The properties of mixtures 자연과학대학 화학과 박영동 교수

Chapter 6 The properties of mixtures 6.1 The thermodynamic description of mixtures Partial molar properties Spontaneous mixing Ideal solutions Ideal dilute solutions Real solutions: activities 6.2 Colligative properties The modification of boiling and freezing points Osmosis 6.3 Phase diagrams of mixtures Mixtures of volatile liquids Liquid-liquid phase diagrams Liquid-solid phase diagrams The Nernst distribution law

The partial molar volumes of water and ethanol at 25°C.

partial molar volume

At 25°C, the density of a 50 per cent by mass ethanol/water solution is g cm -3. Given that the partial molar volume of water in the solution is 17.4 cm 3 mol -1, what is the partial molar volume of the ethanol?

partial molar Gibbs energy, G J

Pressure dependence of G G = H – TS dG = dH – TdS – SdT = Vdp - SdT For liquid or solid, ΔG = VΔp For vapor, ΔG = ∫Vdp = nRT ∫(1/p)dp =nRT ln(p f /p i ) ΔG m = RT ln(p f /p i ) Chap. 5

The Gibbs energy of mixing of two perfect gases of two liquids that form an ideal solution.

Chap. 4 The entropy change with isothermal expansion

The entropy of mixing of two perfect gases of two liquids that form an ideal solution.

Raoult's law: pA =xApA*pA =xApA*

Figure 6.6Figure 6.6 The partial vapour pressures of the two components of an ideal binary mixture are proportional to the mole fractions of the components in the liquid. The total pressure of the vapour is the sum of the two partial vapour pressures. The partial vapour pressure of a substance in a liquid mixture is proportional to its mole fraction in the mixture and its vapour pressure when pure: Raoult’s law

CS 2 is more volatile certain composition makes the solution more volatile

Figure 6.6Figure 6.6 The partial vapour pressures of the two components of an ideal binary mixture are proportional to the mole fractions of the components in the liquid. The total pressure of the vapour is the sum of the two partial vapour pressures. The partial vapour pressure of a substance in a liquid mixture is proportional to its mole fraction in the mixture and its vapour pressure when pure: Raoult’s law: for Ideal solution, esp. for solvent

chemical potential of a solvent A present in solution at a mole fraction x A is

At equilibrium, chemical potential of any given component is same everywhere.

Henry’s law, for ideal solutes

The experimental partial vapour pressures of a mixture of trichloromethane, CHCl 3 (C), and propanone, CH 3 COCH 3 (acetone, A),

The chemical potential of the solute has its standard value when the molar concentration of the solute is 1 mol dm −3 (that is, ).

G = H – TS dG = dH – TdS – SdT = Vdp – SdT dμ = V m dp – S m dT μ*μ* μ*+ RT ln x A -S m (s)ΔT -S m (l)ΔT RT ln x A {S m (l) - S m (s) }ΔT = RT ln x A μ s = μ*– S m (s) dT μ l = μ*– S m (l) dT + RT ln x A

μ*+ RT ln x A μ*μ* Sm(g)ΔTSm(g)ΔT Sm(l)ΔTSm(l)ΔT {S m (l) - S m (g) }ΔT = RT ln x A μ g = μ*– S m (g) dT μ l = μ*– S m (l) dT + RT ln x A

μ A (x A =1, p) μ A (x A, p+ Π ) μ A (x A =1, p) = μ A (x A, p+ Π )

p A = x A p A * = a p A * p B = x B p B * = (1-a) p B * a'= p A /(p A + p B ) = a p A * /(a p A * + (1-a) p B * ) = a p A * /( p B * + a( p A * - p B * )) Understanding fractional distillation

a'= p A /(p A + p B ) = a p A * /(a p A * + (1-a) p B * ) = a p A * /( p B * + a( p A * - p B * )) a' = aX/(1+a(X-1)) where X = ( p A * / p B * ) a'= y A = mole fraction in vapor a= x A = mole fraction in liquid Liquid-Vapor Composition and fractional distillation

A: more volatile substance B: less volatile substance 나오는 것은 A, 남는 것은 B

lever rule and phase diagram

low-boiling(positive) azeotrope repeated distillation can never produce a distillate that is richer in constituent X than the azeotrope 끓어 나오는 것 은 Azeotrope, 남는 것은 A 나 B

high-boiling(negative) azeotrope 공비 ( 共沸 ) 혼합물 끓어 나오는 것 은 A 나 B 이지 만, 남은 것은 Azeotrope