Well, actually we probably could. And I find this a puzzle myself, why research into this isn't given more priority. First, if it is just oxygen you don't need plants, a strain of green algae called Chlorella which apparently is ideal for this, takes up CO2, produces oxygen, has very little by way of any other requirements except sunlight. Then in a later development, they now use Spirulina which works like Chlorella but is also edible by humans, which Cholorella is not.

There were early Russian experiments that showed that you just need eight square meters of algae to provide all the oxygen needed for a human being.

That may seem a lot, but algae can be stacked in trays above each other and then you use artificial light for the illumination. This worked just fine on the ground, supplied Russian volunteers with enough oxygen to breath throughout the six months duration of their longest experiments. They have also been able to grow some of their own food as well in these simulated closed system conditions.

And - modern LED lights like this are about an order of magnitude more efficient than the earlier ones

I figured out, a modern LED grow light like this would need about 4.8 kW to supply lighting for the algae for a crew of six.

This is the early Russian experiment which used Chlorella - which is great for producing algae but is more or less inedible.

More recent experiments use Spirulina

This is the idea of the Melissa project. It differs from BIOS-3, in more use of microbes and - basically high grade composting. While for BIOS-3 they burn the plant wastes in an oven. Both approaches have advantages and disadvantages.

So the ISS would seem to have enough power for lighting to supply to the algae - which you would do with light pipes or similar.

The actual volume of algae needed for one person is very small.

You could also use light collectors like this to collect light from outside the ISS and pipe it into your algae tank using light tubes.

That then would use no power at all, when the ISS is in daylight, as it is a lot of the time.

This would work especially well for BIOS-3, not so useful for Melissa.

This is something that the ESA is testing in space.

Algae and plants can behave differently in orbit. And there is a lot more to life support than just producing oxygen and removing CO2. But it's an important part and I don't understand myself why this Russian system, proved to work on the ground, has never been tested in space.

There was a news story just today about the astronauts eating the first ever food grown in orbit and eaten there (until now they have grown plants but not been permitted to eat them as it was for research).

But this is such a long way away from what has been achieved in these ground based simulations, with all the oxygen and a fair amount of food all produced from plants.

They could grow all their food also, if we find suitable crops for zero g - or else find a way to supply low g levels (say by spinning the containers with the crops).

This shows the Russian experiments again - in the BIOS3 closed system experiments, they produced nearly all their food - needing some supplement, but most of the bulky stuff - from just 13 square meters per person.

So - it's not so hard to produce food also in space. Using hydroponics or aeroponics - high tech methods - but they are used on the ground also, for agriculture, so not so hugely expensive, and in space the expense would be a small part of the cost of getting it up there.

Also - plants tend to be perceived as unreliable - but - we aren't talking about your allotment where a pest or disease of plants can decimate a crop if unlucky. In the ISS or another such system, there are no pests or diseases of plants. Even on Earth in hydroponic facilities, the facilities can be sterilized of them.

So then - plants are in many ways more reliable than machines. Even if your entire algae crop dies through some malfunction - so long as you have a few viable cells, you can grow it again. Try doing that if your machines for making oxygen break down.

In her 2006 masters thesis Living in Space, for the Swedish Physics in Space program at Uppsala university,Maria Johansson compared the Russian BIOS-3 with MELiSSA and the current ISS system.

On the assumption that the ISS uses solar power for BIOS-3 type system, the power requirements, she found, were

ISS: 1.2 kW
MELiSSA 4 kW
BIOS-3 0.92 kW

She finds that the ISS system has least startup mass, of 1.773 metric tons, but much higher supply mass per day of 6.5 kg.

Melissa has most startup mass of 15.711 tons, and supply per day 1.4 kg

BIOS-3 has 6.250 startup mass, and 0.5 kg supply per day.

BIOS-3 if it can be got to work on the ISS, breaks even after two years.

MELISSA breaks even after 7.5 years. But with more use of short lived bacteria, it is more easily controllable.

In any case BIOS-3 was designed for planetary surface habitats originally and not tested in space. So it would need some work for zero g, testing to find which of the plants they used will grow in zero g and what the performance is like - or else you use centrifuges for gravity in space.

MELiSSA is in the early stages of testing in the ISS with small scale experiments with the algae.

For more on this see my
Could Astronauts Get All Their Oxygen From Algae Or Plants? And Their Food Also?

Which I've also made into a kindle ebook

Could Future Astronauts Get All Their Oxygen from Algae and Plants?: And Their Food Also (Amazon)

(have just updated this answer, 27th Sept 2015 - complete rewrite, after the research into the literature I did for the Science20 article and kindle ebook)

Excluding brief periods of high beta angle, the ISS spends almost half of the time in darkness, so insolation is not 24/7.

It takes around 10,000 leaves to provide the oxygen needed for one person. There are 6 people onboard the ISS. 60,000 leaves is a lot of leaves. All of those leaves would need sunlight for photosynthesis to happen, but the ISS doesn't have that many windows. Very little natural sunlight enters the ISS. The main windows in the cupola and lab have to be protected, so their shutters are closed when the windows are not being used. The remaining windows are tiny portholes.

So, you might suggest using artificial light. Okay, but we've already thought about that. The power usage and thermal impacts would be more hassle than the benefit from the plants.

And, we still haven't addressed where we would put all of these plants or where the water would come from to keep these plants healthy. Nor have we addressed the time the crew would have to devote to caring for the plants.

They don't get sunlight 24/7. When their orbit passes around the night side of Earth, they are in darkness.

There have been experiments on using plants to make oxygen, but we can't produce anything like enough in the space that we have. As this article explains, a human being needs about 740 kg of oxygen a year, but to provide that would require seven or eight mature sycamore trees. They take up a lot of space and need a lot of water. Also, most plants are adapted to earth gravity. Nobody knows quite what happens if you try to grow a tree in space.

How many trees are needed to provide enough oxygen for one person?

Water is too heavy to send in large enough quantity. But there is frozen water on Mars. Most plants could not survive the cold, lack of O2, low atmospheric pressure, and the radiation. And although there is CO2 , the Martian “air’, is less than 1% of Earth’s atmospheric pressure. It is way too is too thin to support plant life.

However, cyanobacteria which photosynthesizes can possibly live in Mars-like conditions. And large numbers would not be too heavy. The Great Oxygenation Event on Earth 2.45 billion years ago was caused by cyanobacteria.

“Planetary researchers at the German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt; DLR) simulated the conditions on Mars for 34 days and exposed various microorganisms to this environment. "During this period, the lichens and bacteria continued to demonstrate measurable activity and carry out photosynthesis," “The water required for this process is present in the morning and evening of the Martian day, when humidity condenses as precipitation across the surface, and the organisms can absorb it”. Surviving the conditions on Mars This is the sort of polar lichen that did fine in Mars conditions.

Polar and high altitude lichens have also been found able to survive Mars conditions. Lichens are a symbiotic relationship between fungi and algae (plants) or cynobacteria. Lichen have been even able to survive the vacuum of space. Lichen survives in space Lichens are macroscopic. They photosynthesize. They are multicellular and they are eukaryotes. They are well known to live in the most extreme environments. In the experiment during the Foton-M2 space mission they were exposed to vacuum, wide fluctuations of temperature, the complete spectrum of solar UV light and bombarded with cosmic radiation for 14 days. Analysis post flight showed a full rate of survival and an unchanged ability for photosynthesis.

Also, bacterial life survives high in the stratosphere on Earth which has an atmospheric pressure, and temperature and radiation similar to Mars. Janibacter hoylei sp. nov., Bacillus isronensis sp. nov. and Bacillus aryabhattai sp. nov., isolated from cryotubes used for collecting air from th... - PubMed - NCBI

Methanogens which make methane in conditions without oxygen have also been found to be able to live in Mars-like conditions. Some use CO2 and hydrogen to make methane and water. In some places they get that H from reactions in basaltic rocks. Methane (and water vapor) are much better greenhouse gases than carbon dioxide. With enough methane released, Mars would warm, releasing frozen CO2 and then melting water. Earth organisms survive under low-pressure Martian conditions

However, even if we can find organisms that will produce oxygen by photosynthesis on Mars in thousands of years (or more), the bigger problem will be keeping the atmosphere from being from being lost into space by solar winds and destoryed by radiation. Mars has no magnetosphere to protect the atmosphere. The lack of a magnetosphere is thought to be one reason for Mars's thin atmosphere. Mars’ magnetic field - DTU Space

Mostly, this has been answered. As one who has written numerous columns about settling Mars and also a novel on the same topic, I’ll add my 2-cents worth.

Plants will not grow on Mars. The air, at ~1% of our atmospheric pressure is too thin to support plant life. The low pressure and cold will effectively freeze-dry any plant and so killing it very dead. Seeds will not fare any better, although they could remain viable until planted in a more favorable environment.

Our atmospheric pressure here on Earth is about 1,000 millibars. On Mars, it’s around 10 millibars depending upon location. Of the Earth’s air, 400 ppm (these days!) is CO2. That’s about 0.4 millibars. The oxygen is just above 20% or 200 millibars. If you transformed all of the CO2 into O2, you wouldn’t even get close to breathable. (Note that Mars had greater partial pressure of CO2 than the Earth does.)

In simplest terms, there’s not enough CO2 in the atmosphere of Mars to turn into O2 for us to breathe, not even close.

With respect to the way the question is phrased, why bother with separate space ships. They probably wouldn’t land near enough to each other to be useful. Seeds are much lighter than the water required. Still, the water would quickly freeze and then sublimate into the atmosphere, not even making a dent on the dryness there.

Much about Mars is conjecture among the general population and based on science fiction books and movies. The most recent one to gain fame is The Martian. This book has several misleading concepts. For example, how can 1% atmosphere blow over a space ship (must be very light or poorly balanced)? How can a Mars wind pick up poles and blow them, like javelins, into a person penetrating the suit and skin? How can you grow potatoes in toxic soil?

Mars is very, very hard to settle. It’s an odd place with red skies and blue sunsets. There is no visible life there. For the next 100 years (give or take a number of decades), it will look the same unless some magic or powerful energy source comes along so that we can fix the atmosphere and heat up the planet.

My book takes the most optimistic view possible and extrapolates that. It assumes that money is not a serious obstacle and that we can get to Mars and on its surface safely, neither of which is guaranteed today.

Even my solution to oxygenating the air is a reach but at least possible with existing technology. It will not reach full breathability unless we are very lucky. Instead, it will give us maybe 20–40% of where we must go — again, if we are lucky. But that’s huge. Mars would no longer be a virtual vacuum for life.

Incidentally, the cold is overstated due to the low atmospheric pressure. The air will have little heat extracting ability. It’s just too thin. Heat is more important than temperature when settling Mars. Cosmic rays also pose a problem for plants as well as people.

Mars is tough.

EDIT: Some have referred to bacteria (or archaea) for Mars. That is correct. Seeds no; bacteria yes. However, at the low temperatures, low moisture, wan sunlight, and toxic soil composition, photosynthetic bacteria as we know them would grow too slowly to impact atmospheric composition seriously in our lifetimes. Perhaps, someone can engineer a bacterium that can overcome all of these issues. It is odd, though, that Mars has no such bacteria on its surface today as it had millions of years to use natural selection and evolution to create them.

EDIT 2: I neglected to mention that plants breathe. That is, they use oxygen to respire and create energy both when it’s dark and when seeds germinate. No oxygen; no germination.

EDIT 3: Please note that the absence of a magnetosphere implies the absence of a planetary magnetic field. It is the magnetic field that blocks the solar wind, not the magnetosphere. Your boat makes a bow wave as it travels through the water. The magnetosphere is like that wave. The boat is like the magnetic field. Upon which would you prefer to travel?

If there were a magnetic field on Mars, the atmospheric pressure would be ever so slightly higher — a few millibars if memory serves. The solar wind without a magnetic field did accelerate the loss of atmosphere a few billion years ago, but the primary driver was thermal loss due to a low gravitational field. That atmosphere would be gone today either way. Building a new atmosphere without a magnetic field would be fine if you could build one at all. It would be nice to block the solar wind but not catastrophic if you did not.

Here’s the real story. If you could create a real, breathable atmosphere on Mars, the other things would be child’s play in comparison. Do not hold your breath. Breathe!

There have been numerous experiments into plant growth in space. It's important to scientists on the ground because it can help us better understand how plants function which can help us to grow food more efficaciously. It's also important to NASA, because when we finally start sending astronauts away from low Earth orbit, they may need to grow their own food and maintain their own regenerable atmosphere.

Gravity is not the only difference between the Earth environment and the ISS environment. In the closed atmosphere of a spacecraft, volatile organic compounds (VOCs) can accumulate. VOCs need to be scrubbed from the air or seed production will suffer. There are elevated radiation levels that can cause mutations and affect growth. An experiment on Mir, that involved storing tomato seeds in space for six years found mutation rates up to 20 times higher in the space seeds than in the control seeds stored on the ground. And there are the spectral effects of using only electric lighting.

Because plants also respire, we have to have fans to circulate the air around the plants so that they don't suffocate on their own exhalations. Even failed experiments can provide us with better understanding. An experiment to study plant lignin failed to produce healthy plant materials but taught us more about providing effective air movement.

In the absence of weight, there is poor water and air movement through the rooting media. One complication we've discovered is that in microgravity, the water distributes evenly throughout the soil. This can actually prevent air from reaching the roots. That's why 'Veggie' uses wicks - so that water is only distributed to selected areas. It's also why a lot of study has gone into selecting the best soils. Fine grained soils hold too much water and coarse soils hold too much air.

Tropism is a growth response between a plant and external stimulus. There are numerous forms of tropism and understanding each of them greatly affects our abilities to grow healthy plants. One of the cool things about experimenting on the ISS is that we can study each form of tropism in isolation. On Earth, gravity tends to overwhelm the other influences.

Gravitropism is when the external stimulus is gravity. Plants have a hormone called auxin. In a gravity environment, if a plant is oriented on its side, auxin will accumulate in the stem and stimulate cell expansion that will result in the stem bending to point upwards so that the stem grows towards light (the sun). Similarly, auxin prevents cell elongation in the roots and that encourages roots to grow downwards.

When plants grow, they do so in an oscillatory or helical manner called circumnutation. We can easily see this in vines that grow around an object. An interesting experiment was done aboard the ISS to study this in the absence and presence of gravity in the space environment. Arabidopsis plants were grown from seeds in space and observed both in the normal microgravity environment and in a centrifuge that simulated 0.8 g. While under the 0.8 g, the plants experienced circumnutation amplitudes 5-10 times as high as in microgravity. Within the endodermis of the planet there are gravisensing cells. On a larger scale, this may mean that vines cannot twine in space.

An interesting thing learned from studying cucumber growth in space involves a structure called a peg that develops immediately after germination, between the root and stem. This peg has long been observed and the scientists were interested to see if it was dependent on gravity. What they learned was that each seed is structured to grow two pegs - one on each side - but in the presence of gravity, only one peg develops, whereas both are activated in microgravity.

Studies indicate that a plant's perception of gravity is related to the presence of starch in the organelles within the cell structure of the roots. Roots with starch appear to be more sensitive to gravity that roots that are missing the starch.

Hydrotropism is when the external stimulus is water. Cucumber plants are particularly dependent on gravity to initiate growth. An experiment called Hyrop Tropi was conducted in the Japanese laboratory aboard ISS, in 2010. The experiment was designed to investigate two major objectives; one was to see if roots of cucumber seedlings would bend toward water when they grow in microgravity, and the other was to identify Auxin-regulated genes. This was a neat example of an experiment that needed microgravity. It would be difficult to study the role of water on Earth, because we can't easily remove the effects of gravity, but in space we could ensure that water was the only stimulus. Here's a brief summary of the results, from the principal investigator:

The results showed that roots hydrotropically bent toward the moistened plastic foam under microgravity conditions, whereas they grew straight along the direction of gravitational force under 1G conditions. The hydrotropic response in microgravity appeared to be greater in the NaCl chamber compared with that in H2O chamber, but they did not differ statistically. Furthermore, CsIAA1 gene differentially expressed in the hydrotropically bending roots; the expression was much greater on the concave side than on the convex side. On the other hand, no asymmetric expression of CsIAA1 in the roots grown under 1G conditions were detected. These results revealed that roots become very sensitive to moisture gradients in microgravity and that auxin redistribution and differential auxin response take place during hydrotropic response. Also, the results imply that the hydrotropic response can be used as a means of root growth regulation for plant production in space. (Hydrotropism and Auxin-Inducible Gene expression in Roots Grown Under Microgravity Conditions)

Phototropism is when the external stimulus is light. In some of the pictures from space you'll notice that the lighting is red-blue in the plant habitat. Red-blue light that has been deemed most efficacious for photosynthesis.

Other tropisms that can be studied are chemotropism (chemicals), thigmotropism (touch), and electrotropism (electric fields)

In April, a SpaceX cargo vehicle delivered a plant growth chamber that the payload investigators call 'Veggie'. The astronauts will use it to grow foods. 'Veggie' utilizes small bags of soil with inserted wicks to provide water. Here's a video explaining the experiment:

One area that we don't yet have a lot of understanding is how much the spaceflight environment will influence metabolite production. Metabolites affect flavor and nutritional quality. The plan is to return early 'Veggie' crops to Earth to study the metabolites.

Here's another video about plant experiments aboard ISS:

The U.S. Segment transports oxygen in NORS (Nitrogen Oxygen Recharge System) tanks that are carried as cargo in visiting vehicles, such as the Japanese HTV, OrbitalATK’s Cygnus, and SpaceX’s Dragon. Here is a picture of Kate Rubins working with a NORS tank.

The Russian Segment transports oxygen to the ISS in three forms. Each Progress resupply vehicle has a compressed gas transfer tank, water that is transported up can be split by a device called Electron into oxygen and hydrogen, and as a backup there are SFOG (Solid Fuel Oxygen Generator) candles that are lithium-perchlorate based.

Is it technically possible?

Yes.

Do you really want that as your primary life support system?

Probably not.

I grow this happy little water fern called Azolla. For two people’s oxygen needs you need about 16 square meters of Azolla. [1] Scale that up to 48 square meters for the 6 members of a fully staffed ISS.

It’s a water plant, so I need 48 1x1x0.1 meter trays, and water to fill them up. That’s 4800 kilos of water, plus the mass and space of the trays, plus the LEDs to light them, and enough electrical power to keep them running. That’s a lot of upmass, but we’re going to ignore that.

I also choose to ignore that the water will float right out of the trays, so I need some quantity of artificial gravity to hold it down.

I’m also going to ignore how much humidity that much exposed water and plant material will throw into the air.

I’m also going to ignore that I lose a fair amount of astronaut time to taking care of the plants.

In terms of physical volume it could fit in the inflated BEAM module, so space-wise it is feasible.

Day zero of the new life support system we stock the plants in the trays. It works! Everyone is happy. (A little damp, smelling slightly of cabbage, but happy.) Bonus, the plants are edible!

Now some sort of glitch happens. It could be a fire, electrical problem, space pirates, some weird plant disease, or (most likely) I mis-measure a nutrient solution. Overnight half the plants die.

That’s okay, they’ll recover. These little plants are awesome and can regenerate from a 50% loss in just a few days. The big problem is that I have to have enough buffer capacity to stay alive while I’m waiting for the life support system to regrow. You end up needing a huge reserve capacity or an electrochemical backup system because of the many unpredictable failure modes of biological systems.

The most surprising thing I learned from researching closed life support systems was how downright sexy an on-off switch could be. Being able to cold start your life support in minutes instead of days or weeks is incredibly handy.

Please don’t think the idea is doomed though. We’ll definitely need a plant based system for long term colonization. i.e. Mars. It’s just a matter of more research.

1 - Liu, Xiaofeng, et al. "Research on some functions of Azolla in CELSS system." Acta Astronautica 63.7-10 (2008): 1061-1066.

The average human exhales almost a kilogram of CO2 (480 liters) each day, and there are six people on the International Space Station. As the level of CO2 rises, people can experience symptoms such as nausea, dizziness, headaches, and depression. We need to scrub CO2 from the air.

There are two primary devices to perform this function on the ISS. On the Russian Segment there is воздух "Vozdukh" (literally translates as 'air') (located in the SM) and on the US Segment there is CDRA (Carbon Dioxide Removal Assembly) (located in the Lab).

Both devices utilize the same principle. The devices utilize two beds: a desiccant bed to remove moisture and an adsorbent bed to remove carbon dioxide. The desiccant bed is needed because the adsorbent bed requires dry air to work properly.

The "dirty air" is blown through a silica gel. That gel removes water vapor. It also heats the air a bit, and since the adsorbent bed needs cool-dry air, the air is cooled before entering the adsorbent bed. The adsorbent bed is composed of Zeolite. Zeolite is an aluminosilicate. It is crystalline and highly porous. This type of material is called a molecular sieve. The pore size can be controlled by regulating the electrostatic field that results from the negative charge of the aluminum. Adjusting pore size allows filtering of different substances. We're only interested in filtering out carbon dioxide.

"Clean air" comes out the other side of the adsorbent bed. That air is pumped back into the cabin. A vent is the opened that exposes the adsorbent bed to the vacuum of space. The vacuum removes all the carbon dioxide and thus regenerates the bed to be used again at the next cycle. The water vapor from the desiccant bed is put back into the cabin atmosphere. We have a different piece of equipment that is designed to regulate humidity.

Nominally, Vozdukh is primary and can scrub the air for a six person crew. It uses less power than CDRA. CDRA serves as a backup and for additional support when the crew complement is higher (such as when there was a visiting shuttle crew). As a further backup for contingency cases, the Russian Segment also has LiOH canisters that can adsorb contaminants.

The ISS grows some plants using artificial light but it is more experimentation than relying on them for food or oxygen. They have the plants in a container and water them with a syringe. That is because of zero-g making watering, etc. an issue.

An actual greenhouse would greatly benefit from artificial gravity. There have been many concepts for a large wheel or cylinder that rotates as a permanent space station perhaps in the L-5 Lagrange point. Lagrange points are stable orbits that will not decay over time.

The space station concepts include dirt inside similar to Earth terrain except in space and you are on the inside of a cylinder or wheel with the ground above you in all directions. It would need to have windows to allow sunlight in but it would have to have good UV filtering. The UV is space is fatal to plants and not good for humans. The windows also might be mirrored rather than direct light. That could greatly reduce gamma rays. Gamma rays don’t reflect on a mirror; they go right through it.

It could look something like this:

Or this:

However, both show way too much housing and too little farmland. According to a 1970’s study you need 4,000 square feet of farmland per person to grow enough food. That is also about the amount you need to recycle our CO2. You would also need paths to work the land and storage areas for the food. That means the population density is about 10 people per acre so it would be a very large structure for even a couple of hundred people.

Note that artificial light is energy prohibitive. Enough LED lighting to grow food for 10 people is about 1.5 megawatts. Therefore you are much better off with direct (or reflected) sunlight.

The ISS has a recycling system that uses a Sabatier reactor and electrolysis. The electrolysis splits water into hydrogen and oxygen. The oxygen is added to the atmosphere.

2H2O -> 2H2 + O2

The hydrogen is fed into the Sabatier reactor. CO2 is pulled out of the air and combined with the hydrogen to make methane and water. The water is recycled back through the electrolysis. It provides half of the water. The other half is either brought along or used from the slight excess of water they have.

CO2 + 4H2 -> CH4 + 2H2O

Note that the water recycling is quite effective, not 100% but quite good. The way NASA sends food they have 28% water content in it which provides an excess of about 0.25 kg per day per crew, which is almost all the water needed to recycle the CO2.

The methane is vented overboard.

This idea is a common one in Science Fiction - but it is not without problems.

1. For long distance travel - you’ll be moving further and further from the sun - so the plants will be getting insufficient sunlight for photosynthesis. When plants can’t photosynthesize (eg at night) - they actually consume oxygen and produce CO2 - just like animals do. So once you’re out past (say) the orbit of Mars - you’re going to either need to use shade-loving plants - or you’ll have to use artificial “grow lights” or large focussing collection mirrors to gather sunlight over a larger area.
2. In zero-g - you can’t just spray water onto the top of the soil - which is why most people who work on this kind of problem talk about “soilless hydroponics”.
3. Plants that are harvested for food will gradually consume nutrients from the soil that must be replenished. Fertilizer is one way to do that - but hauling large amounts of that stuff in a weight-limited spacecraft is going to be a huge problem. Super-efficient recycling could solve the problem - but maintaining closed-system recycling where NOTHING is lost is very, very difficult. You’d have to recycle 100% of human waste - solids and liquids. If an astronaut ever died - their body would have to be 100% recycled. This is technologically very difficult.
4. Just having large windows to collect sunlight would be problematic because cosmic and solar radiation goes right through glass. Shielding the plants from those radiation sources without also blocking the sunlight that they need is difficult. It might be better to collect sunlight with solar panels and use their output to power “grow-lamps” that efficiently provide light in just the frequencies that plants need.
5. Going back to the recycling problem - there are always parts of a plant that are inedible to humans…but all of that waste material would need to be recycledl

Well to start you'd probably want separate systems for food and oxygen. There is virtually no overlap between the best food crops and the best oxygen producers. What's more any time you're trying to manage closed cycle life support you're likely to run into issues with positive feedback destabilizing the whole thing in a frighteningly short period of time. We still haven't fully cracked this problem, admittedly, but what progress we have made suggests that isolating certain functions in discrete, more easily controlled systems greatly reduces the risk.

So, let's start by looking at that oxygen. Rather than the large, leafy plants you may be imagining we'd be better served with something called an algae based bioreactor. To start you have a big tank of water infused with nutrients. The tank includes a grow light, a stirring mechanism (particularly vital if dealing with micro gravity) and some kind of system to enable gas exchange. Since again we have to assume this thing will be operating in microgravity at some point the traditional methods of either leaving one end of the tank open to the air or bubbling gas up through the water from the bottom and letting buoyancy sort it out probably won't cut it, so a system of semi-permeable membranes that let oxygen and CO2 pass through without letting the water out may be the best bet here. Then, you introduce live algae cultures to the tank.

As anyone who's seen an algae bloom can tell you, those little buggers reproduce at an astonishing rate once they've been fed. So all you need to do is pump the air in your ship along those membranes. The algae will pull as much carbon dioxide as they can out of that air and use it to multiply, eventually turning the inside of the tank into a mass of thick sludge which will periodically need to be partially drained and replaced with new nutrients. But as a bonus, said sludge can be used as a nutritional supplement, feedstock for growing edible fungi, or even fertilizer for hydroponics with the right processing.

So, now that we've got our air figured out, what about food?

So one of the biggest issues with farming is that it requires a LOT of water. Water is heavy and very difficult to work with in the absence of gravity, both of which are problematic for a spacecraft. Anything we can do to cut down on the amount we need is good here. Which brings us to aeroponics. In terms of water usage, aeroponics is one of the best ways to grow plants. Rather than suspending their roots in a growth medium like dirt or a vat of liquid nutrients, high pressure sprayers just continually mist the roots so that only get what they need. While you would need to find a good way to contain the mist to protect the rest of your spacecraft’s equipment and make sure you're not wasting water unnecessarily, the potential mass savings alone make them a very tempting solution for any spacecraft.

What I would propose is a conveyor system where the plants are all mounted on what are essentially gigantic luggage carousels that move them around the farm throughout the day. These carousels would pass through multiple misting chambers. Once a batch of crops arrived in these chambers they would seal themselves up and flood themselves with a nutrient rich mist, using fans to make sure the entire plant received a dose. Once the process was done regular air would get cycled in while filters reclaimed excess moisture and nutrients. Then the chamber opens again and the next batch of crops moves into position. The advantage of the conveyor is that you could also use this to control how much light the plants got, a necessity if you plan to use natural light as your can't always expect a regular day/night cycle outside of a planet.

When I worked in the space program in the 1960's, there were two processes to get CO2 to split into Oxygen and Carbon. The first and easiest used the Sabatier reaction.
4H2 + CO2-----> CH4 + 2H2O
The H2 was obtained by electrolysis of H2O condensed out of the air.
2H2O --------> 2H2 +O2

The other method was the Bosch reaction
CO2 + 2H2 ------> C + 2H2O
Humans in their respiration emit about 1-2 lb of CO2 and 2 lb of H2O every day. Extra water would provide the Hydrogen for the reactions and some of the Oxygen.

In the 60's the sabatier reaction was easy to do and the CH4 was planned to be dumped and or used as reaction control gas. I wrote a paper on the use of liquid NH3 insted of H2O as a source of H2.

Later in the 80's the Russians did get a Bosch reactor to work in their space station though they were not trouble free.

In the apollo program LiOH was used to convert exhaled CO2 and H2O into LiHCO3 and O2.

Oxygen is transported into space station from earth by cargo craft and stored.
But for emergency use they have oxygen candles which make Oxygen by chemical action.Vika or TGK is an oxygen generating system for spaceflight.[1] It is a SFOG, or solid-fuel oxygen generator, a kind of chemical oxygen generator.[1] It has been used on the retired Mir space station and the International Space Station.[1] It was originally developed byRoscosmos to supplement the Elektron oxygen system on Mir.[1] A Vika module, also known as a "candle", contains about one liter of lithium perchlorate and can provide oxygen for one person for 24 hours.[1]

Carbon dioxide (CO2) is a metabolic byproduct of respiration. The average human exhales almost a kilogram of CO2 (480 liters) each day, and there are six people on the International Space Station. As the level of CO2 rises, people can experience symptoms such as nausea, dizziness, headaches, and depression. We need to scrub CO2 from the air.

There are two primary devices to perform this function on the ISS. On the Russian Segment there is воздух "Vozdukh" (literally translates as 'air') (located in the SM) and on the US Segment there is CDRA (Carbon Dioxide Removal Assembly) (located in the Lab).

Both devices utilize the same principle. The devices utilize two beds: a desiccant bed to remove moisture and an adsorbent bed to remove carbon dioxide. The desiccant bed is needed because the adsorbent bed requires dry air to work properly.

The "dirty air" is blown through a silica gel. That gel removes water vapor. It also heats the air a bit, and since the adsorbent bed needs cool-dry air, the air is cooled before entering the adsorbent bed. The adsorbent bed is composed of Zeolite. Zeolite is an aluminosilicate. It is crystalline and highly porous. This type of material is called a molecular sieve. The pore size can be controlled by regulating the electrostatic field that results from the negative charge of the aluminum. Adjusting pore size allows filtering of different substances. We're only interested in filtering out carbon dioxide.

"Clean air" comes out the other side of the adsorbent bed. That air is pumped back into the cabin. A vent is the opened that exposes the adsorbent bed to the vacuum of space. The vacuum removes all the carbon dioxide and thus regenerates the bed to be used again at the next cycle. The water vapor from the desiccant bed is put back into the cabin atmosphere. We have a different piece of equipment that is designed to regulate humidity.

Nominally, Vozdukh is primary and can scrub the air for a six person crew. It uses less power than CDRA. CDRA serves as a backup and for additional support when the crew complement is higher (such as when there was a visiting shuttle crew). As a further backup for contingency cases, the Russian Segment also has LiOH canisters that can adsorb contaminants.

Q: How can we get oxygen in the space if we settle in the space?

From a factory.

Oxygen is the third most abundant element in the galaxy, after hydrogen and helium. It’s just free oxygen—oxygen that isn’t chemically bound to anything—that’s rare.

As long as we have plenty of energy, we’ll always have plenty of oxygen. We just need to build machines to free it from its chemical bonds.

My guess is that someone will point out that we can also recycle oxygen, but that’s the same thing. For example, on Earth, animals exhale oxygen bound to carbon in the form of carbon dioxide, and plants use solar energy to crack CO2 apart and release oxygen. Anywhere we build a closed ecosystem, we can use plants to do at least some of the work, but anywhere that isn’t practical, we can use machinery.

Indeed, today’s nuclear submarines make oxygen by cracking water and dumping the hydrogen overboard.

Because that is not how the process works. Oxygen is created on the ISS and submarines by electrolysis of water. Passing an electric current between two electrodes in distilled water. One electrode will collect Hydrogen, one Oxygen (H2O). The oxygen will be used but the hydrogen expelled.

Scrubbers remove the CO2 from the air.

The most straightforward way of removing the gas is to vent it. But it must first be captured through a chemical reaction in a carbon dioxide “scrubber”.

Traditionally, scrubbers use soda lime (a mixture of chemicals including calcium hydroxide, sodium hydroxide and potassium hydroxide) or amines (a derivative of ammonia) to lock onto CO2 molecules.

But in space where every gram counts, lithium hydroxide is used in scrubbers because it has a low molecular weight. When the CO2 reacts with lithium hydroxide it creates create lithium carbonate and water.

While this is the primary scrubber type on the space station it’s a back-up on a submarine.

Scrubbers of all types involve chemical reactions that have the added benefit of producing water, which could be used for drinking or to fuel the oxygen generator.

Good question, but things are never quite that simple.

1. Mars is too cold for Earth plants to survive. Even lichens would almost certainly die. You'd first need to increase the thickness of the Martian atmosphere, to get more greenhouse warming going. That would take a LOT of CO2 and water - far more than a spaceship load. Edit added: Something else that is crucial: all plants have aerobic metabolisms, so they would suffocate in the Martian atmosphere. There are photosynthetic bacteria that have anaerobic metabolisms, so you would want to use them instead of green plants. (Sorry, this is the second edit on this paragraph!)
2. Because of the temperature, water on Mars that didn't evaporate would freeze solid. There is no water in the Martian atmosphere to speak of, and there won't be unless the planet warms up. A lot.
3. Even if you could get photosynthesis going, organisms would be rather quickly destroyed by hard UV radiation from the sun: you need a good bit of oxygen in the atmosphere in order to make an ozone shield. See also Is it really true that life couldn't survive on Earth's surface if the ozone layer didn't exist? If so, why?
4. In order to protect living cells from UV before there's enough oxygen to form an ozone layer, you need substantial oceans of water for them to grow in. See #2.

Sorry, it just wouldn't work. For a biological package probe to do your terraforming for you, you need two things: (a) a world that's already warm enough for substantial amounts of liquid water on the surface, and (b) a lot of time: at least several centuries.

What you are asking is part of a life support system, ECLSS. The International Space Station Environmental Control and Life Support System (ECLSS) is a life support system that provides or controls atmospheric pressure, fire detection and suppression, oxygen levels, waste management and water supply. The highest priority for the ECLSS is the ISS atmosphere, but the system also collects, processes, and stores waste and water produced and used by the crew—a process that recycles fluid from the sink, shower, toilet, and condensation from the air.

Now lets answer your question, one by one.
Carbon Dioxide:-
An important aspect of air revitalization for life support in spacecraft is the removal
of carbon dioxide from cabin air. Several types of carbon dioxide removal systems are in use in spacecraft life support. These systems rely on various removal techniques that employ different architectures and media for scrubbing CO, such as permeable membranes, liquid amine, adsorbents, and absorbents. Sorbent systems have been used since the first manned missions.
Currently, Carbon dioxide and trace contaminants are removed by the Air Revitalization System. This is a NASA rack, to be placed in Tranquility, designed to provide a Carbon Dioxide Removal Assembly (CDRA), a Trace Contaminant Control Sub-assembly (TCCS) to remove hazardous trace contamination from the atmosphere and a Major Constituent Analyzer (MCA) to monitor nitrogen, oxygen, carbon dioxide, methane, hydrogen, and water vapor. The Air Revitalization System was flown to the station aboard STS-128 and was temporarily installed in the Japanese Experiment Module pressurised module. The system is scheduled to be transferred to Tranquility now that the module has arrived and was installed during Space Shuttle Endeavour mission STS-130

A CDRA is a regenerative system whose principal operation utilizes 4 beds. Each bed ORU contains a desiccant bed and a CO, sorbent bed hence desiccant / adsorbent bed ORU. The system relies on one desiccant bed to condition the air prior to entry into the adsorbent bed. The adsorbent bed selectively removes the COP, and the air travels through the second desiccant adsorbent bed to replace the humidity.

Oxygen:-
Although oxygen is produced at ISS, but they also have bottled oxygen as backup.
This is the method used to prepare oxygen:-
Electrolysis of water (H2O) is the main method to generate oxygen aboard the ISS. Water is split into oxygen (O2) and hydrogen (H2). The oxygen is vented into the breathable cabin air system, known as the Oxygen Generation System(OGS), while the explosive hydrogen is vented externally.
The station’s football-field-sized solar arrays are the power source to electrolyse the water. Each day the OGS continuously provides between 2.3 and 9kg (5 to 20lbs) of oxygen. The OGS and CDRA are a component of the ISS life support system, known as ECLSS or Environmental Control and Life Support System, located in the US Destiny module. The Elektron system aboard the Russian Zvezda service module performs the same vital electrolysis service for the ISS crew. The Electron system was also used aboard the Russian Mir Space Station.

Finally I would conclude with this basic flow-chart of ECLSS. This will resolve all such queries.

More detail on ECLSS is available on ISS ECLSS
You can more read about the CDRA from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050210002.pdf

Oxygen levels are maintained within ISS using a variety of mechanisms:

Cargo vehicle resupply

The Russian Progress vehicles and European ATV vehicles are each equipped with air tanks to maintain their own pressurized environments. While those vehicles are docked to the ISS, those tanks can be manually vented to release the air into ISS. US segment cargo vehicles can also support to some degree.

Portable Repress Unit (БНП)

For contingency cases, there are two high-pressure air tanks in the Russian Service Module transfer compartment. That air can be used to repressurize modules.

Elektron & OGS

The US has equipment called OGA (Oxygen Generating Assembly) and the Russians have equipment called Elektron. They both use electrolysis to separate waste water into oxygen and hydrogen. The oxygen is used to replenish the atmosphere and the hydrogen is vented. Both have been problematic pieces of equipment, and so do not meet all their needs.

Solid Oxygen Generator (ТГКs)

The solid oxygen generator is a device that holds a lithium perchlorate pellet. When electricity is applied, an exothermic reaction results in pure oxygen being released. One cartridge can produce 600 liters of oxygen.

Airlock Tanks

The US Airlock also has high-pressure oxygen tanks that can be used to recharge the vehicle.

Not immediately. The problem is that while a tree takes in CO2 during daylight hours, it also takes in O2 during all hours for respiration. That’s right, the planet builds up carbohydrates by photosynthesis and then tera=s them down as fuel for growth and transpiration. A lot of the carbs go into wood, but more are used up.

These two systems are essentially independent; the O2 give out by photosynthesis is not banked for use burning carbs; it is simply released into the atmosphere. On Mars, they would disperse and spread all over the planet; good luck in collecting enough for the tree to survive. In general, trees are overall carbon sequestrators - they cull CO2 and make wood out of it. Of course, the decay process every year at leaf fall and the final rotting of the wood potentially returns all the CO2 to the atmosphere.

You will need a substantial oxygen partial pressure before trees can be used outdoors.

There are other problems that Earth-grown trees are not equipped to handle. Perhaps a few centuries of gene splicing will fix that. Yeah, that’s right - GMOs to Mars!!!

In principle, we can. There are multiple techniques that can do it.

Pragmatically, all of those methods require significant complexity, particularly if you want them to operate automatically. More to the point, they all require substantial amounts of power, and the carbon needs to be removed in one form or another.

Now, in applications where power is plentiful and there's benefit in being independent of resupply for extended periods (such as nuclear subs and space stations), such methods may be worth it, and are, in fact, the subject of research. But in most applications, it's much cheaper to just swap in new oxygen cylinders.

It could do this with plants, but it's not their priority.

With plants, the basic equation is
6CO2 + 12 H2O -> C6H12O6 + 6O2 + 6 H2O

Where the oxygen comes from water and the oxygen from the CO2 ends up in more H2O.

Indirectly that H2O from the CO2 might eventually end up as O2 if it gets taken up for photosynthesis later on, but this is not splitting it directly.

See Plants Don't Convert CO2 into O2 and Page on lamission.edu (see page 5 there for a useful diagram of how it works).
(Thanks to Daniel Spector for correcting me here)

You could split the CO2 completely to C and O2, by using laser light: Making oxygen before life.

And there are other technological ways of splitting CO2 to get one of the oxygen atoms from it, see Richard Gorman's answer to Why can't the ISS split astronaut's exhaled CO2 and recycle the oxygen?

Anyway, I'll continue here with the photosynthesis approach.

To make oxygen from CO2 via photosynthesis they would need to dedicate an entire module to growing green algae. Or if they set aside three modules to the task, they could grow most of their food in them, and as a biproduct, also create all the oxygen they need from plants. In theory anyway. Experiments on the ground by the Russians showed that this is possible. The main question would be whether the same methods work in orbit. For instance dwarf wheat, which they used in the ground experiments had disappointing yields in zero g.

That could just be a matter of choosing the right species for zero g. Or for that matter, (just my own idea, not seen it in the literature) - why not have containers for the plants around the exterior of the module, that spin around the center, like a tumble drier, at whatever spin rate is needed to get enough gravity for healthy growth of the plants?

The thing is that the ISS is not primarily designed for doing studies like this. If you set aside three modules for growing its own food, that's three modules that can't be used for their zero gravity experiments and spacecraft systems. Even one module would be more than they would consider acceptable for this.

The mass requirement for the water needn't be great. The obvious thing for a space station is to use aeroponics, where the roots of the plants are suspended in an atmosphere of water vapour plus nutrients. This uses almost no water at all.

The air in the ISS needs to be kept very dry to prevent microbial growth which is a problem in space stations, microbial films, for long duration multi year stations like MIR or the ISS. But that just means that the atmosphere of the growing chamber would need to be isolated from the rest of the ISS.

Indeed you could condense the water that forms inside any container with growing plants (due to plant transpiration) and use that to supply water back to the ISS, so it could help with purification of the water.

The power requirements for supplying artificial light for the algae is within the capabilities of the ISS. It was 48 kW for xenon lights for green algae for six crew - that's a total of 8 m2 of algae per crew member and 200 - 300 watts illumination per square meter. But with modern LED technology that could be reduced to a tenth or less.

For instance, just checking commercially available high efficiency grow lights available to aeroponic / hydroponic growers in 2015: this High Efficiency Green Energy Full Spectrum SMD LED Plant Grow Light for Indoor Gardening, Aeroponic and Hydroponics - uses 20 watts of power to illuminate 0.2 square meters. It is recommended for crops that require bright sunlight such as lettuces here: Top 10 Best LED Grow Lights: The Heavy Power List. That would be 800 watts for 8 square meters, or 2.4 kilowatts for the light needed for algae for a crew of six. Or if they grow all their own food, three times that, 7.2 kW.

The current total power supply for the ISS is 120 kW International Space Station (ISS) power system

So in principle they could generate all their oxygen, it would seem. The main difficulty there would seem to be space rather than power supply.

Or you could use natural sunlight and go all the way and have an "artificial greenhouse" in space. If you can do it in the vacuum conditions of the Moon or on Mars, you can surely also do it as a space module, and it is a natural place to test the technology first. You'd probably have it at a lower pressure than the ISS as plants can make do with much lower atmospheric pressure than humans which could simplify the technology a bit. For instance in this NASA challenge they suggest a quarter of of Earth normal for a greenhouse for Mars or in Space. Deployable Greenhouse

If this was their priority, then either they could get all their oxygen this way - or else - they would turn up some issue with this approach. If we have a future space station focused on human factors and preparation for long term interplanetary flight and missions on the Moon and around other planets without resupply from Earth, this would surely be a priority.

For more on this, see, Robert Walker's answer to Why can't plants be used in the ISS to take in carbon dioxide and give out oxygen so that oxygen content inside the ISS remains almost constant instead of taking air from earth to fill in the tanks of the ISS?

And for the methods currently used to create oxygen on the ISS: Robert Frost's answer to How is oxygen generated on the ISS?

See also my Science20 blog post: Lettuces Now, What Next - Could Astronauts Get All Their Oxygen And Food From Algae Or Plants?

If we put plants on Mars exposed directly to the carbon dioxide-rich environment, will they produce oxygen?

No, the plants directly exposed to Mars’ atmosphere will be freeze-dried and killed. Mars’ environment has several problems for terrestrial plants:

1. Near-vacuum conditions. Plants will quickly lose water and other volatiles, hence the drying.
2. Cold, to the point the plants would freeze solid.
3. Lack of oxygen. Plants’ metabolism requires oxygen at night to process the food made with photosynthesis and carbon dioxide during the day.

And that assumes you at least put the plants in planters with nutrient-rich soil and water. Otherwise you can add “lack of nutrients” and “lack of water” to the reasons the plants are killed by the Martian environment.

I typically watered mine using a syringe. We were doing an experiment growing basil and lettuce seeds. They came to me onboard ISS in a pre-made container, the same as young students were using on Earth. The idea was that they would do what I would do, and then come up with ideas as to how the container/system could be made better.

I turned it into a football game of sorts…, Iowa State University vs. the University of Nebraska. As the plants germinated/grew, I would assess points scored in touchdowns, etc. Each week of the experiment was a quarter of the “game,” and I would then post scores, including halftime. It was tremendous fun until I determined that the procedure I was given for the experiment was flawed. It had me water too frequently which led to some moldy plants. Eventually they all died, and I became an instant failure.

Keep lookin’ up!

What's the need to extract breathable oxygen from carbon dioxide here on Earth. We already have plenty of oxygen to breath which is produced by plants, phytoplanktons, algae,etc. naturally.

If you are talking about to reduce carbon content in our atmosphere then that would be the part of other process which will require a lot more than extracting oxygen from carbon dioxide from a machine.

Talking about MOXIE present on preserverance rover, it produces oxygen at very low rate and it's for test purposes. If we build huge machines at large scale like that on earth just to produce oxygen then also it can't fulfill the needs of normal population and it's not even needed because as I mentioned above there is plenty of oxygen in our surroundings. Also, it will be so expensive to operate and maintain. However, machine like MOXIE at large scale is needed on Mars to produce breathable oxygen as the oxygen demand on Mars is limited.

If you’re asking about Mark Watney’s world, you’re mixing current science fact and fiction as Andy Weir’s book and the film adaptation portrayed it.

In both the film and book of “The Martian,” astronaut Mark Watney’s life hangs in the balance in the long-term survival by three devices that sustain his life within his artificial habitat and home, the Hab.

• Oxygenator: This device generated oxygen to breathe by conversion of the thin Martian air. If this device failed for too long, Mark would suffocate.
• Atmospheric Regulator (AREC): This device watched the mixture of gases in the Hab, removing carbon dioxide as needed.
• Water Reclaimer: This device cleans waste water for reuse.

Similar devices are in place in reality, today, aboard the International Space Station. These life support devices are not quite as efficient as Watney’s, but they do similar things, recycling most of the air and water aboard.

But these ISS systems do have limits in efficiency, which occasionally must be topped off with fresh supplies of water and oxygen from uncrewed resupply spacecraft.

However, neither the ISS or Watney’s fictional version of NASA have machinery which uses cyanobacteria or plankton or any other means for life support yet.

Nor would venting gases or bacteria into the Martian atmosphere help. While Mars is Earth-line in geology, its day and orbital tilt, it’s far colder and smaller. Water would evaporate. Bacteria would die (and you’d tick off the planetary scientists still looking for ancient, authentic evidence of Martian microbial life with rovers).

With no magnetic field, the solar wind blows away the Martian atmosphere, leaving it thin, and irradiates the surface to uninhabitable levels without protection.

Terraforming is a dream science that isn’t practical right now. Frankly, if we could terraform Mars, we wouldn’t need to do it, because we could use the same means to reinvigorate a much more habitable world: our own Earth. Planetary-scale transformations just won’t happen without a lot of work and several lifetimes for even a small change. Without some means of providing a magnetic field to Mars, any attempts to improve the atmosphere would literally be blown away.

https://www.nasa.gov/centers/marshall/pdf/104840main_eclss.pdf

Next-generation life-support system heading to Space Station

Advance closed loop system uses solar power from the solar panels to break down water into hydrogen and oxygen. The oxygen is breathed.

Solar Panels aboard the ISS power electrolysis

2 H2O + energy → 2 H2 + O2 [1]

So for a kg of hydrogen and 8 kg of oxygen from 9 liters of water requires 6.83 kWh of electricity with electrolysis at 65% efficiency. This is enough oxygen to supply 4 people. That’s 285 Watts continuous power over 24 hours per person.

CO2 + 4 H2 → CH4 + 2 H2O [2]

Now two kg of hydrogen absorb 11 kg of carbon dioxide produced by 4 people per day. This produces 4 kg of methane and 9 liters of water. The water is recycled to the electrolysis process above. The methane is pyrolysed using 15 watts of microwave energy continuous.

CH4 + energy → C +2 H2 [3]

The hydrogen is recycled in the 2nd step.

The carbon soot is used to absorb odours and water contaminants.

Chemical Kinetics of Methane Pyrolysis in Microwave Plasma at Atmospheric Pressure

Producing Hydrogen by Plasma Pyrolysis of Methane

So, oxygen is recovered.

Water has a similar cycle and is constantly reused.

Food is dehydrated and reconstituted from powders and concentrates. Food is about 85% water generally - which varies by food type. 109 kg of food concentrate per year make 727 kg of food products per year. So, for a 3 year flight, food totals 2.17 tons per person. Water and air are totally recycled. A total of 300 Watts powers the system - which comes from sunlight.

Apollo Era Food

Skylab Food

Space Station Food

SpaceX BFR Champagne

Space Colony Food