Never did the Alka-Seltzer experiment. I would think it would eventually pop the lid off, since when you drop it in water it forms lots of bubbles. As more gas bubbles form, the pressure inside the container will keep going up. When it is greater than the friction force of the lid, it would start to move the cover. Once you get a tiny opening to the outside air, the gas bubbles above the liquid would start rushing out very fast to the outside. The higher the pressure and the smaller the opening of this break, the faster the air molecules will travel. The momentum force generated by billions of fast moving molecules would be very strong and cause the top to break open. You would also get a loud pop sound too, since the fast moving air would be traveling faster than the speed of sound, causing a mini-sonic boom.
If the lid was on super tight, or the container was a sealed reinforced metal box, I think the gas pressure generated would at some point become high enough to go back into the water, so you would get even more carbonation. You would reach an equilibrium point where the gas pressure would stabilize with it escaping the water and going back in it too. This equlibrium pressure would be related to the partial pressure of CO2 gas. If the container was not strong enough, it could easily explode, so never do this experiment on a tighttly sealed container. It can be extremely dangerous. Even if you are using something with a top that can pop-off, you must wear safety glasses, since it could cause serious eye inuries.
I did not look up the answer and just based things on my basic science knowledge. Not sure how Alka-Seltzer makes bubbles. My best guess would be CO2 gas bubbles. They could have a mixture of sodium bicarbonate separated by some type of dry acid on the other side. When it is dropped in water, the dry acid would react with the NaCO3.
NaCO3 + HCl + H2O -> CO2 (gas) + NaCl (table salt) + H2O
(did not bother to balance the equation)
I think they add some aspirin in it too to help with headaches or other aches.