Gedankenexperiment in thermodynamics: what is wrong? Good day.
A notion of chemical potential teaches us, that a chemical reaction
$A+B \to C$
at finite tempereture actually goes in both directions
$A+B \rightleftharpoons C$
and the intensity of a given diection depends on:
1) Temperature
2) Energy difference E(A+B) versus E(C)
For my argument it is enough that it exists in both directions.
Let me assume A, B and C are gasses and A has the smallest molecules, B intermadiate and C the biggest ones.
I put A,B,C in a box and an quilibrium settles. Then I use a molecular sieve to extract A, I prevent A from going back to the box by using a vacuum-cleaner. A new equilibrium with excess of B comes into the place. I use (for a differential time where no more A passes) a molecular sieve with bigger holes to extract B. Then alternating sieves frequently I extract A and B, colling down the pool. 
Is that possible?
I think it contradicts the second law of thermidynamics... I create A and B by cooling the pool. Then I can combust A and B....
Let us say $A=H_2$, $B=O_2$ and $C=H_20$ - it would lead to "energyless" dissociation of water.
What is wrong with my arguments? :


*

*"Bothdirectional" chemical reactions are a fact.

*Existence of molecular sieves is a fact...
Thanks
 A: Assuming the reverse reaction (the endothermic one) will happen under the conditions of the presumably thermally isolated box, it will reduce the temperature inside the box. As the temperature decreases, the probability of this reverse reaction occurring will decrease, since it is not energetically favourable, so the reaction will become slower and slower as time passes.
Your suggestion is to speed it up by inducing a favourable chemical potential by extracting the left hand molecules using a sieve. This will generate a chemical potential difference across the molecular sieve, and to ensure that you are extracting the correct molecules using your vacuum cleaner (i.e. to stop them from going back through the sieve), you will need to apply a larger chemical potential difference than the one across the sieve. This energy you will need to supply to your vacuum cleaner will increase as the conditions for the reverse reaction become less and less favourable.
These "free energy" problems generally boil down to achieving a level of engineering efficiency that is impossible. Your system needs to be perfectly thermally isolated, and your vacuum cleaner needs to be lossless in order to get a net energy loss of zero (there is no question of gaining energy from the process).
