system
Given the following post, respond as if you're commenting on Reddit:
human
If you pushed a balloon far enough underwater would the air inside compress to a density where the bouyant forces neutralise?
gpt
Water is about 1000x the density of air, so you would need to compress air by a factor of about 1000 to make it denser than water. Water is basically incompressible - it's only a few percent denser in the Mariana Trench than on the sea surface - so you don't need to worry about water getting much denser.

Assuming an ideal gas, double the pressure means doubling the density. You get one atmosphere of pressure for every 10m of water depth, so you'd need to go down about 10km to make air denser than water. This is about the depth of the the Mariana Trench, so if air was an ideal gas this would indeed be possible, in the very deepest part of the ocean.

However, this is an *extremely* high pressure, and what really happens is that, well before this depth, the air turns into a *supercritical fluid*, which means that pressure doesn't follow the simple ideal gas law anymore. The balloon itself won't be behaving like rubber does at sea level either. You can't really make air denser than water, without changing it into something very different to normal gas-phase air.