1

Handout of Physical Chemistry Experiments

（Part I）

□Experiments 1 and 2 Control and application of thermostatic bath Measurement of liquid

viscosity

□ Experiments 3 Heat of Combustion

□ Experiments 4 Vapor Pressure of a Pure Liquid

□ Experiments 5 Binary Liquid–Vapor Phase Diagram

□ Experiments 6 Binary Alloy Phase Diagram

□ Experiments 7 Measurement of Ammonium Carbamate Decomposition Pressure

Student ID

Class

Name

Teaching & Research Institute of Physical Chemistry

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Specifications of Physical Chemistry Experiments

According to our experience, there are some key issues which need your particular attention as follow. 1． Each experiment is performed by two students as a team. Although

each team member may have his/her own responsibility during the experiment, everyone needs to understand the whole experimental procedure and techniques adopted.

2． Prior to the experiments, you are requested to be clear about the

experimental objective and theories involved in the experiments. It will be helpful to have a whole picture of the experimental procedure in your mind. Don’t simply copy the textbook when you prepare your experimental report.

3． It is necessary to take a notebook to the lab for the recording of

experimental log and the raw data in the table which is designed by yourself before experiment. Room temperature and atmospheric pressure are required for every experiment. Hence, you are suggested to record these two data which will be needed for the analysis of experimental data and preparation of report. Don’t use pencil to record data. You are asked to report the experiments as it is. Honesty is one of the key requirements for science.

4． Don’t be satisfied with following the instruction during experiment.

You are encouraged to explore the reasons and improvement for the experiment. Curiosity always is the driving force of science development.

5． It’s your responsibility to clear your experimental bench after

experiment. Throwing solid waste to the sink is forbidden. Be respectful to the environment.

6． Prepare your experimental report dependently. Copying others is forbidden.

Hope everyone enjoys with our experiments and have your own gains

about the objectives and application of theory.

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Experiments 1 and 2 Control and application of

thermostatic bath Measurement of liquid viscosity I、Experimental objectives 1. Understand the structure, temperature controlling and application of thermostatic bath. 2. Learn one of the methods for the determination of liquid viscosity.

II、Theory

1. Thermostatic bath It is often necessary to maintain a constant temperature. The importance of this

type of control in experimental physical chemistry is illustrated by the fact that most physical chemistry experiments require temperature control of some kind. Many physical quantities such as rate constants, equilibrium constants, and vapor pressures are sensitive functions of temperature and must be measured at a known temperature that is held constant to within 0.1 K or better.

There are two basic methods of achieving a constant temperature: 1. Phase equilibrium is maintained at constant pressure between two phases of a

pure substance or three phases of a two-component system (eutectic). 2. A temperature sensor provides a feedback signal to control the input of heat (or

refrigeration cooling in some cases) in order to maintain the temperature close to any arbitrary desired value.

Method 1 is the simplest approach; method 2 is more flexible and generally more useful.

The water bath, equipped with stirrer, temperature sensor, control circuit, and heater, provides the most commonly used means of temperature control in the range 15 to 80 oC. The tank should be constructed of welded stainless steel; the inclusion of glass windows in two or more sides is a convenience but complicates the design. The thermometer, temperature controller, and stirrer are best mounted in the middle; this arrangement leaves the ends free for experimental work. There should be adequate provision for mounting rods and clamps to support flasks, dielectric cells, etc. Depending on the experiment being done, two or four sets of apparatus can be operated in a single bath of this size. The bath should be provided with the following items.

Stirrer. The bath fluid must be well stirred in order to avoid temperature gradients within the bath. A large centrifugal water circulator, driven by a motor, provides adequate stirring. It should be positioned carefully so that the effluent stream will cause efficient circulation throughout the entire tank.

Thermometers. The sensor probe should be placed in the bath in a central location removed from the heater and stirrer units. If a single cell or sample holder immersed in the bath is the only object of interest, the probe should be placed near this cell but not touching it. The measuring thermometer should be placed in good thermal contact with the cell or sample holder if there is only one or positioned close to the location of multiple cells.

4

Figure 1 Illustration of thermostatic bath

1- The tank; 2-Heater; 3-Stirrer; 4-Tthermometer；5- Mercury temperature meter；6- Temperature controller；7- Backman thermometer

Heater. 24 A single copper-sheathed immersion heater of 250-W capacity is

adequate for temperature control up to about 30 C. It is recommended that the heater be positioned low in the bath and in the effluent stream from the stirrer. At higher temperatures a second heater may be needed. In this case one can be maintained at a constant power and the other can be regulated by the temperature controller, or both can be controlled, depending on their power ratings, the temperature desired, and other design factors. Blade heaters sheathed in stainless steel have longer time constants than copper-sheathed tube types and will not give as good temperature control, but they can be used as unregulated constant-power heaters.

Temperature controller. Large water baths are typically provided with controllers of moderate resolution (say 0.1 to 0.5 K), but much better constancy ( 0.1 K or less) can be achieved.

The most important method of achieving temperature control is to use a sensitive thermometer that generates an electrical signal, such as a resistance thermometer, thermistor, or thermocouple. Comparison of this signal with a reference signal that establishes the set point provides an error signal to a feedback circuit that controls the power to the heater. Thus any temperature deviation from the desired value detected by the sensor will be corrected automatically. Mercury temperature meter functions as temperature controller in this experiment. Backman thermometer is used to read the accurate temperature.

With a proportional controller, the heater power supplied to the system is changed by an amount proportional to an error signal corresponding to the temperature difference ( Ts-T ); see Fig. 2. The controller output can be either time proportionating or current proportionating; only the latter will be considered here, as it is the more commonly used mode. Proportional controllers provide a fast response and show very little cycling about the set point, which means better temperature control. Two disadvantages are a steady-state offset from the set-point temperature and the presence of damped oscillations associated with a change in the set point

5

Figure 2. On–off controller behavior; the temperature variation observed after a

step increase in the set-point temperature from Ts′to Ts . Note the long-term oscillation that persists about Ts. The heater power W can have only two values: 0 or W max.

The offset can be reduced by decreasing the proportional band PB (i.e., increasing the controller gain), but there is a limit to this approach since instability in the form of undamped oscillations will occur at too high a gain.

The overshoot oscillations occurring after a change in set point can be reduced greatly by adding to the simple proportional control a second control signal proportional to the time derivative of the temperature. This feature “anticipates” the magnitude of future error signals and smooths out overshoot oscillations. The offset problem could of course be eliminated by a manual reset of the set-point value. However, this can be done automatically by adding an integrating control feature, for which the control signal is proportional to the integral of the error signal. As long as there is any difference between the control temperature and the set-point temperature, a small corrective change in the heater power will occur to slowly reduce this difference to zero. Figure 11 illustrates the behavior of systems with proportional derivative (PD) or proportional + integral + derivative (PID) controllers. Note that there are also proportional + integral (PI) controllers.

Figure 3. Response of a system with ( a ) proportional + derivative (PD) control

and (b) proportional + integral + derivative (PID) control when the gain is 15 percent of the critical gain. Part ( c ) shows the response with PID control when the gain is 50 percent of the critical gain, a practical limit for good regulation.

The sensitivity of thermostatic bath: max minSensitivity

2

T T−=

2. Coefficient of viscosity

6

It is a general property of fluids (liquids and gases) that an applied shearing force that produces flow in the fluid is resisted by a force that is proportional to the gradient of flow velocity in the fluid. This is the phenomenon known as viscosity.

It is conveniently measured, in the case of liquids, by determination of the time of flow of a given volume V of the liquid through a vertical capillary tube under the influence of gravity. For a virtually incompressible fluid such as a liquid, this flow is governed by Poiseuille’s law in the form

4

8

r P

Vl

π τη =

Clearly, viscosity is proportional to r4 (r is the radius of capillary). However, accurate measurement of capillary radius is difficult. Usually, we take a reference liquid (distilled water in this experiment) measuring the relative viscosity. According to the viscosity of reference, the viscosity of targeted liquid can be derived. During the experiment, two liquids (1 denotes targeted liquid and 2 for reference liquid) flow through the vertical capillary tube

1 1 1 1 1

2 2 2 2 2

P

P

η τ ρ τη τ ρ τ

= =

Hence, the relative viscosity relates with the densities and times flowing through the capillary tubes. Measuring the flowing times, get the densities of two liquids and viscosity of reference liquid from textbook, viscosity of targeted liquid can be obtained.

Figure 4. Viscosimeter

III、Procedure (1) Thermostatic bath 1．Fill sufficient water，set up the thermostatic bath。（It was prepared by the technician already）

Capillary

b

a

Tube A

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2. Set the temperature of thermostatic bath to 30oC。 ① （Presetting） Screw the black cap of mercury temperature meter presetting the temperature and at this step allow the setting temperature 1-2 oC lower than target temperature. Switch on the power source (switch on two heaters) and stirrer allowing the bath to heat up. ② （Accurate setting）Check the mercury temperature meter. If the temperature is lower than the target temperature after the system stop heating, then tune the mercury temperature meter slowly to get the accurate setting temperature. 3. After the temperature reaches the target temperature, wait for 5-10 min and then start the experiment. 4. Determination of sensitivity of thermostatic bath Place the Backman thermometer near the wall of water tank. Start the stopwatch, read and record the temperature denoted as T1 (Backman thermometer) every one minute . Place the Backman thermometer at the center of water tank. Start the stopwatch, read and record the temperature denoted as T2 (Backman thermometer) every one minute . (2) Viscosity determination 1．Set the temperature of thermostatic bath to 30oC。 2. (a)Pipette the 10 mL ethanol into the tube A of viscosimeter (see Figure 4). Put rubber tubes to capillary tube (Be careful with the tube and do not break it). Immerse the viscosimeter in the water bath for at least 10 min (Make sure fiducial mark a should be in the water bath).

(b) By suction with a pipette bulb through the rubber tube on capillary tube, draw the solution up to a point well above the upper fiducial mark a. (During the suction, no bulbs are allowed).

(c) Release the suction and measure the flowing time between the upper (a) and lower (b) marks with a stopwatch or timer. Obtain two or more additional runs with the same filling of the viscosimeter. Three runs agreeing within about 0.3 s should suffice. (Note: maintain the viscosimeter vertical in the waterbath!) 3. Dry the viscosimeter in the furnace. 4. Determine the viscosity of water with the same method. 5. Return the viscosimeter to the furnace.

IV、Data Recording and Analysis 1. Data recording （Thermostatic bath）

(a) Record the room temperature, atmospheric pressure and experimental temperature.

(b) Read and record the temperature of thermostatic bath (Backman thermometer) every one minute.

2. Sensitivity

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From the Figure, the sensitivity of thermostatic bath

T near the wall of bath tank= 30.0±Sensitivity of T1; T at the center of

tank=30.0±Sensitivity of T2.

3. Determination of viscosity

V、 Discussion（Attach the figures）

1. The mechanism of temperature controlling for thermostatic bath?

2. What are the major factors influencing the sensitivity of thermostatic bath? How

to increase the sensitivity?

3. What’s the role of tube B in Figure 4?

4. Discuss the major factors affecting the accuracy of viscosity determination.

5. Can we use two different viscosimeters during experiments?

41.170 39.9940.088

2

−= =

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Appendix Density, viscosity and surface tension of water

Water Ethanol

t/℃ d/(g•cm-3) η/(10-3Pa•s) γ/(mN•m-1) t/℃ d/(g•cm-3)

0

5

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

40

50

60

0.99987

0.99999

0.99973

0.99963

0.99952

0.99940

0.99927

0.99913

0.99897

0.99880

0.99862

0.99843

0.99823

0.99802

0.99780

0.99756

0.99732

0.99707

0.99681

0.99654

0.99626

0.99597

0.99567

0.99224

0.98807

0.96534

1.787

1.519

1.307

1.271

1.235

1.202

1.169

1.139

1.109

1.081

1.053

1.027

1.002

0.9779

0.9548

0.9325

0.9111

0.8904

0.8705

0.8513

0.8327

0.8148

0.7975

0.6529

0.5468

0.3147

75.64

74.92

74.22

74.07

73.93

73.78

73.64

73.49

73.34

73.19

73.05

72.90

72.75

72.59

72.44

72.28

72.13

71.97

71.82

71.66

71.50

71.35

71.18

69.56

67.91

60.75

0

5

10

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

0.80625

0.79872

0.79788

0.79451

0.79367

0.79283

0.79198

0.79114

0.79029

0.78945

0.7886

0.78775

0.78691

0.78606

0.78522

0.78437

0.78352

0.78267

0.78182

0.78097

0.78012

0.77927

0.77841

0.77756

0.77671

0.77585

0.775

0.77414

0.77329

10

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Experiments 3 Heat of Combustion

I、Experimental objectives In this experiment, you will measure the standard enthalpy of combustion of

benzoic acid and use its known heat of combustion to determine the heat capacity of a bomb calorimeter. Once the calorimeter has been calibrated, the enthalpy of combustion will be measured for an unknown sample, naphthalene, and compared to the literature value for this compound. Specific Aims • The purpose of this experiment is to learn to use a bomb calorimeter, and to understand the data that is measured with this instrument. • A standard sample, benzoic acid, with a known heat of combustion will be used to calibrate your calculations – this will determine the heat capacity of the calorimeter. • Once this is known, the heat of combustion will be determined for an unknown sample, naphthalene. • Compare your results to literature values for the heat of combustion of sucrose. • Prepare long lab report. II、Background and Theory

In your Physical Chemistry coursework you have learned that the enthalpies of reactions can aid in predicting the likelihood of a chemical reaction occurring. In this lab, you will use an instrument called a “bomb calorimeter” to measure the heat evolved during the combustion of a sample at a constant volume. Calorimetry is an integral category of physical and analytical chemical techniques, and is especially important to the study of fuels and food chemistry – yes, those “calories” listed on your candy bar wrapper are measured by cooking the candy bar in a calorimeter.

Figure 1 The bomb calorimeter.

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The bomb calorimeter is shown schematically in Figure 1. The calorimeter consists of a metal reaction chamber that is immersed in a water bath with a known volume of water. The metal reaction chamber, or “bomb cell”, maintains a constant volume and allows the heat generated in its interior to be transferred efficiently to the surrounding bath. Inside this chamber, the sample is ignited by passing electrical current through a “fuse” wire. In the combustion process, some, but not all, of the fuse wire is also consumed. The interior of the reaction chamber is pressurized with oxygen to ensure efficient combustion of the material of interest. The water bath is insulated from the outside environment to prevent transfer of heat beyond the water bath.

Therefore the bomb calorimeter is an adiabatic system. From the First Law of Thermodynamics, we know that the change in internal energy (ΔU) in a system is given by the sum of the work done on the system (w) and the energy transferred to the system as heat (q).

ΔU = q +w (1)

For example, if 12 kJ of work is done on a system in the form of mechanical compression, and 6 kJ of energy escapes from the system into the surrounding environment (not a closed system), then the change in internal energy ΔU is 12 kJ – 6 kJ = 6 kJ. The bomb calorimeter is a unique instrument because it provides a closed system (or nearly so for our purposes), which does not allow heat to escape into the surrounding environment (q = 0). In addition, the interior of the bomb is very rigid and able to withstand large expansion pressures (even explosions, hence the “bomb” part of its name) without changing its volume (dV = 0). Upon ignition, the heat released by combustion of the sample is equilibrated through the walls of the bomb cell into the surrounding water bath where a temperature increase is recorded as a function of time. The temperature increase of the system is proportional to the heat of combustion of the sample, and they are related through a constant of proportionality. For the chemical reaction occurring inside the bomb cell (constant volume), the change in internal energy is equal to the product of the heat capacity of the sample (CV) with the change in temperature (dT) inside the bomb cell:

ΔU = CV •ΔT (2)

However, in this experiment, the temperature change is measured in the water bath, and the observed temperature increase must then be related to the heat released inside the bomb cell. Therefore, we must determine the heat capacity of the calorimeter (Ccal) by combusting a sample with a known mass and heat of combustion. This is a calibration procedure that will determine the accuracy of your measured heat of combustion for an unknown sample in the second part of this experiment. Ccal is defined as:

C st st wirecal

H m e

T

• +=

∆ (3)

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where Hst is the known heat of combustion of the standard sample (in calories per gram), mst is the carefully measured mass of the standard sample (in grams), ewire is the heat of combustion of the fuse wire (in calories), and ΔT is the measured change in temperature (in degrees C).

After ignition, a typical plot of water bath temperature as a function of time is shown in Figure 2. Just before ignition, the recorded temperature is designated Tinitial, and the temperature at the time when the temperature stops increasing is designated Tfinal. To compensate for any change in temperature that was occurring independent of the combustion, we define the rates of temperature change over the 5 minutes before ignition and the 5 minutes after the temperature stopped changing as r1 and r2, respectively. Finally, we define the time required for the temperature to reach 60% of its maximal change as t1, and the time between the 60% increase and full increase as t2. These variables are all labeled for clarity on Figure 2. From the measurement of these six variables, the adjusted temperature rise can be calculated as:

Figure 2 Typical plot of water bath temperature as a function of time.

ΔT =Tfinal -Tinitial - (r1 • t1)- (r2 • t2) (4)

Once Ccal is determined with a standard sample (benzoic acid), the heat of combustion can be determined for an unknown sample (naphthalene) from:

cal wireT C e

Um

∆ • −∆ = (5)

where Ccal is the heat capacity of the calorimeter determined in the first part of this

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experiment and m is now the measured mass of the unknown sample (naphthalene).

III、Apparatus The apparatus used to measure your heats of combustion is the bomb calorimeter

described above. An oxygen tank is supplied to allow pressurization of the bomb cell. The temperature will be read off periodically and the temperatures are recorded in your lab notebook. A pellet press is provided to prepare a solid pellet of your samples before combustion in the calorimeter. The TA will demonstrate the correct usage of the pellet press. An analytical balance is used to measure the mass of the pellets to be analyzed, and a ruler is used to measure the amount of fuse wire before and after combustion.

IV、Procedure

Preparing the sample and charging the oxygen bomb (1) The benzoic acid comes in pre-made pellets, simply choose one and be sure to

record its mass. The naphthalene will need to be prepared using the pellet press. See a TA for hints on operating the press.

(2) Weigh the 20 cm cotton wire and 10 cm fuse wire. Winding cotton wire and fuse wire together. Weigh tem together again.

(2) Attach the fuse to the bomb: Set the bomb head on the support stand and fasten a 10 cm length of fuse wire between the two electrodes. Insert the ends of the wires into the eyelet at the end of each electrode stem and push the cap downward to pinch the wire into place. Place the fuel capsule with its weighed sample in the electrode loop and bend the wire downward toward the surface of the charge. It is not necessary to submerge the wire in a powdered sample. In fact, better combustion will usually be obtained if the loop of the fuse is set slightly above the surface. When using pelleted samples, bend the wire so that the loop bears against the top of the pellet firmly enough to keep it from sliding against the side of the capsule. It is also good practice to tilt the capsule slightly to one side so that the flame emerging from it will not impinge directly on the tip of the straight electrode. (3) Close the bomb: Care must be taken not to disturb the sample when moving the bomb head from the support stand to the bomb cylinder. Check the sealing ring to make sure it is in good condition and moisten it with a bit of water so that it will slide freely into the cylinder. For easy insertion, push the head straight down without twisting and leave the gas release valve open during this operation. Set the screw cap on the cylinder and turn it down firmly by hand to a solid stop. (4) Fill the bomb: The oxygen filling connection should already be attached to the oxygen tank. The pressure connection to the bomb is made with a slip connector on the oxygen hose which slides over the gas inlet fitting on the bomb head. Slide the connector onto the inlet valve body and push it down as far as it will go. Close the outlet valve on the bomb head; then open the oxygen tank valve no more than

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one-quarter turn. Open the filling connection control valve slowly and watch the gauge as the bomb pressure rises to the desired filling pressure (usually 10 atm., never more than 30 atm.), then close the control valve. Release the residual pressure in the filling hose by pushing downward on the lever attached to the relief valve. The gauge on the oxygen cylinder should now return to zero.

Operating the Calorimeter (1) Fill the calorimeter bucket with 2000(+/- .5) mL of water every time you do a run. (2) Set the bucket in the calorimeter (3) Set the bomb in the calorimeter bucket: Attach the lifting handle to the two holes

in the side of the screw cap and lower the bomb into the water with its feet spanning the circular upraised guides in the bottom of the bucket. Be very careful with the bomb so as not to disturb the sample. Remove the handle and shake any drops of water back into the bucket; then push the two ignition lead wires into the terminal sockets on the bomb head (the other end of the ignition wires should be attached to the ignition unit, one wire attached to the 10 cm lead and the other to the middle (ground), be careful not to remove any water from the bucket with your fingers.

(4) Set the cover on the jacket with the thermometer facing toward the front. Turn the stirrer by hand to be sure that it turns freely; then slip the drive belt onto the pulleys and start the motor.

(5) Turn on the paperless recorder. Push the “start” button to start record temperature. (6) Let the stirrer run for 5 minutes to reach equilibrium before starting a measured

run. (7) Stand back from the calorimeter and fire the bomb (be sure ignition unit is

plugged in!) by pressing the ignition button and holding it down until the indicator light goes out. Normally the light will only glow for about 20 second but release the button within 5 seconds regardless of the light. Continue to stand clear for 30 seconds after firing.

(8) The bucket temperature will start to rise within 20 seconds after firing. This rise will be rapid during the first few minutes; then it will become slower as the temperature approaches a stable maximum. If no temperature rise is observed in 1 min, you failed the ignition. Then you need to reload the sample again.

(9) Initially temperature increase with time. Then it achieves a highest value before it drops with time. Record the temperature for at least 7 min after reaching highest temperature. Stop the paperless recorder. Save your data in the computer ortherwise your data will be overwritten by new data.

(10) Remember to repeat the experiment with naphthalene after your first run with benzoic acid.

Cleaning Up (1) After the last temperature reading, stop the motor, remove the belt and lift the

16

cover from the calorimeter. Wipe the thermometer bulb and stirrer with a clean cloth and set the cover on the support stand. Lift the bomb out of the bucket; remove the ignition leads and wipe the bomb with a clean towel. (2) Open the knurled knob on the bomb head to release the gas pressure before attempting to remove the cap. This release should proceed slowly over a period of not less than one minute to avoid losses. After all pressure has been released, unscrew the cap; lift the head out of the cylinder and place it on the support stand. Examine the interior of the bomb for soot or other evidence of incomplete combustion. If such evidence is found, the test will have to be discarded. (3) Remove all unburned pieces of fuse wire from the bomb electrodes; straighten them and measure their combined length in centimeters. Subtract this length from the initial length of 10 cm to obtain the net amount of wire burned. (4) Remember to repeat the experiment with naphthalene after your first run with benzoic acid.

V、Data Analysis

Plot your recorded temperatures as a function of time. The plot should look similar to Figure 2 above. Use a non-linear regression in Excel to fit the data through the region from the ignition point until the temperature stops rising. From this fit you can interpolate to determine the time when the temperature has changed by 60%, which will allow you to determine t1 and t2. The rates of change before ignition and after plateau, r1 and r2, can be determined from a linear fit to the data points in these two regions. For your calculations, the known value of the heat of combustion of benzoic acid is 6318 calories/gram, and the heat generated from the fuse wire is 2.3 cal/cm.

VI、Discussion Questions 1. If your measured heat of combustion for sucrose is not identical to the literature

value, what are some of the possible reasons for this discrepancy (sources of error)? In fact, we have omitted some of the details in performing a “careful” calorimetric experiment that would improve your accuracy. What are some of the procedures that could have been included in this lab to improve your measured value accuracy?

2. Is the rate of temperature change after ignition in the bomb calorimeter the same or different for the combustion of benzoic acid versus sucrose and why?

3. In your data analysis usage of equation 4, explain why you need to know the rate of temperature change before ignition and after the temperature plateau (in other words, what is the purpose of the “- r1t1 - r2t2” part)?

4. Compare the heat of combustion of benzoic acid (provided below) to that measured in this experiment for sucrose. What molecular information does this

17

provide? If you wanted to develop a machine that ran on solid fuel, would it be more advantageous to use benzoic acid or sucrose as your fuel source? Justify your answer from a thermodynamic perspective.

5. In the first sentence of this lab manual chapter we mention enthalpies of reactions, and we proceed through the chapter as if enthalpies are equivalent to the ΔU that we measure for our unknown sample. In fact, ΔU is not quite equal to ΔH. What is the relationship between these quantities (give an equation)? Then describe, in words, the difference between a change in internal energy and a change in enthalpy.

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Experiments 4 Vapor Pressure of a Pure Liquid

I、Experimental objectives In this investigation we will examine the relationship between vapor pressure and

temperature by considering the properties of water, at various temperatures and within a vacuum apparatus. II、Background and Theory

The vapor pressure of a substance is the equilibrium gas phase pressure of the substance that is established when its rate of evaporation from the condensed phase becomes equal to its rate of condensation from the gas phase.

A(l) ↔ A(g) The vapor pressures of pure liquids and solutions are very important and useful physical property data. The measurement of the variation of vapor pressure with temperature is a very common method for determining the molar enthalpy of vaporization (ΔvapH(m)) for liquid systems. Comparison of the vapor pressure of a pure solvent with the vapor pressure of the solvent above a solution allows the activity of the solvent to be calculated

The Clausius- Claperyon equation (eq.1) is commonly used to obtain ΔvapH(m) from vapor pressure data.

vap (m)

2

Hdp

dT RT

∆= (1)

This equation assumes that the vapor phase is ideal and that the molar volume of the liquid phase is much smaller than the molar volume of the gas phase. Most vapor pressure data fits well into these assumptions. Equation 1 can be integrated once an assumption is made aboutΔvapH(m). If ΔvapH(m) is taken to be constant, then the indefinite integral of equation 1 gives:

vap (m)lnH

p CRT

−∆= + (2)

The enthalpy of vaporization can be determined from the gradient of the plot of ln p versus 1/T. III、Experimental Procedure

The following apparatus can be used to determine the vapor pressure of a liquid at various temperatures. The liquid sample (water) is introduced into the distillation flask though feeding 8 and seal with a plug (It was ready). (1) Turn on the manometer (14 in Figure 1) allowing preheating for 2 min. Set the zero point (Make sure the system is exposed to air and the zero reading means the pressure difference between system and air is zero).

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Figure 1. Apparatus 1-Heater；2- Liquid riser；3-Equilibrium chamber；4- Thermometer；5- Sampling tube for liquid；6- Sampling tube for gas phase；7- Condenser；8-Feeding；9- Magnetic bar；10- Magnetic stirrer；11-Power source；12-Buffer；13、16- Cork；14- Manometer；15- Vacuum pump

(2) Leak test. Vacuum the system to around -45 kPa and wait for 10 min. If the

change of reading is less than 0.25 kPa, the system can be considered to be leak free. Otherwise, consult with the tutor or TA.

(3)Switch on the cooling water for the condenser (7). Turn the power source to zero volt and rate of magnetic stirrer to the minimum, then switch on the power.

(4) Close cork 16 and turn on the vacuum pump. Open cork 13 and vacuum the system to around -42~-43 kPa, close cork 13.

(5) Tune the stirrer to a suitable stirring rate (Do not stir too vigorously). Adjust the position of stirrer to achieve stable and uniform stirring.

(6)Adjust the output voltage of power source (There is a black mark for proper output volt). Water is heating up.

(7)After dozens of minute, water boils. Further adjust the output voltage to get a condensation rate in condenser 7 of 6~10 drops/min. When the temperature (Thermometer 4) maintain stable, record the temperature and the corresponding vacuum pressure (manometer 14).

(8) Increase the pressure in the system by 3-5 mmHg (around 6 kPa) by allowing a small amount of air to enter through tap B slowly. As the pressure in the system increases, boiling will stop. It is now necessary to increase the heating to start the boiling again. Record the new boiling point and the corresponding pressure. To fulfill the above purpose, fill little air to the system by slowly open cork 13, increasing the system pressure by about 6.0 kPa . Repeat step (7).

(9) Repeat step (8) until the system pressure is close to atmospheric pressure. (around 6 experimental points).

(10) After experiment, tune the output voltage to zero. Tune stirring rate to the minimum. Switch off the power. Turn off cooling water. Clean up your desk.

Liquid level

Water in

Water in

20

IV、Data Analysis

The pressure reading of the manomer Pm is a measure of the difference between the atmospheric pressure Pa and the pressure inside the flask P.

P = Pa - Pm The atmospheric pressure is read directly on a Fortin Barometer, and corrected to

273.15 K.

Plot ln P versus 1/T. Apply the linear least squares method to obtain the gradient and evaluate the uncertainty.

Calculate the enthalpy of vaporization of water.

Determine from your graph the normal boiling point of water (the temperature at which the vapor pressure is 101.3 kPa). V、Discussion Atmospheric pressure is read from a barometer. How to correct to 273.15 K? Appendix The Fortin barometer is simply a single-arm, closed-tube mercury manometer equipped with a precise metal scale (usually brass). The bottom of the measuring arm of the barometer dips into a mercury reservoir that is in contact with the atmosphere. The mercury level in this reservoir can be adjusted by means of a knurled screw that presses against a movable plate (see Fig. 2 ). When the meniscus in the reservoir just touches the tip of a pointed indicator, the zero level is properly established and the pressure can be determined from the position of the meniscus in the measuring arm. Both the front and back reference levels on a sliding vernier are simultaneously lined up with the top of this meniscus in order to eliminate parallax error, and the height of the arm can be read to the nearest tenth of a millimeter using the vernier scale. A thermometer should be mounted on or near the barometer, since the temperature must be known in order to make a correction for thermal expansion. The metal scale on

most barometers is made of brass (linear coefficient of thermal expansion 1.84 × 10-5

K-1 ) and is usually graduated so as to read correctly at 0°C. A table of barometer corrections over the range 16 to 30°C and 720 to 800 mm is given in Appendix. High-precision work also requires corrections for the effect of gravity, residual gas pressure in the closed arm, and errors in the zero position of the scale. Since these usually amount to only a few tenths of a millimeter, they will not be discussed here.

21

Figure 2. Detailed sketch of a Fortin barometer. Uncorrected reading shown is 79.02 cm.

P = Pobs(mm,T) – Δ (Δ denotes the values in the above table).

22

Experiments 5 Binary Liquid–Vapor Phase Diagram

I、Experimental objectives (1) To construct a liquid/vapor temperature-composition (T-X) phase diagram for a binary mixture of cyclohexane and ethanol. (2) Understand the structure, mechanism, application of Abbe refractometer for the determination of solution composition. II、Background and Theory

Binary mixtures of two volatile liquids exhibit a range of boiling behavior from ideal, with a simple continuous change in boiling point with composition, to nonideal, showing the presence of an azeotrope and either a maximum or minimum boiling point. In this experiment, the properties of a binary mixture of cyclohexane and methanol will be investigated by studying the change in boiling point with composition. You will construct a boiling point diagram and identify any nonideal behavior in the system.

For ideal mixtures of liquids, the composition of the vapor phase is always richer in the component with the higher vapor pressure. According to Raoult's Law, the vapor pressure of component A is given by

pA = xA pA* (1) where xA is the mole fraction of A in solution and pA ∗ is the vapor pressure of pure A. Actual vapor pressures can be greater or less than those predicted by Raoult's Law, indicating negative and positive deviations from ideality (Figure 1). These deviations from Raoult’s law are often ascribed to differences between “heterogeneous” molecular attractions (A – – – B) and “homogeneous” attractions ( A – – – A and B – – – B ). Thus the existence of a positive deviation implies that homogeneous attractions are stronger than heterogeneous attractions, and a negative deviation implies the reverse. This interpretation is consistent with the fact that positive deviations are usually associated with positive heats of mixing and volume expansions on mixing, while negative deviations are usually associated with negative heats and volume contractions. In some cases, the deviations are large enough to produce maxima (Figure 2 (a)) or minima (Figure 2 (b)) in the boiling point and vapor pressure curves. At the maximum or minimum, the compositions of the liquid and vapor phases are the same, but the system is not a pure substance. This results in an azeotrope, a mixture which boils with constant composition. A distillation will not be able to completely separate the two components. Either the distillate or the residue will eventually reach the azeotropic composition and no further separation will occur.

23

Figure 1. Vapor compositions during distillation of a system with small positive deviations from Raoult’s law.

Figure 2. Schematic vapor-pressure and boiling-point diagrams for systems showing (a) a strong positive deviation and (b) a strong negative deviation from Raoult’s law.

Simple distillation can be used to obtain a boiling point diagram so long as some method exists to analyze both the distillate and the residue. In practice, several mixtures of differing composition of the two liquids are distilled and samples of both the distillate and residue are taken. The temperature (boiling point) of each distillation

24

is recorded and the composition of both the distillate and residue is determined. The analysis method should provide a measurement which changes significantly and continuously over the entire range of concentration, from one pure liquid to the other pure liquid. In many cases, the refractive index provides a suitable measure of concentration. A calibration curve must be obtained using known mixtures. The refractive index of an unknown mixture is then measured and the composition obtained using the calibration curve. III、Experimental Reflux apparatus

Figure 3. Inclined ebulliometer

1-Heater；2- Liquid riser；3-Equilibrium chamber；4- Thermometer；5- Sampling tube for liquid；6- Sampling tube for gas phase；7- Condenser；8-Feeding；9- Magnetic bar；10- Magnetic stirrer；11-Power source

You will use inclined ebulliometer to establish liquid-vapor equilibrium. The recondensed vapor from the condensor drops back into the container, and some of it collects above the stockcock at port 6. We use a pipet filler to draw a small quantity of liquid (~1 mL) into the liquid sampler, and collect the sample from port 5. We will use a thermometer placed in the inclined ebulliometer as shown to record the temperature of the vapor phase. For accurate temperature readings, it is important to have good boiling. Control this using the transformer with proper voltage.

Refractometer (See introduction attached!)

You will use an Abbe refractometer to measure the refractive index, n of the samples. Good technique is essential to get reliable results in this experiment. This instrument requires precise temperature control. It is also very important not to scratch the glass surfaces. Do not touch pipet tips to the glass, and wipe it only with optical quality tissues, not paper towel! The refractive index is the ratio of the speed

25

of light in vacuum compared to the speed of light in the sample (the speed of light is reduced in matter). We use this method for the cyclohexane-ethanol system because there is a large difference in the refractive index of cyclohexane and ethanol, so the composition of mixtures can be easily and quickly determined by this method. To do this, you must prepare a calibration curve: You can plot the calibration curve with the data listed in Table 1. However, it is the calibration curve at 15 oC, and therefore you need to further calibrate the difference in refractive index between 15 oC and your experimental temperature (Room temperature) with pure cyclohexane or ethanol. As room temperature varies with time, you need to carry out this calibration every 30 min.

Table 1 Refractive index of cyclohexane-ethanol solutions at 15 oC (Xc denotes the molar concentration of cyclohexane)

XC 0.00 0.054 0.0929 0.1726 0.2820 0.3667

n 1.3630 1.3681 1.3718 1.3788 1.3870 1.3930

XC 0.4639 0.5678 0.6683 0.6736 0.8742 1.000

n 1.4002 1.4060 1.4116 1.4126 1.4223 1.4282

IV、 Procedure (1) Calibration of refractometer

Use pure cyclohexane or ethanol to calibrate the refractometer. The calibration value (the difference of refractive index between 15 oC and room temperature) can be expressed as Δn(I+T) = n(refractive index of pure cyclohexane or ethanol at room temperature) – (refractive index of pure cyclohexane or ethanol at 15 oC). As room temperature varies with time, you need to carry out this calibration every 30 min during experiment. Note: I means the instrument error, while T denotes the error caused by temperature.

(2) Calibration of thermometer Use pure cyclohexane or ethanol to calibrate the thermometer with their boiling

points under atmospheric pressure. You will 14 cyclohexane-ethanol solutions to construct the phase diagram. They will be investigated in 14 inclined ebulliometers respectively. Therefore, you need to calibrate 14 thermometers with pure cyclohexane or ethanol. Determine the boiling points of cyclohexane or ethanol under atmospheric pressure over 14 inclined ebulliometers, the calibration value of each thermometer can be calculated asΔT = T (Measured) – T(Calculated). T(Calculated) is derived from Antoine equation with the experimental pressure (atmospheric pressure). (3) Prepare 14 cyclohexane-ethanol solutions with different concentrations and their

corresponding boiling points roughly vary from boiling point of pure ethanol → 76 → 74→ 72→ 70→ 67→ 65→ 67→ 70→ 72→ 74→ 76→ 78→ boiling point of pure cyclohexane.

(4) Introduce these 14 solutions into inclined ebulliometers (marked with 1 to 14). You can fill the solution from port 8 in Figure 3 or port 7 (the condenser) to

26

achieve the liquid lever as shown in Figure 3. (5) Turn on the cooling water of the condenser. (6) Tune the stirrer to a suitable stirring rate (Do not stir too vigorously). Adjust the

position of stirrer to achieve stable and uniform stirring. (7) Turn the transformer to zero volt, then switch on the power. Adjust the output

voltage of transformer (There is a black mark for proper output volt). Boiler is heating up. Carefully controlling the heating (output volt) to give a steady drip of condensation off the tip of the condenser when boiling (6 drips/min). Allow several minutes after boiling for the apparatus to equilibrate. Equilibrium is reached when the temperature is approximately constant. However, in practice the temperature readings may move up and down by a few tenths of a degree in a cycle. Try to record the highest temperature reached once this cycle is established for each mixture.

(8) Measure the temperature, record it in your notebook, and take samples of the liquid phase and the vapor phase in clean, labelled containers.

(9) Measure the n value of liquid phase and the vapor phase using the refractometer. (10) Repeat steps 7-9, measure the n value of liquid phase and the vapor phase using

the same refractometer. V、Data Recording and Analysis 1. Data recording Record the n values of liquid phase (nl) and the vapor phase (ng) from different refractometers. Meanwhile record the corresponding Δn(I+T) and ΔT values. 2. Data analysis (1)Plot the calibration curve with n as x-axis and Xc as y-axis. Fit the curve.

(2) Calculate 15

i,l or g

o C

n according to 15

i,l or g

o C

n = RT

i,measurede for l or gn - Δn(I+T).

(3) Get the Ti = Ti (Measured) –ΔTi

(4) According to your calibration curve and 15

i,l or g

o C

n calculate the concentration of cyclohexane (Xc, l) in the liquid phase and (Xc, g) in the gasephase. (5) Make a graph of Ti vs Xc, l and Ti vs Xc, g, but record them on the same graph, as is common in textbooks. This is more difficult than most graphs you have prepared, in that there are two sets of values to be used on the x-axis (Xc, l and Xc, g) and only one set of data to be used on the y-axis (T). To do this in Excel: • Begin by simply clicking in a cell where you wish to create a graph (don’t select the data first). • Click on the graph icon on the menu bar as usual, and select XY (Scatter), click the example graph showing data markers without lines, and click the Next button. • In the next dialog, click the Series tab, then the Add button. • Click inside the X Values box, then select your Xc, l data. • Click inside the Y Values box, then select your T i data. • Now click the Add button again, and create a second data series with Xc, g and Ti in the same way.

Because of the scatter in the data, it is usually best to draw the best line through the data points by hand on the printout, rather than add lines in Excel.

Find the values of T and Xc at the azeotrope. Compare these to the literature

27

(64.6 oC, Xc=0.56). (CRC Handbook) VI、Discussion 1. What type of deviation from ideality (if any) does this system show? Rationalize this behavior in terms of the intermolecular forces expected for this system. 2. How could one separate the components in an azeotrope? One of the most important azeotropes is that formed in the ethanol-water system. Find the composition of this azeotrope (use the literature) and also find a method for "breaking" this azeotrope. It must be possible since we can buy 100% ethanol and 100% water! 3. Use the literature to find a binary mixture whose azeotropic mole fraction is roughly 0.50. 4. A similar experiment can be conducted to obtain a solid/liquid temperature-composition phase diagram. For solid/liquid systems, eutectics may form rather than azeotropes as is the case for liquid/vapor systems. Discuss the similarity between a eutectic and an azeotrope. Appendix REFRACTOMETERS

The term refractometer is applied principally to instruments for determining the index of refraction of a liquid, although instruments also exist for determining the index of refraction of a solid. The index of refraction n for a liquid or an isotropic solid is the ratio of the phase velocity of light in a vacuum to that in the medium. It can be defined relative to a plane surface of the medium exposed to vacuum as shown in Fig. S1 a; it is the ratio of the sine of the angle øv a ray of light makes with a normal to the surface in vacuum to the sine of the corresponding øm in the medium:

It is common practice to refer the index of refraction to air (at 1 atm) rather than

to vacuum for reasons of convenience; the index referred to vacuum can be obtained from that referred to air by multiplying the latter by the index of refraction of air referred to vacuum, which is 1.00027.

The index of refraction is a function of both wavelength and temperature. Usually the temperature is specified to be 20 or 25°C. The former is more in accord with past practice, but the latter is somewhat easier to maintain with a constant-temperature bath under ordinary laboratory conditions. The wavelength is usually specified to be that of the yellow sodium D line (a doublet, 589.0 and 589.6 nm), and the index is given the symbol nD.

28

Figure S1 Reflection and refraction at an interface: ( a ) øm < øcrit ; ( b ) øm = øcrit ; ( c ) øm1= øm2 > øcrit.

Most refractometers operate on the concept of the critical angle øcrit; this is the angle øm for which øv (or øair ) is exactly 90° (see Fig. S1 b ). A ray in the medium with any greater angle øm1 will be totally reflected at an equal angle øm2 as shown in Fig. S1 c. The index of refraction is given in terms of the critical angle by

where cl is the phase velocity of light in the liquid. In a refractometer the critical angle to be measured is that inside a glass prism in contact with the liquid, since the index of refraction of the glass is higher than that of the liquid. Therefore

where ng is the index of refraction of the prism glass and øg is the critical angle in the glass. By trigonometry it can be shown that the index of refraction of the liquid is given by

where γ is the prism angle (angle between the two transmitting faces) and δ is the angle of the critical ray in air with respect to the normal to the glass–air prism face (see Fig. 10 ).

29

Figure S2 Essential features of an immersion refractometer. The behavior of the critical ray is shown in detail, since this represents the basic principle of almost all refractometers.

The most precise type of refractometer is the immersion refractometer. It contains a prism fixed at the end of an optical tube containing an objective lens, an engraved scale reticule, and an eyepiece. It also contains an Amici compensating prism (see below). In use, the instrument is dipped into a beaker of the liquid clamped in a water bath for temperature control. A mirror in the bath or below it reflects light into the bottom of the beaker at the requisite angle and with some angular divergence. The field of view is divided into an illuminated area and a dark area, as shown in Fig. S2 ; the scale reading that corresponds to the boundary-line (critical-ray) position is read and referred to a table to obtain the refractive index. This instrument is capable of measuring the refractive index to ±0.00003. Its scale normally covers only a small range; a set containing several refractometers or detachable prisms is required to cover the ordinary range of refractive indexes for liquids (1.3 to 1.8).

30

Figure S3. Schematic diagram of an Abbe refractometer. The most commonly used form of refractometer is the Abbe refractometer, shown

schematically in Fig. S3 . This differs from the immersion refractometer in two important respects. First, instead of dipping into the liquid, the refractometer contains only a few drops of the liquid held by capillary action in a thin space between the refracting prism and an illuminating prism. Second, instead of reading the position of the critical-ray boundary on a scale, one adjusts this boundary so that it is at the intersection of a pair of cross-hairs by rotating the refracting prism until the telescope axis makes the required angle d with the normal to the air interface of the prism. The index of refraction is then read directly from a scale associated with the prism

31

rotation. The Abbe refractometer commonly contains two Amici compensating prisms,

geared so as to rotate in opposite directions. An Amici prism is a composite prism of two different kinds of glass, designed to produce a considerable amount of dispersion but to produce no angular deviation of light corresponding to the sodium D line. By use of two counterrotating Amici prisms, the net dispersion can be varied from zero to some maximum value in either direction. The purpose of incorporating the Amici prisms is to compensate for the dispersion of the sample so as to produce the same result with white light that would be obtained if a sodium arc were used for illumination. This is achieved by rotating the prisms until the colored fringe disappears from the field of view and the boundary between light and dark fields becomes sharp. It should be borne in mind that the dispersion of a sample is not always exactly compensated, for dispersion is not exactly defined by a single parameter for all substances. The most precise results are obtained with illumination from a sodium arc, the Amici prisms being set at zero dispersion.

The Abbe refractometer is less precise (±0.0001) than the immersion refractometer and requires somewhat less exact temperature control (±0.2°C). For this purpose water from a thermostat bath is circulated through the prism housings by means of a circulating pump. Alternatively, tap water is brought to the temperature of a thermostat bath by flow through a long coil of copper tubing immersed in the bath and is then passed once through the refractometer and down the drain.

The procedure for the use of an Abbe refractometer is as follows: 1. If a sodium arc is being used, check to see that it is operating properly. The sodium arc should be treated carefully and should be turned on and off as infrequently as possible. It should be turned on at least 30 min before use. 2. Check to see that the temperature is at the required value by reading the thermometer attached to the prism housing. 3. Open the prism (rotate the illuminating prism with respect to the stationary refracting prism). Wipe both prism surfaces gently with a fresh swab of cotton wool dampened with acetone. Caution: The prisms must be treated with great care, since scratches will decrease the sharpness of the boundary and permanently reduce the accuracy of the instrument. 4. When the prism surfaces are clean and dry, introduce the sample. In some models the refracting prism surface is horizontal and faces upward. In this case place a few drops of the liquid sample on the refracting prism and move the illuminating prism to the closed position. Other models have a prism configuration like that shown in Fig. S3. In that case bring the prisms into the closed position first and then squirt a small amount of sample into the filling hole. 5. Rotate the prism until the boundary between the light and dark fields appears in the field of view. If necessary, adjust the light source or the mirror to obtain the best illumination. 6. If necessary, rotate the Amici prisms to eliminate the color fringe and sharpen the boundary. 7. Make any necessary fine adjustment to bring the boundary between the light and

32

dark fields into coincidence with the intersection of the cross-hairs. 8. Turn on the lamp (if any) that illuminates the scale, and read off the value of the refractive index. 9. Open the prism and wipe it gently with a clean swab of cotton wool, dampened with acetone. When it is dry, close the prism.

If the sample is very volatile, it may evaporate before the procedure is completed. In this case or in the event of drift, add more sample.

One of the worst enemies of the refractometer is dust. A gritty particle may scratch the prisms badly enough to require their replacement. The cotton wool used for wiping the prisms should be kept in a covered jar. Each swab of cotton wool should be used only once and then discarded. Do not rub the prisms with cotton wool, and do not attempt to wipe them dry; if streaks are left when the acetone evaporates, wipe again with a fresh swab dampened with fresh solvent. Do not use lens tissue on the prism surfaces. Finally, the instrument should be protected with its dust cover when not in use, and the table on which the instrument is used should be kept scrupulously clean.

For adjustment of the scale, a small “test piece” (a rectangular block of glass of accurately known index of refraction) is usually provided with the refractometer. The illuminating prism is swung out and the surface of both the refracting prism and the test piece are carefully cleaned. They are then carefully brushed with a clean camel’s-hair brush (which is normally kept in a stoppered container) and inspected at grazing incidence to detect particles of dust or grit. A very small drop (ca. 1 mm 3 ) of a liquid (such as 1-bromonaphthalene or methylene iodide) that has a higher refractive index than the refracting prism is placed on the test piece, and the latter is then carefully pressed against the refracting prism and carefully moved around to spread the liquid. The reading of refractive index is made in the usual way. If it is not in agreement with the true value of the test piece, an adjustment of the instrument scale is made or a correction is calculated.

The procedure for determining the index of refraction of an isotropic solid sample is similar; like the test piece, it must have at least one highly polished plane face.

The refractometer is essentially an analytical instrument, used to determine the composition of binary mixtures (as in Exp. 14) or to check the purity of compounds. Its most common industrial application is in the food and confectionery industries, where it is used in “saccharimetry”—the determination of the concentration of sugar in syrup. Many commercially available refractometers have two scales: one calibrated directly in refractive index, the other in percent sucrose at 20°C.

The refractive index of a compound is a property of some significance in regard to molecular constitution. The molar refraction, , is a constitutive and additive property; for a given compound it may be approximated by the sum of contributions of individual atoms, double bonds, aromatic rings, and other structural features.

33

Experiments 6 Binary Alloy Phase Diagram

I、Experimental objectives The objective of this experiment is to obtain the cooling curves for several bismuth-tin alloys and use this information in conjunction with the lead-thin phase diagram to determine the chemical composition of each alloy. Experimentally determine the lead-tin (Bi-Sn) equilibrium phase diagram to demonstrate phase equilibrium in a binary system. II、Background and Theory

Binary alloys are metals comprised of two or more elemental metals. There are three main forms of binary alloys: solid solution, multi-phase mixture, and compound. A solid solution is a binary alloy in which the bonding strength between metals A and B is between that of A-A and B-B. This results in a random positioning of atoms throughout the microstructure of the alloy.

A multi-phase mixture results when the A-A and B-B bonds are stronger than the A-B bonds, which results in metals A and B forming clumps of contiguous atoms, minimizing the rate at which A-B bonding occurs.

A compound is when the desire for A to bond to B is greater than A-A and B-B, which results in maximizing the rate at which A-B bonds occur. This means that a compound is formed, characterized by A bonding with B.

In a solution where any amount of metal A can dissolve into metal B such that the atoms of metal A are positioned in the B lattice at random, and vice versa, the diagram shown in Figure 1: (Cu-Ni Phase Diagram).

Figure 1 Cu-Ni Phase Diagram.

34

Any weight percentage of copper or nickel can dissolve into each other, without losing the random positions in each other’s lattice. A phase diagram represents the phases that exist in a certain solution depending on the temperature and the weight percentage composition of the elements or molecules that comprise the solution. When the phase is completely solid or completely liquid, finding the temperature of each of the elements simply involves looking at the weight percentage that corresponds to the point on the graph.

If the temperature and composition rests within the α + L phase, then the tie line rule is used to determine both the weight percentage of each phase, and the weight percentage of each of the elements in each phase. For example, if the temperature is 1200° Celsius in a copper-nickel solution, and the weight percentage of nickel is 25 percent, then a tie line is drawn as shown in Figure 2:

Figure 2 Tie Line Method. The percentage composition of the liquid at 1200° Celsius and 25 percent weight composition of nickel is found using Equation 1 below:

−=

−30 25

45.45%30 19

(1)

Thus, the percentage liquid is 45.45 percent. The percentage of solid in the solution is found by subtracting the percentage liquid from 100, resulting in 54.55 percent solid.

The percent composition of copper and nickel in both the solid and the liquid solutions can be found by following the tie line over to the solidus and liquidus lines, and determining the weight percentage of nickel and copper at those points. The liquid phase of the alloy is 19 percent nickel, while the solid phase of the alloy is 30 percent nickel. The weight percentages at the solidus line represent the composition of

35

the solid phase, while the weight percentages at the liquidus line represent the composition of the liquid phase. Detail on Multiphase Mixtures

The bismuth-tin mixture that is heated and cooled in this experiment was an example of a multi-phase mixture, because the bond between the two elements was weaker than the bond between the elements and themselves. Only a limited amount of bismuth can dissolve into tin, and the vice versa. Because of the limitation in the phases that occur, a more complex phase behavior happens as the temperature and the composition changes in a multiphase alloy. Figure as: Binary Eutectic Phase Diagram shows the diagram that occurs for a multiphase mixture.

Figure 3 Binary Eutectic Phase Diagram

On the far left of the diagram in Figure 3, the α phase occurs. The maximum

amount of B that can be dissolved in a solution of A is shown at the joining of the left solidus and solvus lines. The maximum amount of A that can be dissolved in B is shown at the joining of the right solidus and solvus lines. Once these points have been passed, the rest of A and B takes the form of a lamellar structure, or a structure consisting of layers of alternating α and β phases.

As a liquid cools past the liquidus line, particles of α or β begin to form, depending on the composition of the mixture. Once the temperature drops below that of the eutectic point, and the composition of α or β is beyond that of saturation, the rest of the material solidifies in the form of a lamellar structure.

If a liquid cools exactly through the eutectic point, no α or β particles form. A pure lamellar structure forms with the complete lack of particles. Coring

As a solution cools, the composition of the particles will not remain uniform throughout. The weight percentages of the different phases change continuously with the temperature, so the outer regions of α phase particles will have a different composition of a certain element than the inner regions of α phase particles. Figure 4: How Coring Works.

36

Figure 4 How Coring Works.

Figure 4 above shows that, as the liquid cools just below the liquidus transition,

the α particles forming are a slightly lower weight percentage of B than they are after further cooling. The percentage of B slowly gets higher. Thus, the α particles forming will have a varying amount of composition of the different elements depending on how far into the middle the particles are. Constructing a Phase Diagram

As a mixture cools, the slope of the line goes through several different changes, depending on the composition of the alloy. For example, Figure 4: Cooling of a Multiphase Mixture.

Figure 5 Cooling of a Multiphase Mixture.

In Figure 5 above, as the liquid phase passes through the liquidus line, the cooling slows as the α particles form. Then, as the eutectic structure forms, the cooling stops, and the cooling curve flattens out, as the material undergoes a eutectic reaction, turning the rest of its liquid phase into a lamellar structure consisting of α and β phases.

A phase diagram can be found by looking for temperatures T1 and T2, where the slope of the cooling becomes more shallow, and where the slope flattens out completely, at several different weight percentages of A and B. Since theory predicts that bismuth and tin cannot perfectly dissolve into each other at varying percentages,

37

and that there do exist saturation points, a binary eutectic phase diagram is expected to be produced.

III、Procedure for Determining the Bismuth-Tin Phase Diagram

The following steps outline what is necessary to conduct the bismuth-tin phase diagram experiment. 1. Prepare three Sn and Bi mixtures (100g) with Bi weight percentages of 80%, 58%

and 30% using the electronic scale. In addition, weigh 100 g pure Sn and Bi respectively. Then, these five samples are placed into five Pyrex test tubes. The samples are covered with paraffin oil preventing from oxidation of Sn and Bi. Insert a small glass tube into Pyrex test tubes providing room for thermocouple. Also fill some paraffin oil to the small tube to achieve good thermal conductivity for thermocouple (It has done by the lab).

2. Set the desired temperature on the temperature controller (The left dashboard on the temperature controller which is responsible for the temperature of heating furnace). The setting temperature should be at least 50 oC higher than the melting or transition temperature of each sample. Switch on the heating furnace.

3. Place one of the Pyrex test tubes into the heating furnace and melt the sample. Insert the left thermocouple into the small glass tune in the Pyrex test tubes. During the melting, stir the melt with this small glass tube gently. After all sample is melted, Wait until the temperature increase to a temperature 50 oC higher than the sample’s melting or transition temperature (See Table 1 for each sample). Then, take out the thermocouple and transfer the test tube to the cooling furnace. Insert the right thermocouple into the small glass. Switch on the paperless recorder. Push the “Start button” start to recording. To accelerate the cooling rate, you can push the “Cooling Fan” button. During the cooling, stir the sample with the small glass in it until the small glass tube is difficult to be moved. When the temperature drops to the desired temperature as shown in Table 1 for each sample, Stop the paperless recorder. Save your data in the computer. (During the cooling, you can place another sample to the heating furnace getting ready for the next coring).

4. Repeat step 2 and 3 for other samples. Table 1 Approximate melting or transition temperature of each sample and desired cooling temperature

Sample Melting or transition temperature, oC cooling temperature, oC 100% Bi 271 230 80%Bi 210 115 30% Bi 190 115 58%Bi 135 115

100%Sn 232 200

38

IV、Data Recording and Analysis 1. Open the cooling curve in the computer; click the curve at different positions retrieving data points and print. Go to http://srdata.nist.gov/its90/download/type_k.tab converting the thermoelectric voltages to corresponding temperatures. 2. Calibrate the thermocouple with the melting point of Bi or Sn you measured and standard Bi melting point (271 oC) or Sn (232oC). 3. List the composition and its corresponding transition temperature in a table. Combine the following data (Table 2) to your table. Draw binary alloy phase diagram. Denote the meanings of points, lines and areas. Table 2 Supplementary data for your experiment Bi mass percentage, % Transition temperature, oC

5.3 225 205 60 11.6 216 179 100 21.0 202 135

V、Discussion 1.What conditions determine equilibrium in binary systems? 2.Why does the BiSn system exhibit a eutectic binary equilibrium phase diagram? 3.How do cooling rates influence the experimental phase equilibrium in the Bi-Sn system? 4.How can phase diagrams be utilized for engineering applications?

39

Experiments 7 Measurement of Ammonium

Carbamate Decomposition Pressure

I、Experimental objectives (1) The purpose of this experiment is to calculate the equilibrium constant, Kp, for a chemical reaction at several temperatures and to use these values to calculate the thermodynamic properties of the reaction. (2) Learn to use vacuum technique for experiment. II、Background and Theory In this experiment, the thermodynamic properties of the decomposition of ammonium carbamate, will be determined by measuring the equilibrium vapor pressure as a function of temperature. Ammonium carbamate decomposes to form carbon dioxide and ammonia as shown in the equation below.

NH2COONH4(s) → 2NH3(g) + CO2(g) If all the gases involved in the reaction can be treated as ideal gases, the standard equilibrium constant KΘ

can be expressed as

Where, pNH3 and pCO2 are the partial pressure of NH3 and CO2 at equilibrium at temperature of T; pΘ is the standard pressure. Assuming the total pressure of the system is p at equilibrium, then

3NH

2

3p p=

2CO

1

3p p=

Combine the above three equations, we derive

At determined temperature, the total pressure of the system keeps to constant due to equilibrium, and this pressure is also called as decomposition pressure. Hence, if we measure the decomposition pressure at certain temperature, the equilibrium constant KΘ

can be obtained according to the above equation. Equilibrium constant changes with temperature.

If the temperature varies moderately, r mH∆

can be considered as a constant. Then

3 2

2NH COp pKp p

=

2 32 1 43 3 27

p p pKp p p

= =

总 总 总

2

ln r mHd KdT RT

∆=

40

the function of KΘ versus temperature is expressed as

Measure several KΘ

at different temperatures and Plot ln K vs 1/T, we get a straight line.

r mH∆ can be calculated according to the slope.

Then r mG∆ and r mS∆ can be derived according to

III、Apparatus

Figure 1. Apparatus

ln r mHK CRT∆

= − +

lnr mG RT K∆ = −

( ) /r r rm m mS H G T∆ = ∆ −∆

41

Figure 2. Pressure gauge

IV、Procedure （1） Turn on the manometer allowing preheating for 2 min. Set the zero point

(Make sure the system is exposed to air and the zero reading means the pressure difference between system and air is zero).

（2） Connect dried pressure gauge as shown in Figure 2 with rubber pressure hose as shown in Figure 1. Close Cock 1. Turn on Cock 2 and vacuum the system. Run leak test.

（3） After leak test, turn on cock 1 exposing the system to the air. Take off the Pressure gauge and fill ammonium carbamate to the ball a. Pipette little Hg to the U tube of pressure gauge, see figure 2. (Important note: Pipetting Hg should be conducted over a china plate avoiding the losing of Hg to the environment.)

（4） Carefully connect pressure gauge with rubber pressure hose again. (Do not mix ammonium carbamate with Hg during connecting!) Immerse the pressure gauge in the water bath. Set the temperature to 25 oC. Switch on the vacuum pump. Sweep the air out of the bulb by cautiously and slowly reducing the pressure in the ballast bulb by turn off cock 1 and slowly turn on cock 2. After 2 min, turn off cock 2 and turn on cock 1 very gently introducing small amounts of air to the system until both branches of U tube have the same Hg levels. Watch the Hg levels. If they keep the same level for 5 min, record the temperature and reading of manometer.(Note: During the vacuuming, firstly cock 2 can be opened partially for 1 min. Then turn on cock 2 fully avoiding the suction of Hg.)

（5） To establish that all the air has been removed from the isoteniscope, cautiously reduce the pressure in the ballast bulb by vacuuming for 1 min again. According to step (4), record the pressure again.

（6） If the successive decomposition pressure readings are in good agreement (the difference is less than 266.65 Pa), increase the temperature by 5 oC. After several minutes, carefully admit small amounts of air from cock 1 until both branches of U tube have the same Hg levels. If they keep the same level for 5 min, record the temperature and reading of manometer. With the same method, measure the decomposition pressures of 35oC, 40oC and 45 oC.

（7） After experiment, introduce air to the system and return the pressure gauge.

V、Data recording and Analysis

42

(1) Data recording 1) Record room temperature. 2) Record the atmospheric pressure and calibrate. 3)Record the readings of manometer at different temperatures, pmeasure. (2)Analysis 1) The decomposition pressure can be calculated according to pdecom. = patmo.-pmeasure.

patmo. denotes the calibrated atmospheric pressure. pmeasure is the reading of manometer(also called △P). Compare the pdecom. with the values calculated by pdecom. = -2741.9/T +11.1448. (pdecom. with the unit of mmHg)

2) Calculate KΘand r mG∆ for different temperatures.

3) Plot ln KΘ vs 1/T (Kelvin), derive r mH∆

.

4) Calculate r mS∆ for all the temperatures.

VI、Discussion 1. Before we measure the decomposition pressure, why do we need to sweep the air

out of the sample bulb? If the air is not completely vacuumed, does it affect the measurement of KΘ?

2. How to know the equilibrium is achieved for the decomposition reaction？ If equilibrium is not achieved，does it affect the measurement?

3. Is it necessary to control the temperature accurately? How to evaluate the effect of temperature?

4. Why do we need to admit air to the system very slowly? Otherwise, what consequence can be resulted?

5. If the temperature keeps constant, after few minutes, Hg levels are not the same sometimes. Why?