viewed as shifting bonds as well as adding them. In the former case, that's still at least somewhat representative of the original sun-energy donation to the cause.


Note that the dissolved organics like methane (natural gas) are probably a mix of decomposed plant material and compounds produced under that same heat and pressure. If you want to get a sense of what those are, read up on making coke from coal for use in steel making.


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