《物理化学 Physical Chemistry》课程教学资源（英文版）Phase Equilibrium（Binary mixtures）

Phase equilibrium binary mixtures Chemistry 331

Chemistry 331 Phase Equilibrium Binary mixtures

liq vap eq. in Binary Mixtures Both the liquid and the vapor phase are binary mixtures of a and b xA, X B are the mole fractions in the liquid yA, yB are the mole fractions in the vapor PA,pAre the le partial pressures in the vapor Chemistry 331

Chemistry 331 liq  vap Eq. in Binary Mixtures • Both the liquid and the vapor phase are binary mixtures of A and B. • x A, x B are the mole fractions in the liquid. • y A, y B are the mole fractions in the vapor. • p A, p B are the partial pressures in the vapor

Ethyl Acetate in Acetic Anhydride 800 700 600 500 300 200 100 0.0 02 04 06 0.8 1.0 Chemistry 331 thyl acetate

Chemistry 331 Ethyl Acetate in Acetic Anhydride 0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 xethyl acetate p /torr

Raoult's law The vapor pressure of a substance varies linearly with its mole fraction in solution. I Raoult's law becomes exact as xa> Raoult's law becomes increasingly valid as the components of the mixture become more structurally similar Chemistry 331

Chemistry 331 • The vapor pressure of a substance varies linearly with its mole fraction in solution.\ pA= xA pA * • Raoult’s Law becomes exact as xA →  • Raoult’s Law becomes increasingly valid as the components of the mixture become more structurally similar. Raoult’s Law

n-Pentane in Methyl Acetate 600 500 300 200 100 0 0.0 0.2 0.4 0.6 1.0 pentane Chemistry 331

Chemistry 331 n-Pentane in Methyl Acetate 0 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 p /torr xpentane

Ideal solution model uA(=uA 8), at equilibrium uA(D=uA+Rtin(palp) uA(=uA+RTIn(palp)+rTinx HA(D=UA+RTInxa where ua is the chemical potential of the pure liquid Chemistry 331

Chemistry 331 Ideal Solution Model         A A A A A A A A A A A A l g l RT p p l RT p p RT x l RT x ( ) ( ) ( ) ln( / ) ( ) ln( / ) ln ( ) ln * * = = + = + + = + , at equilibrium 0 0 0 0 where A * is the chemical potential of the pure liquid

Ideal heat of mixing △G mixing nAua+nBuB-naua+bUb) nRTInxtnBrtinxB a △S uXIn 1g=nGInx+nprInx 18 ˇB △H=△G…+TS=0 muxing muxing muxing Chemistry 331

Chemistry 331 Ideal Heat of Mixing      G n n n n n RT x n RT x S G T n R x n R x H G T S mixing A A B B A A B B A A B B mixing mixing p A A B B mixing mixing mixing = + − + = + =       = + = + =       ( ) ln ln ln ln * * 0

Molecular basis for ideal sol'ns In pure liquid a, there are only A-A interactions In pure liquid b, there are only B-b interactions D In solutions of a and b there are A b interactions as well 0 says that all 78 three interactions are of equal strength Chemistry 331

Chemistry 331 Molecular Basis for Ideal Sol’ns. • In pure liquid A, there are only A-A interactions. • In pure liquid B, there are only B-B interactions. • In solutions of A and B, there are A-B interactions as well. ▪ Hmixing= 0 says that all three interactions are of equal strength

Ethyl acetate- Acetic Anhydride 800 700 600 500 Ptotal 400 Ethyl acetate 300 200 Pa drid 0.0010.20.3040.506070809 1.0 Chemistry 331

Chemistry 331 Ethyl Acetate - Acetic Anhydride 0 100 200 300 400 500 600 700 800 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p /torr xethyl acetate pacetic andydride pethyl acetate ptotal

n-Pentane and methyl Acetate 600 total 400 Pp pentane 300 200联 FE-I methyl acetate 100 0.0 0.2 0.4 0.6 0.8 0 Chemistry 331 pentane

Chemistry 331 n-Pentane and Methyl Acetate 0 100 200 300 400 500 600 0.0 0.2 0.4 0.6 0.8 1.0 xpentane p /torr pmethyl acetate ppentane ptotal