Chemical Education Today
Letters The Reaction Quotient Is Unnecessary To Solve Equilibrium Problems
The Limitation of a Qualitative Reasoning In this Journal there has been a discussion about the necessity of the reaction quotient for solving equilibrium problems (1–4). Especially, the contribution of Robert Lederer (3) caught my attention, and I tried to do his experiment with 0.2 M acetic acid. Having created a situation like the one described by Lederer, namely a bulb that did not light up when the electrodes were immersed in the solution, I did not notice an increase of the conductivity when diluting the solution to 0.1 M as the bulb still did not burn. This was what I expected, because there is a shift of equilibrium to the side of the ionized products, but the concentration (or activities) after dilution will be smaller than at the start of the experiment, although it will not be twice as small. I agree with Lederer that the total amount of ions in the solution will be greater than before diluting, but the actual conductance of the liquid is the result of the concentrations (or activities) and not of their total amount. This point is not recognized by Paul Matsumoto in his reaction (4). I fully agree with him that the dissociation of the acetic acid will be complete in an endless dilution, but this does not mean that this endless diluted solution, which, in fact, will be water, will be a good conductor. In this discussion we can have a look at the conductance measurements of MacInnes and Shedlovski (5), whose results are also listed in Robinson and Stokes (6). In the box below, some of their values of the equivalent conductance at various molarities of the acetic acid are listed. Acetic Acid Molarity/10᎑3 M
Ion Concentration /10᎑4 M
Equivalent Conductance
000.028014
00.15107
390.02
001.028310
01.27270
388.94
012.829000
04.75910
387.41
100.000000
13.49600
385.29
200.000000
18.99200
384.41
These values show how the actual concentrations drop off, but slower than the initial acetic acid molarity. Although MacInnes and Shedlovski did not report on a concentration of 1.0 M, we can assume that the shift in the values listed also will hold good for this concentration. The reasoning given by Robert Lederer is a good qualitative one, but in this case a more precise look would be necessary. Literature Cited 1. Matsumoto, P. S. J. Chem. Educ. 2005, 82, 406–407. 2. Silverstein, T. P. J. Chem. Educ. 2005, 82, 1149. 3. Lederer, R. J. Chem. Educ. 2005, 82, 1149.
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4. Matsumoto, P. S. J. Chem. Educ. 2005, 82, 1150. 5. McInnes, D. A.; Shedlovski, T. J. Am. Chem. Soc. 1932, 54, 1429–1438. 6. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths: London, 1959. Michiel Vogelezang Radboud University Nijmegen Institute for Teacher and School (ILS)
[email protected] The author replies: I agree with Michiel Vogelezang’s letter regarding Lederer’s demonstration using a light-bulb conductivity apparatus (1), where the dilution of a 1.0 M acetic acid solution to a 0.5 M solution produced an (apparent) unanticipated increase in the solution’s conductance. The focus of our exchange (1, 2) was my earlier paper (3) and not on rationalizing Lederer’s demonstration. In a subsequent analysis, I calculated the concentration of the ions in the system containing 0.5 M versus 1.0 M acetic acid using an “ICE” table (3, 4). The results show that the dilution of a 1.0 M acetic acid solution increases the percent ionization of acetic acid and decreases the concentration of the sum of all ions in solution. As the solution’s conductance depends on the concentration of ions in solution (5), a decrease in the concentration of ions in solution would decrease the solution’s conductance, which is inconsistent with Lederer’s observations (1). Thomas Newton (6) measured a lower conductance in a 0.5 M acetic acid solution than in a 1.0 M solution, which I was able to confirm. The box below shows the solution conductance as a function of the depth of electrode immersion and the concentration of acetic acid. The conductivity measurement apparatus consists of a gel box power supply (which displays the voltage and current in the system), wires with alligator clips, and a pair of graphite electrodes (0.25 in. diameter rods, 2.7 cm apart). Depth of Electrode Immersion in Solution/cm
Conductance at 1.0 M Acetate/mS
Conductance at 0.5 M Acetate/mS
1
1.52
1.13
4
6.06
5.07
These experimental measurements are inconsistent with Lederer’s observations (1). Without specific information on Lederer’s experimental protocol and equipment, I am unable to resolve the contradiction between Lederer’s observations and the conductivity measurements or my calculations. A possible explanation could be an increase in the surface area of the electrodes in contact with the solution upon dilution (5, 6; see boldface items in the box above). Other factors may be electrode geometry (6, 7).
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Journal of Chemical Education
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Chemical Education Today
Letters Literature Cited 1. 2. 3. 4.
Lederer, R. J. Chem. Educ. 2005, 82, 1149. Matsumoto, P. S. J. Chem. Educ. 2005, 82, 1150. Matsumoto, P. S. J. Chem. Educ. 2005, 82, 406–407. Brown, T. L.; LeMay, H. E.; Bursten, B. E. Chemistry. The Central Science, 7th ed.; Prentice Hall: Upper Saddle River, NJ, 1997. 5. Hille, B. Elementary Properties of Ions in Solution. In Ionic Channels in Excitable Membranes, 2nd ed.; Sinauer Associates, Inc.: Sunderland, MA, 1992; Chapter 10. 6. Newton, T. personal communication. 7. Jovov B, Wills, N. K.; Lewis S. A. Am. J. Physiol. 1991, 261: C1196–1203. Paul Matsumoto Galileo Academy of Science & Technology 1150 Francisco Street San Francisco, CA 94109
[email protected] The author replies: After having received three responses to my letter (contending an increase in conductivity when diluting a weak acid), all contradicting my conclusion, I endeavoured to perform the demonstration again. More attention to detail and variable controlling did in fact show that there was no increase in illumination of the light-bulb apparatus. If the elec-
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trode height in the solution is not strictly controlled, the illumination does appear to alter. I thank those who wrote me with their concerns and data, and appreciate being set straight on this concept. Never to old to learn… Rob Lederer Dr. E. P. Scarlett High School 220 Canterbury Dr. S.W. Calgary, AB T2W 1H4 Alberta, Canada
[email protected] Editor’s Note The discussion of conductivity of aqueous solutions of acetic acid may have been influenced by subconscious recollections of an experiment different from the one described in Rob Lederer’s original letter. Like pure water, pure acetic acid is a relatively poor electrical conductor and will not cause a light-bulb conductivity apparatus to light. The University of Wisconsin–Madison lecture demonstrator, Jim Maynard, placed a conductivity tester in glacial acetic acid and several aqueous solutions of different concentrations, taking care to maintain the same electrode surface area throughout. The result, as shown by photographs in the Supplemental Material,W is that the bulb lights brightest when the concentration of acetic acid is about 5 mol/L. Both above and below that concentration the bulb is dimmer, and no glow can be seen for glacial acetic acid and for concentrations of 0.1 mol/L and below.
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