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