Yes I mean headspace as far as bottles and kegs, but it was in direct correlation to brite tanks/carb vessels
Bottles and kegs - If you carb a beer to 2.5 volumes of CO2, that means at 9psi at 34 degrees the beer will maintain 2.52 volumes of CO2
now, transfer that same liquid into a bottle or keg. Unless you re-pressurize the keg or bottle to 9psi, the dissolved volume of CO2 and the headspace will want to equalize pressure, meaning the extra CO2 that was under pressure in solution will now break out of solution and fill up that headspace and re-pressurize the keg/bottle, meaning less dissolved volume of CO2 in your beer. Hence equal pressures.
Same thing applies in a brite tank, except what I am basically doing is bubbling CO2 through a solution under pressure, to forcefully get that CO2 into solution, i.e. force carbing a keg, or force carbing in a brite tank. Difference is, in a brite tank, because I am constantly adding CO2 and increasing pressure from the bottom, I have to constantly relieve pressure from the top to allow the CO2 to pass through the solution. The amount of headspace directly relates to how quickly I can carbonate that beverage in that manner in a brite tank. The more headspace, the faster it carbs, because the less beer there is. So you cant just set it and forget it.