Thermodynamics

812 | Thermodynamicsorory A,gas sidey A,liquid sideGas: ALiquid: By A,gas side y A,liquid sideP A,gas side————PGas A y A,liquid sideTABLE 16–2Henry’s constant H (in bars) for selected gases in water at low to moderatepressures (for gas i, H P i,gas side /y i,water side ) (from Mills, Table A.21, p. 874)Solute 290 K 300 K 310 K 320 K 330 K 340 KH 2 S 440 560 700 830 980 1140CO 2 1,280 1,710 2,170 2,720 3,220 —O 2 38,000 45,000 52,000 57,000 61,000 65,000H 2 67,000 72,000 75,000 76,000 77,000 76,000CO 51,000 60,000 67,000 74,000 80,000 84,000Air 62,000 74,000 84,000 92,000 99,000 104,000N 2 76,000 89,000 101,000 110,000 118,000 124,000P A,gas side = Hy A,liquid sideFIGURE 16–23Dissolved gases in a liquid can bedriven off by heating the liquid.Strictly speaking, the result obtained from Eq. 16–22 for the mole fractionof dissolved gas is valid for the liquid layer just beneath the interface,but not necessarily the entire liquid. The latter will be the case only whenthermodynamic phase equilibrium is established throughout the entire liquidbody.We mentioned earlier that the use of Henry’s law is limited to dilutegas–liquid solutions, that is, liquids with a small amount of gas dissolved inthem. Then the question that arises naturally is, what do we do when the gasis highly soluble in the liquid (or solid), such as ammonia in water? In thiscase, the linear relationship of Henry’s law does not apply, and the molefraction of a gas dissolved in the liquid (or solid) is usually expressed as afunction of the partial pressure of the gas in the gas phase and the temperature.An approximate relation in this case for the mole fractions of a specieson the liquid and gas sides of the interface is given by Raoult’s law asP i,gas side y i,gas side P total y i,liquid side P i,sat 1T2(16–23)where P i,sat (T) is the saturation pressure of the species i at the interface temperatureand P total is the total pressure on the gas phase side. Tabular dataare available in chemical handbooks for common solutions such asthe ammonia–water solution that is widely used in absorption-refrigerationsystems.Gases may also dissolve in solids, but the diffusion process in this casecan be very complicated. The dissolution of a gas may be independent ofthe structure of the solid, or it may depend strongly on its porosity. Somedissolution processes (such as the dissolution of hydrogen in titanium, similarto the dissolution of CO 2 in water) are reversible, and thus maintainingthe gas content in the solid requires constant contact of the solid with areservoir of that gas. Some other dissolution processes are irreversible. Forexample, oxygen gas dissolving in titanium forms TiO 2 on the surface, andthe process does not reverse itself.The molar density of the gas species i in the solid at the interfaceri,solid side is proportional to the partial pressure of the species i in the gasP i,gas side on the gas side of the interface and is expressed asri,solid side P i,gas side 1kmol>m 3 2(16–24)