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