Also remember that living cells also have pressure constraints outside of simple chemical equilibrium. Even if the gas is reasonably inert, like nitrogen, hundreds of psi, if the vessel can hold it, will begin to disrupt cell structures and inhibit or kill yeast.
If the latter is the case, Is there a simple formula I can use to calculate the amount of yeast to sugar ratio given a volume that will tell me the resulting PSI?
This is deceptively easy, but unfortunately, likely very incomplete. We can determine how what quantity of gas we get from any reaction, but with side reaction of the sort found in living things, and with the non-ideal behavior of gasses -- both under pressure and because CO2
reacts with water, calculations are likely to go nowhere fast.