An investigation of the use of mathematical models to explore the chemical aspects of physiological systems; this deals with the theoretical and computational aspects of understanding the chemistry of human physiological function. The question of existence of solutions to problems having unbounded constraint sets is investigated by relating their existence (or nonexistence) to a property of a solution to an auxiliary chemical equilibrium problem with a bounded constraint set. An example system is selected consisting of gases in contact with an aqueous buffer solution at a uniform total hydrostatic pressure and temperature. The numerical problem of determining the amount of C02 to be added to achieve a specified partial pressure of CO2 in the gas phase, and its effects on the composition of the total system, is solved by using a procedure suggested by the concept of unbounded constraint sets, requiring 2.8 seconds on an IBM 7044 using a FORTRAN IV program. Findings may apply to design of artificial life-support systems needed in extraterrestrial environments related to Air Force missions. 25 pp. Ref.