Carbon dioxide scrubbing & plant life

So we were watching Apollo 13 the other night, and during the scene where the team of engineers has to work to fit the square peg into the round hole (literally) to scrub the CO2 (I don’t know how/if we can do subscripts, but you get the idea) out of the spacecraft, the following question came up: Why would they not just load up the spacecraft with some plants prior to launch? Plant “inhales” CO2, “exhales” O2, everyone is happy. How efficient/inefficient is this process, i.e. How much plant life would you need to to keep 3 grown men alive in a closed capsule, assuming an infinite supply of water & sunlight to keep photosynthesis working…?

This sort of thing has been proposed for long-term missions such as trips to mars (and the stay there); I think it would be pretty much essential for that, but on shorter missions closer to Earth, it probably isn’t worth the hassle - plants take up a lot of room, make for extra weight, need looking after and, perhaps most importantly, you need a heck of a lot of them to produce enough oxygen for the crew.

I think it’s more likely to be tanks of algae (particularly if they can be harvested and turned into food) than oak trees.

According to this factoid, a patch of grass 25 feet on a side (625 sq ft) generates enough oxygen for one person. So you’d need a good-sized lawn to provide enough oxygen for the crew, and that’s not something you can stick in a space capsule. There’s just no place to store the mower, and you’d need a humongously long hose to water it.

It may be that some organisms such as algae could produce oxygen faster and in a smaller space than grass, but any such mechanism would still be heavier and more cumbersome than could be justified by a relatively short mission.

6CO2 + 6H2O + energy --> 6O2 + C6H12O6

is the photosynthesis equation. So the question is given that we have enough water how much energy is needed for 1 CO[sub]2[/sub] molecule? The number I could find says 8000kJ for 1 glucose molecule so that’s 1333kJ of energy per mole. A single breath has about .01 moles of CO[sub]2[/sub]. Now if you breathe 10 times per minutes that’s .16 breaths per minute. For three guys that’s 0.005 moles. The energy needed to keep equilibrium would be 666kJ/s. Now for internal lighting of 60 W/m[sup]2[/sup] you would need a surface are of 11 m[sup]2[/sup]. That’s a square 10ftx10ft of leaves

These numbers assume a lot (like my math). Such as perfect absorption of the light, no interference between leaves and it does not take into account the mass of the rest of the tree and the various support requirements it requires.

See what I mean.
666 kJ —> 666J