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.
Parts
» COMPUTATIONAL MECHANICS and APPLIED ANALYSIS
» Explicit and Implicit Functions and Total Differentiation
» Exact (Perfect) and Inexact (Imperfect) Differentials
» Intermolecular Forces and Potential Energy
» Internal Energy, Temperature, Collision Number and Mean Free Path
» Vector or Cross Product r The area A due to a vector product
» First Law for a Closed System
» First Law For an Open System
» STATEMENTS OF THE SECOND LAW
» Cyclical Integral for a Reversible Heat Engine
» Irreversibility and Entropy of an Isolated System
» Degradation and Quality of Energy
» SINGLE–COMPONENT INCOMPRESSIBLE FLUIDS
» Evaluation of Entropy for a Control Volume
» Internally Reversible Work for an Open System
» MAXIMUM ENTROPY AND MINIMUM ENERGY
» Generalized Derivation for a Single Phase
» LaGrange Multiplier Method for Equilibrium
» Absolute and Relative Availability Under Interactions with Ambient
» Irreversibility or Lost Work
» Applications of the Availability Balance Equation
» Closed System (Non–Flow Systems)
» Heat Pumps and Refrigerators
» Work Producing and Consumption Devices
» Graphical Illustration of Lost, Isentropic, and Optimum Work
» Flow Processes or Heat Exchangers
» CLASSICAL RATIONALE FOR POSTULATORY APPROACH
» Generalized Legendre Transform
» Van der Waals (VW) Equation of State
» Other Two–Parameter Equations of State
» Compressibility Charts (Principle of Corresponding States)
» Boyle Temperature and Boyle Curves
» Three Parameter Equations of State
» Empirical Equations Of State
» State Equations for Liquids/Solids
» Internal Energy (du) Relation
» EXPERIMENTS TO MEASURE (u O – u)
» Vapor Pressure and the Clapeyron Equation
» Saturation Relations with Surface Tension Effects
» Temperature Change During Throttling
» Throttling in Closed Systems
» Procedure for Determining Thermodynamic Properties
» Euler and Gibbs–Duhem Equations
» Relationship Between Molal and Pure Properties
» Relations between Partial Molal and Pure Properties
» Mixing Rules for Equations of State
» Partial Molal Properties Using Mixture State Equations
» Ideal Solution and Raoult’s Law
» Completely Miscible Mixtures
» DEVIATIONS FROM RAOULT’S LAW
» Mathematical Criterion for Stability
» APPLICATION TO BOILING AND CONDENSATION
» Physical Processes and Stability
» Constant Temperature and Volume
» Equivalence Ratio, Stoichiometric Ratio
» Entropy, Gibbs Function, and Gibbs Function of Formation
» Entropy Generated During an Adiabatic Chemical Reaction
» MASS CONSERVATION AND MOLE BALANCE EQUATIONS
» Evaluation of Properties During an Irreversible Chemical Reaction
» Criteria in Terms of Chemical Force Potential
» Generalized Relation for the Chemical Potential
» Nonideal Mixtures and Solutions
» Gas, Liquid and Solid Mixtures
» Availability Balance Equation
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