A 1 lb Coleman propane cylinder holds 248 liters of propane gas at STP. To hold that same volume of air (assuming a tank volume of 1l), the tank pressure would need to be 248 ATM (3645 PSI). The actual pressure inside the tank is only around 145 PSI, though, because unlike air propane condenses into a liquid under moderate pressure. If you want to store a large volume of gas in a small space and you don't care what that gas is, propane seems like a good option.
This is the same principle behind canned air: the cans actually contain refrigerant gasses like R-134a and R-152 — which makes you wonder why you need a license which requires three years of on the job training to do refrigeration work with the same gasses. You can often find what chemicals are actually in consumer products by searching for the product name plus "SDS." Here's the SDS for the top canned air duster on Amazon. Similarly, instant freeze spray is just butane (its boiling point of -1C is better suited to this than R-134A's -26C boiling point or propane's -42C boiling point), and Airsoft propellant gas is often just propane.
Assembled Propane Tank to Tire Filling Adapter
Anyway, I don't own a bicycle air pump, so instead of buying one like a reasonable person, I purchased a set of adapters to instead fill my bike tires with propane. Overall, what I came up with is more convenient to use and cheaper (ignoring the ongoing cost of propane) than a normal air pump, but it turns out that, at least for my inner tubes, propane leaks out faster than air. Also, this can be very unsafe if used improperly. I recommend not building your own propane to Schrader valve adaptor. If you turn the bottle upside down while filling, liquid propane can enter the tire and then uncontrollably expand until the tire explodes.
It turns out that you can actually buy small single use cylinders of propane intended refilling bike tires on the trail, so filling your tires with propane isn't totally crazy. These cylinders are small, though (40 gram), so the risk of catastrophically over-inflating a tire is significantly reduced.
Three parts were needed for this unsafe assembly of adapters:
Parts for Propane Tank to Tire Filling Adapter
The adapter is able to fill tires extremely quickly with a full or mostly full tank. The propane rapidly boils to meet the pressure demand and its temperature rapidly drops. With less full tanks where the heat capacity of the propane isn't high enough to handle the rapid heat loss, the output pressure will stall and the flow rate will be limited by the heat flow into the cylinder. From a propane pressure-enthalpy chart, you can tell that if the pressure is stalled at 30 PSIG (44 PSIA) the temperature of the propane inside the tank has to be around 10F. This is why you can sometimes see frost on a propane tank that is supporting a high flow rate in already cold conditions.