Thermodynamics Ideal Gases/Perfect Gases a Gases. Agas is a fluid which has no intrinsic shape, e and which expands indefinitely to fill any container ● in which it is held. Ideal gases 1. The amount of substance of which it is comprised, n(mole 2. The temperature of the gas, T (Kelvin) 3. The pressure of the gas, P(Pascal) 4. The volume occupied by the gas
Ideal Gases/Perfect Gases Gases: A gas is a fluid which has no intrinsic shape, and which expands indefinitely to fill any container in which it is held. Ideal Gases: 1. The amount of substance of which it is comprised, n (mole) 2. The temperature of the gas, T (Kelvin) 3. The pressure of the gas, P (Pascal) 4. The volume occupied by the gas, V (m3 ) Thermodynamics
Chapter 1 Ideal Gases/Perfect Gases The four parameters are not e indepeodantng them are expressed in the gas laws a Gas Laws 1. Boyles law: Pv=constant at constant T and n e2. Charles law: VacT at constant P and n 3. Avogadros Principle: Von at constant P and T Ideal Gas Law /Perfect Gas Equation Pv=nRT R is gas constant (1.18)
Ideal Gases/Perfect Gases Gas Laws: 1. Boyle’s law: PV=constant at constant T and n 2. Charles’ law: VT at constant P and n 3. Avogadro’s Principle: Vn at constant P and T Chapter 1 The four parameters are not independent. The relations among them are expressed in the gas laws. Ideal Gas Law/Perfect Gas Equation: PV = nRT R is gas constant (1.18)*
Chapter 8 Real gases
Chapter 8 Real Gases
Physical Chemistry Real gases Compression Factors Real gases do not obey the perfect gas equation exactly. The real gas is expressed as the compression factor a ehavior of a measure of the deviation from ideality of the be P (,1RT (8. 200K .20C CH, 500K N 1000K CHA 1000K 200K P 100200300 300600900
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: RT PV Z P T m ( , ) (8.1) Real Gases Z P 200 K 500 K 1000 K 200 K 1000 K 0 300 600 900 3 2 1 0 CH4 Z P H2 0 100 200 300 1.2 1 0.8 0 0 oC N2 CH4 Physical Chemistry
Physical Chemistry Real gases Real Gas equations of State P+ RT (8.2) RT a 6 K van der Waals equation Ideal Gas Law/ Perfect Gas Equation PV=rt PV=nRT (1.18)
Real Gas Equations of State (V b) RT V a P m m − = + 2 2 m Vm a V b RT P − − = (8.2) van der Waals equation Ideal Gas Law/Perfect Gas Equation: PV = nRT (1.18)* PVm = RT Physical Chemistry Real Gases
Physical Chemistry Real gases 三:实际气体的状态方程 范德华( Van der waals)方程 V{yn⊙ RT PV=RT a/v to correct the effect of intermolecular attractive forces on the gas pressure b: the volume excluded by intermolecular repulsive forces 式中a/V是压力校正项,即称为内压力;b是 二体积校正项,是气体分子占有的体积
范德华（Van der Waals）方程 式中 是压力校正项，即称为内压力； 是 体积校正项，是气体分子占有的体积。 b 2 m a V/ V b RT V a P m m ( + )( − ) = 2 PVm = RT Physical Chemistry Real Gases 实际气体的状态方程 : to correct the effect of intermolecular attractive forces on the gas pressure 2 m a V/ b: the volume excluded by intermolecular repulsive forces
Physical Chemistry Real gases Real Gas equations of State Redlich-Kwong Equation RT a Vm-b y(m +b)t (8.3) Virial equation of state PV=RTI1+ BT) C(T) D(T (8.4) The limited accuracy of the data allows evaluation of only Br and sometimes CT)
Virial Equation of State = + + 2 + 3 + ( ) ( ) ( ) 1 m m m m V D T V C T V B T P V R T (8.4) Redlich-Kwong Equation 1/ 2 V (V b)T a V b RT P m m m + − − = (8.3) Physical Chemistry Real Gases Real Gas Equations of State The limited accuracy of the data allows evaluation of only B(T) and sometimes C(T)
Physical Chemistry Real gases Virial Equation of state Power series in l/v PV=RT1+ B(1),C()D(T (8.4) Power series in p PVm=R7[l+B(m)P+C()P+D(7)P+…](85) B=BRT, C=(B+CRT 8 RT tB low P (8.7) RT RT (8.2) P a Z v k RTYo 1-b/V RTV vdw ga ras RT
Virial Equation of State [1 '( ) '( ) '( ) ] PVm = RT + B T P +C T P 2 + D T P 3 + (8.5) 2 2 2 B = B'RT , C = (B' +C')R T (8.6) B P RT Vm = + low P (8.7) m m m m m m RTV a RTV b V a V b V Z RT PV − − − = − = = 1 / 1 vdW gas 2 m Vm a V b RT P − − = (8.2) RT Vm Physical Chemistry Real Gases = + + 2 + 3 + ( ) ( ) ( ) 1 m m m m V D T V C T V B T P V R T (8.4) Power series in 1/Vm Power series in P
Physical Chemistry Real gases Gas Mixtures For a mixture of two gases, 1 and 2, use a two-parameter equation, a=x a,+2x,x,(a, a,) 2+xa, and b=x, 6,+x,b,( 8.10) x and x,: the mole fractions of the components b: a weighted average of b, and b a: related to intermolecular attractions (a,a2) 2: intermolecular interaction between gases 1 and 2 mean molar volume (8.11)
Gas Mixtures 2 1 1 2 2 2 2 1/ 2 1 1 2 1 2 2 1 a = x a + 2x x (a a ) + x a and b = x b + x b (8.10) For a mixture of two gases, 1 and 2, use a two-parameter equation, (8.11) tot m n V V mean molar volume Physical Chemistry Real Gases 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
Physical Chemistry Real gases s Condensation T,W↓ li L+V 2000 →W( saturated K liquid)→>Y( liquid), P↑V Isotherms ofh,o
Isotherms of H2O P Vm 400 oC U R J N Y 374 oC 300 oC 200 oC H2O L + V L V L G H T S K M W Condensation T < 374 oC gas condenses to liquid when P T = 300 oC R(vapor)→S(satura ted vapor), P, V S(saturated vapor)→W(saturated liquid), P→, V W(saturated liquid)→Y(liquid), P , V Physical Chemistry Real Gases