Chemical Education Today
Letters A Soap-Making Suggestion Soap-making procedures for student laboratories, such as those recently published in this Journal, generally involve a filtration step (1). Unfortunately, the reaction mixture tends to clog the filter paper in the Büchner funnel. A plastic scrubbing sheet, Scotch-Brite or its equivalent, may be cut to fit the bottom of the Büchner funnel and used instead of filter paper. (If twopiece plastic Büchner funnels are used, the connecting sleeve of the top part can be used to trace a circle of the appropriate size.) These filter pads are coarse enough to allow rapid filtration but fine enough to hold curdy soap and are reusable. (The remainder of the scrubbing sheet need not go to waste, being good for blocking the holes in the bottoms of flower pots, if you or a friend grow plants.) Literature Cited 1. de Mattos, Marcio C. S.; Nicodem, David E. J. Chem. Educ. 2002, 79, 94. Phanstiel, Otto, IV; Dueno, Eric; Wang, Queenie Xianghong. J. Chem. Educ. 1998, 75, 612.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Oct/abs1345_1.html Full text (HTML and PDF) with links to cited JCE articles Ben Ruekberg Department of Chemistry University of Rhode Island Kingston, RI 02881
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Chemical Education Today
Letters Manual Data Processing in Analytical Chemistry: Linear Calibration Most current analytical textbooks (1) describe the statistical concepts and formulas on which data processing in analytical chemistry is based. Classical univariate statistics provides well-established equations (2) that thoroughly deal with these issues. Most science students are familiar with Excel spreadsheets. However, in the author’s experience, translating statistical equations into Excel formulas is not straightforward for students. In particular, assessing which of Excel’s statistical functions perform the calculation that corresponds to the classical equations and determining how to calculate errors from Excel statistical function outputs are not trivial exercises. To help students make the jump from theory to practical data processing, I have used this teaching approach. First step, list all the concepts and formulas involved and prepare a lesson in which all these concepts are explained as though they were completely new. The explanation should be simplified and yet still rigorous. Second step, write a data processing worksheet and show the students how the equations explained in the lesson correspond to the worksheet’s input and output cells. As a practical example, I have created an Excel spreadsheet for applying the calibration straight-line method and the standard-addition straight-line method. Generic data are used and attention is focused on data processing. A lesson giving the complete explanation of the two worksheets included in the spreadsheet is also provided. The spreadsheet and the relevant lesson are available in the online material. These teaching tools are currently used in the first-semester analytical chemistry course, in which students learn the basics on univariate statistics and how to apply them to quantitative analytical chemistry.
It is my personal experience that the teaching approach I propose helps students make the transition from theory to application. At the end of the course, at least 80% of the students are able to correctly use two basic statistical Excel functions: LINEST for calculating regression lines and TINV for calculating Student’s t values. LINEST outputs a 3 × 2 matrix: finding the meaning of the elements of the matrix using the Excel help function is not straightforward. TINV is easy and powerful because is avoids wasting time searching through statistical handbooks. Literature Cited 1. Skoog, D. A.; West, D. M.; Holler, F. J.; Crouch, S. R. Fundamentals of Analytical Chemistry, 8th ed.; Brooks/Cole: Belmont, CA, 2004. 2. Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, 1st ed.; John Wiley and Sons: New York, 1984.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Oct/abs1346.html Abstract and keywords Full text (HTML and PDF) Supplement Lessons and worksheets
Excel spreadsheet data Dora Melucci Department of Chemistry “Giacomo Ciamician” University of Bologna Via Selmi 2 I-40126 Bologna, Italy
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Journal of Chemical Education • Vol. 85 No. 10 October 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
Chemical Education Today
Letters Using Graphics Calculators and Spreadsheets in Chemistry: Solving Equilibrium Problems
Literature Cited
Solving equilibrium problems is a standard part of the chemistry curriculum. For example, the equilibrium expression
< NH3>2 < N 2> 3
K
(1)
gives rise to the rational polynomial
d
2 x 2 x f
3x
3
K
(2)
where d is the initial concentration of N2, f is the intial concentration of H2, and x is the variable related to the change in the concentrations of the reactants and products. Modern freshman general chemistry texts and upper-level physical chemistry texts use either the quadratic method (see ref 1) or the method of (successive) approximations (see ref 2) to solve numerical equilibrium problems such as eq 2. Both methods represent no significant advances in teaching and learning methodology for over sixty years and both methods present difficulties, but especially to students who are weak in mathematics. Furthermore, since mathematical operations are time-consuming, generally educators are forced to set numerical assessment tasks that foster low-level thinking skills. There has been some use of spreadsheets for multiple equilibria problems (3) or use of Newton’s method to solve single-equilibrium problems (4). Donato has proposed using graphics calculators to graph a rearranged version of eq 2 (5). All of these approaches require some degree of mathematical manipulation. Graphics calculators and spreadsheets can be used to directly graph or to tabulate (6–9) the unarranged left-hand side of eq 2, giving rise to several methods of solving equilibrium problems. Essentially one selects that value of x, for which the numerical value of the unarranged left-hand side of eq 2 equals the numerical value of the right-hand side: these methods are detailed in the online material. The use of such technology in this and other areas of chemistry (10–16), empowers novice students, especially those who lack confidence in their mathematical ability. The main feature of the tabular and graphical approaches is that students perform no numerical calculations and no mathematical manipulation, thus avoiding the learning difficulties experienced by students who are weak in mathematics and enabling students of all abilities to achieve at least some success (17). The approaches are fast and can be generalized to equilibria of any molecularity. It has been noted elsewhere (10–16) that the use of technology in chemistry enables students to do numerical experiments, thus moving equilibrium calculations from tedious mathematical exercises into the realm of experimental science. The graphical and tabular approaches allow students to explore the equilibrium concept, which is an important part of discovery and learning (6).
1. Lehfeldt, R. A. A Text-Book of Physical Chemistry; E. Arnold: London, 1899; p viii. 2. Lowry, T. M.; Cavell, A. C. Intermediate Chemistry, 5th ed.; MacMillan: London, 1947. 3. Carter, D. R.; Frye, M. S.; Mattson, W. A. J. Chem. Educ. 1993, 70, 67. 4. Joshi, B. D. J. Chem. Educ. 1994, 71, 551. 5. Donato, H., Jr. J. Chem. Educ. 1999, 76, 632. 6. Pólya, G. How To Solve It; A New Aspect of Mathematical Method, 2nd ed.; Princeton University Press: Princeton, 1971. 7. Pólya, G. Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving; Wiley: New York, 1962. 8. Goldenberg, P. Multiple Representations: A Vehicle for Understanding Understandings. In Software Goes to School; Perkins, D. N., Schwartz, J. L., West, M. M., Wiske, M. S., Eds.; Oxford University Press: New York, 1995; pp 155–171. 9. Kaput, J. Technology and Mathematics Education. In A Handbook of Research on Mathematics Teaching and Learning; Grouws, D., Ed.; Macmillan: New York, 1992. 10. Lim, K. F. J. Computer Chem. 2006, 5, 139. http://www.sccj.net/ publications/JCCJ/v5n3/a02/abst.html (accessed May 2008). 11. Lim, K. F.; Coleman, W. F. J. Chem. Educ. 2005, 82, 1263. 12. Lim, K. F. Aust. J. Educ. Chem. 2004, 64, 24. 13. Lim, K. F. J. Chem. Educ. 2005, 82, 145. 14. Lim, K. F. Using Spreadsheets in Chemical Education To Avoid Symbolic Mathematics. In CCCE Newsletter: Using Computers in Chemical Education; Spring 2003; Paper 5. http://www.eclipse. net/~pankuch/Newsletter/Pages_NewsS03/S2003_News.html (accessed May 2008). 15. Lim, K. F. Using Spreadsheets To Teach Quantum Theory to Students with Weak Calculus Backgrounds. In Maths for Engineering and Science; Hirst, C. Ed.; LTSN MathsTEAM: Edgbaston, U.K., 2003; p 24. 16. Lim, K. F. New Directions in the Teaching of Physical Sciences 2003, 1, 16. 17. Riddell, S.; Tinklin, T.; Wilson, A. Disabled Students in Higher Education: Perspectives on Widening Access and Changing Policy; Routledge: Abingdon, U.K., 2005.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Oct/abs1347.html Abstract and keywords Full text (HTML and PDF) Links to cited URLs and JCE articles Supplement Details of using graphical and tabular approaches to solve equilibrium problems Kieran F. Lim (
)
School of Life and Environmental Sciences Deakin University Geelong, Victoria 3217, Australia
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