Do photosynthesis and respiration violate the law of conservation of energy?

Question

I don't know, if it's a physics question, biology or chemistry question but anyways here it is:

I have been taught that to produce one molecule of glucose in photosynthesis, 18 ATP molecules are used up, but that in respiration, oxidation of the same glucose molecule releases 38 ATP molecules. I just can't seem to wrap my head around it. Where are these extra 20 ATP molecules coming from (or in other words extra 20 units of energy)?

I know there's a whole lot of reactions occurring in the cell that utilize energy, but the reactions of photosynthesis and respiration are reversible and I don't think the path to make or break glucose actually matters with respect to the amount of energy used or released in the processes. Glucose always remains glucose so of course writing the same reactions in reverse orders shouldn't change the energy used/given out in the reaction.

I really can't understand why it should it depend on the path by which glucose is used or made as many people have told me.

So in my opinion these two processes do seem to violate the law of conservation of energy, so please help!

Answer 1

With slight adjustments to the scientific wording, what the poster states is in effect:

1. “…to produce one molecule of glucose in photosynthesis, 18 ATP molecules are used up hydrolysed”

and

2. “…oxidation of the same a glucose molecule releases phosphoryates 38 ADP molecules to ATP”

These statements are both correct…

…but the logical fallacy arises because the first one is incomplete.

In the context of energy production and utilization, it is essential to add:

…and 12 molecules of NADPH are used (i.e. oxidized to NADP)

This is because 1 molecule of NADPH is energetically equivalent to 3 molecules of ATP.
(Oxidative phosphorylation will convert NADPH + 3ADP to NADP⁺ + 3ATP).

Hence it takes 54 ATP equivalents to synthesize a molecule of glucose, but one only gets (approx) 38 molecules of ATP from oxidizing glucose.

If you think right back to the light reactions of photosynthesis, the photons of light energy are used to do two things — phosphorylate ADP to ATP, and to reduce NADP⁺ to NADPH.

Answer 2

Where are these extra 20 ATP molecules coming from (or in other words extra 20 units of energy)?

The sun. They are provided by high energy photons emitted by the sun. Those photons excite electrons into being in a higher energy state, and that higher energy electron state is harnessed and changed into high energy chemical bonds, like in ATP.