厦门大学：《物理化学 Physical Chemistry》课程电子教案（PPT教学课件，英文版）chapter09-2 Solutions

Chapter 9 Solutions

Chapter 9 Solutions

Physical Chemistry Solutions Ideal solutions A solution where the molecules of the various species are so simiar to one another that replacing molecules of one species with molecules of another species will not change the spatial structureor the intermolecular interaction energy in the solution To prevent change on mixing B Bat t, i Ca, B-B, C-C and C, the size and shape of B P P molecules= those ofc The intermolecular interaction B+c B-B. C-C energies should be essentially the same for B-B. B-C. and c atT. P B-C pairs of molecules

Ideal Solutions Solutions A solution where the molecules of the various species are so similar to one another that replacing molecules of one species with molecules of another species will not change the spatial structure or the intermolecular interaction energyin the solution. B at T, P C at T, P B + C at T, P B-B, C-C B-B, C-C, B-C To prevent change on mixing B and C, the size and shape of B molecules  those of C The intermolecular interaction energies should be essentially the same for B-B, B-C, and C￾C pairs of molecules. Physical Chemistry

Physical Chemistry Solutions Ideal solutions When two liquids b and c whose molecules resemble each other closely are mixed at constant t and p, the experimental Ami G is Am G=RT(ghr+noRthn xo) (9.39) From the molecular definition, the B attic at T formation of an ideal solution from P P pure components at constant Tand p △U=0 mIx B+c △V=0 atT. P △mxH=△mU+Pmn2V=0

Ideal Solutions Solutions When two liquids B and C whose molecules resemble each other closely are mixed at constant T and P, the experimental mixG is From the molecular definition, the formation of an ideal solution from pure components at constant T and P ( ln ln ) mix B B C C  G = RT n x + n RT x (9.39) mixU = 0 mixV = 0 mixH = mixU + PmixV = 0 Physical Chemistry B at T, P C at T, P B + C at T, P

Physical Chemistry Solutions Ideal solutions For ideal gases nrR(n Vr/v)(vclv (3.32) For ideal solutions m B m c B mb, C m c C mB nn+n B m B Amis=-nBRhnxB-ncrhn xc △G=△H-7AS △H=0 mX Ami G=RT(ng+nrtIn xo) (9.39)

Ideal Solutions Solutions (ln / ) ln( / ) * * mixS = −nB R VB V − nC R VC V (3.32) * , * Vm,B =Vm C * , * * ( ) V =VB +VC = nB + nC Vm B For ideal gases For ideal solutions * , * , * * , * , VB = nB Vm B VC = nC Vm C = nC Vm B mix B B C C  S = −n Rln x − n Rln x ( ln ln ) mix B B C C  G = RT n x + n RT x (9.39) mixG = mixH −TmixS mixH = 0 Physical Chemistry

Physical Chemistry Solutions Ideal solutions For ideal solutions AmiG=RT(nBhnxB+ndRThnxc) (9.39) For ideal solutions(ideal liquid or solid mixtures) containing the gas constant R? R applies not only to the zero-pressure limit of a gas P R= nt But also to entropy S=khn P+a (3.52) Boltamann's constant r=kN Avogadro constant And other fundamental equations of statistical mechanics!

Ideal Solutions Solutions For ideal solutions For ideal solutions (ideal liquid or solid mixtures) containing the gas constant R? ( ln ln ) mix B B C C  G = RT n x + n RT x (9.39) nT PV R = R applies not only to the zero-pressure limit of a gas A R = kN But also to entropy And other fundamental equations of statistical mechanics! S = k ln P+a (3.52) Boltzmann’s constant Avogadro constant Physical Chemistry

Physical Chemistry Solutions Ideal solutions For ideal solutions △nG=RT( n In x+ n rtIn x() (9.39) △mnG=G-G=∑n∑nA (9.32) △G=RT ∑ ∑nA=∑ n,(u+ RTIn x) (9.40) u;=u(T, P)+RTInx; ideal solution (941) Thermodynamic definition of an ideal solution

Ideal Solutions Solutions For ideal solutions ( ln ln ) mix B B C C  G = RT n x + n RT x (9.39) Thermodynamic definition of an ideal solution:  = − = −i i i i mixG G G ni i n * *   (9.32)  = i mix i i G RT n ln x  = + i i i i i i i n n ( RT ln x ) *   (9.40) i i (T,P) RT ln xi ideal solution *  =  + (9.41) Physical Chemistry

Physical Chemistry Solutions Ideal solutions u=u(T, P)+RT In x, ideal solution (9.41) Thermodynamic definition of an ideal solution A solution is ideal if the chemical potential of every component in the solution obeys(9.41) for all solution compositions and for a range of T and p. Molecular definition of an ideal solution A solution where the molecules of the various species are so similar to one another that replacing molecules of one species with molecules of another species will not change the spatial structure or the intermolecular interaction energy in the solution

Ideal Solutions Solutions Thermodynamic definition of an ideal solution: A solution is ideal if the chemical potential of every component in the solution obeys (9.41) for all solution compositions and for a range of T and P. i i (T,P) RT ln xi ideal solution *  =  + (9.41) Molecular definition of an ideal solution: A solution where the molecules of the various species are so similar to one another that replacing molecules of one species with molecules of another species will not change the spatial structure or the intermolecular interaction energy in the solution. Physical Chemistry

Physical Chemistry Solutions tHermodynamic Properties of Ideal solutions Standardstate For an ideal liquid solution, pure liquid i at t and p For an ideal solid solution, pure solid i at Tand P u;=ui(T, P)+RTIn xi ideal solution (9.41) 共1=1+RTnx deal solition (9.42) 1≡(T,P) ideal solution 9.43) The degree superscript denotes the standard state and the star superscript indicates a pure substance

Thermodynamic Properties of Ideal solutions Solutions i i (T,P) RT ln xi ideal solution *  =  + (9.41) Standard States For an ideal liquid solution, pure liquid i at T and P For an ideal solid solution, pure solid i at T and P i i RT ln xi ideal solution *  =  + (9.42)* ( , ) ideal solution * i T P o i   (9.43)* The degree superscript denotes the standard state and the star superscript indicates a pure substance. Physical Chemistry

Physical Chemistry Solutions Mixing Quantities u=u;+rehn x idealsolution (9.42) △nG=G-G=∑n(G1-Gmn)cons.7,P(932 G (9.22) TPn △mnG=1-A=RT∑nhx1 const.T,P ideal solution (944) Same as Ami G=RT(nB n xB+ncrt'n xo) (9.39

Mixing Quantities Solutions i i RT ln xi ideal solution *  =  + (9.42)* G G G n G G const T P i m i i mix i ( ) . , * , *   − = − (9.32) i i T P n i j i n G G               , , (9.22)* ideal solution (9.44) G RT n x const T P i mix i i i i ln . , *  =  −  =  ( ln ln ) mix B B C C  G = RT n x + n RT x (9.39) Same as Physical Chemistry

Physical Chemistry Solutions tHermodynamic Properties of Ideal Solutions Mixing Quantities △nCG=A1-A=R∑ n In x. consi.T,P(94) Since 0<x<1 We have Inx. <0 △G<0 (941) An irreversible(spontaneous) process at constant T, P 0△G P 9.34 n Amis G in(.44)is independent of P △V=0 ideal solution, const. T, P(9.45)

Thermodynamic Properties of Ideal Solutions Solutions We have 0  xi 1 (9.41) Mixing Quantities mixV = 0 ideal solution, const. T, P (9.45) An irreversible (spontaneous) process at constant T, P. G RT n x const T P (9.44) i mix i i i i ln . , *  =  −  =  Since ln xi  0 mixG  0 T ni mix mix P G V ,          = − (9.34) mixG in (9.44) is independent of P Physical Chemistry