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It's my understanding that aerobic cellular respiration is summarized in the formula $C_6H_{12}O_6+O_2→CO_2+H_2O+ATP$ (unbalanced). The glucose is thrown through a series of chemical reactions, ultimately resulting in the binding of a phosphate group to ADP to form ATP to store energy, and the carbon dioxide is a byproduct of this process. At the very end of this chain, though, there's a few electrons left hanging, and the oxygen is used to bind these to loose protons to form water.

It is also my understanding that the primary purposes of the lungs are to intake $O_2$ and exhale $CO_2$ for this process and their role in speech.

Assuming this is all correct, are the secondary, minor functions of the lungs important enough that if there was a way to siphon the $e^-$ and $CO_2$ to some other function and find something else to allow the larynx to work we wouldn't need to breathe?

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There's a fairly large misconception here. The huge amount of energy that's available from respiration, and which drives the synthesis of ATP, in fact comes from that reaction that you consider secondary, and that's the transfer of electrons to oxygen.

If you want to think of it as two separate reactions, then the first one $$Glucose + 12\ {NAD}^+ + 6 H2O ⇌ 6 CO_2 + 12 NADH$$ releases about 10 times less energy than the second one: $$6 O_2 + 12 NADH ⇌ 12 NAD^+ + 12 H_2O$$

The reason you get something resembling 30 ATP from a glucose molecule is because oxygen is such a great electron acceptor.

Many microbes can in fact use molecules other than oxygen as the electron acceptor, but in general it is much less energetically efficient than using oxygen.

You could try equilibrator for estimating the free energy available from various chemical reactions. First reaction and second reaction from above as examples.

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  • $\begingroup$ That was not at all what I had in mind with secondary purposes. I was referring to the various substances it filters out of the blood, which I assumed could easily have been delegated to the kidneys. I had completely forgotten about that part of cellular respiration. Thanks! $\endgroup$ – user25069 Jul 14 '16 at 22:29

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