C' liquid

If a liquid having the composition c' is cooled, the liquid merely cools till it reaches the point C.

At the point C, a solid compound, having the same composition as the liquid starts separating.

This temperature, the congruent melting point of the compound, remains constant till the entire liquid phase freezes. On further cooling, the temperature of the solid decreases. Thus, the cooling pattern of the liquid of composition c' is similar to that of a pure component. The formula of the compound formed is Mg (Zn)₂ which corresponds to the composition c'.

CB and CD give the freezing point curves of Mg (Zn)2. Addition of zinc depresses the freezing point of Mg(Zn)2 and the temperatures at which the solid compound Mg (Zn)2 will begin to freeze (separate) from various liquids, composition lying between B and G, fall on the curve CB.

Zn+Melt

Mg(Zn)

2

+Melt

Mg+Mg(Zn)

2

Zn+Mg(Zn)

2

Temperature →

Mg

+ Melt

Pure Zn Pure Mg

A

B

C

D

E

F G

H I

J K Composition →

C'

liquid

liquids having their composition lying between H and D. The curve CD gives the depression in the freezing point of Mg (Zn)2 due to the addition of Mg. B is an eutectic point at which solid zinc and solid Mg (Zn)₂ are in equilibrium with liquid of composition B. Similarly at D, another eutectic point, solid magnesium and solid Mg(Zn)₂ are in equilibrium with liquid of composition D.

Phase diagrams, such as that of Mg-Zn system (Figure 10.3.6), can be considered to be made up of two simple eutectic diagrams placed side by side. There is the simple eutectic phase diagram of zinc and Mg(Zn)2 on the left of the line cc' and that of Mg and Mg(Zn)2 on the right.

Theoretically, the curves BC and DC should meet to give a sharp point at C. But normally a rounded maximum is observed as shown in the phase diagram (Figure 10.3.6). This is because the compound formed is usually not very stable and dissociates partly. The dissociation products in the liquid phase depress the actual melting of the compound resulting in a rounded melting point.

Table 10.3.6.1 gives a description of the phase diagram (Figure 10.3.6) of the magnesium – zinc system.

Table 10.3.6.1Description of the phase diagram for magnesium – zinc system

A (420^oC) Freezing point of Zinc C=1, P=2, F=0 Fixed T

E (651^oC) Freezing point of Mg C=1, P=2, F=0 Fixed T

C (590^oC) Freezing point of Mg(Zn)₂ C=2, r=1, P=2,F=0 Fixed T and composition

B Eutectic point (Zn,

Mg(Zn)2, liq. Of composition B)

C=2, P=3, F=0 Fixed T and composition

D Eutectic point (Mg,

Mg(Zn)2, liq of composition D)

C=2, P=3, F=0 Fixed T and composition

AB Freezing point curve of Zn, crystallization of Zn begins

C=2, P=2, F=1 T or

composition

BC and CD Crystallization of Mg(Zn)2

begins

C=2, P=2, F=1 T or

composition

ED Crystallization of Mg begins

C=2, P=2, F=1 T or

composition

Area ABFA Zn ^liquid

(composition given by AB)

C=2, P=2, F=1 T or

composition

Area CBGC Mg(Zn)₂ ^liquid

(composition given by CB)

C=2, P=2, F=1 T or

composition

Area CHDC Mg(Zn)2 ^liquid

(composition given by CD)

C=2, P=2, F=1 T or

composition

Area EDIE Mg ^liquid

(composition given by ED)

C=2, P=2, F=1 T or

composition

Area below FBG Solid mixtures of Zn and Mg (Zn)₂

C=P, P=2, F=1 T or

composition

Area below HDI Solid mixtures of Mg and Mg (Zn)2

C=2, P=2, F=1 T or

composition

Area above ABCDE Liquid containing Zn and Mg

C=2, P=1, F=2 T and composition

In many systems, the two components combine to form more than one compound. In such cases, the phase diagram has a curve similar to BCD for each and every compound. A few examples of systems forming more than one congruent melting compound are included in the table 10.3.6.2.

melting point.

System

A m.pt./^oC B m.pt./^oC

Compound m.pt./^oC

Gold 1064 Tin 232 AB 425

CaCl₂ 777 KCl 776 AB 754

Urea 133 Resorcinol 110 AB ~103

Benzamide 125 Resorcinol 109 AB ~89

Acetamide 79 Phenol 41 AB₂ 43

Silver 961 Strontium 757 A4B 781

A5B3 760

AB 680

A2B2 665

Aluminium 657 Magnesium 650 A3B4 463

Potassium 63.6 Antimony 613 A₃B 812

AB 605

The Sodium chloride-water system

Sodium chloride-water is a system in which the two components form a solid compound which is not stable up to its true melting point and hence decomposes before reaching it. The compound decomposes to give another solid and a solution. The composition of the solid formed is different from that of the original compound. Infact, the compound does not have a true melting point. The dehydrate of sodium chloride, NaCl.2H2O, the compound formed in this system decomposes to give anhydrous sodium chloride and a solution. The temperature at which this decomposition reaction takes place is known as the incongruent melting point of the compound. It is also known as the peritectic (Greek; melting around) temperature or transition temperature.

The compound is said to undergo a transition or peritectic reaction or incongruent fusion.

NaCl.2H2O

NaCl + Solution

At the peritectic temperature, the number of degrees of freedom of the system is zero (C=2, P=3, F=C+1-P, F=2+1-3=0), the system, thus, is invariant. The peritectic reaction takes place at a definite temperature and is reversible. The melt (or the solution) also has a definite composition.

In such a peritectic reaction, the new solid formed may be a pure component as in this system, or may be a congruent or incongruent melting new compound. The melting point of this solid is always more than that of the compound from which it is formed. The phase diagram of the NaCl- H2O system is given in Figure 10.3.7.

Figure 10.3.7: The phase diagram for sodium chloride – water system

A C

B C'

E F

G

H I

J Unsaturated solution

a

a'

ice + solution

a''

a'''

b' b

c'''

c''' d'''

d'' d' d

G'

e'' e' e

NaCl + solution

NaCl +

NaCl.2H2O

NaCl.2H2O

+ solution

ice + NaCl.2H2O

Mass % NaCl

Temperature

O 40

The freezing point of water is represented by A in the phase diagram. Addition of sodium chloride lowers the freezing point of water along AB. The curve AB, hence, is the freezing point curve of water. In the area ABEA, ice is in equilibrium with a solution of sodium chloride in water, the composition of which is given by the curve AB. The point G' corresponds to the composition of the compound NaCl.2H₂O. On heating, this compound remains in the solid state until the point G at temperature t_p (peritectic temperature) is reached. At the point G, the following reaction occurs:

NaCl.2H₂O

NaCl + Solution

The point G, therefore, represents the incongruent melting point of the system. The system is invariant at this point G as NaCl.2H₂O is in equilibrium with anhydrous NaCl and a solution of composition given by the point C (F=C+1-P, F=2+1-3=0). As NaCl separates from NaCl.2H2O at the peritectic temperature G, the solution with which it is in equilibrium should be less rich in NaCl and hence its composition should lie to the left of point G, say, C. Line CG is a part of the tie line drawn at point G. A system anywhere on this line has NaCl.2H2O, NaCl and solution of composition C in equilibrium.

If the heating of NaCl.2H₂O at G is continued, the decomposition to give NaCl continues and the temperature remains constant till the reaction is over. Further heating causes an increase in temperature of the system which is NaCl in equilibrium with solution. The system becomes univarant (F=C+1-P=2+1-2=1). At temperatures more than the peritectic temperature, only NaCl exists in equilibrium with solution. CD is a part of the freezing point curve of solid NaCl as it extends beyond D but ends at C.

Curve BC can also be called the solubility curve of NaCl.2H2O and CD is a part of the solubility curve of anhydrous NaCl. Solutions of NaCl in water having mass % NaCl more than that represented by point C show a halt on cooling when they reach the temperature at C.

The freezing point curves, AB, of water and BC, of NaCl.2H₂O meet at B, the eutectic point of the system. There are three phases, ice, NaCl.2H₂O and solution, in equilibrium at this point and hence it is an invariant point (F=C+1-P=2+1-3=0). The area CBFGC has NaCl.2H₂O in equilibrium with solution whose composition is given by the curve CB whereas NaCl and NaCl.2H₂O exist in equilibrium in the area GG'IJG. This can be explained on the basis of the peritectic reaction:

NaCl + Solution

^NaCl.2H2O

The reaction between NaCl and solution takes place at a constant temperature till either all the NaCl or all the solution has been consumed. If NaCl is present in a quantity more than that required to convert the whole of the solution into NaCl.2H2O, then the system will have after the reaction NaCl.2H2O, and the excess NaCl in equilibrium. If on the other hand, NaCl is present in a quantity less than that required, then the system will have after the reaction NaCl.2H2O and the excess solution in equilibrium. A point on the right of the line GG' represents excess of NaCl whereas between C and G deficiency of NaCl.

If a solution of NaCl in water represented by a is cooled, then at a' ice starts separating and the solution with which it remains in equilibrium is given by the curve AB. The lever rule gives the ratio of the quantity of ice to that of solution. As it cools to a'', NaCl.2H₂O, also starts separating.

system is invariant. On further cooling to, say, a''', the temperature of ice and the eutectice, a mixture of ice and NaCl.2H2O, decreases to a'''. The cooling curve of the system at a, thus, exhibits a break at the temperature a' and a halt at a''.

On the other hand, if a system at b, an unsaturated solution of NaCl in water, is cooled, the temperature of the solution decreases along bB and at B both ice and NaCl.2H₂O start separating.

The temperature remains constant till the entire solution solidifies to give the eutectic mixture of ice and NaCl.2H2O. The cooling curve of the system at b(eutectic composition) has only a halt at temperature B followed by the cooling of the eutectic mixture.

A slightly more concentrated solution of NaCl in water represented by c' cools till the point C is reached, when NaCl.2H₂O starts separating. As cooling continues, more and more NaCl.2H₂O separates and the dihydrate is in equilibrium with solution whose composition is given by the curve BC. The ratio of the quantity of the dihydrate to the solution is given by the lever rule.

When the temperature c'' is reached, ice also separates alongwith the dihydrate forming the eutectic mixture. The temperature remains constant till the entire solution, composition given by B, freezes to form the eutectic mixture which then cools to c'''.

When a system at d cools to d', anhydrous NaCl starts separating and continues to separate on further cooling, the solid remaining in equilibrium with solution, its composition given by the curve CD. At d'', the peritectic reaction starts and continues at constant temperature till the solid NaCl disappears. The system has now NaCl.2H2O in equilibrium with the solution, whose composition is given by C. Further cooling results in the separation of more and more NaCl.2H2O with the composition of the solution moving along the curve CB. When d''' is reached, solution has composition B and eutectic mixture of ice and NaCl.2H2O separates.

Temperature remains constant till the entire solution freezes to give the eutectic mixture, the temperature of which decreases on further cooling. Thus the cooling curve of a solution at d shows a break at d', a halt at d'' and another halt at d'''.

Let us next takes the system e and cool it. The system at e is made up solid NaCl and solution, composition given by CD. As it cools, more and more NaCl separates and at e', solid NaCl and the solution of composition C undergo peritectic reaction to give NaCl.2H₂O. Temperature remains constant at e' till the completion of the reaction. Further cooling lowers the temperature of NaCl.2H₂O. Table 10.3.7.1 describes the phase diagram 10.3.7.

Table 10.3.7.1Description of the phase diagram for sodium chloride – water system

A(0^oC) Freezing point of H2O

B Eutectic point (ice, NaCl.2H2O, solution B) -21.1^oC, 23.3 mass% of NaCl.

C(0.15^oC) Peritectic point (NaCl, NaCl.2H₂O, solution C)

AB Freezing point curve of ice

BC Freezing point curve of NaCl.2H2O

CD Freezing point curve of NaCl.

HA Solid water (ice). Liquid water beyond A on the line HA.

GG' Solid NaCl.2H2O

CGJ A point on this line represents NaCl and NaCl.2H₂O in equilibrium with solution C.

EBF A point on this line represents ice and NaCl.2H₂O in equilibrium with solution B.

Area AEBA Ice solution (composition given by AB)

Area to the right of DCGJ NaCl solution (composition given by CD)

Area of BCGFB NaCl.2H₂O solution (composition given by BC)

Area below GJ NaCl and NaCl.2H₂O

Area above ABD Unsaturated solution

Cooling produced by freezing mixtures

Freezing mixtures are obtained by adding salt to ice, usually sodium chloride to ice. The low temperatures obtained in these freezing mixtures can be explained by using the NaCl.2H2O phase diagram.

below 0^oC and some ice melts. If this system is maintained under adiabatic conditions, then the melting of ice reduces the temperature of the ice, sodium chloride mixture. If sufficient quantity of the salt is added, then the temperature of the system drops to the eutectic temperature of - 21.1^oC. At this temperature ice, solid salt and solution of composition B are at equilibrium. The temperature remains constant as long as all three phases coexist in equilibrium. The invariance of the system at the eutectic point enables one to use eutectic mixtures as constant temperature baths. Table10.3.7.2 gives the eutectic temperature and composition of some ice salt systems.

Table 10.3.7.2 Eutectic temperatures of a few ice-salt systems

Salt ~Eutectic temperature/^OC ~Mass% of anhydrous salt in eutectic

NaCl -21 23

KCl -11 20

NH4Cl -15 20

KI -23 52

NaBr -28 40

NaI -32 39

Action of salt in melting ice formed on pedestrian paths and streets can be interpreted by the phase diagram. If enough salt is added to ice, say at -2^oC, to take the system to a point just above a', where the stable state is solution, then we expect all the ice to melt, temperature of the system remaining constant.

A good freezing mixture is one that has a low eutectic temperature, a high endothermic heat of solution of the salt, the ability of the components to form an intimate mixture and cheap, non toxic components. The most commonly used salt is common salt in a freezing mixture as it is cheap and easily available. Both the melting of ice and the endothermic dissolution of salt contribute to lowering in temperature of a freezing mixture. In the case of NaCl-ice mixture, the lowering in temperature is almost due to the fusion of ice as the heat of solution of NaCl is very low. CaCl2.6H2O – ice is a good freezing mixture as the eutectic temperature of this system is - 55^oC and CaCl2.6H2O has a high endothermic dissolution.

Dry ice (solid CO2) mixed with alcohol, acetone or ether forms a good freezing mixture with temperatures reaching below -70^oC.

The Ferric chloride - Water system

The ferric chloride – water is an example of a two component system in which the two components are completely miscible in the liquid phase and form a number of congruent melting compounds.

Ferric chloride forms four stable hydrates, Fe₂Cl₆.12H₂O, Fe₂Cl₆.7H₂O, Fe₂Cl₆.5H₂O and Fe₂Cl₆.4H₂O.Fe₂Cl₆ is used instead of FeCl₃ to avoid fractional number of molecules of water of crystallization. When several congruent melting compounds are formed in a system, a maximum is obtained for each as shown in the phase diagram for the system in Figure 10.3.8. The description of the phase diagram is given in Table 10.3.8.1.

Figure 10.3.8: The phase diagram for ferric chloride – water system

The freezing point of water is represented by A and the freezing point curve of ice by AB.

Systems at C, E, G and I are the congruent melting dodecahydrate, heptahydrate, pentahydrate and tetrahydrate respectively. At the respective congruent meeting points, the solid hydrates are in equilibrium with aqueous solutions of the same composition as the corresponding hydrates.

The eutectic temperatures are given by B, D, F, H and J and their values are -55^oC, 27.4^oC, 30^oC, 55^oC and 66^oC respectively. The temperatures at the congruent melting points C, E, G and I are 37^oC, 32.5^oC, 56^oC and 78.5^oC respectively. There are tie lines at B, D, F, H and J connecting solidus lines.

Fe2Cl6.12H2O Fe2Cl6.7H2O Fe2Cl6.5H2O Fe2Cl6.4H2O

Temperature →

solution

a b c d e f g h i j k

D' D D''

F' F F''

H' H H''

B' B B''

A

C

E

G

I

K

J J'' J'

C' E' G' I'

Water Mole %Fe2Cl6 → Fe2Cl6

Table 10.3.8.1 Description of the phase diagram for ferric chloride-water system

A Freezing point of water (0^oC)

C Congruent melting point of dodecahydrate (37^oC)

E Congruent melting point of heptahydrate (32.5^oC)

G Congruent melting point of pentahydrate (56^oC)

I Congruent melting point of tetrahydrate (78.5^oC)

B Eutectic point: Ice dodecahydrate solution B(-55^oC)

D Eutectic point: dodecahydrate heptahydrate solution D(27.4^oC)

F Eutectic point: heptahydrate pentahydrate solution F(30^oC)

H Eutectic point: pentahydrate tetrahydrate solution H(55^oC)

J Eutectic point: tetrahydrate anhydrous salt solution J(66^oC)

CC' Solid dodecahydrate

EE' Solid heptahydrate

GG' Solid pentahydrate

II' Solid tetrahydrate

AB Freezing point curve of ice

BCD Solubility curve of dodecahydrate

DEF Solubility curve of hepta hydrate

FGH Solubility curve of pentahydrate

HIJ Solubility curve of tetrahydrate

JK Solubility curve of anhydrous salt

Areas

ABB'A Ice Solution (composition given by AB)

BCB'B Dodecahydrate Solution (given by BC)

DCD'D Dodecahydrate Solution (given by DC)

DED''D Heptahydrate Solution (given by DE)

FEF'F Heptahydrate Solution (given by FE)

FGF''F Pentahydrate Solution (given by FG)

HGH'H Pentahydrate Solution (given by HG)

HIH''H Tetrahydrate Solution (given by HI)

JIJ'J Tetrahydrate Solution (given by JI)

Right of J''JK Anyhydrous salt Solution (given by JK)

Areas below

B'BB'' Ice+dodecahydrate

D'DD'' Dodecahydrate+ heptahydrate

F'FF'' Heptahydrate+ Pentahydrate

H'HH'' Pentahydrate+ tetrahydrate

J'JJ'' Tetrahydrate+ Anyhydrous salt

Area above ABCDEFGHIJK

Liquid (solution of FeCl₃ in water)

Isothermal evaporation of solution:

If a solution represented by point a (Figure 10.3.8) on being subjected to evaporation under constant temperature conditions moves along abcd to the point k, a sequence of changes takes place. These changes are given in Table 10.3.8.2.

Table 10.3.8.2 Isothermal evaporation of solution

a to b Ferric chloride solution gets slightly more concentrated.

at b Separation of Fe2Cl6.12H2O starts.

b to c More of the dodecahydrate separates. Composition of the solution remains unchanged at b. There is decrease in the volume of the solution.

at c Solution disappears completely and the system has only Fe2Cl6.12H2O.

c to d Dodecahydrate solution, composition given by d. As the system moves towards d, more and more of the solution is formed, amount of solid left decreases.

at d Solid decahydrate disappears and there is only solution.

d to e Unsaturated solution.

At e Fe2Cl6.7H2O starts separating.

e to f More heptahydrate separates. Solution composition remains unchanged at e. Volume of the solution decreases.

At f Complete solidification to Fe2Cl6.7H2O occurs

f to g Again solution appears, solution having composition g, volume of the solution increases, amount of Fe2Cl6.7H2O decreases.

At g Fe₂Cl_6.7H₂O disappears. There is only solution.

g to h Unsaturated solution

At h Fe₂Cl_6.5H₂O starts forming.

h to i More Fe₂Cl_6.5H₂O separates. Volume of solution (composition h) decreases.

At i Complete solidification to Fe2Cl6.5H2O occurs.

i to j Conversion of pentahydrate to tetrahydrate takes place.

At j Conversion to tetrahydrate gets completed.

j to k Conversion of tetrahydrate to anhydrous ferric chloride occurs.

If evaporation is continued, pure anhydrous ferric chloride is obtained.

Copper sulphate – water system

While discussing solid-liquid equilibria, we assumed the pressure on the system to be high enough that no vapour was present. At lower pressures vapor, may be present if one or more of the constituents is volatile. An important example of a solid-vapor equilibrium is the equilibrium between salt hydrates and water-vapor. We will take up for discussion the copper sulphte-water system

Figure 10.3.9: Vapour pressure – composition graph of CuSO4-H2O system (25^oC)

We will examine how the vapor pressure of the CuSO4- H2O system varies with the concentration of CuSO4 at a fixed temperature. Figure 10.3.9 gives the vapor pressure – composition diagram of this system at 25^oC. Point a gives the vapor pressure of pure water at 25^oC. The vapor pressure of water gets lowered along the curve ab as anhydrous copper sulphate is added to liquid water. At b the solution is saturated with respect to the pentahydrate, CuSO₄. 5H₂O. Along bc, there are 3 phases in equilibrium at constant temperature, CuSO₄. 5H₂O, saturated solution of CuSO₄ in

i liquid

liquid+CuSO

4

.5H

2

O

Vap + Liquid

b sat soln+CuSO

4

.5H

2

O

c

d e

f

g h Vap+CuSO

4

.5H

2

O

Vap+CuSO

4

.3H

2

O

Vap+CuSO

4

.H

2

O Vap+CuSO

4

7.85

4.32

0.017

CuSO4.5H2O+CuSO4.3H2O CuSO4.3H2O+CuSO4.H2O CuSO4.H2O+CuSO4.

Pressure/mmHg

a

H

2

O Mass% CuSO4 CuSO

4