Do the equilibrium constants have units? A discussion on how general chemistry textbooks calculate and report the equilibrium constants

Authors

  • Juan Quílez-Pardo Universitat Jaume I

Keywords:

Equilibrium constants, General chemistry text books, Definition, Calculation and Units

Abstract

An analysis of the literature concerning the dimensionality of equilibrium constants reveals that this topic manifests as a controversial issue. Based on this previous examination, this work studies if general chemistry textbooks accurately define and calculate equilibrium constants. In order to evaluate those textbooks, in the first part of this study the experimental equilibrium constants, Kp and Kc, and the thermodynamic equilibrium constant, Kº, are defined. Also, the equations that relate each constant to the other two are given. In the specific presentation of these quantities, an example is discussed both performing their accurate calculation and reporting them using the proper units. In the second part of this study, it is examined the way both first-year university chemistry textbooks and pre-university chemistry textbooks determine equilibrium constants, concentrating on how they handle the units of these quantities. Many textbooks treat Kp and Kc as dimensionless quantities. This misleading assumption is caused by a problem in the terminology used as in many cases Kp (or Kc) plays the role Kº. In order to avoid this misleading treatment of the equilibrium constants some suggestions are provided.

References

Abrantes, L.M. & Nieto de Castro, C. (1985). O conceito de constante de equilíbrio – suaintroduçao. Boletim Sociedade Portuguesa de Química, 19, 21-23.

Adamson, A. W. (1975). Understanding Physical Chemistry. New York: Benjamin.

Andrés, D. M., Antón, J. L., Barrio, J. I., de la Cruz, M. C. & González, F. (2000). Química. Madrid: Editex.

Antonik, S. (1993). Aspects dimensionnels de la constante d’équilbre en phase gazeuse. Usage des tables de thermodynamique. Bulletin de l’Union des Physiciens, 87, 909-917.

Atkins, P. W. (1989). General Chemistry. New York: Scientific American Books.

Atkins, P. & de Paula, J. (2010). Atkins’ physical chemistry. Oxford: Oxford University Press.

Atkins, P. W. & Jones, L. L. (2010). Chemical Principles. The Quest for Insight. New York: Freeman and Company.

Barrio, J. I. & Belmonte, M. (1992). Química COU. Reacción. Madrid: SM.

Barrio, J. I., Sánchez, A., Bárcena, A. I. & Caamaño, A. (2016). Química 2. Madrid: SM.

Belmonte, M. (1999). Química 2. Barcelona: Ediciones del Serbal.

Bergqvist, A., Drechsler, M., De Jong, O. &Rundgren, S. N. C. (2013). Representations of chemical bonding models in school textbooks – help or hindrance for understanding, Chemistry Education Research and Practice, 14, 589 – 606. DOI: 10.1039/C3RP20159G

Boggs, J. E. (1958). The logarithm of “ten apples”. Journal of Chemical Education, 35(1), 30-31. DOI: 10.1021/ed035p30

Borge, J. (2015). Reviewing some crucial concepts of Gibbs energy in chemical equilibrium using a computer-assisted, guided-problem-solving approach, Journal of Chemical Education, 92(2), 296–304. DOI: 10.1021/ed5005992

Brenon-Audat, F., Busquet, C. & Mesnil, C. (1993). Thermodynamique Chimique. Paris: Hachette.

Brown, C. & Ford, M. (2014). Higher Level Chemistry, 2nd ed.; Harlow: Pearson.

Burrows, A., Holman, J., Parsons, A., Pilling, G. & Price, G. (2017). Chemistry. Introducing inorganic, organic and physical chemistry. Oxford: Oxford University Press.

Caamaño, A. &Obach, D. (2000). Química 2. Barcelona: Teide.

Caamaño, A., Obach, D. & Servent, A. (1991). Química COU. Barcelona: Teide.

Cakmakci, G. (2009). Emerging issues from textbook analysis in the area of chemical kinetics. Australian Journal of Education in Chemistry, 70, 31-38.

Cardona, A. R., Pozas, A., Martín, R. & Ruíz, A. (2003). Química 2. Madrid:McGrawHill.

Carriedo, G. A., Fernández, J. M. & García, M. J. (2016). Química 2. Madrid: Paraninfo.

Castillo, J., Ogaz, R., Merino, C. & Quiroz, W. (2016). An ontological and epistemological analysis of the presentation of the first law of thermodynamics in school and university textbooks, Chemistry Education Research and Practice, 17, 1041-1053. DOI: 10.1039/C6RP00105J

Centellas, F. A. (2008). Algunesreflexions al voltant del tractament de l’equilibriquímic en el batxillerat. Educació Química, 1(1), 10-16.

Chang, R. (2000). Physical chemistry for the chemical and biological sciences. Susalito: University Science Books.

Climent, M. D., Domingo, R.,Latre, F., Sanz, V., Silla, E., Soler, V.& Viché, J. (1989). Química de COU. Una perspectiva práctica. Valencia: Cespusa.

Copley, G. N. (1958). Letter to the Editor. Journal of Chemical Education, 35(7), 366-367. DOI: 10.1021/ed035p366

Cox, J. D. (1982). Notation for states and processes, significance of the word standard in chemical thermodynamics, and remarks on commonly tabulated forms of thermodynamic functions. Pure & Applied Chemistry, 54, 1239–1250.

Cox, G. A., Dixon, D., Morris, R. & Roberts, J. P. (1979): Does K have units? Education in Chemistry, 16, 101.

Delorme, P. (1985). A propos des constants d’équilibre. Bulletin de l’Union des Physiciens, 79, 1087-1092.

Depovere, P.& Weiler, J. (1993a). Mise au point a propos du caractère dimensionné ou indimensionné des constants d’équilibre. Association Belge des Professeurs de Physique et Chimie, 117, 107-112.

Depovere, P. & Weiler, J. (1993b). Réflexions concernant “le dimensionnement ou le non dimensionnement” des constantes d’équilibre. Réponse des auteurs, Association Belge des Professeurs de Physique et Chimie, 119, 234.

DeVoe, H. (2016). Thermodynamics and Chemistry. www.chem.umd.edu/thermobook.

Domingo, R. & Silla, E. (1991). Exercicisnumèrics en química. València: Generalitat Valenciana.

Drechler, M. & Schmidt, H. J. (2005). Textbooks’ and teachers’ understanding of acid-base models in chemistry teaching. Chemistry Education Research and Practice, 6(1), 19-35. DOI: 10.1039/B4RP90002B

Eltinge, E. M. & Roberts, C. W. (1993). Linguistic content analysis: A method to measure science as inquiry in textbooks. Journal of Research in Science Teaching, 30(1), 65-83. https://doi.org/10.1002/tea.3660300106

Engel, T. & Reid, P. (2012). Physical Chemistry. Englewood Cliffs: Prentice Hall.

Ewing, M. B., Lilley, T. H., Oloffson, G. M., Rätzsch, M. T. &Somsen, G. (1994). Standard quantities in chemical thermodynamics. Pure & Applied Chemistry, 66(3), 533-552.

Fernández, E. (2016). Selectividad 2015. Pruebas de acceso a la Universidad: Química. Madrid: Anaya.

Fernández, A. & Pérez, C. (2004). Química Schaum bachillerato. Madrid: McGrawHill.

Fidalgo, J. A. & Fernández, M. R. (2005). Problemas de Química. 2º de Bachillerato. León: Everest.

Freeman, R. D. (1985). Conversion of standard thermodynamic data to the new standard-state pressure. Journal of Chemical Education, 62(8), 681-686. DOI: 10.1021/ed062p681

Freemantle, M. (1991). Chemistry in Action. London: MacMillan.

García, J. A., Lozano, R. &Teijón, J. M. (1991): Problemas de Química de Selectividad. Madrid: Tebar Flores.

García, T. & García-Serna, J. R. (2003). Química. Barcelona: Edebé.

Gil, V. M. S. & Paiva, J. C. (1999). Equilibrium constant units revisited. Chemical Educator, 4(4), 128-130.

Goedhart, M. J. & Kaper, W. (2002). From chemical energetics to chemical thermodynamics. In Gilbert, J., De Jong O., Justi, R., Treagust, D. & Van Driel J. (eds.), Chemical Education: Towards research-based practice (pp. 339-362). Dordrecht: Kluwer.

Goldberg, D. E. (2001). How to solve word problems in chemistry. New York: McGraw Hill.

Gordus, A. A. (1991). Chemical equilibrium. The thermodynamic constant. Journal of Chemical Education, 68(2), 138-140. DOI: 10.1021/ed068p138

Guardia, C., Menéndez, A. I. & de Prada, F. (2009). Química 2 Solucionario. Madrid: Santillana.

Harris, W. F. (1978). The Plethora of Equilibrium Constants. Chemsa, 4, 170-172.

Harris, W. F. (1982). Clarifying the concept of equilibrium in chemically reacting systems. Journal of Chemical Education, 59(12), 1034-1036. DOI: 10.1021/ed059p1034

Henry, A. J. (1967). The dimensions of physical quantities. Education in Chemistry, 4, 81-86.

Illana, J., Araque, J. A., Liébana, A. & Teijón, J. M. (2016). Química 2. Madrid: Anaya.

Jespersen, N. D.; Brady, J. E. &Hyslop, A. (2012). Chemistry. The Molecular Nature of Matter. Hoboken: Wiley.

Justi, R. & Gilbert J. K. (2002). Models and modelling in chemical education. In Gilbert, J., De Jong, O., Justi, R., Treagust, D. & Van Driel, J. (eds.). Chemical education: towards research-based practice (pp. 213–234). Dordrecht: Kluwer.

Khine, M. S. (2013). Critical Analysis of Science Textbooks. Evaluating Instructional Effectiveness. Dordrecht: Springer.

López, J. A. (2000). Problemas de Química. Madrid: Prentice Hall.

Laidler, K. J. (1990). Units of an equilibrium constant. Journal of Chemical Education, 67(1), 88. DOI: 10.1021/ed067p88.1

Levine, I. (2009). Physical chemistry. New York: McGraw-Hill.

Matta, G. F., Massa, L., Gubskaya, A. W. & Knoll, E. (2011). Can one take the logarithm or the sine of a dimensioned quantity or a unit? Dimensional analysis involving transcendental functions. Journal of Chemical Education, 88(1), 67-70. DOI: 10.1021/ed1000476

McQuarrie, D. A. & Simon, J. D. (1997). Physical chemistry: a molecular approach. Susalito: University Science Books.

Mills, I. M. (1989). The choice of names and symbols for quantities in chemistry. Journal of Chemical Education, 66(11), 887-889. DOI: 10.1021/ed066p887

Mills, I. M. (1995). Dimensions of logarithmic quantities. Journal of Chemical Education, 72(10), 954-955. DOI: 10.1021/ed072p954

Mills, I., Cvitas, T., Homann, K., Kallay, N. & Kuchitsu, K. (1983). Quantities, units, and symbols in physical chemistry. Oxford: Blackwell.

Molyneux, P. (1991). The dimensions of logarithmic quantities: Implications for the hidden concentration and pressure units in pH values, acidity constants, standard thermodynamic functions, and standard electrode potentials. Journal of Chemical Education, 68(6), 467-469. DOI: 10.1021/ed068p467

Moncaleano, H. (2008).La enseñanza del concepto de equilibrio químico. Análisis de las dificultades y estrategias didácticas para superarlas. Doctoral Dissertation. Departament de Didàctica de les CiènciesExperimentals. Universitat de València.

Moore, J. W.,Stanitski, C. L., Wood, J. L.,Kotz, J.C.&Joesten, M. D. (1998). The Chemical World. Concepts and Applications. Orlando: Saunders.

Morcillo, J. & Fernández, M. (1991). Selectividad. Pruebas de 1990: Química. Anaya: Madrid.

Morcillo, J., Fernández, M. & Carrión, V. E. (1998). Química 2, Madrid: Anaya.

Mortimer, R. G. (2000). Physical chemistry. San Diego: Hartcourt.

Oxtoby, D. W., Gillis, H. P. & Campion, N. H. (2012). Principles of Modern Chemistry. Belmont: Brooks/Cole.

Pedrosa, M. A. & Dias, M. H. (2000). Chemistry textbook approaches to chemical equilibrium and student alternative conceptions. Chemistry Education Research and Practice, 1(2), 227-236. DOI: 10.1039/A9RP90024A

Pekdağ, B. & Azizoğlu, N. (2013). Semantic mistakes and didactic difficulties in teaching the ‘‘amount of substance’’ concept: a useful model. Chemistry Education Research and Practice, 14, 117 – 129. DOI: 10.1039/C2RP20132A

Pethybridge, A. D. & Mills, I. M. (1979). Answer to: does K have units? Education in Chemistry, 79, 191.

Petrucci, R. H., Harwood, W. S., Herring, G. E. & Madura, J. (2006). General Chemistry: Principles and Modern Applications. New Jersey: Prentice-Hall.

Petrucci, R. H., Herring, G. E., Madura, J. & Bissonnette, C. (2017). General Chemistry: Principles and Modern Applications. New Jersey: Prentice-Hall.

Quílez, J. (2012). First-year university chemistry textbooks’ misrepresentations of Gibbs energy. Journal of Chemical Education, 89(1), 87-93. DOI: 10.1021/ed100477x

Quílez, J. (2016). Kp does not play the role of the thermodynamic equilibrium constant, K: a discussed example on general chemistry textbooks’ misrepresentations. Chemistry: Bulgarian Journal of Science Education, 25(6), 815-825.

Quílez, J. & Solaz, J. J. (1995). Students’ and teachers’ misapplication of Le Châtelier’s principle. Implications for teaching chemical equilibrium, Journal of Research in Science Teaching, 32(9), 939-958. https://doi.org/10.1002/tea.3660320906

Quílez-Díaz, A. & Quílez-Pardo, J. (2015). Avoiding general chemistry textbooks’ misrepresentations of chemical equilibrium constants. African Journal of Chemical Education, 5(2), 72-86.

Quintero, G. (1987). Le Châtelier – right or wrong? Journal of Chemical Education, 64(12), 1069. DOI: 10.1021/ed064p1069.2

Raff, L. M. (2001). Principles of physical chemistry. Englewood Cliffs: Prentice-Hall.

Raff, L. M. (2014).Spontaneity and Equilibrium: Why “ΔG < 0 Denotes a Spontaneous Process” and “ΔG = 0 Means the System Is at Equilibrium” Are Incorrect? Journal of Chemical Education, 91(3), 386-395. DOI: 10.1021/ed400453s

Ronneau, C. (1993). Reflexions concernant “le dimensionnement ou le non dimensionnement” des constantes d’équilibre. Association Belge des Professeurs de Physique et Chimie, 119, 231-233.

Rosenberg, R. M.&Kotz, I. M. (1999). Spontaneity and the equilibrium constant: advantages of the Planck function. Journal of Chemical Education, 76(10), 1448-1451. DOI: 10.1021/ed076p1448

Sanger, M. J. & Greenbowe, T. J. (1999). An analysis of college chemistry textbooks as sources of misconceptions and errors in electrochemistry. Journal of Chemical Education, 76(6), 853-860. DOI: 10.1021/ed076p853

Silbey, R. J., Alberty, R. A. & Bawendi, M. G. (2005). Physical chemistry. Hoboken: Wiley.

Simón, B., García-Serna, J. & Romero, J. J. (2016). Química 2. Barcelona: Edebé.

Sözbilir, M. (2004). What makes physical chemistry difficult? Perceptions of Turkish chemistry undergraduates and lecturers. Journal of Chemical Education, 81(4), 573-578. DOI: 10.1021/ed081p573

Spencer, J. N., Bodner, G. M. & Rickard, L. H. (2008). Chemistry. Structure and Dynamics. New York: Wiley.

Treptow, R. S. (1999). How thermodynamic data and equilibrium constants changed when the standard-state pressure became 1 bar. Journal of Chemical Education, 76(2), 212-215. DOI: 10.1021/ed076p212

Tulip, D. & Cook, A. (1993). Teacher and student usage of science textbooks, Research in Science Education, 23(1), 302–307. https://doi.org/10.1007/BF02357074

Tykodi, R. J. (1986). A better way of dealing with chemical equilibrium. Journal of Chemical Education, 63(7), 582-585. DOI: 10.1021/ed063p582

Vemulapalli, G. K. (1993). Physical chemistry. Englewood Cliffs: Prentice-Hall.

Vickerman, C. (1979). Answer to: does K have units? Education in Chemistry, 79, 191-192.

Wright, P. G. (1979). Answer to: does K have units? Education in Chemistry, 79, 192-193.

Zubiaurre, S. & Arsuaga, J.M. (2007). Selectividad. Pruebas de 2006: Química. Anaya: Madrid.

Zumdahl, S. S. & Zumdahl, S. S. (2007). Chemistry. Boston: Houghton Mifflin.

Zumdahl, S. S. & DeCoste, D. J. (2018). Chemical Principles. Boston: Cengage Learning.

Downloads

Published

10/12/2019

How to Cite

Quílez-Pardo, J. (2019). Do the equilibrium constants have units? A discussion on how general chemistry textbooks calculate and report the equilibrium constants. International Journal of Physics &Amp; Chemistry Education, 11(3), 73–83. Retrieved from https://www.ijpce.org/index.php/IJPCE/article/view/51