Developing and Using a Computer Simulation of LiquidâVapor

Article Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

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Developing and Using a Computer Simulation of Liquid−Vapor Transitions to Improve Students’ Assimilation of Concepts Related to the Behavior of Real Gases David Zorrilla,†,‡ Jesús Sánchez-Márquez,*,† Víctor García,† and Manuel Fernández†

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Departamento de Química-Física, Facultad de Ciencias, Campus Universitario Río San Pedro, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain ‡ IMEYMAT: Institute of Research on Electron Microscopy and Materials of the University of Cádiz, 11510 Puerto Real, Cádiz, Spain S Supporting Information *

ABSTRACT: Teaching and understanding the concepts related to ideal gases and their transformations is relatively uncomplicated. However, for science and engineering students, reaching an understanding of and assimilating the concepts related to real gases and their transformations is a more difficult goal. Backed by their considerable experience teaching this aspect of chemistry, the authors have developed UCA-GAS, computer software that takes account of all the characteristics of the problem. A methodology is proposed on the basis of a laboratory activity that makes the concepts related to the behaviors of gases and their changes in state much easier to assimilate. To evaluate the usefulness of this activity, a starting hypothesis related to the use of the software and laboratory activity was proposed and tested by means of an experiment involving a group of undergraduate students. KEYWORDS: Second-Year Undergraduate, Laboratory Instruction, Computer-Based Learning, Gases

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INTRODUCTION

2. The second concept is the critical temperature (Tc). For example, in the transition of CO2 from gas to liquid, the liquid phase cannot be obtained at temperatures above 31.1 °C regardless of how much the pressure is increased. This postulates that every gas has a Tc above which it cannot be liquefied merely by applying pressure. It is important that students understand the special character of the critical isotherm (and its temperature, Tc), as well as the concepts of saturated vapor and liquid. They must also assimilate the following: the concept of vapor for gases that are in equilibrium with their liquids below the critical temperature; that all states are a mixture of liquid and vapor below the saturation curve; and that for a substance to be able to change its phase, it is necessary to supply or extract a certain amount of heat, bearing in mind that if a phase change occurs at constant pressure, this heat does not result in an increase in temperature and is called latent heat. Students have to make a special effort to really understand these concepts rather than simply memorize them. 3. In 1873, the Dutch physicist Johannes Diderik van der Waals made two simple modifications to the equation for ideal gases (PV = nRT) that made it possible to explain the

A great deal of research has been performed on the best way to help science students assimilate and understand the concepts related to gases.1−3 The problem of how to teach this particular topic more effectively lies in the large number of concepts and interrelations that students have to internalize.4 This, added to the “invisible” nature of gases and their properties, means that students require a high level of ability for abstract thinking in order to understand this topic properly.5,6 Several previous studies highlight the fact that a large percentage of students enrolling in university courses hold misconceptions regarding ideal gases and have little knowledge of how real gases behave.7,8 Consequently, many students fail to fully understand the behavior of real gases during their courses. These problems often become apparent in classes such as Physical Chemistry I (thermodynamics) at the University of Cádiz, although this issue is evident at many other Spanish universities. Teaching the following concepts in particular can be problematic: 1. The first concept is the behavior of a gas under pressure at different temperatures and the fact that it is possible to liquefy a gas at room temperature through the application of high pressure. For example, when learning about liquid air, students clearly have difficulty imagining how an “invisible” gas that is so important to their daily life can be transformed into something liquid and ponderable. © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: November 14, 2018 Revised: June 5, 2019

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DOI: 10.1021/acs.jchemed.8b00939 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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Figure 1. Compressibility factor vs pressure for several gases (left) and for a gas at different temperatures (right).

equilibrium of the two phases when a gas undergoes liquefaction. Students must draw the conclusion that the equation for ideal gases only properly represents gas behavior at sufficiently low pressures or sufficiently high temperatures. To predict the behavior of matter outside those limits, more sophisticated equations of state are necessary, such as those of van der Waals among many others. 4. The final concept is the compressibility factor, Z = Pv̅/RT (where v̅ is the molar volume). This parameter is used to study the deviation of a gas from its ideal behavior and can be expressed in relation to the critical point as

changes to the temperature, volume, or number of moles of the selected gas, and it is possible to evaluate the pressure as a function of the variables chosen using three gas models: the ideal gas model, the van der Waals model, and the Peng−Robinson model. However, although it produces comparative graphs, it does not have a graphical user interface that displays how each parameter varies, which was considered important during the design phase of UCA-GAS to reduce the cognitive load on the students. (b) Gas Law Simulator:10 a web application that uses JavaScript and flash. It has an intuitive graphical interface in which the different parameters can be varied. However, it does not have a database with real gas parameters as only the ideal gas model has been implemented, and therefore it is not possible to compare different gas models. (c) Gas Law Simulation Kinetic Molecular Theory:11 a web application designed using HTML5. It has an intuitive graphical interface, but the management of the graphics are not very intuitive, and it only uses ideal gases. (d) Ideal Gas Law Simulation:12 a very basic simulator for ideal gases only. (e) Gas Properties:13 a very intuitive Java application. However, it has no display of graphics and is limited to ideal gases. To facilitate the transfer of knowledge, some authors have proposed performing theoretical calculations of the properties of real gases using software.14,15 However, UCA-GAS has been specifically designed with a visual and intuitive environment that makes it easy to use, thus reducing the capacity for abstract thinking required by students that have to assimilate the concepts mentioned above. The software is intended for use with laboratory practice, comprising a series of activities of increasing difficulty. The students have the support of the UCAGAS software to facilitate the visualization of the concepts under study. Consequently, the teaching and learning difficulties mentioned above are minimized, allowing the students to assimilate the concepts better. The psychological theories proposed to improve the transmission of scientific knowledge are not always easy to apply because they often lack detailed guidance on the design of teaching−learning processes at a specific level.16 With the guided activity designed in this paper (see the section Development of the Proposed Laboratory Practice) and the virtual and interactive support provided by the created software (see the section UCA-GAS Software), it is possible to go from a behaviorist educational model, the traditional approach to

critical factor Zc =

Pcvc RTc

for the ideal gas Z = 1. Figure 1 shows the compressibility factor versus pressure for various gases and for a gas at different temperatures. Both the teaching staff and students at the Science Faculty of the University of Cádiz have highlighted the difficulties involved in the effective teaching and learning of concepts traditionally taught in a face-to-face class in which the presentation of the theory is followed by its application to specific problems. Students mentioned these difficulties during their tutoring hours throughout the year, and the teachers in charge of the subject recorded them. The students’ inferior performance in this subject with regard to others was a further indicator. Their unsatisfactory assimilation and comprehension of these concepts was tested in coursework and in the final exam. Therefore, the aim of this paper is to propose laboratory practice supported by software, UCA-GAS, which allows for changes in the educational methodology in order to improve the teaching and learning of concepts related with real gases. This laboratory practice is intended to support the theoretical classes with the aim of improving students’ assimilation of the concepts and thus their performance in the subject. When we proposed the development a computer simulator for ideal gases and before starting the design phase of the software, similar software with the characteristics required for the intended aim was practically unavailable on the market. A study of the current market to determine the most relevant gas simulators available nowadays and their characteristics is given below: (a) GasSim:9 a web tool for modeling and simulating gases containing a database with 76 gases. Its interface allows B



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Figure 2. Comparison of isotherms using the van der Waals equations of state (red) and the ideal gas equations (blue) for 1 mol of N2 at 100 K. The continuous horizontal red line is located by the Maxwell equal area rule.

in Chemistry at the University of Cádiz that were studying Physical Chemistry I (thermodynamics). This experiment had the following phases: 1. The software was designed taking into account the opinions of five expert chemistry educators (with at least 8 years of experience teaching this subject) regarding the suitability of the program for the intended objective. The experts were interviewed during the design phase of UCAGAS. The program also had to fulfill some essential functions of educational software (instruct, inform, stimulate critical participation, etc.). To this end, we used qualitative methods, such as conducting interviews with the expert educators in this subject, and quantitative methods in the form of questionnaires. The information obtained was then used to develop the UCA-GAS software (see the section UCA-GAS Software). 2. A practical guide was produced (see the section Development of the Proposed Laboratory Practice) in which a series of activities was proposed following the philosophy of increasing difficulty. This made it possible to reduce the learning curve of the use of the UCA-GAS software and enhance the educational nature of the program through a constructivist model. 3. A previous knowledge questionnaire was developed to assess the students’ assimilation of the desired concepts after the theoretical classes but before the proposed laboratory practice. The questionnaire was then completed again after the laboratory practice. Thus, it was possible to evaluate the performance of the students after the laboratory practice and compare that with how they performed after receiving only theoretical classes. An opinion questionnaire was also designed to assess the students’ perception of the level of suitability and usefulness of the laboratory practice and the software used in the learning process.

teaching this subject, to a constructivist model. Therefore, taking advantage of the reduction in abstraction skills required from the students and the decrease in cognitive load in the transfer of scientific concepts, resulting from the use of a combination of virtual and other classroom resources,17 we have proposed a laboratory practice with a philosophy of increasing difficulty that uses UCA-GAS as a learning tool. In this way, it is easier for students to draw their own conclusions. The interactivity that the program provides leads to a more learner-centered experience and makes it easier for students to grasp the concepts of how real gases behave in a problem-based learning environment. The proposed practice has been elaborated taking into account the recommendations of different authors regarding the creation of educational models that facilitate the transmission of scientific knowledge.18−20

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RESEARCH QUESTIONS In this study, we investigate the following research questions related to real gases in Physical Chemistry I: 1. How do students embrace the simulation software proposed in the activity and detailed below to improve their learning process? 2. Do students assimilate the concepts related to real gases better after undertaking the proposed activity to support the theoretical classes? Once the “problem” was determined in detail, the hypothesis proposed in this study was that the laboratory practice performed with the specially designed sof tware as a resource to support the theoretical classes facilitates students’ ef fective learning of the concepts related to real gases.

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METHODS To evaluate the hypothesis, an experiment was performed involving 62 second-year students of the Undergraduate Degree C



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Figure 3. Calculation of the error propagated using Monte Carlo simulations with artificially generated errors following a normal distribution.

Figure 4. UCA-GAS GUI for performing interactive simulations of simple thermodynamic processes.

4. The results obtained through the questionnaires were analyzed to draw conclusions about the actual performance of the students and their perception of the usefulness of the laboratory practice and its supporting software in their learning process. Thus, it was possible to test the hypothesis proposed.

Monoatomic gases: He, Ne, Ar, Kr, and Xe Diatomic gases: H2, D2, F2, O2, Cl2, Br2, I2, HD, HF, HCl, and CO Polyatomic gases: H2O, D2O, NH3, CO2, CH4, CF4, CCl4, CH3OH, C6H5CH3, and n-C6H14

UCA-GAS SOFTWARE The UCA-GAS software is a computer code developed to facilitate the learning of the laws and behaviors of gases. In addition, it is a tool for the use of different equations of state. The program was written in the VISUAL BASIC programming language with an operating environment enabling the design of an intuitive and user-friendly graphical interface. The software installer for Windows XP, Vista, 7, 8, and 10 can be downloaded free of charge at ref 21. The gases directly available for calculations with the proposed software are

In addition, the following equations of state for real gases have been introduced: the Berthelot equation,22 the Dieterici equation,23−25 the Redlich−Kwong equation,26−31 the Redlich−Kwong−Soave equation,32−39 the Peng−Robinson equation,40−46 the van der Waals equation,47,48 and the Virial equation.49 By choosing the right equation and looking in the literature for the necessary parameters, the software enables the behavior of any other gas to be studied.50,51 Among other calculation capabilities, the software allows users to graphically represent and compare several isotherms corresponding to different temperatures or different equations of state for different gases (see Figure 2). The software also makes it possible to perform Monte Carlo type numerical

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Figure 5. Results obtained from the initial and final questionnaires to assess students’ performance (n = 62). The scale of the questionnaires ranged from 0 (no knowledge of the item or ability to use the item) to 5 (excellent knowledge or ability).

simulations52 using data sets with artificially generated errors (see Figure 3). The objective of these simulations is the analysis of the error propagated53−57 by the calculations of the model. The random initial errors in the simulations are considered to follow a normal distribution. A code based on a routine from Numerical Recipes58 is used to obtain a normally distributed deviate with zero mean and unit variance. This routine is based on the Box Muller transformation, which uses a source of uniform deviates. Regarding the calculation speed, the formula is normally calculated very quickly, meaning that a large amount of random numbers can be used with a reasonable calculation time. In addition, a graphical interface has been included (see Figure 4) that allows users to perform interactive simulations of simple thermodynamic processes (isothermal, isobaric, and expansions and compressions).

because of the nature of the topic to be transmitted. Therefore, the simulation focused on enhancing the visualization of the concepts to be transmitted. 2. We have focused on reducing to a minimum the learning curve needed by the students to manage this new tool. The nature of the experiments on this subject can be laborious, and there is a risk of increasing the cognitive load on the students. Thus, we allow the students to focus on the concepts to be learned and take advantage of the POGIL methodology. 3. As we focused on making the software easy to manage, it is very intuitive and accessible for students. We encouraged students to use it for the duration of the course, facilitating self-learning and thereby helping the students to retain the knowledge acquired during the laboratory practice permanently. 4. The laboratory practice proposed is more general because it not only allows students to acquire complex, new concepts but also to (1) observe known phenomena, (2) make observations that lead to discoveries about models through generalization, and (3) solve open problems. The general objective of the proposed laboratory practice is that science students effectively assimilate the concepts related to real gases. In order to achieve this general objective, the practice has been divided into more specific subobjectives, for which activities have been defined. The subobjectives are 1. Understand the nonideal behavior of gases. 2. Acquire the computer media skills required to simulate the behavior of matter. 3. Assimilate and internalize the concept of critical point and be able to relate and use it to determine the parameters of a van der Waals type equation of state. 4. Understand the concept of equations of state, be able to determine which model best represents a given gas, and be able to estimate its deviation from ideality.

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DEVELOPMENT OF THE PROPOSED LABORATORY PRACTICE In this phase of the work, we propose a set of activities that follow a process-oriented guided inquiry learning (POGIL) philosophy59,60 to some extent. The activities follow a structured inquiry approach in which the students have limited knowledge and do not know the results of the experiments. The teacher’s role is to guide the students, who make decisions about specific procedures according to the data obtained. This methodology, which includes periods of reflection, has been applied to other concrete concepts of Physical Chemistry.9 However, the laboratory practice (a complete learning guide has been included in the Supporting Information) proposed in this paper has some distinctive elements: 1. We considered the aspects related with the visual transmission of information to be an important motivational factor of the laboratory practice. Even if the practice were carried out experimentally, it could not be guaranteed to be the most appropriate way to reduce the capacity for abstraction required by the students E



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Figure 6. The means of the results obtained from the satisfaction survey performed by 62 students, where value 1 is completely dissatisfied or not useful in the learning process and 5 is completely satisfied or very useful in the learning process.

van der Waals models) with errors controlled by the UCA-GAS software. In order to improve the students’ assimilation of the concepts related to real gases, this practice could be repeated as homework or in the laboratory with a different gas or equation of state.

5. Estimate the error made in the predictions with the gas models. To achieve these objectives, we propose six activities (developed in the Supporting Information). Activity 1

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The main objective of this activity is to create a visual representation of the concepts for students in order to reduce the capacity of abstraction required in the following activities.

RESULTS AND DISCUSSION

Questionnaire 1

This questionnaire includes specific evaluation questions and was developed to assess the students’ knowledge of the different topics covered in the activities in the proposed practice. The students completed it before and after carrying out the practice to determine whether it had the expected effect. Figure 5 shows the average performance ratings obtained by the students in relation to the following items: 1. Understanding of the nonideal behavior of gases. 2. The correct use of equations of state different to that of the ideal gases. 3. The suitable application of predictive models in the simulation of the behavior of matter. 4. The correct way to study and interpret phase changes in the isotherms of a real gas. 5. The proper use of the compressibility factor (Z) for studying the deviation from ideality of a real gas. 6. The ability to obtain the critical point of a real gas and understand the concept. 7. The ability to obtain and analyze the error committed in a model by numerical simulation. Figure 5 shows two sets of bar graphs. Those in garnet are the average values obtained immediately prior to performing the laboratory activity, and those in orange are the values obtained after the practice. Significant increases in the values can be observed in all the items but especially in points 5, 6, and 7, which correspond to the use of the compressibility factor, obtaining the critical point, and analysis of the error committed, three of the most important objectives. It is also relevant to point

Activity 2

In this activity, we introduce the students to the different behaviors of ideal and real gases and to interpretation of the van der Waals equation and how it shows the liquid−vapor transition. Activity 3

Then, the students have to verify that the real behaviors of gases approach ideal behaviors when the temperature increases and provide an explanation of that behavior. Activity 4

Following the last activity, the students have to determine, as accurately as possible and using the simulator, the temperature at which the gas under study can be liquefied again by applying pressure. Activity 5

In order to facilitate the assimilation of the big differences in behavior for ideal gases and real gases, the students have to plot Z(P, T) versus P for a temperature higher than Tc for the selected gas. They must use at least five different values of P (apart from P = 0) and determine the areas (1) where the correction applies to the molecular volume and (2) where the molecular interaction prevails. Activity 6

In order to understand the magnitude of the errors made in these types of calculations, the students, for the assigned gas under study, have to generate random values (using the ideal gas and F



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out that the global performance with regard to knowledge and the ability to apply the concepts related to real gases increased from the 44.3% when this knowledge was taught face-to-face in theory and problem-solving classes to 75.9% after the students performed the proposed laboratory practice. As Figure 5 shows, the errors are relatively small in comparison with the changes in the results, indicating that the results are statistically significant.

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Questionnaire 2

AUTHOR INFORMATION

Corresponding Author

In addition, a satisfaction survey was conducted to assess the students’ perception of their achievement of the objectives proposed and of how the laboratory practice contributed to their learning process. Figure 6 shows the average values achieved on the survey for the following items: 1. The nonideal behavior of real gases has been extensively covered. 2. The proper use of predictive and interpretative models has been practiced and properly applied to simulate the behavior of matter. 3. The ability to study phase changes in real gases by using graphical representations of its isotherms. 4. The ability to obtain the critical point of a gas and its relationship with the parametrization of a van der Waals type equation. 5. The ability to analyze the equation of state that best represents a specific gas and to estimate its deviation from ideality. 6. The ability to estimate the error made in calculations with ideal and real gas state equations. As Figure 6 shows, the students’ ratings are extremely high, especially in point 4, related to obtaining the critical point of a gas. It is relevant to mention that despite the errors represented in the graph, the values obtained in the survey provide qualitative results that support the conclusions obtained.

*E-mail: [email protected]. ORCID

Jesús Sánchez-Márquez: 0000-0001-9498-1361 Víctor García: 0000-0002-9868-8194 Notes

The authors declare no competing financial interest.

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REFERENCES

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CONCLUSIONS According to the results obtained from the surveys, the hypothesis proposed in this work has been satisfactorily confirmed. The performance of the students was assessed, and very satisfactory results were found regarding the concepts studied in depth. The concepts were well assimilated after students used the models for the simulation of the behavior of matter, determined the most adequate equation of state for each problem, and analyzed the error achieved when applying the different models. A significant increase was also observed in the students’ perception of the usefulness with regard to their levels of knowledge of the various topics covered: nonideal gas behavior, use of equations of state, application of predictive models, study of phase change, use of the compressibility factor (Z), obtaining of the critical point, and estimation and analysis of the error committed in the calculations with the models. Therefore, we can conclude that the UCA-GAS software is a valuable educational resource that enables students to engage in useful laboratory practice to support theoretical classes, and it results in better understanding of the concepts pertaining to real gases.

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Complete lab workshop guide, designed to initiate the students in gas concepts and help them acquire critical thinking in the calculation of critical values and boiling temperatures for some gases with real equations of state and in the simulation and estimation of error (PDF, DOCX)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00939. G



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