Unsure about whether $\rm CO_2$ significantly displaces Oxygen?

Question

Caves can have high concentration of $\rm CO_2$ and cause suffocation. I thought it's because the denser $\rm CO_2$ displaces Oxygen in lower ground. However, in a typical daily condition where both are nearly ideal gas, their spatial distribution should be decided by a boltzmann factor $e^{-\beta m g h}$ and should be independent of each other. The oxygen concentration per volume should be independent of $\rm CO_2$, but pressure is increased with more $\rm CO_2$ (which can messed up pressure-dependent respiration processes).

Is this line of reasoning correct? I'm a bit unsure about this because the CO2-displacing-oxygen argument sounds familiar to me.

Another example is that googling "why firefighters use $\rm CO_2$ to distinguish fire" gives results "Carbon dioxide is denser than oxygen. So when you spray the carbon dioxide on fire, it sinks under the oxygen, separating the fire from oxygen". Assuming the searched answer is correct (decreasing temperature from liquid $\rm CO_2$ is not necessary). Then it seems to contradict the idea that both O2 and CO2 are ideal gas in typical condition.

Answer 1

The increased concentration of carbon dioxide in caves is not due to its greater density.

Oxygen is a very reactive gas and will quickly react with organic matter to produce carbon dioxide. The air you exhale has about 4% carbon dioxide due to the oxygen reacting with you! Fortunately for us, plants convert carbon dioxide back to oxygen as a side effect of photosynthesis and where air can circulate freely air currents mix oxygen produced by plants back into the atmosphere around us.

In a cave there may be no way for air to mix with the atmosphere outside the cave, so when organic matter in the cave decays the carbon dioxide produced is stuck there. So the level builds up due to chemical processes not due density differences.

This isn't universally the case. Most of the caves I explored in my pot holing days had water flowing through them and the water transported oxygen in and carbon dioxide out. A lot of caves also have a significant air flow due to the wind blowing over vents to the surface and producing a pressure differential. However there are caves where no such gas transport occurs and carbon dioxide can build up to dangerously high levels.