Chapter 8Real Gases

Compression FactorsReal gases do not obey the perfect gas equation exactly. The measure of the deviation from ideality of the behavior of a real gas is expressed as the compression factor Z:(8.1)Real GasesPhysical Chemistry

Real Gas Equations of State(8.2)van der Waals equationReal GasesPhysical Chemistry

Van der Waals Equation of StateReal GasesPhysical Chemistryb: the volume excluded by intermolecular repulsive forces

Virial Equation of State(8.4)Redlich-Kwong Equation(8.3)Real GasesPhysical ChemistryReal Gas Equations of StateThe limited accuracy of the data allows evaluation of only B(T) and sometimes C(T).

Virial Equation of State(8.5)(8.6)(8.7)low PvdW gasReal GasesPhysical ChemistryPower series in 1/VmPower series in P

Gas Mixtures(8.10)For a mixture of two gases, 1 and 2, use a two-parameter equation, Real GasesPhysical Chemistryx1 and x2: the mole fractions of the componentsb: a weighted average of b1 and b2a: related to intermolecular attractions(a1a2)1/2: intermolecular interaction between gases 1 and 2

Isotherms of H2OPVm400 oCURJNY374 oC300 oC200 oCH2OL + VLVLGHTSKMWCondensationT < 374 oCgas condenses to liquid when PT = 300 oCR(vapor)S(saturated vapor), P, VS(saturated vapor)W(saturated liquid), P, V W(saturated liquid)Y(liquid), P , VReal GasesPhysical Chemistry

t/ADC0.006110.01solidgasliquidOP / 10 5 Pa374.2218 atm H2O phase diagram: P T 99.9741 atm0.0024IRSYTfTbT3Real GasesPhysical Chemistry

400 oCCondensationT 374 oCNo amount of compression will cause the separation out of a liquid phase in equil. with the gas.T = 374 oCCritical temperature TcCritical pressure PcCritical volume Vm,cCritical constantsReal GasesPhysical ChemistryFig. 8.3

Critical constantsCritical T (Tc), Tc(CO2)=304.2 KCritical P (Pc), Pc(CO2)=7.38 MPaCritical molar V (Vm,c), Vm,c(CO2)=9410-6 m3mol-1Real GasesPhysical Chemistry

Table 8.1 Critical ConstantsReal GasesPhysical Chemistry

FluidThere is a continuity between the gaseous and the liquid states. In recognition of this continuity, the term fluid is used to mean either a liquid or a gas. An ordinary liquid can be viewed as a very dense gas. Only when both phases are present in the system is there a clear-cut distinction between liquid and gaseous states. For a single-phase liquid system it is customary to define as a liquid a fluid whose temperature is below Tc and whose molar volume is less than Vm,c.If these two conditions are not met, the liquid is called a gas. So a further distinction between gas and vapor can be made, but these two words are used interchangeably in this book.Real GasesPhysical Chemistry

Supercritical fluidA supercritical fluid is one whose T and P satisfyA supercritical fiquid usually has liquidlike density but its viscosity is much lower than typical for a liquid and diffusion coefficients in it are much higher than in liquids. T > Tc and P > PcReal GasesPhysical Chemistry

Supercritical fluidSupercritical CO2 is used commercially as a solvent to decaffeinate coffee.Real GasesPhysical ChemistryCO2

Critical data and equations of stateDifferentiating the van der Waals equation (8.2)andAt the critical point:(8.12)Application of the conditions (8.12) givesand(8.13)Real GasesPhysical Chemistry

Critical data and equations of stateDivision of the first equation in (8.13) by the second yieldsFrom van der Waals equation:(8.14)Use of (8.15) in the first equation in (8.13) givesand(8.16)(8.15)Real GasesPhysical Chemistry

Critical data and equations of stateSubstitution of (8.15) and (8.16) into (8.14)(8.14)gives(8.16)(8.15)(8.17)Real GasesPhysical Chemistry

Critical data and equations of stateSubstitution of (8.15) and (8.16) into (8.14)Three equations for two parameters, a and b(8.16)(8.15)(8.17)(8.18)vdW gasReal GasesPhysical Chemistry

Critical data and equations of stateCombination of (8.15) to (8.17)(8.16)(8.15)(8.17)(8.19)Real GasesPhysical ChemistryPredicts the compressibility factor at the critical pointVan der waals equation

Critical data and equations of state(8.19)ideal gas(8.20)(8.21)(8.22)R-K equationReal GasesPhysical ChemistryVan der waals equation

Selected equations of stateReal GasesPhysical Chemistry

Selected equations of stateReal GasesPhysical Chemistry

The law of corresponding statesThe critical constants are characteristic properties of gasesThe reduced variables of a gas by dividing the actual variable by the corresponding constant. The observation that the real gases at the same reduced volume and reduced temperature exert the same reduced pressure is called the law (principle) of corresponding states.(8.27)reduced pressurereduced volumereduced temperature(8.28)Real GasesPhysical Chemistry