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Part 2: No energy is stored in a carbon atom, in a chemical sense. Now, this is what I has come upon me just this morning as I was reflecting on this question:

What stores energy in chemistry? It came upon me that the statement "bonds store energy" is very flawed. Thus, I am afraid I would have to say that Zhe is wrong in his comments. But neither is it correct to say "free atoms (or bonded atoms) store energy". As much as I would not like to use this analogy to answer this question for possible points of contention regarding the relevancy, I feel nevertheless that it is appropriate: Consider two simple bar magnets (i.e. magnetic dipoles) which are attracted to each other. What holds them together is a magnetic force. To pull them apart, we input energy into them as work in order to overcome the force. This system of magnetic dipoles is analagous to how atoms are bonded to each other, just that the force of attraction between the two atoms are much more complex and that the nature is electrostatic, not magnetic (of course, we now know that magnetism is very closely linked to electric charges in physics but that is not important for this discussion).

Part 2: No energy is stored in a carbon atom, in a chemical sense. Now, this is what I has come upon me just this morning as I was reflecting on this question:

What stores energy in chemistry? It came upon me that the statement "bonds store energy" is very flawed. Thus, I am afraid I would have to say Zhe is wrong in his comments. But neither is it correct to say "free atoms (or bonded atoms store energy". As much as I would not like to use this analogy to answer this question for possible points of contention regarding the relevancy, I feel nevertheless that it is appropriate: Consider two simple bar magnets (i.e. magnetic dipoles) which are attracted to each other. What holds them together is a magnetic force. To pull them apart, we input energy into them as work in order to overcome the force. This system of magnetic dipoles is analagous to how atoms are bonded to each other, just that the force of attraction between the two atoms are much more complex and that the nature is electrostatic, not magnetic (of course, we now know that magnetism is very closely linked to electric charges in physics but that is not important for this discussion).

Part 2: No energy is stored in a carbon atom, in a chemical sense. Now, this is what has come upon me just this morning as I was reflecting on this question:

What stores energy in chemistry? It came upon me that the statement "bonds store energy" is very flawed. Thus, I am afraid I would have to say that Zhe is wrong in his comments. But neither is it correct to say "free atoms (or bonded atoms) store energy". As much as I would not like to use this analogy to answer this question for possible points of contention regarding the relevancy, I feel nevertheless that it is appropriate: Consider two simple bar magnets (i.e. magnetic dipoles) which are attracted to each other. What holds them together is a magnetic force. To pull them apart, we input energy into them as work in order to overcome the force. This system of magnetic dipoles is analagous to how atoms are bonded to each other, just that the force of attraction between the two atoms are much more complex and that the nature is electrostatic, not magnetic (of course, we now know that magnetism is very closely linked to electric charges in physics but that is not important for this discussion).

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Note that this is an edited answer. I have realised that there was initially a very severe error in my answer. Please re-read if you have not read this edited version.

In chemistry, we purely look at the energies stored in bondsthe process of bond breaking and bond formation when we look at energetics, as Zhe aptly pointed out in the comments. Thus, free atoms, such as a carbon atom, do not "store energy". As you have clarified in the comments, you wish to know, "in the context of the reaction $\ce{C + O2 -> CO2}$, where the realesedreleased energy comes from, how it is stored in carbon, and how does it become warmth". In my response, I will tackle this 3-part question. Note that I will not consider nuclear chemistry and the interactions of subatomic particles, other than the particle chemists are most concerned about - the electron.

Part 1Part 1: In the combustion of elemental carbon, energy is given off by the exothermic formation of two strong carbon-oxygen double bonds (endothermic), while the oxygen-oxygen double bond is broken (exothermic). The overall enthalpy change of the reaction is exothermic as the sum of the bond energies of the bonds formed is greater than that of the bonds broken. Thus, energy is released from the reaction.

Part 2Part 2: No energy is stored in a carbon atom, in a chemical sense. Bonds areNow, this is what I has come upon me just this morning as I was reflecting on this question:

What stores energy in chemistry? It came upon me that the statement "bonds store energy" is very flawed. Thus, I am afraid I would have to say Zhe is wrong in his comments. But neither is it correct to say "free atoms (or bonded atoms store energy". As much as I would not like to use this analogy to answer this question for possible points of contention regarding the relevancy, I feel nevertheless that it is appropriate: Consider two simple bar magnets (i.e. magnetic dipoles) which are attracted to each other. What holds them together is a magnetic force. To pull them apart, we input energy into them as work in order to overcome the force. TheyThis system of magnetic dipoles is analagous to how atoms are bonded to each other, just that the electrostatic interactionsforce of attraction between the nucleartwo atoms are much more complex and that the nature is electrostatic, not magnetic (of course, we now know that magnetism is very closely linked to electric charges in physics but that is not important for this discussion).

So going back to relevant examples, which would illustrate my next important point as to explain where energy changes comes from. Consider the chemical energy stored in food. We say that there is a chemical potential energy (at a very basic level of physics). But is that true? Does food and electronsmany fuels store energy? That may be correct from the point of view of the bonding atomsfuel undergoing reaction. Why do I say so? Remember: It is the process of bond formation and bond breaking that give off energy. Bonds themselves do not store energy. Only from reactions would we observe energy changes as energy is given off or taken in by the reactants to form products.

Part 3Let's go back to the combustion of elemental carbon. Using this perspective, neither carbon, nor carbon dioxide, nor oxygen store energy. The substances in the final and initial state do not store energy. In the process of bond formation and bond breaking, that energy is given off or taken in by the system.

Why do bonds not store energy? Well... bonds are merely electrostatic forces of attraction, in the most elementary sense. How can a force store energy?

Even if you don't believe the rest of my low-level explanation, please at least take away one thing: Bonds don't store energy.

Part 3: In chemistry, the energy is very often given off as heat in exothermic reactions. However, they can also be given off as light energy or sound energy.

In chemistry, we purely look at the energies stored in bonds when we look at energetics, as Zhe aptly pointed out in the comments. Thus, free atoms, such as a carbon atom, do not "store energy". As you have clarified in the comments, you wish to know, "in the context of the reaction $\ce{C + O2 -> CO2}$, where the realesed energy comes from, how it is stored in carbon, and how does it become warmth". In my response, I will tackle this 3-part question. Note that I will not consider nuclear chemistry and the interactions of subatomic particles, other than the particle chemists are most concerned about - the electron.

Part 1: In the combustion of elemental carbon, energy is given off by the exothermic formation of two strong carbon-oxygen double bonds (endothermic), while the oxygen-oxygen double bond is broken (exothermic). The overall enthalpy change of the reaction is exothermic as the sum of the bond energies of the bonds formed is greater than that of the bonds broken. Thus, energy is released from the reaction.

Part 2: No energy is stored in a carbon atom, in a chemical sense. Bonds are what store energy. They are the electrostatic interactions between the nuclear charges and electrons of the bonding atoms.

Part 3: In chemistry, the energy is very often given off as heat in exothermic reactions. However, they can also be given off as light energy or sound energy.

Note that this is an edited answer. I have realised that there was initially a very severe error in my answer. Please re-read if you have not read this edited version.

In chemistry, we purely look at the energies in the process of bond breaking and bond formation when we look at energetics, as Zhe aptly pointed out in the comments. Thus, free atoms, such as a carbon atom, do not "store energy". As you have clarified in the comments, you wish to know, "in the context of the reaction $\ce{C + O2 -> CO2}$, where the released energy comes from, how it is stored in carbon, and how does it become warmth". In my response, I will tackle this 3-part question. Note that I will not consider nuclear chemistry and the interactions of subatomic particles, other than the particle chemists are most concerned about - the electron.

Part 1: In the combustion of elemental carbon, energy is given off by the exothermic formation of two strong carbon-oxygen double bonds (endothermic), while the oxygen-oxygen double bond is broken (exothermic). The overall enthalpy change of the reaction is exothermic as the sum of the bond energies of the bonds formed is greater than that of the bonds broken. Thus, energy is released from the reaction.

Part 2: No energy is stored in a carbon atom, in a chemical sense. Now, this is what I has come upon me just this morning as I was reflecting on this question:

What stores energy in chemistry? It came upon me that the statement "bonds store energy" is very flawed. Thus, I am afraid I would have to say Zhe is wrong in his comments. But neither is it correct to say "free atoms (or bonded atoms store energy". As much as I would not like to use this analogy to answer this question for possible points of contention regarding the relevancy, I feel nevertheless that it is appropriate: Consider two simple bar magnets (i.e. magnetic dipoles) which are attracted to each other. What holds them together is a magnetic force. To pull them apart, we input energy into them as work in order to overcome the force. This system of magnetic dipoles is analagous to how atoms are bonded to each other, just that the force of attraction between the two atoms are much more complex and that the nature is electrostatic, not magnetic (of course, we now know that magnetism is very closely linked to electric charges in physics but that is not important for this discussion).

So going back to relevant examples, which would illustrate my next important point as to explain where energy changes comes from. Consider the chemical energy stored in food. We say that there is a chemical potential energy (at a very basic level of physics). But is that true? Does food and many fuels store energy? That may be correct from the point of view of the fuel undergoing reaction. Why do I say so? Remember: It is the process of bond formation and bond breaking that give off energy. Bonds themselves do not store energy. Only from reactions would we observe energy changes as energy is given off or taken in by the reactants to form products.

Let's go back to the combustion of elemental carbon. Using this perspective, neither carbon, nor carbon dioxide, nor oxygen store energy. The substances in the final and initial state do not store energy. In the process of bond formation and bond breaking, that energy is given off or taken in by the system.

Why do bonds not store energy? Well... bonds are merely electrostatic forces of attraction, in the most elementary sense. How can a force store energy?

Even if you don't believe the rest of my low-level explanation, please at least take away one thing: Bonds don't store energy.

Part 3: In chemistry, the energy is very often given off as heat in exothermic reactions. However, they can also be given off as light energy or sound energy.

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In chemistry, we purely look at the energies stored in bonds when we look at energetics, as Zhe aptly pointed out in the comments. Thus, free atoms, such as a carbon atom, do not "store energy". As you have clarified in the comments, you wish to know, "in the context of the reaction $\ce{C + O2 -> CO2}$, where the realesed energy comes from, how it is stored in carbon, and how does it become warmth". In my response, I will tackle this 3-part question. Note that I will not consider nuclear chemistry and the interactions of subatomic particles, other than the particle chemists are most concerned about - the electron.

In chemistry, energy changes arise due to two key processes: the formation of a chemical bond and the breaking of a chemical bond, where the term "chemical bond" refers to any of the following: ionic bond, covalent bond, metallic bond and intermolecular force of attraction (although some may dispute this). Bond formation is an exothermic process while the breaking of a bond is endothermic. This is rather intuitive as energy is needed as input to overcome the force of attraction between atoms. The exothermic bond making process may not be so intuitive. However, you can simply think of it as an application of the conservation of energy: If bond breaking is established to absorb energy, the opposite would give off an equivalent amount of energy. Another intuitive explanation why this is so comes from a very important chemical principle: Chemical systems, in general, prefer to be in the more stable state (i.e. a lower-energy state). Thus, bond formation and exothermic reactions, in general, are favoured thermodynamically.

Part 1: In the combustion of elemental carbon, energy is given off by the exothermic formation of two strong carbon-oxygen double bonds (endothermic), while the oxygen-oxygen double bond is broken (exothermic). The overall enthalpy change of the reaction is exothermic as the sum of the bond energies of the bonds formed is greater than that of the bonds broken. Thus, energy is released from the reaction.

Part 2: No energy is stored in a carbon atom, in a chemical sense. Bonds are what store energy. They are the electrostatic interactions between the nuclear charges and electrons of the bonding atoms.

Part 3: In chemistry, the energy is very often given off as heat in exothermic reactions. However, they can also be given off as light energy or sound energy.

Regarding your more difficult query about why energy is given off during bond formation, you can refer to my very brief explanation in Para 2. However, I fail to give you a detailed answer. Although I find no fault in Wikipedia's explanation based on the greater delocalisation of electrons upon bond formation, I do not believe that it is the main reason. Certainly, the strong attractive forces of the nucleus must be involved as well.