厦门大学：《物理化学 Physical Chemistry》课程电子教案（PPT教学课件，英文版）chapter06 Reaction Equilibrium in Ideal Gas Mixtures

Physical chemistr Chapter 6 Chapter 6 Reaction Equilibrium in Ideal gas mixtures

Chapter 6 Reaction Equilibrium in Ideal Gas Mixtures Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture Chemical Potential of a pure Ideal gas dG=-SdT+vdP (436) dT+y dP G one-phase pure (4.86)2 substance TP H=1m=/ dp P isothermal, pure ideal gas , du=rt ddp u(T, P2)-u(T, P)=rt'hn u=u(T)+RTho p isothermal, pure ideal gas(6.1) pure ideal gas, Po=l bar(6.2)

Chemical Potentials in an Ideal Gas Mixture Chemical Potential of a Pure Ideal Gas dG = −SdT +VdP (4.36) dP P RT d Vm dP        = = isothermal, pure ideal gas   = 2 1 2 1 1 P P dP P d RT 1 2 2 1 ( , ) ( , ) ln P P  T P −  T P = RT isothermal, pure ideal gas (6.1) o o P P  =  (T) + RT ln pure ideal gas, P o1 bar (6.2) dGm = d = −Sm dT +Vm dP m i (4.86)* T P G n G , , i i =             one-phase pure substance Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture For a pure ideal gas RT G=H-S Hm=f(T) - RTE P/P Sm=f(p) →>-0asP>0 2RTI Fig. 6. 1 T is fixed

Chemical Potentials in an Ideal Gas Mixture Fig. 6.1 T is fixed P/Po  -  o 0 1 2 3 RT -RT -2RT  = Gm = Hm −TSm H f (T) m = S f (P) m =  → − as P → 0 For a pure ideal gas Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture An ideal gas mixture (1)PV=n,orRT' Ideal gas mixture at 2)The mixture is separated by Tand p thermally conducting rigid membrane permeable to gas i only, and P=x, p P≡x.P membrane Pure gas po=1 bar mixture at and T (T,P2x12x2,…)=14(T,xP)=p1(T,P) Fig 6.2 ideal gas mixture (6.3)

Chemical Potentials in an Ideal Gas Mixture Fig. 6.2 ( , , , , ) ( , ) ( , ) * * i 1 2 i i P i T Pi  T P x x  =  T x =  An ideal gas mixture Ideal gas mixture at T and P Pi  xi P * Pi Pure gas mixture at and T membrane (1) PV = ntotRT (2) The mixture is separated by thermally conducting rigid membrane permeable to gas i only, and Pi  xi P P bar o 1 ideal gas mixture (6.3) Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture (T,P2x1,x2,…)=4(T,xP)=1(T,P) ideal gas mixture Ideal gas (6.3) mixture at Tand p No intermolecular interaction, no effect on u from other gases in the mixture P≡x.P membrane Pure gas mixture at A1=°(7)+RTh and T deal gas mixture P≡1br (64) Fig 6.2 The fundamental thermodynamic equation

Chemical Potentials in an Ideal Gas Mixture Fig. 6.2 ( , , , , ) ( , ) ( , ) * * i 1 2 i i P i T Pi  T P x x  =  T x =  Ideal gas mixture at T and P Pi  xi P * Pi Pure gas mixture at and T membrane ideal gas mixture (6.3) o o i i i P P  =  (T) + RT ln ideal gas mixture P o 1 bar (6.4)* The fundamental thermodynamic equation No intermolecular interaction, no effect on from other gases in the mixture. i Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 Chemical potentials in an ideal gas mixture For an ideal gas mixture RT 1=f(7) - RTE po=1 bar 2RTI Fig 6.1 (modified)

Chemical Potentials in an Ideal Gas Mixture Fig. 6.1 (modified) Pi /Po i - i o 0 1 2 3 RT -RT -2RT ( ) ( ) T G , T o m i o i = f (T) o i = P bar o 1 For an ideal gas mixture Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 E Ideal Gas Reaction equilibrium For the ideal-gas reaction aA+becc+dD (436) 2vu=0 the equilibrium condition aua +buB=cuc+dup Cuc+dup-auA -buB=0 u;=u ()+RTIn (64) cuo +crTIn C+duo +drT In-D aua-aRT In A-buB-bRThn=0

Ideal Gas Reaction Equilibrium For the ideal-gas reaction aA+bB cC+dD (4.36) i  i i = 0 the equilibrium condition A B C d D a +b = c +  cC + d D − a A −b B = 0 o o i i i P P  =  (T) + RT ln (6.4)* ln ln 0 ln ln − − − − = + + + o o B o B o A A o o D o D o C C P P b bRT P P a aRT P P d dRT P P c cRT     Physical Chemistry Chapter 6

Physical Chemistry Chapter 6 Ideal gas reaction equilibrium cuc +crTInC+dup +drT'hn qu -aRT In A-buB-bRT'h =0 cuc +dup --bu RT(chn 。+dlh anA-bIn-D (6.5) P △G=∑vGmn=∑(7)=+d2-a-b the equilibrium condition b △G=-RT|lh In h P

Ideal Gas Reaction Equilibrium ( ln ln ln ln ) (6.5) o B o A o D o C o B o A o D o C P P b P P a P P d P P RT c c d a b − + − −  +  −  −  = ln ln 0 ln ln − − − − = + + + o o B o B o A A o o D o D o C C P P b bRT P P a aRT P P d dRT P P c cRT     o B o A o D o i C i o i i o i m T i o GT  G , , =  (T) =c + d − a −b                −       −       +       = − b o B a o A d o D c o o C P P P P P P P P G RT ln ln ln ln Physical Chemistry Chapter 6 the equilibrium condition

Physical Chemistry Chapter 6 Ideal Gas Reaction Equilibrium △G0=-R(h PA P △G°=-RTh/( P P P K po=1 bar (6.7) P P △G=- rt In K

Ideal Gas Reaction Equilibrium (6.6) (6.7) (ln ln ln ln ) b o B a o A d o D c o o C P P P P P P P P G RT        −       −       +       = −                                        = − b o B a o A d o D c o C o P P P P P P P P G RT ln b o B a o A d o D c o C o P P P P P P P P P K                          P bar o 1 Physical Chemistry Chapter 6 o P o G = −RT ln K

Physical Chemistry Chapter 6 Ideal gas reaction equilibrium d P P (6.7) B P P the equilibrium condition △G=- RTIn kp ∑vAH1=0 ∑vH=∑[+Rr 0 ∑v(O+RPa=0 (68) ∑(a1+b)=∑a+∑b Ca=C

Ideal Gas Reaction Equilibrium o P o G = −RT ln K (6.7) b o B a o A d o D c o C o P P P P P P P P P K                          P bar o 1 [ ln ] 0 , =          = + o o i eq i i i i i i P P     RT ( ) ln 0 , =         +  i o o i eq i i i P P   T RT (6.8)  + =  + i = i i i i i i i (ai bi ) ai b and ca c a Physical Chemistry Chapter 6  = 0 i  i i the equilibrium condition