In the Classroom

438 Journal of Chemical Education • Vol. 84 No. 3 March 2007 • www.JCE.DivCHED.org

In introductory chemistry courses, students encountervarious types of relationships among properties of matter.Published literature has demonstrated that analogies from lifeexperiences help students comprehend those relationshipstaught in an introductory chemistry course (1–6). When arelationship links more than two variables and is somewhatcomplicated, such as Coulomb’s law, students struggle. Mostpopular text books have adequate discussion about the influ-ence of charges and sizes of ions on a number of physicalproperties including lattice energy, melting point, and solu-bility of ionic substances (7, 8). A clear understanding of therelationships presented by Coulomb’s law is necessary for stu-dents to comprehend the effects of sizes and charges of ionson physical properties of ionic substances. An example fromlife experience that is parallel is presented here.

As a mathematical equation, Coulomb’s law may be ex-pressed as follows:

Fq q

d1 2

2∝ (1)

or

F =k q q

d1 22 (2)

where F is the force (attraction or repulsion) between twocharged particles, q1 and q2 are the magnitudes of chargeson the particles, d is the distance between the charges, and kis the proportionality constant. Thus, according to this law,the force between two charged particles is directly propor-tional to the magnitudes of the charges and is inversely pro-portional to the square of the distance between them.1

It is the author’s experience that the majority of studentsin an introductory chemistry class are familiar with the pro-cess of covering floors with tiles. Most commercial floor tilesare sold as squares, with sides measuring 1, 1.5, or 2 in. Todetermine the number of tiles needed to cover a rectangular

room, one needs to know the length and width of the roomand the size of the tile. The data in Table 1 illustrate how thenumber of tiles is dependent upon the length and width ofthe room and the size of the tile.

A comparison of cases 1 and 2 in Table 1 demonstratesthat the number of tiles needed is directly proportional tothe length of the room while a comparison of cases 2 and 3shows that the number of tiles is directly proportional to thewidth of the room. However, when we compare the data incases 3, 4 and 5, we notice an inverse relationship betweenthe number of tiles needed and the size of the tile. When thesize of the tile is doubled, as in cases 3 and 4, the number oftiles is reduced by a factor of 4. An examination of cases 3and 5 reveals that when the size of tile is halved, the numberof tiles is increased by a factor of 4. These observations dem-onstrate that the number of tiles needed is inversely propor-tional to the square of the size of the tile used. The teachermay choose to illustrate the process using overhead transpar-encies and color coded mini square tiles.

A comparison of cases 1 and 2 in Table 2 demonstratesthat force is directly proportional to the magnitude of charge1 (q1) while a comparison of cases 2 and 3 shows that theforce is directly proportional to the magnitude of charge 2(q2). However, when we compare the data on cases 3 and 4,we notice an inverse relationship between the force and dis-tance between the charges. When the distance is doubled, asin cases 3 and 4, the force is reduced by a factor of 4. Theforce is inversely proportional to the square of the distancebetween the charged particles. Data on Table 2 relevant toCoulomb’s law show a definite parallel relationship to the onesassociated with determining the number of tiles in Table 1.Students at this point are convinced that the relationshipsfound in Coulomb’s law are no more complex than layingsquare tiles to cover the floor of a room. Students seem torelax when they realize that this type of complex relation-ship exists not just in science but in real life as well.

Known-to-Unknown ApproachTo Teach about Coulomb’s LawP. K. ThamburajDepartment of Chemistry, Ohio University Center, Zanesville, OH 4370; thambura@ohiou.edu

Applications and Analogiesedited by

Arthur M. LastUniversity College of the Fraser Valley

Abbotsford, BC, Canada

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In the Classroom

www.JCE.DivCHED.org • Vol. 84 No. 3 March 2007 • Journal of Chemical Education 439

Note

1. The author is indebted to one of the reviewers for suggest-ing the sketch shown in Figure 1. The sketch illustrates that whenthe distance between two charged particles increases, the area ex-periencing the lines of force also increases. Point “A” on the sketchrepresents the position of a charged particle. When the distance isdoubled (For example, when AC = 2 AB) the area experiencingthe force is quadrupled (4 squares vs 1 square) and the intensity ofthe force is reduced to one fourth.

Acknowledgment

The author appreciates the help of Pramod Kanwar atOhio University Center in Zanesville, Ohio in drawing thesketch.

Literature Cited

1. Fortman, John J. J. Chem. Educ. 1993, 70, 649.2. Fortman, John J. J. Chem. Educ. 1994, 71, 848.3. Umland, Jean B. J. Chem. Educ. 1984, 61, 1036.4. Thamburaj, P. K. J. Chem. Educ. 2001, 78, 915–916.5. Haim, L.; Corton, E.; Kocmur, S.; Galagovsky, L. J. Chem.

Educ. 2003, 80, 1021–1022.6. Cain, Linda. J. Chem. Educ. 1986, 63, 1048.7. Kotz, J. C.; Treichel, P., Jr. Chemistry and Chemical Reactivity,

5th ed.; Thomson: Belmont, CA, 2003; pp 93, 329–331.8. McMurry, J.; Fay, R. C. Chemistry, 3rd ed.; Prentice Hall: Up-

per Saddle River, NJ, 2001; pp 213–214.

Figure 1. Sketch illustrating that when the distance between twocharged particles increases, the area experiencing the lines of forcealso increases.