Chapter 8 Real Gases

Compression Factors Physical Chemistry Real Gases Compression Factors Real 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) Z P H2 0 100 200 300 1.2 1 0.8 0oC N2 CH4 Z P 200 K 500 K 1000 K 0 300 600 900 3 2 1 CH4

Real Gas Equations of State Physical Chemistry Real Gases Real Gas Equations of State (8.2) van der Waals equation Ideal Gas Law/Perfect Gas Equation: PV = nRT (1.18)*

Van der Waals Equation of State Physical Chemistry Real Gases Van der Waals Equation of State : to correct the effect of intermolecular attractive forces on the gas pressure b: the volume excluded by intermolecular repulsive forces

Real Gas Equations of State Physical Chemistry Real Gases Real Gas Equations of State Redlich-Kwong Equation (8.3) Virial Equation of State (8.4) The limited accuracy of the data allows evaluation of only B(T) and sometimes C(T).

Virial Equation of State Physical Chemistry Real Gases Virial Equation of State Power series in 1/Vm (8.4) Power series in P (8.5) (8.6) low P (8.7) (8.2) vdW gas

Gas Mixtures Physical Chemistry Real Gases Gas Mixtures For a mixture of two gases, 1 and 2, use a two-parameter equation, (8.10) x1 and x2: the mole fractions of the components b: a weighted average of b1 and b2 a: related to intermolecular attractions (a1a2)1/2: intermolecular interaction between gases 1 and 2 (8.11) mean molar volume

Condensation Physical Chemistry T < 374 oC P H Real Gases Condensation T < 374 oC P H gas condenses to liquid when P H2O T = 300 oC Y G R(vapor)S(saturated vapor), P, V U T S W M R 400 oC S(saturated vapor)W(saturated liquid), P, V  J N 374 oC L V 300 oC L 200 oC L + V W(saturated liquid)Y(liquid), P , V K Vm Isotherms of H2O

H2O phase diagram: P — T Physical Chemistry solid liquid gas Real Gases H2O phase diagram: P — T D C 218 atm Y I solid liquid S P / 10 5 Pa 1 atm R gas 0.00611 A O 0.0024 0.01 99.974 374.2 Tf T3 Tb t/℃

Condensation Physical Chemistry T  374 oC Isotherms of H2O P Vm U R J Real Gases Condensation T  374 oC Isotherms of H2O P Vm U R J N Y 374 oC 300 oC 200 oC H2O L + V L V G H T S K M W Fig. 8.3 No amount of compression will cause the separation out of a liquid phase in equil. with the gas. 400 oC T = 374 oC Critical temperature Tc Critical pressure Pc Critical volume Vm,c Critical constants

Critical T (Tc), Tc(CO2)=304.2 K Physical Chemistry Real Gases Isotherms of CO2 {P} {Vm,c} T3 c Tc g b a l T1 T2 Critical constants Critical T (Tc), Tc(CO2)=304.2 K Critical P (Pc), Pc(CO2)=7.38 MPa Critical molar V (Vm,c), Vm,c(CO2)=94×10-6 m3·mol-1

Table 8.1 Critical Constants Physical Chemistry Real Gases Table 8.1 Critical Constants Species Tc / K Pc / atm Vm,c / cm3·mol-1 Ar 150.7 48.3 74.6 Ne 44.4 27.2 41.7 N2 126.2 33.5 89.5 H2O 647.1 217.8 56.0 D2O 643.9 213.9 56.2 H2S 373.2 88.2 98.5 CO2 304.2 72.88 94.0 HCl 324.6 82.0 81.0 CH3OH 512.5 80.8 117

Fluid Physical Chemistry Real Gases Fluid There 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.

Supercritical fluid T > Tc and P > Pc Physical Chemistry Real Gases Supercritical fluid A supercritical fluid is one whose T and P satisfy T > Tc and P > Pc A 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.

CO2 o Supercritical fluid C Physical Chemistry Real Gases CO2 -60 -40 -20 20 40 60 80 100 B 5 10 15 25 30 35 -56.6 ℃ t c=31.06 t/ o C gas liquid solid 200 300 400 500 600 700 800 900 1000 1100 1200 p /MPa P c =7.38MPa A 0.518MPa Supercritical fluid Supercritical CO2 is used commercially as a solvent to decaffeinate coffee.

Critical data and equations of state Physical Chemistry Real Gases Critical data and equations of state At the critical point: (8.12) Differentiating the van der Waals equation (8.2) and Application of the conditions (8.12) gives and (8.13)

Critical data and equations of state Physical Chemistry Real Gases Critical data and equations of state From van der Waals equation: (8.14) Division of the first equation in (8.13) by the second yields (8.15) Use of (8.15) in the first equation in (8.13) gives and (8.16)

Critical data and equations of state Physical Chemistry Real Gases Critical data and equations of state Substitution of (8.15) and (8.16) into (8.14) (8.15) (8.16) (8.14) gives (8.17)

Critical data and equations of state Physical Chemistry Real Gases Critical data and equations of state Substitution of (8.15) and (8.16) into (8.14) (8.15) (8.16) (8.17) Three equations for two parameters, a and b vdW gas (8.18)

Critical data and equations of state Physical Chemistry Real Gases Critical data and equations of state Combination of (8.15) to (8.17) (8.15) (8.16) (8.17) Predicts the compressibility factor at the critical point (8.19) Van der waals equation

Critical data and equations of state Physical Chemistry Real Gases Critical data and equations of state Van der waals equation (8.19) ideal gas R-K equation (8.20) (8.21) (8.22)

Selected equations of state Physical Chemistry Real Gases Selected equations of state Equation Critical constants Perfect gas van der Waals Berthelot

Selected equations of state Physical Chemistry Real Gases Selected equations of state Equation Critical constants Perfect gas R-K virial

The law of corresponding states Physical Chemistry Real Gases The law of corresponding states The critical constants are characteristic properties of gases The reduced variables of a gas by dividing the actual variable by the corresponding constant. (8.27) reduced pressure reduced volume reduced temperature 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. (8.28)