determination of the solid-liquid phase diagram for...

University of Waterloo Chemical Engineering Department

ChE101: Chemical Engineering Concepts 2: Laboratory

Experiment #1:

Determination of the Solid-Liquid Phase Diagram for Naphthalene-Biphenyl Using Thermal Analysis

Hilary Lockie 20168263

Group #1 Hilary Lockie Performed: May 13th, 2005 Alvin Wan Submitted: May 24th, 2005 Adil Habib

1.0 INTRODUCTION 1.1 Objective: The purpose of this experiment is to use thermal analysis to study

naphthalene-biphenyl (two combined components) to determine the freezing point of the

system at atmospheric pressure. From the experiment, it will be possible to develop the

resulting solid-liquid phase diagram.

1.2 Theoretical Principles:

• Gibbs Phase Rule

The Gibbs phase rule is a method of calculating degrees of freedom of a system.

Degrees of freedom are the intensive properties (independent of system size) for the

system. The phase rule is given by the following equation:

π−+= cDF 2 (1)

where: DF = degrees of freedom (intensive properties)

c = number of chemical species

π = number of phases in the system

In a system with two components and two phases, like the naphthalene-biphenyl

mixture used in this lab, the degree of freedom is 2 (2 + 2 components – 2 phases).1

• Freezing Point

The freezing point of a solution indicates the point at which a solid begins to form as

the solution cools. This is a determined point that depends on the composition of the

solution.

• Lever Rule

The lever rule provides a method for finding the fraction of liquid and vapor (or solid,

in the case of this lab) in a two-phase, two-component system when the temperature

and pressure are known, as well as the overall composition.

The fraction of the masses of the phases is found through the following equation:

LF

FS

xxxx

SL

−−

= (2)

where: L and S are the mass of the liquid and solid phases, respectively

xS, xL and xF are the mass fractions of the solid phase, liquid phase

and total mixture

These are all calculated with respect to one component of the solution.1

• Phase Diagrams

Phase diagrams are graphs that give information on the equilibrium temperature and

pressure for a particular compound. The equilibria occur for the solid-liquid plateau,

liquid-vapor plateau and solid-vapor plateau. In this experiment, the phase diagram is

shown for the solid-liquid equilibrium point, and varies from 100% composition of

naphthalene to 100% composition of biphenyl. Further examples of this particular type of

phase diagram are in the ChE101 lab manual and in the preliminary report questions.

Theoretical phase diagrams can be developed from the following equation:

mKT ff =∆ (3)

where: ∆Tf is the freezing point depression

Kf is a proportionality constant

m is the molality (mol solute/kg solvent)1

• Cooling Curves (from the ChE101 lab manual)

Cooling curves have characteristics that are distinct:

(a) The rate of cooling lessens with time, since the cooling process releases heat from

the system. The curve will become less steep.

(b) A plateau occurs at the eutectic temperature (lowest possible for solidification). The

temperature stays constant until all of the liquid has solidified, at which time the solid

finishes cooling.

(c) A sudden dip and rise in temperature can occur from supercooling the liquid. The

solution cools below its normal freezing point and becomes unstable, so solidification is

sudden. This is avoidable by continuously stirring the liquid.

Test tube

Naphthalene-biphenyl mixture

H2O (boiling)

Hot plate

Beaker

H2O

Test tube equipped with thermocouple

Temperature regulator Stirrer

Naphthalene-biphenyl mixture

Temperature controlled water bath

2.0 EXPERIMENTAL

2.1 Apparatus:

Apparatus 1: Hot Water Bath

Apparatus 2: Controlled Temperature Water Bath

Chemical materials include reagent grade naphthalene and biphenyl (See next section

for safety data for these chemicals).

2.2 Procedure:

Procedure is as outlined in the ChE101 lab manual.

Figure 2.1: Hot Water Bath

Figure 2.2: Controlled Temperature Water Bath

3.0 SAFETY 3.1 Biphenyl Major handling and hazard issues with biphenyl stem from its organic nature, and its

effect on the environment. Biphenyl is toxic to aquatic organisms and can cause long

term damage. This means that the chemical should be disposed of in an organic waste

container. It is also an irritant for the eyes, respiratory system and skin, so lab workers

should be cautious to avoid inhaling the fumes and should wear protective eyewear at all

times, and gloves when handling the chemical in potentially hazardous situations (i.e. if

the biphenyl is in an open container).

First aid procedures for contact with skin or eyes are to wash the area extensively

with large volumes of water. In the case of skin contact, soap is also recommended. In a

case of inhalation, remove the person to an area of fresh air. In case of ingestion, wash

mouth out with copious amounts of water and contact poison control.

3.2 Naphthalene

Naphthalene, like biphenyl, is very hazardous to the environment and should be

disposed of in an organic waste container. It is an irritant like biphenyl, to the eyes, skin

and respiratory system. Lab workers should be cautious to avoid inhaling fumes, and

should wear protective eyewear and gloves when handling the chemical.

First aid procedures are the same as with biphenyl. Poison control should be

contacted in cases of dermal contact, eye contact or ingestion. Area of contact should be

washed extensively with water and clothing should be disposed of in a safe manner.

Naphthalene has a flash point of 80°C, so it should be kept away from hot plates and

other areas of high heat. In case of a flare-up, the fire can be extinguished with water or

a fire extinguisher. The fumes from ignited naphthalene are toxic, so extreme care

should be taken to avoid fire.

3.3 Other Hazards

Other aspects of the experiment that could be potentially dangerous include the hot

water being used to heat the chemicals and the hot plate. Workers should be cautious to

keep hands well away from hot surfaces and mixtures, and should use appropriate

handling devices (gloves, test tube tongs, etc.) when necessary.

4.0 RESULTS AND DISCUSSION 4.1 Results:

Table 4.1: Composition of Naphthalene-Biphenyl for Each Test

Mixture Mass (g) Naphthalene

Mass (g) Biphenyl

Total Mass (g) Start Temperature (°C)

1 17 0 17 85 2 17 3 20 80 3 17 7 24 70 4 17 14 31 60 5 0 18 18 75 6 2 18 20 70 7 6 18 24 60 8 12 18 30 45

By plotting the freezing curve for each of the eight mixtures (graphs and tables in

Appendix C), the freezing point for each mixture can be found. In the graphs in Appendix

C, the freezing point is plotted by a horizontal dotted line. In turn, these temperatures are

put together to create Figure 4.1.

Table 4.2: Freezing Point of Naphthalene-Biphenyl Mixtures

Mixture 1 2 3 4 5 6 7 8 Freezing Point Tf (°C) 80.8 72.5 63.3 51.8 69.3 62.3 49.6 38.0

%wt Biphenyl 0 15 30 45 100 90 75 60

Figure 4.1: Naphthalene-Biphenyl Liquid-Solid Phase Diagram

Naphthalene-Biphenyl Solid-Liquid Phase Diagram

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

%wt Biphenyl

Tem

pera

ture

Tf (

°C)

Solid Naphthalene = Liquid Mixture

Solid Biphenyl = Liquid Mixture

Solid Naphthalene and Solid Biphenyl

Liquid Mixture

E TE

Melting Point of Naphthalene

Melting Point of Biphenyl

4.2 Discussion:

From this diagram, it can be shown that the melting point of naphthalene is

approximately 81°C and that of biphenyl is approximately 69.5°C. These values are quite

accurate compared to the sample data given, giving error of only about 1% from the data

table. From physical property tables, the actual melting point of naphthalene is 80.0°C1

and of biphenyl is 70°C2. This means the data gathered in the experiment are also

precise. The eutectic point was found to be 38°C. This was not as accurate as the

melting point temperatures (it was off by 2.3°C from the sample data). This difference

can be accounted for by experimental errors.

The difference between the freezing points plotted for 15%, 30% and 45% biphenyl

and the solid-liquid equilibrium line is larger than expected. This could be because the

experiment was halted prematurely for these mixtures, so the temperature was not as

low as it should have been. It is also possible that the compounds did not contain the

right percentage of biphenyl (this is discussed in Sources of Error), so the temperature

would be accurate for the amount of biphenyl the mixture contained. Mixture 4, in

particular, was stopped when the temperature began to drop at 0.1°C per second as

opposed to 0.2 - 0.3°C each second (Figure C1.4).

Overall, the results appear fairly precise. None of the values stray too far from the

fitted line of equilibrium. This can be used to conclude that there were no extreme errors

in calculations or measurements.

4.3 Sources of Error:

• There were a few sources of error in this experiment, but the largest source

involved the mixing of chemicals. Each time more biphenyl was added to the

compound, some residue was left in the plastic tray. Another aspect of this

occurred because, as the experiment progressed, the temperature was lowered.

This caused the solution, while in liquid form, to solidify on the upper portion of

the test tube. This inhibited the stirring and lessened the volume of the solution

that was being cooled to the freezing point.

• To accommodate for solution solidifying at the top of the test tube, it would be

useful to use either bigger test tubes or less substance so the test tube does not

become overfilled – and can therefore be completely submerged into the water

bath to above the level of the solution. This way, all of the solution melts each

time more solid chemical is added.

• Test tube tongs and a scale closer to the laboratory site would be beneficial for

safety concerns. Workers used bare hands (or latex gloved hands) to carry hot

test tube, increasing the risk of burns. Carrying chemicals across the room is also

potentially hazardous should one trip. A shorter distance minimizes that risk.

5.0 CONCLUSIONS • The solid-liquid phase diagram for naphthalene-biphenyl is shown in figure 4.1. It

reflects closely the sample data given, and the freezing points of both

components are precise to reference numbers.

• Error from loss of substance accounted partially for variances in points from the

melting (freezing) point line.

• The eutectic point calculated from this lab is approximately 38.0°C. Melting point

of biphenyl was calculated to be about 69.5°C and that of naphthalene was about

81°C.

6.0 REFERENCES 1. Felder and Rousseau, Elementary Principles of Chemical Processes (Third Edition),

Wiley, USA: 2000.

2. “Biphenyl,” http://en.wikipedia.org/wiki/Biphenyl, 27 Apr 2005, accessed 23 May 2005.

APPENDIX A

Sample Calculations

(PreLab Questions)

Cooling Curve for a Mixture of 17g Naphthalene and 3g Biphenyl

70

72

74

76

78

80

82

84

86

88

0 20 40 60 80 100 120 140 160 180 200 220 240

time (s)

tem

pera

ture

(°C

)

1.1 Determining Mixture Freezing Points

(1)

(2) Judging from the location of the approximate temperature plateau that occurs at 160s

into the cooling process, it appears that the freezing point of the mixture is approximately

72.5°C (72.4°C from the table of values).

Figure B2: Cooling Curve for a Mixture of 17g Naphthalene and 3g Biphenyl


30

35

40

45

50

55

60

65

70

75

80

85

0 10 20 30 40 50 60 70 80 90 100

Weight Percent Biphenyl

Free

zing

Poi

nt T

f (°C

)

1.2 Generating the Naphthalene-Biphenyl Solid-Liquid Phase Diagram

(3)

(4) Lines AE and BE are freezing point curves. The freezing point for each chemical

(either naphthalene or biphenyl) lessens when more of the opposing chemical is added.

Point E is the eutectic point, the point at which the freezing point is the lowest for any

composition of the mixture. It occurs when there is 60% by weight of biphenyl (40%

naphthalene).

Below line BE and above line C, solid naphthalene can exist in equilibrium with the

liquid mixture of the two chemicals. This is true below the line AE and above line C for

solid biphenyl and the solution.

Above BEA, the chemicals exist in liquid phase only.

Below line C, the chemicals exist in solid phase only.

Line C is the temperature (40°C) at which solid biphenyl and solid naphthalene can

exist in equilibrium with the liquid mixture.

Melting Point of Naphthalene

Melting Point of Biphenyl

E

Solid Biphenyl ⇋ Liquid Mixture

Solid Naphthalene and Solid Biphenyl (no liquid)

A

B

C

Solid Naphthalene ⇋ Liquid Mixture

Bs BL P

Figure B3: Naphthalene-Biphenyl Solid-Liquid Phase Diagram

(5) At the point where the mixture is 65% naphthalene (35% biphenyl) and 50°C, there

are two phases present: solid naphthalene and liquid solution. According to the phase

rule (1), there are two degrees of freedom. This means that the temperature and the

mass fraction of naphthalene solid are unique.

T = 50°C wt% Biphenyl = 0.35

Using the Lever Rule (2):

153

10350

4503503500 .

..

...

=−−

=−

−=

SL

To find the weight percentage of liquid and solid components:

22254

100 ..

=

By this information, it can be determined that the weight percentage of the liquid phase

is 77.8% and of the solid phase is 22.2%.

APPENDIX B

Lab Questions

1. Define intensive and extensive properties and give 5 examples of each.

An intensive property is a characteristic of a reaction or process that is independent

of the size of the system. Examples of intensive properties include temperature,

pressure, density, mole fraction and mass fractions. An intensive property can be

identified as such if it is the same for any section of the system compared to the system

as a whole.

An extensive property is the opposite of an intensive property. These depend on the

size of the system. Examples of these include volume, mass, surface area, energy (J)

and number of moles of substance. When a section of the system has a different value

for a property than the whole system, the property is extensive. 2. (a) Why is “time” not a “degree of freedom” when using the phase rule?

Since time is changing rapidly, it is not an intensive property. Time is, indeed,

constant over the whole system, but it never remains at one point, or slows, unlike other

intensive properties (pressure, temperature, density). Time also is unrelated to the

characteristics of the system. For example, the density of a system can remain constant

regardless of how much time has pass. (b) Using the phase rule, determine the number of degrees of freedom at the eutectic point.

22222 =−+=−+= πcDF

Therefore, the number of degrees of freedom at the eutectic point is 2. The two intensive

properties that can be used to solve the system are temperature and mass fraction. 3. Explain the use of the “lever rule” in working out material balances and illustrate on the phase

diagram shown in these instructions.

The lever rule makes it possible to calculate the amount of liquid and the amount of

solid (or vapour, in some cases) at a certain temperature and mass fraction. A tie-line is

drawn, like the one on the diagram in the lab manual (Figure 1 in the experiment 1

section). The tie-line is drawn horizontal at the temperature point and, in the case of

solid-liquid phase diagrams, goes from the y-axis to the melting point line. A vertical line

it then drawn at the mass fraction point and goes up to the tie-line. The distance from the

y-axis to the tie-line in a ratio to the distance from the tie-line to the melting point line

gives the ratio of liquid to solid. This is demonstrated in the following diagram.

Figure D3.1: Method of Using Lever’s Rule to Calculate Amount of Liquid and Amount of Solid

4. How does supercooling affect the accuracy of the data obtained from cooling curves?

Supercooling occurs when a solution is colder than its freezing point but still in liquid

form. When a solution becomes supercooled, the temperature needs to rise before the

solution can solidify. This creates a dip in the graph that should, technically, not exist. 5. Why must the temperature difference between the contents of the sample and the cooling

water in the jacket be kept constant (at about 3°C)?

The temperature of the solution needs to drop slowly and consistently to avoid

supercooling the mixture. It is also much more difficult to observe the cooling curve if the

temperature is dropping too rapidly. The solid-liquid plateau may only occur for a few

seconds if the solution is cooling too fast. Finally, if the temperature is not cooled

consistently, the graph of the cooling curve will not be reflective of the actual cooling

curve of the mixture. 6. Explain the cooling curves of mixtures 6, 7 and 8 with reference to the phase diagram.

Mixtures 6, 7 and 8 are all composed of 18g of biphenyl with a smaller amount of

naphthalene. As more naphthalene is added, the freezing point of the mixture is

lessened. In this particular experiment, all three of these mixtures reached a

supercooled state before solidifying. At any given point on the line connecting the

freezing point of the three mixtures, the solution is in equilibrium with solid biphenyl, with

no solid naphthalene present.

Tie-Line

Melting Point Line

AS AL A

Mass Fraction

Temp.

AS-A = L A-AL = S

Figure D7.1: Naphthalene-Biphenyl Liquid-Solid Phase Diagram


30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

%wt Biphenyl

Tem

pera

ture

Tf (

°C)

7. What are the compositions and weights of the phases present at equilibrium when a mixture of

20% biphenyl is at (a) 80°C (b) 60°c and (c) 30°C. The weight of the system is 12.7kg.

(a) At point A, when the temperature is 80°C and the composition of the mixture is 20%

weight of biphenyl, all components are in the liquid phase. This means that the

composition is 20% liquid biphenyl and 80% liquid naphthalene. The masses, if the total

mass is 12.7kg, are 2.54kg biphenyl and 10.16kg naphthalene.

(b) At point B, the lever rule needs to be applied to find the amount of solid and liquid.

The solution is in equilibrium with solid naphthalene at this point. Using the lever rule:

1222

090200

2902002000 .

.

...

.==

−−

=−−

=BLB

BBSSL

Subsequently, to find the percent composition:

%.

311222

100=

+

Therefore, there is 31% solid naphthalene and 69% liquid solution. The mass of the solid

naphthalene is therefore 3.937kg and the mass of the liquid solution is 8.763kg. Since

the mass composition of the total solution including the solid should remain the same,

the percentage of liquid biphenyl is 20%, or 1.753kg and the percentage of liquid

naphthalene is 49%, or 7.010kg.

A

B BS

C

BL


30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100

%wt Biphenyl

Tem

pera

ture

Tf (

°C)

(c) At point C, the solution is entirely solid phased. The mass percentage of solid

naphthalene is 80% and of solid biphenyl is 20% and the masses are 10.16kg and

2.54kg, respectively. 8. In a sketch of the phase diagram, choose a point halfway between the melting point of biphenyl

and the eutectic temperature. Explain what happens as a lab worker adds biphenyl to a solution

beginning at 100% naphthalene if it remains at the constant temperature.

• A – system is 100% solid naphthalene

• B – solid naphthalene and liquid biphenyl exist

• C – system reaches equilibrium of naphthalene solid and naphthalene/biphenyl

solution at melting point of naphthalene, which is the constant given temperature

• D – liquid solution of naphthalene and biphenyl

• E – system reaches equilibrium of liquid solution and solid biphenyl at melting

point of biphenyl, which is the constant given temperature

• F - solid biphenyl and liquid naphthalene exist (also potentially residual liquid

biphenyl)

Figure 8.1: Naphthalene-Biphenyl Solid-Liquid Phase Diagram

A

B F

C E D

APPENDIX C

Raw Data

Mixture 1: 17g Naphthalene

80

80.5

81

81.5

82

82.5

83

83.5

84

84.5

85

85.5

0 20 40 60 80 100 120 140 160

Time t (s)

Tem

pera

ture

T (°

C)

Figure B1.1: Mixture 1 – 17g Naphthalene, No Biphenyl

Mixture 2: 17g Naphthalene, 3g Biphenyl

72

73

74

75

76

77

78

79

80

81

0 50 100 150 200 250

Time t (s)

Tem

pera

ture

T (°

C)

Figure C1.2: Mixture 2 – 17g Naphthalene, 3g Biphenyl



Mixture 3: 17g Napthlalene, 7g Biphenyl

62

63

64

65

66

67

68

69

70

71

0 50 100 150 200 250 300 350

Time t (s)

Tem

pera

ture

T (°

C)


50

51

52

53

54

55

56

57

58

59

60

61

0 50 100 150 200 250 300 350 400

Time t (s)

Tem

pera

ture

T (°

C)

Figure C1.5: 18g Biphenyl, No Naphthalene

Figure C1.6: 2g Naphthalene, 18g Biphenyl

Mixture 5: 18g Biphenyl

69

70

71

72

73

74

75

76

0 50 100 150 200 250 300

Time t (s)

Tem

pera

ture

T (°

C)


61

62

63

64

65

66

67

68

69

70

71

0 50 100 150 200 250 300 350

Time t (s)

Tem

pera

ture

T (°

C)




45

47

49

51

53

55

57

59

61

0 50 100 150 200 250 300 350 400

Time t (s)

Tem

pera

ture

T (°

C)


37

38

39

40

41

42

43

44

45

46

0 50 100 150 200 250 300 350

Time t (s)

Tem

pera

ture

T (°

C)

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