The properties of mixtures

자연과학대학 화학과박영동 교수

Chapter 6 The properties of mixtures

6.1 The thermodynamic description of mixtures

6.1.1 Partial molar properties 6.1.2 Spontaneous mixing 6.1.3 Ideal solutions 6.1.4 Ideal dilute solutions 6.1.5 Real solutions: activities

6.2 Colligative properties

6.2.6 The modification of boiling and freezing points 6.2.7 Osmosis

6.3 Phase diagrams of mixtures

6.3.8 Mixtures of volatile liquids 6.3.9 Liquid-liquid phase diagrams 6.3.10 Liquid-solid phase diagrams 6.3.11 The Nernst distribution law

=

The partial molar volumes ofwater and ethanol at 25°C.

partial molar volume

At 25°C, the density of a 50 per cent by mass ethanol/water solution is 0.914 g cm-3. Given that the partial molar volume of water in the solution is 17.4 cm3 mol-1, what is the partial molar vol-ume of the ethanol?

partial molar Gibbs energy, GJ

Pressure dependence of G

ch05f01

G = H – TSdG = dH – TdS – SdT = Vdp - SdT

= V

For liquid or solid, ΔG = VΔp

For vapor, ΔG = ∫Vdp = nRT ∫(1/p)dp=nRT ln(pf/pi)

ΔGm = RT ln(pf/pi)

Chap. 5

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

Chap. 4The entropy change with isothermal expansion

ch04f04

2

12 2 2

1 1 1

2 2

1 1

1

1

ln ln

S dqT

p nRdw dV dVT T V

V pnR nRV p

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

Raoult's law:

pA =xApA*

Figure 6.6  The partial vapour pressures of the two components of an ideal binary mix-ture are proportional to the mole fractions of the components in the liquid. The total pres-sure of the vapour is the sum of the two par-tial vapour pressures.

The partial vapour pres-sure of a substance in a liquid mixture is propor-tional to its mole fraction in the mixture and its vapour pressure when pure:

Raoult’s law

CS2 is more volatile

certain composition makes the solution more volatile

Figure 6.6  The partial vapour pressures of the two components of an ideal binary mix-ture are proportional to the mole fractions of the components in the liquid. The total pres-sure of the vapour is the sum of the two par-tial vapour pressures.

The partial vapour pres-sure of a substance in a liquid mixture is propor-tional 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 xA is

At equilibrium, chemical potential of any given component is same every-where.

Henry’s law, for ideal solutes

The experimental partial vapour pressures of a mixture of trichloromethane, CHCl3 (C), and propanone, CH3COCH3 (acetone, A),

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

G = H – TSdG = dH – TdS – SdT = Vdp – SdTdμ = Vmdp – SmdT

μ*

μ*+ RT ln xA

-Sm(s)ΔT

-Sm(l)ΔT RT ln xA

{Sm(l) - Sm(s) }ΔT = RT ln xA

μs = μ*– Sm(s) dT

μl = μ*– Sm(l) dT + RT ln xA

μ*+ RT ln xA

μ*

Sm(g)ΔT

Sm(l)ΔT

{Sm(l) - Sm(g) }ΔT = RT ln xA

{Sm(l) - Sm(g) }ΔT = RT ln xA

μg = μ*– Sm(g) dT

μl = μ*– Sm(l) dT + RT ln xA

μA(xA=1, p) μA(xA, p+Π)μA(xA=1, p) = μA(xA, p+Π)

pA = xA pA *= a pA

*

pB = xB pB * = (1-a) pB

*

a'= pA /(pA + pB) = a pA * /(a pA

* + (1-a) pB

*)

= a pA * /(pB

* + a(pA *- pB

* ))

Understanding fractional distilla-tion

a'= pA /(pA + pB)

= a pA * /(a pA

* + (1-a) pB

*)

= a pA * /(pB

* + a(pA *- pB

* ))

a'= aX/(1+a(X-1))

where X = (pA * / pB

*)

a'= yA = mole fraction in vapor

a= xA = mole fraction in liquid

Liquid-Vapor Composition and fractional distillation

A: more volatile substance

B: less volatile substance나오는 것은 A, 남는 것은 B

lever rule and phase diagram

low-boiling(positive) azeotrope

repeated distillation can never pro-duce a distillate that is richer in con-stituent X than the azeotrope

끓어 나오는 것은 Azeotrope, 남는 것은 A 나

B

high-boiling(negative) azeotrope공비 ( 共沸 ) 혼합물

끓어 나오는 것은 A 나 B이지만 , 남은 것은 Azeotrope