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Physical Models and Classroom Demonstrations Based on Applying the Hydraulic Analogy to Chemical Equilibrium, Thermodynamics, and Kinetics Dana Lev-Ran

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Physical Models and Classroom Demonstrations Based on Applying the Hydraulic Analogy to Chemical Equilibrium, Thermodynamics, and Kinetics Dana Lev-Ran Florida State University Libraries Honors Theses The Division of Undergraduate Studies 2014 Physical Models and Classroom Demonstrations based on Applying the Hydraulic Analogy to Chemical Equilibrium, Thermodynamics, and Kinetics Dana Lev-Ran Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS & SCIENCES PHYSICAL MODELS AND CLASSROOM DEMONSTRATIONS BASED ON APPLYING THE HYDRAULIC ANALOGY TO CHEMICAL EQUILIBRIUM, THERMODYNAMICS, AND KINETICS By DANA LEV-RAN A Thesis submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for graduation with Honors in the Major Degree Awarded: Summer, 2014 The members of the Defense Committee approve the thesis of Dana Lev-Ran defended on July 29, 2014. ______________________________ Dr. Kenneth A. Goldsby Thesis Director ______________________________ Dean Karen L. Laughlin Outside Committee Member ______________________________ Dr. John G. Dorsey Committee Member ______________________________ Dr. Bridget A. DePrince Committee Member ABSTRACT The hydraulic analogy for electrical circuits is a well-known, if limited, model for understanding potential and current. The work described in this thesis extends this analogy to chemical reactions by constructing apparatuses that model chemical equilibrium and the dynamics of forming kinetic and thermodynamic products in a chemical reaction. The apparatuses were designed so that they could be constructed from readily available and affordable materials by middle or high school students under the supervision of a shop or science teacher. The resulting hydrodynamic models were evaluated qualitatively and quantitatively with respect to the well-established theories of chemical equilibria, kinetics, and thermodynamics. The effectiveness and utility of the hydrodynamic models to illustrate chemical behavior, as well as their limitations, are discussed. iii TABLE OF CONTENTS Abstract................................................................................................................................. iii List of Abbreviations and Symbols....................................................................................... v INTRODUCTION............................................................................................................... 1 Chemical Potential and Potential Applications of the Hydraulic Analogy in Chemistry................................................................................................ 3 The STACT Project............................................................................................................... 4 EXPERIMENTAL............................................................................................................... 6 Hydrodynamic Model for Chemical Equilibrium.................................................................. 6 Hydrodynamic Model for Kinetic and Thermodynamic Products in a Chemical Reaction.............................................................................................. 7 RESULTS AND DISCUSSION.......................................................................................... 11 Hydrodynamic Model for Chemical Equilibrium ................................................................. 11 Equilibrium calculations using K............................................................................. 16 Hydrodynamic Model for Kinetic and Thermodynamic Products in a Chemical Reaction.............................................................................................. 18 SUMMARY.......................................................................................................................... 22 REFERENCES..................................................................................................................... 24 iv List of Abbreviations and Symbols In addition to the abbreviations listed below, standard SI units and abbreviations are used in this thesis. CPVC chlorinated polyvinyl chloride R ideal gas constant cu units of height based on graduate s second cylinder markings sq ft square feet d diameter V volts E electric potential or cell potential V volume F Faraday’s constant VP volume in products cylinder g gravitational constant VR volume in reactants cylinder ΔG Gibbs free energy VT total volume h height ICE Initial-Change-Equilibrium k proportionality constant for water pressure and height above the point of measurement ID inner diameter in inch Keq chemical equilibrium constant K´ hydraulic equilibrium constant L length m mass n number of moles OD outer diameter P pressure PE potential energy PVC polyvinyl chloride r radius v INTRODUCTION The hydraulic analogy for electrical circuits grew out of the early belief that electricity, generally attributed to Benjamin Franklin,1 is a fluid that flows through wires, much like water flows through pipes. By the beginning of the twentieth century, Sir Oliver Lodge had extended this idea to a formal analogy “that was widely used in the first half of the century and is still with us,”2 even though it was generally recognized by then that “the electric force is neither a ‘current’ [in the literal sense] or a ‘fluid’.”3 In spite of the ongoing debate about using the hydraulic analogy4 (and analogies in general5,6) to teach scientific concepts, this analogy continues to appear in introductory texts on electricity and electrical circuits. To understand the lasting appeal of the hydraulic analogy for electrical, one must look beyond the simplicity of the model and its ability to illustrate the invisible dynamics that occur in an electrical circuit, as shown in Figure 1. (a) (b) Figure 1. (a) A pump increases the pressure in the upper pipe and decreases the pressure in the lower pipe, and the difference in pressure between the two sides causes the fluid to flow in a clockwise direction. (b) A battery applies a voltage, and the difference in potential causes electricity to “flow” in a clockwise direction. [Source: C.R. Nave, Current Law and Flowrate, Hyperphysics, Georgia State University, http://hyperphysics.phy- astr.gsu.edu/hbase/electric/watcir2.html (accessed July 24, 2014).] 1 The beauty of this analogy becomes clear when one compares the characteristics of a hydrolytic system with the analogous characteristics of an electrical circuit, including their units. The following table allows a side-by-side comparison. Table 1. Analogous Characteristics of Hydrolytic Systems and Electric Circuits. (Adapted from Easier by Analogy by Jim McNicol.7) Description Hydraulic System Electrical Circuit Basic unit of the mobile component. water molecule electron Quantity of the basic unit. volume (m3 or L) charge (coulomb) Flow = quantity/time volume/time current (ampere) Source of the energy that causes the elevated tank cell/battery flow. or pump or generator Force that causes the flow. pressure (psi, atm, etc.) potential (volt) Resistance to the flow. friction or turbulence resistance (ohm) The two major tenets of the hydraulic analogy for electrical circuits are that (1) electrical current is analogous to flow rate of a liquid (generally presumed to be water), and (2) electrical potential is analogous to (water) pressure. Using the symbol to indicate “is analogous to,” we can write the first analogy as current (charge/time) flow rate (volume/time) (1) where both expressions correspond to quantity/time. Multiplying equation (1) by time gives charge volume (2) consistent with quantities listed in Table 1. The standard unit of charge, the coulomb (C), can be written as energy in joules (J) divided by potential in volts (V).8 J C = (3) V 2 Rearranging equation (3) to express volts as joules divided by coulombs J V = (4) C and rewriting the relationship in terms of the general characteristics in Table 1 gives energy potential = (5) charge Recalling from Table 1 and equation (2) that charge is analogous to volume, we expect that energy/charge should be analogous to energy/volume. energy energy charge volume (6) charge volume Energy divided by volume is also called energy density, or potential energy density, which corresponds to hydrostatic pressure. Therefore, equation (6) becomes potential pressure (7) showing that the two major tenets of the hydraulic analogy for electrical circuits follow directly from statement that charge is analogous to volume, the quantities of “fluid” being circulated in the respective systems. CHEMICAL POTENTIAL AND POTENTIAL APPLICATIONS OF THE HYDRAULIC ANALOGY IN CHEMISTRY Let’s imagine that we did not know that 1 C 1 V = 1 J, or that we did not remember the exact relationship between these units. We could deduce this relationship by considering the equation below used to interconvert the free energy of reaction, G, and potential, E. G = nFE (8) 3 This essential equation can be readily found in any high school chemistry or college textbook.9 Adding typical units to the equation gives G (J/mol) = n(number of e ) F(C/mol e) E(V) (9) Considering only the units, and cancelling units to simplify the relationship yields equation (10) shown below. J/mol = number of e C/mol e V J = C V (10) As before, rearranging this equation J V = C and writing this relationship in terms of the general characteristics gives energy potential = charge which lead in the previous section to the statement that electric potential is analogous to water pressure. Given that we arrived at this conclusion by using an equation for chemical potential,
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