Systems, methods and cartridges for carbonating or otherwise dissolving gas in a precursor liquid, such as water, to form a beverage. A gas source can be provided in a cartridge which is used to generate gas that is dissolved into the precursor liquid. A beverage medium, such as a powdered drink mix or liquid syrup, may be provided in the same, or a separate cartridge as the gas source and mixed with the precursor liquid to form a beverage. The gas source may include a solid molecular sieve formed in beads in which at least 85% of the beads by weight have a size of 0.71 mm to 2.0 mm.
