[Hannah LS (OP)]

Paul asks:

How are they going to get enough oxygen stored for a return journey to mars, even with recycling?

Any ideas?

[chiralSPO]

With recycling, you only need enough oxygen to assure a 20% content in the volume of breathed air. If they are breathing without masks, then the volume of the rooms within the spacecraft need to be filled to 20% with O₂. For instance, if the ship has only one room, with a volume of 600 m³, and is kept at a pressure of 1.0 atmospheres, you would need roughly 735 kg of air, about 150 kg of which would need to be O₂ (the remainder being N₂). If they have oxygen masks, one could use far less. Of course, that would require the ability to recycle the air at the same rate as it is processed by the people on board (scrubbing CO₂ will be at least as important--O₂ levels are safe as low as 18% or so, but if CO₂ levels rise up to 2%, the astronauts will be very uncomfortable!)

[Janus]

The human body uses ~ 550 liters of oxygen per day.  This is as a gas at 0.00143 kg/L.  Liquid oxygen, which is how the oxygen reserve would be stored, has a density of 1.141 kg/L, or ~800 times greater. This means you would need ~ 0.7 L of LOX per day for each person .  This works out to be ~255 L per person per year or just over 1/4 cubic meter. 
Thus a LOX tank the same size as that in the external tank of the space Shuttle (~2/3 the volume of the entire external tank), should hold enough LOX to supply a 20 person crew with 10 years worth of oxygen.

[evan_au]

Water and food are less compressible than oxygen, so I assume they will consume more mass and volume?

Recycling will be important here, too.