Mixture of Gases

2. Mixture of Gases

Consider a gaseous mixture (e.g., of carbon dioxide and oxygen) above a liquid sur-

face. In that case ˆf CO 2 (l) = ˆf CO 2 (g) , and using the ideal solution model

X CO 2 (l) f CO 2 (l)( T,P) = X CO 2 f CO 2 (g) (T,P)

Treating the gases as ideal,

X CO 2 (l) f CO 2 (l) (T,P) = X CO 2 P=p CO 2 ,

X CO sat 2 (l) POY CO 2 (l) P CO 2 =X CO 2 P=p CO 2 , i.e.,

(32) p

X CO sat 2 =p CO 2 /( P CO 2 POY CO 2 (l) ), or

(33) In this case, the total pressure that appears in Eq. (31) is replaced by the partial pres-

sat

CO 2 =X CO 2 (l) P CO 2 POY CO 2 (l) .

sure. In power plants, water exists under large pressures and hence air may be dissolved in it in the boiler drums. Since solubility decreases at low pressures, the air is released in the con- denser sections (Eq. (31)). Oxygen is corrosive to metals, and it, therefore, becomes necessary to remove the dissolved air or oxygen from water prior to sending water to the boiler. Deaera- tors are used to remove the dissolved gases from water. They work by heating the water with steam (P sat increases, Eq. (31)), and then allowing it to fall over a series of trays in order to expose the water film so that the gases are removed from the liquid phase as much as possible.

Another example pertains to diving in deep water. The human body contains air cavi- ties (e.g., the sinuses and lungs). As a diver proceeds to greater depths, the surrounding pres- sure increases. In order to prevent the air cavities from collapsing at greater depths, the divers must adjust the air pressure they breathe in. They do so by manipulating their diving equip- ment to equalize the cavity pressures with the surrounding water pressure. Consequently, the pressurized air gets dissolved in the blood (Eq. (31)). Upon rapid depressurization, in the process of reaching phase equilibrium, the dissolved air is released into the blood stream in the form of bubbles that can be very harmful to human health. Raoult’s Law may be applied to estimate the concentration of air in blood. Similarly when a person develops high blood pres-

sure, the amount of soluble O 2 and CO 2 may increase.

If we assume blood to have the same properties as water, we can determine the solu- bility of oxygen at a 310 K temperature and 1 atm pressure as follows. The vapor pressure data of oxygen can be extrapolated from a known or reference condition to 310 K using Clau-

sius–Clayperon equation (which is valid if (h fg /Z fg ) is constant), namely, ( P sat k /P ref ) = exp ((h fg,k /(R k Z fg,k ))(1/T ref – 1/T)).

(34) The saturation pressure at 310 K can be determined using the relation ln (P sat ) = 9.102 – 821/T

(K) bar, i.e., P sat (310 K) = 635 bar. In air, at 1 atm p O 2 = 0.21 bar, and the resulting solubility of O 2 in water is 300 ppm.

Another example pertains to hydrocarbon liquid fuels (e.g., fuel injected engines) that are injected into a combustion chamber at high pressures ( ≈ 30 bar). The gaseous carbon dioxide concentration in these chambers is of the order of 10%. At 25ºC, the solubility of the dioxide in the fuels is ≈0.1×3 MPa÷61MPa = 0.005. This solubility increases as the pressure is increased.