PHASE EQUILIBRIUM PHYSICAL CHEMISTRY, 2nd year Degree in Pharmacy

2018-2019

PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

1 PHASE RULE

• Phase: part of the system where intensive macroscopic property has the same value.

• Homogeneous system: system consisting of only one phase.

• Heterogeneous system: system consisting of two or more phases.

3 Mª Fernanda Rey-Stolle Valcarce

PHASE RULE

• Gibbs’ Phase Rule

F = C - P+ 2 ind

F : Number of degrees of freedom (independent intensive variables needed to define the system state)

Cind : Number of independent components (number of chemical compounds – number of chemical reactions in equilibrium – number of restrictive conditions)

Cind = C - r - a

4 P : Number of phases Mª Fernanda Rey-Stolle Valcarce

2 PHASE RULE

• Cind : number of independent components

Cind = C - r - a

TOTAL number of Number of restrictive conditions: different chemical species  by reaction stoichiometry  for electroneutrality Number of reactions in equilibrium

5 Mª Fernanda Rey-Stolle Valcarce

PHASE RULE

• P: number of phases

 If components are gases 1 phase

1 phase  If components are liquids several phases

several phases  If components are solids 1 phase

6 Mª Fernanda Rey-Stolle Valcarce

3 PHASE CHANGES

Phase Transitions Gas

Vaporization Condensation

Liquid Deposition Sublimation Melting Freezing

Solid

7 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

4 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS For single-component systems:

F = Cind –P+2 = 1 +2 -P= 3-P

 P = 1 F = 3 - P = 2 P and T

 P = 2 F = 3 - P = 1 P or T

 P = 3 F = 3 - P = 0 Invariant system

• The maximun number of independent intensive variables to define the state of the system is two

9 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS For single-component systems:

F = 3 - P

• When only one phase is present, both the pressure and temperature are independent variables. It corresponds to an area in P-T diagram. • When two phases are present, there is only one pressure for a given temperature and viceversa. It corresponds to a line in P-T diagram. • When three phases are present, there is no variation of the pressure nor temperature. It corresponds to a point in P-T diagram (triple point).

10 Mª Fernanda Rey-Stolle Valcarce

5 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

      G        S        T P  T P

slope   S

12 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

G = μ

Solid Liquid Vapour

17 Mª Fernanda Rey-Stolle Valcarce

6 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

Solid

Vapour

TS

18 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS  First order transition: There is an abrupt change of the first derivatives of G at the transition temperature

H  QP= H ≠ 0 S L⇌ S transition  V ≠ 0 V temperature  S ≠ 0 L⇌ V Tt T ∞ S⇌ V

CP S⇌ S  Q  C P       T P

Tt T 19 Mª Fernanda Rey-Stolle Valcarce

7 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

LINES PRESSURE

LIQUID 2 phases Pb 1 atm SOLID

VAPOUR F = 1 (P or T)

o Tb Tb TEMPERATURE 23 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

LINES PRESSURE

LIQUID 2 phases Pm 1 atm SOLID

VAPOUR F = 1 (P or T)

Tm TEMPERATURE o Tm 24 Mª Fernanda Rey-Stolle Valcarce

8 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

LINES PRESSURE

LIQUID 2 phase

1 atm VAPOUR F = 1 (P or T) SOLID Psub

o Tsub Tsub TEMPERATURE 25 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS Critical point: PRESSURE

Vapour PC Vapour LIQUID Gas

Liquid Liquid SOLID

VAPOUR

TC TEMPERATURE

26 Mª Fernanda Rey-Stolle Valcarce

9 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS Triple point: PRESSURE TRIPLE POINT

LIQUID 3 phases SOLID

PT VAPOUR F = 0

TT TEMPERATURE

27 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

PRESSURE H2O

LIQUID

SOLID

VAPOUR

TEMPERATURE

28 Mª Fernanda Rey-Stolle Valcarce

10 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM FOR WATER

P 374 oC, 218 atm LIQUID

SOLID

0.01 orC, 0.06 atm VAPOUR

T o T o m V T 31 Mª Fernanda Rey-Stolle Valcarce

11 PHASE DIAGRAM FOR WATER

Liquid

STEAM

Temperature, T/K

32 Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM FOR CO2

P 31 oC, 73 atm

LIQUID SOLID

-57 oC, 5.1 atm VAPOUR

o TS T

34 Mª Fernanda Rey-Stolle Valcarce

12 PHASE DIAGRAM FOR SULPHUR

35 Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM FOR HELIUM

36 Mª Fernanda Rey-Stolle Valcarce

13 PHASE DIAGRAM FOR CARBON

37 Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM FOR SILICA

38 Mª Fernanda Rey-Stolle Valcarce

14 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

CLAPEYRON EQUATION

• Applying the condition of phase equilibrium to a component in two phases, α and β:

μα  μβ

dμα  dμβ

dGα  dGβ

-SαdT  VαdP  -SβdT  VβdP

40 Mª Fernanda Rey-Stolle Valcarce

15 CLAPEYRON EQUATION

Sβ dT -Sα dT  Vβ dP  Vα dP

Sβ -Sα  dT  Vβ  Vα  dP

41 Mª Fernanda Rey-Stolle Valcarce

CLAPEYRON EQUATION

 P S  Sα ΔS ΔS ΔH ΔH       T V  Vα ΔV ΔV T ΔV T ΔV

 P ΔH P Phase α   T T ΔV

Phase β It is used mostly in equilibrium: ⇄ T S L and S ⇄ S 42 Mª Fernanda Rey-Stolle Valcarce

16 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

• For most systems:

> 0 <0

 P ΔH  or:  T T ΔV

> 0 > 0 > 0 <0

43 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

• Ice melting:

> 0

 P ΔH  m  T T ΔVm

<0 <0

44 Mª Fernanda Rey-Stolle Valcarce

17 PHASE EQUILIBRIUM INSINGLE- COMPONENT SYSTEMS

PRESSURE H2O

LIQUID

SOLID

VAPOUR

TEMPERATURE

45 Mª Fernanda Rey-Stolle Valcarce

INTEGRATION OF CLAPEYRON EQUATION

• Applying the equation to equilibrium Solid ⇄ Liquid :

 P ΔHm   T T ΔVm

ΔHm dP   dT T ΔVm

46 Mª Fernanda Rey-Stolle Valcarce

18 INTEGRATION OF CLAPEYRON EQUATION

•Considering ΔH and ΔV constant with temperature

ΔHm ΔHm dT   dP  dT  T ΔVm ΔVm T

ΔHm P  log T  C ΔVm

47 Mª Fernanda Rey-Stolle Valcarce

INTEGRATION OF CLAPEYRON EQUATION

Integrated: P

ΔHm   P log T C Hm slope  Δ Vm Vm For water: C

C

Hm slope  log T Vm P

55 log T Mª Fernanda Rey-Stolle Valcarce

19 INTEGRATION OF CLAPEYRON EQUATION

• Finding the definite integrate and considering ΔH and ΔV constant with temperature:

P2 T2 ΔHm ΔHm T2 d T  d P   d T   P1 T1 T1 T ΔVm ΔVm T

ΔHm T P  P  log 2 2 1 ΔVm T1

47 Mª Fernanda Rey-Stolle Valcarce

INTEGRATION OF CLAPEYRON EQUATION

ΔHm T2 P2  P1  log ΔVm T1

ΔHm T ΔP  log 2 ΔVm T1

This equation can also be applied to Solid ⇄ Solid substituing ΔHm by the corresponding change of enthalpy.

48 Mª Fernanda Rey-Stolle Valcarce

20 CLAUSIUS-CLAPEYRON EQUATION

• If one phase is vapour:

 P Hv  Hα 

 T T(Vv  Vα )

• Not considering the molar volume of phase α compared to vapour one:

 P Hv  Hα Hv  Hα    T T(Vv  Vα ) T Vv 51 Mª Fernanda Rey-Stolle Valcarce

CLAUSIUS-CLAPEYRON EQUATION

• If the vapour has ideal gas behaviour:

R T Vv  P • Substituting:

 P Hv  Hα P(Hv  Hα ) P ΔH   2  2  T T Vv R T R T

52 Mª Fernanda Rey-Stolle Valcarce

21 CLAUSIUS-CLAPEYRON EQUATION

 P P ΔH   T R T2

dP ΔH  dT P RT2

53 Mª Fernanda Rey-Stolle Valcarce

CLAUSIUS-CLAPEYRON EQUATION

•Finding the indefinite integral:

dP ΔH  dT  P  RT2

•Considering ΔH constant with temperature

dP dT  ΔH  P  RT2 54 Mª Fernanda Rey-Stolle Valcarce

22 CLAUSIUS-CLAPEYRON EQUATION

Integrated:

ΔH 1 log P    C R T C H slope  - log P R

1 T 55 Mª Fernanda Rey-Stolle Valcarce

CLAUSIUS-CLAPEYRON EQUATION

Diethylether

Chloroform

Water

Carbon tetrachloride

56 Mª Fernanda Rey-Stolle Valcarce

23 CLAUSIUS-CLAPEYRON EQUATION

•Finding the definite integrate:

P2 dP T2 ΔH  dT   2 P1 P T1 RT

•Considering ΔH constant with temperature

P2 dP T2 d T  ΔH   2 P1 P T1 RT

57 Mª Fernanda Rey-Stolle Valcarce

CLAUSIUS-CLAPEYRON EQUATION

Integrated:

P2 ΔH  1 1  log      P1 R  T2 T1 

58 Mª Fernanda Rey-Stolle Valcarce

24 CLAUSIUS-CLAPEYRON EQUATION

• Approximations of Clausius-Clapeyron equation:

 Only the volume of the vapour phase is considered

 ideal gas behaviour

 Enthalpy constant with temperature

59 Mª Fernanda Rey-Stolle Valcarce

CLAUSIUS-CLAPEYRON EQUATION

60 Mª Fernanda Rey-Stolle Valcarce

25 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

GOULDBERG-TROUTON RULE

• Trouton's rule is reached, using Gouldberg rule and Clausius-Clapeyron equation:

o cal Trouton's rule ΔSvap  21 mol K It is followed by non-associated liquids

66 Mª Fernanda Rey-Stolle Valcarce

26 LIQUID-VAPOR EQUILIBRIUM

Kilimanjaro (Tanzania) T (water) = 79 ºC 5895 m, P = 350 mmHg vap 67 Mª Fernanda Rey-Stolle Valcarce

LIQUID-VAPOR EQUILIBRIUM

P ≈ 2 atm

Tvap (water) = 120 ºC

Fast Cooker

Shorter cooking times

69 Mª Fernanda Rey-Stolle Valcarce

27 SOLID-LIQUID EQUILIBRIUM

LYOPHILIZATION:

•Instant coffee:  Avoiding dryness with heating.  Conservation is improved.

70 Mª Fernanda Rey-Stolle Valcarce

SOLID-LIQUID EQUILIBRIUM

CO2: •Dry Ice:

 Smoke and fog effects.

71 Mª Fernanda Rey-Stolle Valcarce

28 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

HIGHER ORDER TRANSITIONS

 Higher order transition :

transition QP=  H = 0 temperature H S  V = 0 V

Tt T  S = 0

73 Mª Fernanda Rey-Stolle Valcarce

29 HIGHER ORDER TRANSITIONS

There are two types: • Second order transitions:

Examples: C P • Transition between normal conductivity and superconductivity of certain metals • Transition between liquid crystal T T phase and gel phase of lipids in t biological membranes There is an abrupt • Denaturation of proteins change of CP,α,κ (Second derivatives of G) at the transition 74 temperature Mª Fernanda Rey-Stolle Valcarce

HIGHER ORDER TRANSITIONS

• Second order transitions: Although Clapeyron equation gives the slope of ANY LINE in P-T phase diagrams of single-component systems:

dP ΔH 0   dT T ΔV 0

in these transitions gives an indetermination

75 Mª Fernanda Rey-Stolle Valcarce

30 HIGHER ORDER TRANSITIONS

• Second order transitions:

There are two Ehrenfest equations that give the slope in second Equations order transitions:

76 Mª Fernanda Rey-Stolle Valcarce

HIGHER ORDER TRANSITIONS

• Lambda Transitions: ∞

CP Examples: • Equilibrium L ⇄ L in He phase diagram .

Tt T

There is no abrupt change of CP at the transition temperature. It begins to grow well before the

transition temperature 77 Mª Fernanda Rey-Stolle Valcarce

31 HIGHER ORDER TRANSITIONS

• Lambda Transitions:

78 Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

32 PHASE DIAGRAM FOR BINARY SYSTEMS

Phase Rule for binary systems F = C +2 - P = 2 +2 - P = 4 - P

Pressure

Fmaximum = 3 Temperature Component mole fraction

If P = cst T – composition diagrams

If T = cst P – composition diagrams

Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

33 PHASE DIAGRAM FOR BINARY SYSTEMS

Three equilibria for binary systems are studied :

 LIQUID ⇄ VAPOUR

 LIQUID ⇄ LIQUID

 SOLID ⇄ LIQUID

Mª Fernanda Rey-Stolle Valcarce

VAPOUR PRESSURE

• VAPOUR PRESSURE: Liquid It is the pressure exerted Ethanol by the vapour of a liquid or solid when both phases are in dynamic equilibrium at a certain Pvapour = Pv equilibrium temperature.

23 Mª Fernanda Rey-Stolle Valcarce

34 IDEAL SOLUTIONS

Vapour-liquid equilibria for (a) pure toluene and (c) pure benzene. Solution (b) is a mixture of equal amounts of toluene and benzene, so the concentration of benzene molecules in the vapour phase is only half as great as above pure benzene. Note also that although the initial amounts of benzene and toluene in the solution were equal, more benzene than toluene escapes to the gas phase because of benzene’s higher vapour pressure. Mª Fernanda Rey-Stolle Valcarce

IDEAL SOLUTION Raoult's Law: The partial vapour pressure of a component in a mixture is equal to the vapour pressure of the pure component at that temperature multiplied by its mole fraction in the mixture.

* l * l P  P x PB  PB xB A A A

Raoult's Law only works for ideal mixtures: • Two types of molecules are randomly distributed • Typically, molecules are similar in size and shape • Intermolecular forces in pure liquids and mixture are similar • Examples: benzene-toluene, n-hexane-n-heptane, ethyl bromide-ethyl iodide, chlorobenzene-bromobenzene Mª Fernanda Rey-Stolle Valcarce

35 IDEAL SOLUTION

* PB * l PA  PA xA P PB P * A * * l PB  PB PB xA PA

XA = 0 XA = 1 * * * l XB = 1 XB = 0 P PB  PA PB xA

35 Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM: P vs x

Constant T

L

● * P PA * l L P vs. xA PA  PA xA

* ● P V B P vs. xA ?

V * * * L P  PB  PA PB xA

L xA Mª Fernanda Rey-Stolle Valcarce

36 IDEAL GAS Dalton’s Law: The pressure of a gas mixture is the sum of the partial pressures of the individual components of the gas mixture.  c   n RT  i c c nRT  i1  niRT P    Pi V V i1 V i1 c P  Pi v i1 ni RT P v i  V  v v xi  P n RT Pi xi P

V Mª Fernanda Rey-Stolle Valcarce

IDEAL GAS

Dalton’s Law:

Mª Fernanda Rey-Stolle Valcarce

37 PHASE DIAGRAM: P vs x Constant T •Dalton's law: V PA  P xA •Raoult's law: * L * * * L V PA xA [PB  PA PB xA ] xA

L V •Expressing xA as a function of xA :

* L * V * * L V PA xA  PBxA  PA PB xAxA

* L * * L V * V PA xA PA PB xAxA  PBxA Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM: P vs x

Constant T

* L * * L V * V PA xA PA PB xAxA  PBxA

* V L PBxA xA  * * * V PA  PA  PB xA

L Substituting xA in Raoult's law:

* * * L P  PB  PA PB xA

* V * * * PBxA P  PB  PA  PB  * * * V PA  PA  PB xA Mª Fernanda Rey-Stolle Valcarce

38 PHASE DIAGRAM: P vs x

Constant T

P*xV  *  *  * B A P PB PA PB  * * * V PA  PA  PB xA

* * * * * V * * * V PAPB  PA  PB PBxA  PA  PB PBxA P  * * * V PA  PA  PB xA

* * PA PB P  * * * V PA  PA  PB xA

Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM: P vs x

Constant T

L

● * P PA

L * * * L P vs. xA P  P  P P x L + V B A B A

* ● PB * * V PA PB Pvs. xA P  P*  P*  P* xV V A  A B  A

L v xA xA Mª Fernanda Rey-Stolle Valcarce

39 PHASE DIAGRAM: T vs x

Constant T Constant P

LIQUID * VAPOUR * TB ● ●P A P L + V L + V T * ● PB

● * LIQUID TA VAPOUR

L xA Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM: T vs x

Lever rule: • A mixture with composition Constant P xA at temperature T1 is in two phases: liquid and vapour. V • The composition of the liquid phase in equilibrium with L + V vapour at temperature T1 is T1 ● ● ● L xA . • The composition of the T vapour phase in equilibrium with the liquid at temperature T is x V. L 1 A • But what is the amount of each phase?

L V xA xA xA X A Mª Fernanda Rey-Stolle Valcarce

40 PHASE DIAGRAM: T vs x

Lever rule: n nL nV x  A xL  A xV  A A n A nL A nV

n nL  nV xL nL  xVnV x  A  A A  A A A n nL  nV nL  nV

L V L L V V xA n  n  xAn  xAn

L L V V xA  xA n  xA  xA n

Mª Fernanda Rey-Stolle Valcarce

PHASE DIAGRAM: T vs x

Lever rule: Constant P

V

L + V T nV T1 ● ● ● nL

L

L V xA xA xA XA Mª Fernanda Rey-Stolle Valcarce

41 PHASE DIAGRAM: T vs x

Constant P

V

T7 ● T ● 6 ● ● ● L V T T5 n n T2 ●

T1 ● L

L V L xA V xA xA L xA V xA XA xA XA Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

42 DISTILLATION

• Simple distillation: part of the vapour formed in the initial stages of the process is extracted and condensed.

DISTILLED ⇒ vapour condensated, richer in the more volatile component RESIDUE ⇒ residual liquid richer in the less volatile component Mª Fernanda Rey-Stolle Valcarce

DISTILLATION

Constant P

V Residue T v l

Distilled

L

XA

XA Mª Fernanda Rey-Stolle Valcarce

43 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

Azeotropes

Azeotrope P T Liquid Pmax Vapour * L + V * TB PA * * PB T L + V A T Vapour min

Liquid Azeotrope

0 1 0 1

XA XA It occurs when AB interactions Eg • carbon disulphide / acetone are weaker than AA and BB •dioxane / water • ethanol / water Mª Fernanda Rey-Stolle Valcarce

44 Azeotropes

Azeotrope P T Vapour Liquid Tmax

P* * A TB L + V * TA * L + V PB

Pmin Vapour Liquid Azeotrope

0 1 0 1

XA XA

It occurs when AB interactions Eg: • chloroform / acetone are stronger than AA and BB ones •nitric acid / water Mª Fernanda Rey-Stolle Valcarce

Azeotropes

Azeotrope of minimum boiling point

T

Vapour  TB In these solutions, the

R   pure components can

l + v  T

T d A

 l + v R  NOT be separated by d Tmin fractional distillation  

Liquid Azeotrope

0 1 XA

DISTILLED ⇒ azeotrope RESIDUE ⇒ pure components Mª Fernanda Rey-Stolle Valcarce

45 Azeotropes

Maximum azeotrope boiling point

T Azeotrope Vapour

Tmax

 R 

 R  In these solutions, the

T d  B  d  pure components can TA  NOT be separated by fractional distillation. Liquid T

0 1 XA

DISTILLED ⇒ pure component RESIDUE ⇒ azeotrope Mª Fernanda Rey-Stolle Valcarce

Azeotropes

Pure Compounds Azeotrope

A Tvap (A) B Tvap(B) % A Tvap(A) /ºC /oC /oC Water 100 Ethanol 78.3 4.0 78.174 Water 100 Acetone 79.6 11.3 73.41

Water 100 Chloroform 61.2 16.0 56.1

Water 100 Benzene 80.2 29.5 69.3

Water 100 Toluene 111 44.4 67.9

Ethanol 78.3 Hexane 68.8 33.2 58.7

Ethanol 78.3 Benzene 80.2 44.0 67.9

Ethyl acetate 78.5 Hexane 68.8 39.4 65.2 Carbon disulphide 46.1 Acetone 56.2 60.8 39.3

Toluene 111 Acetic acid 118 62.5 100.7 Acetone 56.1 Chloroform 61.2 78.5 64.43 Mª Fernanda Rey-Stolle Valcarce

46 Azeotropes

An azeotropic distillation Atmospheric behaves like a pure component, pressure but is NOT a pure component T

Reduced pressure

The azeotropic composition depends on the pressure

0 XA 1

Mª Fernanda Rey-Stolle Valcarce

PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

47 DIAGRAM OF LIQUID-LIQUID PHASE

Constant P 0 XA 1 T Immiscibility 1 phase regions Tc E 2 phases D F G H T1 C   I

2 phases Tc T 1 phase T 0 XA 1 Tc Diagram with Diagram with Minimum Critical Maximum Critical 2 phases Solubility Temperature Solubility Temperature Tc 1 phase

0 XA 1 Diagram with Maximum and Minimum Critical Solubility Temperature Mª Fernanda Rey-Stolle Valcarce

DIAGRAM OF LIQUID-LIQUID PHASE

Constant P • With Maximum Critical Solubility Temperature: Hexane / nitrobenzene Phenol / Water Water / Butanol • With Minimum Critical Solubility Temperature: Water / triethylamine • With Maximum and Minimum Critical Solubility Temperature : Butanol / Water (at high P) Nicotine / Water Mª Fernanda Rey-Stolle Valcarce

48 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

DIAGRAM OF SOLID-LIQUID PHASE

• P =cts  T-composition diagrams

They are classified into:

 Eutectic Systems ⇒The two components are miscible in liquid phase and immiscible in solid phase

 Systems with solid state miscibility:

 Systems with total solid phase miscibility

 Systems with partial solid phase miscibility

Mª Fernanda Rey-Stolle Valcarce

49 DIAGRAM OF SOLID-LIQUID PHASE

EUTECTIC SIMPLE (Constant P):

B cooling curve

T A cooling curve * ● L (A, B) TB

* ● TA B (s) + L (A, B) A (s) + L (A, T ● E E B) A (s) + B (s)

0 XA 1 Mª Fernanda Rey-Stolle Valcarce

DIAGRAM OF SOLID-LIQUID PHASE

EUTECTIC SIMPLE (Constant P):

T T m m   THERMAL BREAK * TB L (A, B) n n o    * TA p p B (s) + L (A, B) r    q  A (s) + L (A, B) s T    E s E A (s) + B (s) THERMAL ARREST  t  t

0 XA 1 time Differential thermal analysis

Mª Fernanda Rey-Stolle Valcarce

50 DIAGRAM OF SOLID-LIQUID PHASE

EUTECTIC SIMPLE (Constant P):

T T m m   * L (A, B) TB THERMAL BREAK n n   * pT A o    o r q    s  B (s) + L (A, B) q A (s) + L (A, B) t    TE t E THERMAL ARREST A (s) + B (s)  u  u

0 XA 1 time

Differential thermal analysis Mª Fernanda Rey-Stolle Valcarce

DIAGRAM OF SOLID-LIQUID PHASE

EUTECTIC SIMPLE (Constant P):

T T m m   L (A, B) * TB n n   * T o o  A    p B (s) + L (A, B) p A (s) + L (A, B) q T    E q E THERMAL ARREST A (s) + B (s)  r  r

0 XA 1 time

Differential thermal analysis Mª Fernanda Rey-Stolle Valcarce

51 DIAGRAM OF SOLID-LIQUID PHASE

EUTECTIC SIMPLE (P constant):

• The thermal arrest is longer for the isopleth

XE to the eutectic composition. • Cooling curves are used to construct the phase diagram.

Mª Fernanda Rey-Stolle Valcarce

DIAGRAM OF SOLID-LIQUID PHASE

EUTECTIC SIMPLE (Constant P):

Mª Fernanda Rey-Stolle Valcarce

52 DIAGRAM OF SOLID-LIQUID PHASE

Pharmaceutical Applications of Eutectic Mixtures http://www.omicsgroup.org/journals/pharmaceutical- applications-of-eutectic-mixtures-2329-6631.1000e130.pdf

Mª Fernanda Rey-Stolle Valcarce

DIAGRAM OF SOLID-LIQUID PHASE

Constant P

Pure Compounds Eutectic

A Tfus(A) / K B Tfus(B) / K % B Tfus / K

Sb 903 Pb 599 81 519

Cd 594 Bi 444 55 417

Si 1685 Al 930 89 851

Mª Fernanda Rey-Stolle Valcarce

53 PHASE EQUILIBRIUM • Phase Rule • Phase Equilibrium in Single-Component Systems:  Phase Diagram  Clapeyron and Clausius-Clapeyron Equations  Trouton's rule  Higher order transitions • Phase Equilibrium in Binary Systems:  L-V Phase Diagram Distillation Azeotropes  L-L Diagram Phase  S-L Phase Diagram (Lab Practices): Simple eutectic • Phase Equilibrium in Ternary Systems (Lab Practices): • Summary and Conclusions

Mª Fernanda Rey-Stolle Valcarce

SUMMARY AND CONCLUSIONS

• FIRST ORDER TRANSITIONS:

Mª Fernanda Rey-Stolle Valcarce

54 SUMMARY AND CONCLUSIONS • PHASE DIAGRAM • CLAPEYRON EQUATION H2O P L  P ΔH S  V  T T ΔV T • CLAPEYRON EQUATION INDEFINITE INTEGRATED water ΔHm P  log T  C ΔVm

• CLAPEYRON EQUATION DEFINITE INTEGRATED

ΔHm T ΔP  log 2 ΔVm T1

Mª Fernanda Rey-Stolle Valcarce

SUMMARY AND CONCLUSIONS

• CLAUSIUS- CLAPEYRON EQUATION INDEFINITE INTEGRATED

ΔH 1 log P    C R T

• CLAUSIUS- CLAPEYRON EQUATION DEFINITE INTEGRATED

P2 ΔH  1 1  log      P1 R  T2 T1 

o cal • TROUTON'S RULE ΔSvap  21 mol K

Mª Fernanda Rey-Stolle Valcarce

55 SUMMARY AND CONCLUSIONS

• HIGHER ORDER TRANSITIONS: SECOND ORDER TRANSITIONS

Ehrenfest equations

Mª Fernanda Rey-Stolle Valcarce

SUMMARY AND CONCLUSIONS

• HIGHER ORDER TRANSITIONS:

LAMBDA TRANSITIONS

Mª Fernanda Rey-Stolle Valcarce

56 SUMMARY AND CONCLUSIONS

V V T * B * L + V TB L + V L + V T L+V * * T TA • Vapour-Liquid Equilibrium T L + V A T L L L

X A 0 1 XA 0 XA 1

•Liquid-Liquid Equilibrium

T * L (A, B) TB T* •Solid-Liquid Equilibrium A A(s) + B(s) + L (A, B) L (A, B) T E E A(s) + B(s) 0 XA 1

Mª Fernanda Rey-Stolle Valcarce

57