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Tuesday, January 21, 2014

Solid-Liquid Phase Diagram - Physical Chemistry - Lu Le Laboratory

Purpose

1.     To investigate the heterogeneous equilibrium between solid and liquid phases of a two-component system.
2.     To construct the phase diagram by measuring the cooling curves.
3.     To determine the eutectic temperature and composition of the mixture.


Principles

        Solid-liquid phase diagrams are of great value in the technical study of alloys, ceramics and in the recovery of a salt by crystallization from a mixture of salts. The binary solid-liquid phase diagram in Figure 1 shows the stability of different phases as a function of temperature at a given pressure. This example shows a case where the two substances are miscible in the liquid state and insoluble in the solid state. In this diagram we are plotting temperature versus the mole fraction of substance B. At the left, the curve intersects at the melting point of pure A or pure B. This is a phenomenon of freezing point depression. The minimum in the freezing-point curve is called the eutectic, and a horizontal line has been draw along the eutectic temperature.


Figure 1.

        To construct a phase diagram for a binary mixture, phase transition temperature data for mixtures of different compositions of the two components must be collected. This can be achieved by recording cooling curves for the different mixtures as shown in Figure 1. Samples containing known amounts of both components are places in containers and heated until completely melting. Then allow it to cool slowly and measure the temperature at regular time intervals. Cooling curve 1 in figure 1 is for pure A. The sample cools at an approximately constant rate. Once the temperature is reached melting point of A, a “halt” is observed in the cooling curve. The temperature of the substance remains constant until all of the sample freezes. Then the temperature drops rapidly again. The same thing happens at the composition of a eutectic (curve 3) and pure B (cooling curve 5). Cooling curve 2 is for a mixture with composition between pure A and the eutectic. On this cooling curve we have a changing point where solid A is crystallizing out. Because the heat evolved by solidification partly offsets the heat lost by radiation and conduction to the cold surroundings, a slow rate of cooling is observed. The melt becomes richer in component B as component A is separating out, and the freezing point of the melting decreases along the curve. When we rich point “b” the liquid has reached the eutectic composition and a “halt” is observed in the cooling curve (line b-c). At this temperature, both pure A and pure B will crystallize together. Since three phases are in equilibrium at constant pressure, the number of degrees of freedom falls to f’ = C- Φ+1 = 2-3+1 = 0. If we continue to remove heat from the mixture the system will remain at eutectic temperature until all of the remaining liquid has solidified. Cooling curve 3 is for a mixture with composition between the eutectic and cooling curve 4 is for a mixture with composition between the eutectic and pure B. For each mixture studied, the cooling curve is examined to determine the temperatures at which changes in slope or plateau occur. A phase diagram is prepared by plotting the points of the corresponding breaks and halts in the cooling curves and connecting these points by smooth curves.
                                             
Chemicals

1.     Tin (metal basis, A.R.)
2.     Bismuth (metal basis, A.R.)


Apparatus

1.     Electronic furnace
2.     Thermocouple
3.     Crucibles
4.     Ebulliometer (use to adjust the thermocouple)
5.     Barometer
6.     Computer and data receiver
7.     Hardened test tube



Procedure

Preparation of Samples
1.     Prepare 0%30%57%80%100%(Bi w/w) Bi-Sn alloy 50g with an analytical balance to nearest 0.0001g.
2.     Add some rosin in the test tube to prevent the sample been oxidized at high temperature.


Drawing Cooling Curves
1.     Set up the apparatus as Figure 2.
2.     Turn the heater on and adjust he voltage until all solids melt. Transfer the crucible out from a hotter furnace to a steel rank to cool down and start recording the temperature.


3.     Repeat these steps for different samples.


Experimental Record

Sample
d.d. H2O
Tin
Bismuth
Melting Point (Literature) (/)
100
232
271
Experimental (/)
99.58
224.44
247.65
Table 1.

Cooling Curve of Samples


Sample Bi/Sn x 100%(w/w)
Bi 0%(w/w)
Bi 29.97%(w/w)
Bi 56.96%(w/w)
Bi 80.00% (w/w)
Bi 99.99% (w/w)
T1 ()
224.44
173.01
131.06
193.47
265.05
T2 ()
-
125.86
-
125.67
-
Table 1. Raw Data

Analysis

    Draw a calibration curve for the thermocouple set:


Calibration curve
 y = -3.01901 + 1.03902*x


Sample Bi/Sn x 100%(w/w)
Bi 0%(w/w)
Bi 29.97%(w/w)
Bi 56.96%(w/w)
Bi 80.00% (w/w)
Bi 99.99% (w/w)
T1 ()
230.18
176.74
130.14
198.00
254.29
T2 ()
-
127.75
-
127.55
-
Table 2. Calibration data

Complete the phase diagram with other known data[1]


Add some colors and sign

      
        Finally, analysis the phase diagram with Gibbs' phase rule: F = C - P + n
 here n=1 because it is at a constant pressure. Then we can get the degrees of freedom of each phase.

Item
Phase (P)
Degrees of Freedom
α
1
1
β
1
1
α+β
1
2
α+L
2
1
β+L
2
1
Liquid phase
1
2
Melting Curve
2
1
Minimum Melting Eutectic Point
3
0


References

[1]   虞覺奇, 易文質. 二元合金狀態圖集. 上海: 上海科學技術出版社, 1995: 250-251
[2]  傅献彩, 沈文霞, 姚天扬. 物理化学, 上册欧4 . 北京:高等教育出版社, 1990:144.
[3]  清华大学化学系物理化学实验编写组. 物理化学实验. 北京:清华大学出版社, 1991.
[4]  Robert C. Wcast Handbook of Chemistry and Physics. Physics. 58th ed. Ohio: CRC Press, 1977.
[5]  朱文涛. 物理化学. 北京:清华大学出版社,1995.
[6] http://www.materials.ucsb.edu/~matclass/101/pdffiles/Lecture_13.pdf




Monday, January 20, 2014

Phase Diagram of Liquid-Vapor Equilibrium in a Binary System - Experiment of Physical Chemistry - Lu Le Laboratory

Purpose

1.     To construct a phase diagram and find the temperature and composition of the azeotrope.
2.     To study the liquid-vapor equilibrium of a binary system.

Principles

        In an idealized system the boiling point of a mixture of two soluble liquids is always between the boiling points of these two pure components. Figure 1-(a) is a typical ideal system. The upper curve is called the dew point curve representing the changing composition of the vapor phase. The lower curve is known as bubble point  curve representing the composition of liquid phase.


Figure 1.

        A number of homogeneous liquid do not obey Raoult’s lawand as a result the phase diagrams would be different. Large positive deviations from Raoult’s law can result in minimum-boiling azeotrope (Fig. 1-(b)) while large negative deviations can lead to maximum-boiling azeotrope (Fig. 1-(c)). In such systems, there exists a particular composition at which both of the liquid phase and the vapor phase have the same composition. This is called an azeotrope mixture.
        A liquid-vapor phase diagram of a binary system can be constructed by using a reflux apparatus. When a mixture of two soluble liquids is heated to a boiling point, the vapor phase is condensed and trapped in the pocket below the condenser. Under equilibrium conditions, the trapped condensate represents the vapor phase while the liquid remaining in the reservoir represents the liquid phase. The composition of the vapor and the liquid will be determined through the use of a calibration curve of refractive index as a function of compositions. An Abbe refractometer is used in this experiment.

Chemicals

1.     Cyclohexane  (A.R.)
2.     Ethanol 99.9% (A.R.)


Apparatus

1.     Ebullimeter
2.     Abbe refractometer


3.     Pipet and sucker
4.     Thermostatic water bath


Procedure

Drawing the Calibration Curve

1.     Prepare 0%10%30%69.5%90.0%96.0%100%(w/w) ethanol-cyclohexane mixtures with an analytical balance to nearest 0.0001g.
2.     Determine the refractive indexes of these mixtures with an Abbe refractometer and prepare the calibration curve of composition-refractive index.

Determine the Composition of Liquid Phase and Gas Phase

1.     Flow the cooling water into the condenser of the ebulliometer.
2.     Turn the heater on and adjust he voltage to about 20~30V until reflux begins. When the liquid is boiling, control the reflux in the lower portion of the condenser (~2cm).


3.     After the thermometer reading is constant, record the temperature and the the pressure of the atmosphere. Then stop heating the mixture.


4.     Suck drops of liquid phase and gas phase(at the bottom of the condenser) out with pipets. Determine the composition by measuring refractive index and using the calibration curve.
5.     Draw a composition –temperature diagram.
   
Experimental Record

Label
Cyclohexane (g)
Ethanol (g)
Mass Fraction of Cyclohexane (MFC)
nD24.1
0%
0.0000
-
0.00000

10%
0.1015
0.9024
10.11057
1.3659
30%
0.3344
0.7231
31.62175
1.3777
69.5%
0.7038
0.2986
70.21149
1.4036
90.0%
0.9130
0.1069
89.51859
1.4188
96.0%
0.9559
0.0492
95.10497
1.4236
100%
-
0.0000
100.00000
1.4270

Mass Fraction of Cyclohexane (MFC)
Tb ()
nD24.1 of liquid phase
nD24.1 of gas phase
0%
78.08
1.3610
1.3614
10%
76.18
1.3627
1.3693
30%
66.83
1.3767
1.3981
69.5%
64.11
1.3966
1.4034
90.0%
64.68
1.4155
1.4056
96.0%
67.58
1.4237
1.4080
100%
79.65
1.4250
1.4250
   
Analysis

(1)  Calibration Curve


Equation
y = Intercept + B1*x^1 + B2*x^2
Adj. R-Square
0.99985
Value
Standard Error
Index of refraction
Intercept
1.36116
2.83E-04
Index of refraction
B1
4.68E-04
1.64E-05
Index of refraction
B2
1.95E-06
1.58E-07

Calibration Curve
y = 1.36116 + (4.68E-04) x + (1.95E-06) x2

        
(2) Determination of the Composition of Gas Phase and Liquid Phase

Mass Fraction of Cyclohexane (MFC)
Tb ()
nD24.1of liquid phase
MFC of Liquid Phase
nD24.1 of gas phase
MFC of Gas Phase
0.0%
78.08
1.3610
-0.3%
1.3614
0.5%
10.0%
76.18
1.3627
3.2%
1.3693
16.3%
30.0%
66.83
1.3767
29.6%
1.3981
62.6%
69.5%
64.11
1.3966
60.5%
1.4034
69.9%
90.0%
64.68
1.4155
85.6%
1.4056
72.8%
96.0%
67.58
1.4237
95.6%
1.4080
76.0%
100.0%
79.65
1.4250
97.1%
1.4250
97.1%


(3) Draw the phase diagram with smooth curve



Azeotrope
64.21
Percentage Weight of Cyclohexane in the Azeotrope
69.9%

        (4) Data Analysis

Experimental Data
Azeotrope
64.21
Percentage Weight of Cyclohexane in the Azeotrope
69.9%

Literature
Azeotrope
64.90
Percentage Weight of Cyclohexane in the Azeotrope
69.5%

Percentage Error
Azeotrope
-1.0%
Percentage Weight of Cyclohexane in the Azeotrope
0.6%


References

[1]  傅獻彩, 沈文霞, 姚天揚. 物理化學, 上冊歐4 . 北京:高等教育出版社, 1990:144.
[2]  清華大學化學系物理化學實驗編寫組. 物理化學實驗. 北京:清華大學出版社, 1991.
[3]  Robert C. Wcast Handbook of Chemistry and Physics. Physics. 58th ed. Ohio: CRC Press, 1977.
[4]  朱文濤. 物理化學. 北京:清華大學出版社,1995.
[5] Ponton, Jack (September 2001). "Azeotrope Databank" (Queriable database). The Edinburgh Collection of Open Software for Simulation and Education, Edinburgh University. Archived from the original on 24 April 2007. Retrieved 24 March 2007.