TitleThe Use of Estimates in Solving Chemical Problems |
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AuthorsProf. Dr. Michael E Green, The City College of New York, United States of America |
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AbstractThe use of approximations in solving problems in the sciences can be vital for students. Order of magnitude estimation also helps with physical understanding of the quantities involved in a calculation. For example, in the first exam in a first-year class in chemistry the student must find the mass in grams of an atom; a couple of students will multiply by Avogadro’s number instead of dividing; for atomic weight around 100, this gives the order of magnitude of the mass of the moon; the moon is big, atoms are small. If the student considered the physical meaning of the mass, this would not be a possible mistake. Another example: calculate the total energy, and potential energy, of a system, and from these find the kinetic energy. If the kinetic energy turns out to be negative, something is wrong; the student should realize this. One place a student is taught an approximation in first year chemistry is finding the ionization of a weak acid; ionization is approximated by taking the square root of the dissociation constant, which only works if the concentration is large compared to the dissociation constant. If the student applies the approximation thoughtlessly, this produces an error. The adequacy of any approximation for accurate use is another concept that must be taught. Part of the use of approximations includes attaching error estimates to answers (sometimes expressed as significant figures). There is a related matter that needs to be taught with the estimates: units must match. A book, “The Use of Estimates in Solving Chemistry Problems” (Green and Garland, 1991, Saunders) went through the quantitative parts of first year chemistry, showing how to estimate answers for all sections. A few examples from more advanced material are included, as this kind of error persists past the first year. |
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Keywordsestimates, introductory chemistry, physical understanding of magnitude |
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CitationGreen, M.E. (2021). The Use of Estimates in Solving Chemical Problems. In M. Shelley, W. Admiraal, & H. Akcay (Eds.), Proceedings of ICEMST 2021--International Conference on Education in Mathematics, Science and Technology (pp. 17-35). Monument, CO, USA: ISTES Organization. Retrieved 12 May 2024 from www.2021.icemst.com/proceedings/10/. |
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