Humans make carbon dioxide. Carbon dioxide is bad for cognition. But plants turn carbon dioxide back into oxygen. And plants are the one true home decoration strategy. So maybe if you get a lot of plants, you can you can keep carbon dioxide in check and keep your brain working?

It's theoretically possible. It's probably just barely possible in practice. But it won't be easy.

People produce ~1 kilogram of carbon dioxide per day. That's around 5.7 × 10²³ molecules or 0.948 moles per hour. (You may remember from high school that a mole is a gigantic number made up to avoid having factors of 10²³ everywhere.) Let's keep it simple and call it one mole per hour.

Meanwhile, plants turn carbon dioxide into oxygen through photosynthesis, i.e. the chemical reaction of (6 water molecules) + (6 carbon dioxide molecules) + (energy) → (1 glucose molecule) + (6 oxygen molecules). The minimum energy physically needed to convert 1 mole of carbon dioxide into glucose and oxygen via this reaction is ~477 kilojoules.

So we've already got a lower bound. Say you have magical plants that somehow channel all incoming energy into photosynthesis with perfect efficiency. They'll need ~477 kilojoules per hour, which converts to a continuous usage of 132.5 watts. ^[1] That's a bit more than what's used by two incandescent light bulbs, which isn't too bad.

But you don't have magical plants. Real plants do photosynthesis through a physical process with two steps, each of which involves four electrons absorbing a photon. That means you need eight photons per carbon dioxide molecule. If you want to tune your lights for maximum efficiency, you should give each photon exactly the minimum energy necessary to excite an electron, which happens to be ~1.8 eV. That corresponds to pure red light with a wavelength of 680 nm, and a continuous usage of 386 watts. ^[2] No physical system using chloroplasts can neutralize your CO₂ using less than that. Somewhat high, but still manageable.

But your houseplants won't be able to grab every single photon that hits them and direct it towards photosynthesis. In practice, ~30% of photons will reflect off the plant, or go through it, or hit some part of the plant other than the chloroplasts. That brings us to 551 watts. ^[3]

And there's another issue. After plants make glucose, what happens to it? Some is used to grow more plant, which permanently sequesters carbon from the environment. But lots is also burned by the plant for the general business of staying alive, releasing the carbon back into the air. The exact amount burned in this way varies based on species and conditions, but around 40% loss reasonable, ^[4] bringing us to 918 watts. ^[5]

That doesn't sound that bad. But have you considered what it would be like to live in the same room with 918 watts of pure red light? In terms of radiant power, that's the same as produced by ~765 incandescent lightbulbs. ^[6] Modern LED grow bulbs are ~50% efficient, meaning you'll actually need to spend ~1836 watts. If you're imagining plants that you can actually see, adjust that upwards again for all the light lost to the room. And if you want to use normal light frequencies instead of living Red Life, then your LED bulbs will be less efficient at creating light and your plants will be less efficient at capturing it. Realistically, we're talking about something like 5,000-10,000 watts, most of which is lost to the room as heat. Imagine five space heaters blasting you on high all the time.

But maybe you're OK living in a tanning booth. Or maybe you'll keep your plants in a perfectly reflective chamber. Or maybe your house has a glass ceiling and infinite free sunlight and free climate control. That's cool. But have you forgotten about your old friend, photosynthetic photon flux density?

Plants can't absorb infinite amounts of light. Chloroplasts take time to "reset" before they can absorb more photons. Your pet fern can only absorb ~52 watts of energy per square meter of leaf surface area. ^[7] So no matter how much light you can produce, if you want to neutralize the carbon dioxide you make, you will need at least 918 / 52 = 17.6 square meters of fern leaf. Picture a 4.2 meter square wall, packed solid with ferns. If there are any gaps, stems, soil, or wall showing, it needs to be even larger. That's the absolute minimum.

But maybe that still sounds OK? Fine. But consider one last barrier: Plants obey the laws of physics [citation needed]. If they remove carbon from the air, they must put that carbon somewhere. The only place it can go other than back into the air is into the plant itself.

The 1 kg of carbon dioxide you produce each day corresponds to 273 grams of elemental carbon. The only way for a plant to hide that is by making more plant. But dry plant matter is only ~50% carbon, and for each gram of dry plant matter, plants have 5-10 grams of water (varying a lot by species). So in order to sequester all the carbon you make, each day you will need to grow around

(1 kg carbon dioxide)
× (0.273 kg elemental carbon / kg carbon dioxide)
× (2 kg dry plant / kg elemental carbon)
× (8.5 kg actual plant / kg dry plant)
= 4.6 kg actual plant.

Your garden must grow that much, every day. That's 140 kg per month. You must prune and discard all that outside, or your garden is not actually sequestering anything.

In conclusion:

1. Build an industrial indoor farm.
2. Weigh it.
3. Wait two weeks.
4. Weigh it again.
5. Divide the increase in weight by your own body mass.
6. That's the fraction of your CO₂ that you're removing from the environment.
7. Open a window.

1. Behold the power of arithmetic:

   (1 mole CO₂ / hour)
   × (477 kJ / mole CO₂)
   = 132.5 watts. ↩︎

2. Again using the power of units:

   (1 mole CO₂ / hour)
   × (8 photons / CO₂ molecule)
   × (1.8 eV / photon)
   = 385.94 watts

   So chloroplasts are at most ~34% (132.5 / 385.94) efficient at channeling the energy in light into photosynthesis. ↩︎

3. I find this 30% number amazingly low. (Well done, evolution.) And perhaps it should be somewhat lower. For one thing, the 30% figure comes from sunlight filtered to the 400-700 nm range. If you've got pure 680 nm light, absorption should be somewhat higher. Also, if photons are absorbed by some part of the plant other than the chloroplasts, they become heat and the energy is gone. But if they're reflected or go through the plant, then they might go on to hit some other plant (provided you have a lot of plants around). If you really have pure 680 nm light and you have very densely packed plants, maybe you could drop this to 10-20%. ↩︎

4. Wikipedia quotes a 35-45% loss just for respiration in the leaf itself. But then this paper shows numbers ranging from 30% to 56% depending on the species and growth rate. ↩︎

5. I've estimated an overall efficiency of 132.5 watts / 918 watts ≈ 14.4%. If you go to Wikipedia, it estimates that ideal leaf efficiency with sunlight is only around 5.4%. That's because sunlight contains a wide band of wavelengths and my calculation assumed an ideal 680 nm source. Around 47% falls outside the 400-700 nm range, and inside that range, around 24% is lost due to higher-energy photons with energy that gets wasted as heat. If you account for that, my estimate becomes 14.4% × (1-0.47) × (1-0.24) = 5.8%, which is close enough for government work. ↩︎

6. A traditional "60 watt" incandescent lightbulb is rated based on the power input. But only around 2% of that energy is actually converted to light. So 918 watts of pure red light isn't what you get from 918 / 60 = 15.3 lightbulbs. It's what you get from 918 / 60 / .02 = 765 lightbulbs. That said, your eyes aren't very sensitive to 680 nm light, so the perceived lux wouldn't be nearly so bad. ↩︎

7. The saturation point of plants is usually given in units of 300 μmol/m²/s. That the number of photons (in micromoles) that can be absorbed, per square meter of leaf, per second. A typical value for a shade-tolerant houseplant would be ~300 μmol/m²/s. If we assume again that the light is 680 nm so that each photon carries 1.8 eV of energy, then ~300 μmol of photons carries 51.92 joules. That's 51.92 joules of energy per square meter of leaf surface, i.e. 52 watts. ↩︎