TECHNOLOGY REPORT pubs.acs.org/jchemeduc
Equilibrator: Modeling Chemical Equilibria with Excel Douglas A. Vander Griend* Department of Chemistry and Biochemistry, Calvin College, Grand Rapids, Michigan 49546, United States ABSTRACT: Equilibrator is a Microsoft Excel program for learning about chemical equilibria through modeling, similar in function to EQS4WIN, which is no longer supported and does not work well with newer Windows operating systems. Similar to EQS4WIN, Equilibrator allows the user to define a system with temperature, initial moles, and then either total pressure or volume. Unlike EQS4WIN, Equilibrator is designed to let the user find the point of equilibrium using a slider to shift the extent of reaction. The program simultaneously calculates the reaction quotient, the Gibbs free energy, G, and ΔG; and immediately updates pertinent graphs for feedback. With so many simultaneous ways to evaluate the position of the reaction with regard to equilibrium, Equilibrator is a superior pedagogical tool for helping students truly understand the basic principles of chemical equilibria. KEYWORDS: First-Year Undergraduate/General, Computer-Based Learning, Hands-On Learning/Manipulatives, Equilibrium, Thermodynamics
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any undergraduate labs study chemical equilibria through modeling. These often include systems such as the Haber Bosch process for the production of ammonia, the rearrangement of N2 and O2 to form NO in a combustion engine, the dimerization of NO2, and the coordination of thiocyanate to aqueous iron(III). The computer program EQS4WIN1 was commonly used to model such equilibria at various pressures and temperatures, but it is no longer supported and does not even work well with Windows XP, let alone Vista.2 Equilibrator is a Microsoft Excel file for learning about chemical equilibria through modeling. It is easy to use and transparent in function, and therefore a superior pedagogical tool for helping students understand the principles of chemical equilibria.
slider, which is used to shift the extent of reaction from maximum reactant to maximum product. Excel could be set up to find this position automatically, but there is considerable pedagogical value in having users determine this point for themselves. As the slider is moved, the reaction quotient, Q, Gibbs free energy, G, and ΔG are calculated directly for all momentary reaction positions. (G is calculated as the integral of ΔG, assuming that ΔG at the point of maximum reactant is zero). Two graphs are also shown on the same sheet below the numerical entries: (i) the initial and momentary pressures (or molarities) are shown as a bar graph (Figure 2), and (ii) the Gibbs free energy is graphed versus the extent of reaction, with the momentary value that corresponds to the slider position superimposed on this curve (Figure 3).c
’ INTERFACE The interface for the reaction between nitrogen and hydrogen to form ammonia is shown in Figure 1. The program takes advantage of many advanced features of Excel. Each chemical system is set on an individual Excel worksheet, which can be easily duplicated and modified to any system of interest. Pulldown menus aid the user in defining the initial state of the system.a Similar to EQS4WIN, Equilibrator allows the user to define a system with exactly three variables: temperature, initial moles, and either total pressure or volume. These are determined in the cells with white background on the interface, and the displayed units are automatically updated through the use of if statements. Excel also provides a password-protected option for preventing alterations to designated cells on a worksheet.b This is especially useful when the program is being used by students. They can see the formula of all the cells, but only change the contents of the ones used to define the initial state of the system and dictate the position of the slider and pull-down menus. Unlike EQS4WIN, which determines the point of equilibrium automatically, Equilibrator is designed to let the user find the point of equilibrium. The key element of the program is the Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
’ CALCULATIONS The program determines the reaction to be at equilibrium when Q is within 0.1% of K (the equilibrium constant). This typically occurs for just one to three positions on the slider scale, which divides the full extent of reaction into 10 000 steps. The slider can be dragged, clicked (20 steps), or stepped with arrows to find the equilibrium position. The extreme left and right positions of the slider come to within one step of zero and maximum extent of reaction, respectively, to prevent division by zero. Ultimately, there are many ways that Equilibrator can be used to determine the point of equilibrium: 1. Minimize the numerical value of the Gibbs free energy. 2. Position the red diamond at the minimum on the curve of the Gibbs free energy. 3. Shift the numerical value of ΔG as close as possible to zero. Published: October 04, 2011 1727
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TECHNOLOGY REPORT
Figure 1. Numerical interface for the Excel-based program, Equilibrator, which is designed to allow students to study the equilibrium position of an arbitrary chemical reaction.
Figure 2. Bar graph comparing reagent quantities of the initial and momentary state: equilibrium (top) or otherwise (bottom).
4. Shift the numerical value of Q as close as possible to that of K. 5. Follow the directions under the slider which will say one of three things: Figure 3. Graph of Gibbs free energy, G, versus the extent of reaction for the entire reaction coordinate, as well as the value for the momentary state: equilibrium (top) or otherwise (bottom).
parameterize the following equation: Because there are many simultaneous ways to evaluate the position of the reaction with regard to equilibrium, Equilibrator is a superior pedagogical tool. Students can visually confirm how these different criteria indicate the same reality. Consequently, the one that makes the most intuitive sense to them can be used as a stepping stone to comprehending the others.
’ ADAPTATION The program has one major disadvantage compared to EQS4WIN: it is not linked to any thermochemical database. For each reaction, information must be provided so that Equilibrator can calculate the equilibrium constant, K, for any temperature. This is managed off-screen to the right on the worksheet where up to six values, (AF) can be entered to
Ln K ¼ A þ B=T þ C ln K þ DT þ ET 2 þ FT 3 At present, Equilibrator has worksheets for the four systems mentioned at the top of the article. If other systems are desired, the existing worksheets can be easily duplicated and modified. In some cases, the instructor could look up the necessary parameters to relate K and T in a database similar to that of JANAF.3 Alternatively, the program can be used to determine the numerical value of K in a context where the equilibrium amounts are being measured. (In this case, the curve of Figure 3 will be shifted until its minimum is at the measured equilibrium point.) If additional sheets are developed, please consider sending them to the author so that he can include them with the program, which will be available on the web. 1728
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TECHNOLOGY REPORT
’ ASSOCIATED CONTENT
bS
Supporting Information Excel sheets containing an introduction, N2O4, NH3, NO, Fe(SCN) reactions, and notes. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ADDITIONAL NOTE a Equilibrator requires the user to allow the macros that govern the slider and drop-down menus. To permanently enable the macros in this program, go to “Excel Options” under the “Office Button” in the upper left-hand corner. Change the trust center settings to enable digitally signed macros. b
Worksheets are protected, meaning end-users can only change the input cells. This can be turned off under Excel’s Review tab with a password (dvg). The status of individual cells can be altered under the “format cells” dialogue. c
Do not use “smoothing” curves for graph as it often confuses the automatically generated axis limits.
’ REFERENCES (1) EQS4WIN: Chemical Equilibrium Software 4 Windows, MathTrek Systems. (2) Mathtrek, Systems. www.mathtrek.com (November 18, 2009). (3) Chase, M. W. Jr.; Davies, C. A.; Downey, J. R., Joint Army Navy Air Force (JANAF) Thermochemical Tables. 3rd ed.; J. Phys. Chem. Ref. Data 1985, 14 (Suppl 1), 1-1856.
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