Reading this will be a waste of time. Especially, if you were attracted to the large cash prize mentioned in the title.
NASA is offering that money, but not in a lump sum. Odds are very low that reading this would be enough to collect even a small part of the prize money.
Mars does not have much atmosphere. What atmosphere it has, is mostly Carbon Dioxide (CO2).
NASA wants to do something with it and wants ideas.
The most obvious thing to do has drawbacks, but let us go over the basics.
They might split carbon dioxide into carbon and oxygen. Creating molecules of carbon, carbon monoxide, and/or oxygen. A supply of oxygen on Mars would be nice.
Electrolysis would do it.
Big prize awards do not go to problems that are easily solved.
What is wrong with electrolysis in this case?
A minor problem is that Mars is cold and has low atmosphere pressure. Making it more costly in energy to pull the molecules apart by electric fields.
A minor problem is that sending things to Mars is costly.
Here is a bigger problem.
Pulling molecules and atoms apart takes energy. Pulled apart, they are like bottle corks bouncing off the ceiling. Once those parts are freed, they have high kinetic energy. Making them reactive.
Possibly corroding the valuable electrodes.
Cars today have catalysts to convert Carbon Monoxide into Carbon Dioxide.
Maybe a catalyst could help turn Carbon Dioxide into breathable oxygen.
I have an idea that would work like a catalyst.
It involves Graphene and possible Nanotubes.
Graphene is like a door or window screen made of connected carbon molecules.
Nanotubes are graphene rolled into a tube shape.
Graphene foil is very good at holding electric charge.
They could induce layers of graphene to hold a cycle of electric charges. Nanotubes could be salted between those layers.
Carbon Dioxide forced into this assembly would have close electric field to induce electrolysis and might also have molecular forces applied to help separate Oxygen from Carbon.
A new type of catalyst which requires a sequence of electric charges onto the layers of graphene.
I would guess that it would be more effective if the Carbon Dioxide was present in large quantity (high pressure).
This is all just theory.
One side thought is that a bank of stacked graphene layers could also be a way to move ions.
Cycling the charge along the layers to push out 'desired Oxygen ions' out of the device.
Cycling a smaller charge to align Carbon-Oxygen molecules as they near the catalyst zone.
I hope I have given you some food for thought, in exchange for wasting your time.