Over the last 100 years, we've witness a never-before-seen rise of 100 parts per million carbon dioxide into our atmosphere. NASA has graphed this for us:
100ppm of CO2 in a cubic meter room has about 755mg of mass. The earth's atmosphere is roughly 5.1 "Exagrams". Air has a mass of roughly 29 grams per mol, and CO2 is roughly 44 grams per mol.
If we want to remove the CO2 from the air, we simply need to remove the 109 00 000 000 000 000 000 000 000 000 000 000 000 000 (1.09 × 10^40) molecules of CO2 that were added over the last century. In grams, that's about 7.96 × 10^14 kilograms of CO2. If you were to take every person alive on earth today and add their mass together, put them on a scale with CO2 on the other end, the weight of CO2 is 350x greater (just the added 100ppm, not the full 400ppm!).
So how do we collect it?
There are no good ways to collect CO2. The problem would be quite different if we had 100,000ppm and needed to bring it down to 90,000ppm, as it would be far easier to extract CO2 from the air. We're forced with discarding over 99.996% of all air processed.
Yet somehow we collect and sell Neon gas, which is 18ppm on in our atmosphere. Argon is collected through a process called "fractional distillation" which is ultimately collecting air, cooling it down to make liquid air, and warming it to just the correct point where only the Neon in the mixture escapes the liquid due to becoming a gas.
Similarly, you could cool the liquid and put it into a centrifuge where mechanical separation of layers would be possible. This is done for blood when creating various blood products (red cells, white cells, plasma, platelets), but may be much more complicated to build the apparatus for.
So, we may have a very expensive way to collect and store a mass of CO2 that is strangely close to as much mass as all the grains of sand on earth combined.
So how do we remove it?
There are no good ways to remove CO2 (change it into some other molecule). Many of these technologies require a slow process in which CO2 reacts with something, which requires you have another secondary mass of at-least 1.09 × 10^40 molecules , but possibly more if you want to capture it instead of a reaction with something.
CO2 doesn't like reacting. Many scientists have found really interesting things that it will react with, and ways to even make useful products, however, nothing seems to have "taken off" just yet. I don't like the idea of reacting CO2 with something as a means to remove 100ppm. I suspect the expense and limited supply of another material will drive up the costs.
Re-think what makes CO2:
Two Oxygen atoms bonded with one Carbon atom. Those bonds each represent 1498 kilojoules of energy for every 44 grams of CO2. Just for fun, let's pretend we're going to blast the Carbon Dioxide with a 100% efficient laser to break those bonds. We would need 2.71 x 10^19 kilojoules of energy, "27.1 Exajoules". Using a laser or any other method, if you want to remove this bond, you need that energy from somewhere. This is far more energy than that given by an atomic bomb (10^9), but fortunately, far less than the Death Star can output (10^32).
We could get that energy in many ways.
We could try using solar power. 5760 kilojoules per day per square meter is reasonable given present solar technology and weather issues. If you covered nearly 1.2 million square kilometers of land (I bumped the number a few hundred thousand to account for service roads and other needs) in solar panels you could generate 6.9 x10^15 kilojoules per year, which means after 33 years of only stopping at nightfall (international participation would really speed things up), we could have removed 100ppm of CO2 from the atmosphere. This project would cost over (but we can hope not much more than) $3.6 Trillion. That's the same expense as 24 International Space Stations (or one really big one). The ISS is the most expensive construction in all of human history.
By the way, 1 million square kilometers is the size of Egypt. Turkey is nearly 783000km, Greenland is nearly 2 million km.
We could go nuclear. Over a 40 year period a typical plant is expected to output something like 1.3 exajoules. There's only 450 online today, and to do it in a 20 year time frame we may need 20 reactors. Obviously the big win here is resources and land mass. There's a big fear with regards to using these as there have been 57 accidents since the Chernobyl disaster, which has left with a region humans should not go for 20,000 years (for reference, the first human cities were founded 8000 years ago). One advantage is that the plants don't have to serve human populations, so they can go places few if any people live.
Fight fire with fire
Perhaps the most shocking option, we could burn oil. We would need to burn 1 633 986 928 barrels, each would release 10kg (if it is diesel) of CO2, a net win (I feel dirty saying that). There's one major problems with this however: That's 1.5x as many barrels as have ever been produced.
Right now about 100 million barrels are made every year, so even if we took 50% of them, we would take about 30 years. Also, such an action would likely cause a global economic collapse and drive the price skyrocketing. If the price was frozen at $50/barrel, it would cost over 75 trillion (suddenly launching 24 space stations sounds like a bargain).
One last problem...
Decomposing CO2 with a laser will create a fine particulate dusting of carbon wherever this happens. At the scale I'm talking about, there will undoubtedly be a massive need to ensure the dust is not introduced into the air in this free form. Lung problems are the least of the concerns.
We have no easy options remaining
The only sane solution that can even remotely get political buy-in and funding is a massive space mirror to deflect the sun. This has other unfortunate results, such as reducing the thing our planet needs to support us, and the on-going maintenance of them.
... one of the proposals was to station one or more wire-mesh "mirrors" in orbit to deflect sunlight back into space or to filter it. The idea was proposed by Lowell Wood, a senior staff scientist at Lawrence Livermore National Laboratory, who calculated that deflecting 1% of sunlight would restore climatic stability, and that that would require either a single mirror 600,000 square miles (1,600,000 km2) in area or several smaller ones. Wood had been researching the idea for more than ten years but considered it so infeasible that it should only be a back-up plan for solving the global warming problem.
(From The Space Mirror on Wikipedia)
If we don't want to live in a future where we have to block out the sun to survive with massive space shades we'll need to get serious innovation behind these problems.
Right now we live in a world where designer air filter masks are on the market and growing in popularity. These pollution issues need real plans to resolve them, and laws with real teeth to prevent more air filter masks from being something new I need to buy.
Note: There may have been some minor errors or amazing technical innovations recently. The point of this article is to bring a focus to the regular person on how serious and challenging this problem is, not to multiply numbers a lot or make exhaustive lists.