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Sorry if this is too elementary, but can someone explain why the following reaction can occur without a net influx of energy from some other process?
$C_6H_{12}O_6 + 6O_2 \to 6 CO_2+6H_2O$
And why does this one need an influx of energy?
$6CO_2+6H_2O\to C_6H_{12}O_6+6O_2$
I’m not quite sure which of two questions you are asking here, but as this is basic to understanding metabolism, I think an answer to both questions will be of most general utility, even if you personally already understand the answer to the first.
[1] The Gibbs Free Energy Change in a chemical reaction determines whether it will proceed spontaneously
If a reaction involves a negative change in Gibbs Free Energy (ΔG), it will proceed spontaneously; if not, an input of energy is needed to drive it.
The breakdown of glucose to carbon dioxide and water has a large –ve ΔG and therefore does not require input of energy — the reverse reaction has an equivalent +ve ΔG and therefore requires an input of energy to drive it.
This basic aspect of chemical reactions emerges from the laws of thermodynamics, and is explained in detail in section 1.3.3 of Berg et al., available on-line.
[2] Reactions that break bonds tend to involve negative changes in free energy
Why does the oxidation of glucose have a –ve ΔG, and its synthesis a positive –ve ΔG? This is because glucose oxidation involves breaking covalent bonds, and its synthesis making covalent bonds.
To understand the thermodynamic contribution of bond energies, the account in section 2.4 of Lodish et al. (available on-line) is recommended. In brief, ΔG = ΔH – TΔS, where H is enthalpy and S is entropy. The bond energies contribute to ΔH, and there is also generally in increase in entropy when two moieties become one, as mentioned in the answer by @MangoPrincess.
Footnotes
Not all chemical or biochemical reactions involve net formation or breakage of bonds — for example molecular rearrangements. In these cases more sophisticated chemical considerations are needed to understand the experimentally determined changes in free energy.
The importance in discussing biochemical reactions in terms of Gibbs Free Energy changes is that an energetically favourable reaction can be coupled to an energetically unfavourable one to drive the latter, and it is the quantitation of the ΔG that allow one to predict or understand this. It is also important as ΔG can be quantitatively linked to oxidation–reduction potentials.
Oxygen has a high electronegativity, in other terms it really likes electrons.
In this scale neon has the highest electronegativity of all elements, followed by fluorine, helium, and oxygen.
These are redox reactions. In the first reaction carbon was oxidized 0 -> +4 and oxygen was reduced 0 -> -2. In the second reaction the reverse happens. Nomen est omen oxygen is an oxidizing agent, so it does not like the reactions where it will be oxidized, since by oxidation it loses electrons. And it likes electrons. Really.
Forcing somebody to do something they don't want, always requires energy, and oxygen is not an exception. ;-)
Just to mention there is always an activation energy regardless of the exothermicity of the reaction. Remember; sugar doesn't burn spontaneously at room temperature... These are multi step reactions and enzymes lower the activation energy of each step, that's why you don't need to invest much by the first reaction. Ofc. a similar reaction can happen by burning sugar, but in that reaction the activation energy is much higher, and it is coming from the heat of the gas flame.
The first reaction is catabolism. It does require some energy input in the beginning ("energy investment" of glycolysis) but ultimately leads to net energy release through "energy payoff" of glycolysis, citric acid cycle, and finally electron transport chain and oxidative phosphorylation.
The final result is oxidation of glucose, and reduction of oxygen.. At various points, electrons transfer to NAD+ and FAD. Then, the reduced forms of these 2 electron carriers (NADH & FADH2) go to the electron transport chain, where electrons transfer to oxygen at the end (reduction of oxygen). Meanwhile, protons were pumped into the intermembrane space to create the proton gradient that drives ATP synthesis.
The second reaction is anabolism. The Calvin Cycle requires energy from ATP and NADPH to create the necessary bonds to build up sugars.
In terms of bioenergetics, degradation of a molecule is exergonic. This is favorable if you think about the second law of thermodynamics: there is more entropy when there are multiple, separate sub-units, while there is more order when one molecule made up of those sub-units. Synthesis of a molecule is endergonic (requiring energy). It IS favorable in the sense that we get sugar to eat and burn in the future.
In summary:
Note my answer leaves out specific details about the processes, but I hope this is basic enough to answer your question!
Source: Lehninger Principles of Biology, David Nelson & Michael Cox
