In the Laboratory
Understanding the Clausius–Clapeyron Equation by Employing an Easily Adaptable Pressure Cooker Monica Galleano,* Alberto Boveris, and Susana Puntarulo Physical Chemistry, School of Pharmacy and Biochemistry, University of Buenos Aires, Junín 956, C1113AAD, Buenos Aires, Argentina; *
[email protected] Designing a physical chemistry laboratory that employs systems of interest to life sciences students is a challenge for an instructor. Experiments for biochemistry and pharmacy majors are numerous and diverse in kinetics. However, thermodynamic laboratory practices are poorly connected with everyday life or professional activity. This situation does not encourage the learning of this area of physical chemistry. A
valve
Time Requirement
valve lid
thermometer safety valve chamber
pressure gauge
The experiment can be carried out in approximately 3 hours, divided as follows:
lid
• Measurement of pressure and temperatures of equilibrium phase under different experimental conditions (1:30 hours)
• Sterilization cycle (1 hour)
• Report (30 minutes)
water
container
C
B
20 mm inner diameter
Equipment
18 mm 30 mm
metallic washer valve lid
46 mm outer diameter
25 mm
3 mm thickness
Figure 1. Schematic representation of the pressure cooker: (A) detailed components, including the pressure gauge and the thermometer added to the lid; (B) the valve lid and the metallic washers used to increase its mass; and (C) as an example, the 35 g washer is represented.
Table 1. Internal Pressure and Equilibrium Temperature as a Function of the Valve Lid Mass
g
Internal Pressurea/ kPa
°C
K
--
101b
100
373
76
156
114
387
Mass/
Description None Original valve lid + 15 g
washerc
Temperature
91
170
118
391
+ 15 g + 20 g washerd
111
183
121
394
washerse
146
209
124
397
167.5
225
126.5 399.5
+ 35 g
+ 91.5 g aInternal
x2
washerf
pressure was calculated as the sum of the atmospheric pressure and the pressure measured by the pressure gauge in each condition. bThis value can be assumed as 101 kPa or measured with the appropriate manometer. cWasher dimensions are 19 mm x 40 mm x 1.5 mm (i.d., o.d., and thickness, respectively). dWasher dimensions are 19 mm x 40 mm x 2 mm. eWasher dimensions are 20 mm x 46 mm x 3 mm. fA 56.5 g washer (27 mm x 60 mm x 3 mm) and a 35 g washer.
276
In this article we present a quantitative analysis of the displacement of phase equilibrium by modifying external pressure. Liquid–vapor phase transition pressure and temperature for water are measured to verify the Clausius–Clapeyron equation. Students analyze the principles governing a pressure cooker and how the pressure cooker can be adapted to function as an autoclave (1) for sterilizing purposes.
The following equipment and materials are needed: pressure cooker, pressure gauge, thermometer, timer, distilled water, heat source (hot plate or Bunsen burner), metallic washers, thermal gloves, glasses, and material to be sterilized. A pressure gauge (a regular oil model with a double scale, 0–2 bars and 0–30 psi) and a bimetal thermometer (model BDTH Badotherm, 0–150 °C) were fitted to the lid of a pressure cooker (10.5 liter capacity; Marmicoc Argentina SACIFA), to read the pressure and the temperature within the chamber (Figure 1A). Holes were drilled in the lid to insert the pressure gauge and the thermometer and both holes were fitted with a brass locknut and synthetic rubber washers on each side of the lid. The pressure indicated by the pressure gauge is the value above atmospheric pressure; to obtain the real chamber pressure it is necessary to add the atmospheric pressure to the gauge value. Commercially available metallic washers were selected to fit in the middle portion of the valve lid. Figure 1B shows how the metallic washers are placed, only resting on the valve lid. The inner diameter of the washer must be 19 to 24 mm for this particular pressure cooker model. When the inner diameter was larger, a smaller washer was added to support it in the correct position. Dimensions and masses of the washers used in this experiment are listed in Table 1. Hazards Pressure cookers are usually equipped with a safety valve that is made from an alloy breakable at 202 kPa of overpressure (approximately 303 kPa of total pressure), which guaranties the safety of the process within the pressure range proposed here. Any changes or modifications to the pressure cooker should be
Journal of Chemical Education • Vol. 85 No. 2 February 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory
tested to make sure that they do not compromise the integrity of the instrument. The manipulation of the pressure cooker must be made with appropriate protection and any component of the equipment should not be manipulated until its temperature reaches room temperature. Students should wear aprons or lab coats and goggles (or any eye protection) and should be advised to avoid direct contact with overheated water vapor because of the risk of burning.
barometric pressure 101 kPa
A
B Pext Pbar 101 kPa
Pext Pbar Pext 101 kPa
Experimental Procedure
Pvap Pext 101 kPa
Pvap 101 kPa
How Does a Pressure Cooker Work? A liquid boils when the vapor pressure of the gas escaping from the liquid is equal to the pressure exerted on the liquid by its surroundings (Pvap = Pext). As a consequence, the boiling point can be manipulated by increasing the external pressure. In a regular cooker, water is exposed to normal external pressure (normal barometric pressure = 101 kPa) and boils at 100 °C (373 K). When the lid is not in its position or the valve is uncovered (Figure 2A), the pressure cooker works as a regular cooker. However, if the valve is covered there will be a change in the inner pressure of the chamber and the liquid–vapor equilibrium point will be displaced (Figure 2B). When the valve is covered, the condition of the system changes because the vapor phase is now restricted to the chamber. As a consequence of the added mass (the valve lid), the pressure raises and the equilibrium between phases is displaced to a higher temperature, resulting in a new boiling point (Figure 2C). The mass of the valve lid determines the pressure inside the chamber because the hole of the valve lets gas escape when the pressure exceeds some fixed value. Excess pressure is eliminated through small quantities of vapor escaping through the valve (Figure 2D) establishing a situation of intermittent constant volume (Figure 2C and 2D).
internal pressure in the chamber constant (101 kPa)
restricted volume
ln P
% vap H R
1 T
c
(1)
where P is the measured pressure (gauge value and atmosphere), T is the measured temperature, R is the gas constant, and c is a variable, a plot of ln P versus (1∙T) results in a straight line with a slope of –Δ vap H∙R (Δ vap H is the enthalpy of vaporization that
D Pext Pbar Pext 101 kPa Pvap Pext 101 kPa
restricted volume
vapor escaping to maintain pressure
internal pressure in the chamber constant ( 101 kPa) Figure 2. Schematic interpretation of water molecules behavior during vaporization process in the pressure cooker. Circles represent water molecules. Pbar indicates barometric pressure (normal = 101 kPa); Pvap indicates the vapor pressure of the liquid; and Pext indicates pressure exerted on the liquid by its surroundings. Conditions C and D will be in equilibrium during the phase change until water converts completely in vapor.
5.6 5.4
ln(P / kPa)
How To Verify the Clausius–Clapeyron Equation? Water is heated in the pressure cooker under different pressures by adding varying washers to the valve lid. First, water heating starts with the valve uncovered. Prior to covering the valve the chamber must be purged or cleansed to ensure the absence of air. When water boils, vapor will displace the air and after a few minutes the vapor escaping through the hole of the valve becomes continuous, indicating that only water is in the chamber. At this point, the valve lid is placed on the valve and the new pressure and temperature of the transition process are measured. After reaching this new equilibrium, the heat source is removed for five minutes, a washer is placed on the valve lid, and the heating is re-started until the next equilibrium point is reached. At the end of 4 or 5 additions or exchanges of different washers students have a correlation between the mass of the modified valve lid and the measured pressure and temperature, as shown in Table 1. According to the Clausius–Clapeyron equation,
C
5.2 5.0 4.8 4.6 4.4 2.45
2.50
2.55
2.60
ź3
(1/T ) / (10
2.65
2.70
ź1
K
)
Figure 3. Natural logarithm of total pressure in the chamber (P) as a function of the reciprocal of the equilibrium temperature (1/T ).
may be taken as constant over a small temperature range, as is the case in this experiment). Under our experimental conditions (Figure 3), the relationship was verified and Δ vap H was estimated as 37 ± 1 kJ∙mol. The uncertainty in the slope is calculated according to ref 2. The experimental value compares favorably with the value from tables (40.4 kJ∙mol).
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 2 February 2008 • Journal of Chemical Education
277
Discussion The effect of pressure on phase equilibrium is usually given in a classroom lecture without any related experimental exercise; however, a few laboratory practices are presented in the literature (5, 6). The main objective of the reported activities is to calculate the enthalpy of vaporization of different liquids. Driscoll (5) reported an experiment that requires a liquid with a vapor pressure about 40 mm of Hg at room temperature, restricting the reagent to toluene, methylcyclohexane, and piperidine. Since all of these compounds are toxic agents, they are not good choices for students’ manipulation. Other experiments (6) use water, but since a temperature of approximately 250 °C is needed, it can be quite dangerous for students’ handling. Additionally, both of the activities require equipment especially designed for the practice. The experiment described in this article requires inexpensive equipment that is easy to obtain and adapt and it is considered safe even for the temperature range of work (100 °C–130 °C) as the liquid is used in the chamber. This exercise was originally developed for a postgraduate course of applied physical chemistry included in the curricula for obtaining the degree of Specialists in Sterilization at this university. In this context, the exercise was successful in demonstrating the physicochemical basis of the autoclave function. The activity can also be an opportunity for integrating previously acquired knowledge, for example, the analysis of the purging step. Dalton’s law should be discussed to understand that all components contribute to the pressure inside the chamber and that the Clausius–Clapeyron equation is valid only if the pressure detected corresponds to a pure component (water), explaining the strict requirement for air elimination. The abstract physical chemistry concepts are partially responsible for the difficulties some students have incorporating basic knowledge. Recently, the discipline has become more interested in the molecular basis of the processes (7) as it is reflected in modern textbooks (8). Thus, a pedagogic approach such as the one presented here (Figure 2) could be useful for comprehension. In addition, instructors can discuss exercises where pressure values should be expressed in different units (atm, mm of Hg, bars, kPa, psi, etc.). Since pressure is often expressed in different 278
220
400
200
396 392
180
388 160 384 140
380
120
376
100
Temperature / K
Sterilization Cycle The second activity is to reproduce a standard sterilization cycle (15 min at 121 °C) (3). The pressure cooker is prepared with 1 L of water. Items to be sterilized (empty plastic vials, partially-filled plastic vials, glass vials or tubes; syringes, etc.) are wrapped in a medical quality paper envelope and are placed into the chamber inside the inner recipient. The lid is adjusted and heating is started. After purging the pressure cooker, additional mass is placed on the valve lid to reach a temperature of 121 °C. Pressure is monitored until reaching approximately 101 kPa of overpressure (corresponding to 202 kPa of inner chamber pressure). At this point the sterilization period begins. After 15 minutes, the heat source is removed and the decrease in pressure and temperature is monitored. A typical sterilization cycle is obtained with the pressure (and temperature) data taken as a function of time (Figure 4). Once the system reaches room temperature, the pressure cooker can be opened and the items retrieved. A careful observation of the objects could lead to a discussion about the resistance of the materials under high temperature and the limitation of wet heat as a sterilization method (4).
Pressure / kPa
In the Laboratory
372 0
10
20
30
40
50
60
Time / min Figure 4. Total pressure in the chamber (●) and equilibrium temperature (○) versus time during a sterilization cycle in the pressure cooker.
basis in many fields, an appropriate distinction in the use of these units would be highly advised for students. Finally, this activity provides the students an opportunity to manipulate, determine, and identify the system conditions: constant volume, constant pressure, or constant temperature. Taken as a whole, this laboratory exercise provides a useful tool to enrich a core concept, usually discussed in a lecture, directly connected with everyday equipment and biomedical applications. Literature Cited 1. Franco, M. A. Papel del Farmacéutico en el Control de la Contaminación Microbiana. In Programa de Educación y Actualización Farmacéutica (PROEF) Tercer Ciclo, Módulo 2, Editorial Médica Panamericana; Buenos Aires, Argentina, 2001; p 67. 2. Colby Chemistry. http://www.colby.edu/chemistry/PChem/notes/ linest.pdf (accessed Nov 2007). 3. Russell, A. D. Sterilization and Disinfection by Heat Methods. In Principles and Practices of Disinfection, Preservation and Sterilization, 3rd ed.; Russell, A. D., Hugo, W. B., Ayliffe, G. A. J., Eds.; Blackwell Science Ltd.: Oxford, 1999; p 629. 4. Alwood, M. C. Medical Applications of Thermal Processes. In Principles and Practices of Disinfection, Preservation and Sterilization, 3rd ed.; Russell, A. D., Hugo, W. B., Ayliffe, G. A. J., Eds.; Blackwell Science Ltd.: Oxford, 1999; p 657. 5. Driscoll, J. A. J. Chem. Educ. 1980, 57, 667. 6. PHYWE series of publications, Laboratory Experiments, Physics, PHYWE SYSTEME, 37070 Göttingen, Germany. http://www. nikhef.nl (accessed Nov 2007). 7. Zielinsky, T. J.; Schwenz, R. W. Chem. Educator 2004, 9 (2), 108–121. DOI: 10.1333/s00897040771a. http://chemeducator. org/bibs/0009002/920108tz.htm (accessed Nov 2007). 8. Atkins, P. W; de Paula, Julio. Atkins’ Physical Chemistry, 7th ed.; Oxford University Press: Oxford, 2004.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Feb/abs276.html Abstract and keywords Full text (PDF) with links to cited URLs and JCE articles Figure 2 in color Supplement Student handouts and instructor notes Information about pressure units
Journal of Chemical Education • Vol. 85 No. 2 February 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
