of the ph to the levels lethal to most ans closed form mathematical models usable in design of a shipboard system from any set of given specifications are presented a list of symbols used in the equations is as follows c concentration of carbon dioxide in the water including ions produced by electrolytic dissociation k h henry 39 s law constant for oxygen 39 79 u00d7 10 u2212 6 n co2 number of moles of carbon dioxide in the bubble p co2 partial pressure of carbon dioxide in the bubble superscript 0 refers to quantities in the gas bubble when it is first introduced into the tank subscript 0 refers to quantities in the water at the time t 0 the system analyzed places a mixture of nitrogen and carbon dioxide with a relatively small fraction of oxygen in contact with ballast water the oxygen level in the ballast water is assumed to have reached equilibrium with air as a result of prolonged contact and therefore would contain a concentration of oxygen sufficient to support a wide spectrum of life forms the objective is to reduce the oxygen content to a low level by interchange with the gas mixture the gas is bubbled through the ballast water which assures uniform distribution of dissolved gas throughout the ballast tank thus diffusion within the tank can be neglected.