The author replies to Silverstein and Lederer.

While my paper states that the reaction quotient (Q) is not needed to solve equilibrium problems, it does not imply that Q is not valuable. In fact, when I teach this topic to my AP chemistry class, I initially use Q to solve the problem, then mention the alternative method described in the paper. Q is valuable in solving problems involving Le Châtelier’s principle (2), as well as how a reaction with a positive ∆G° value with an appropriate value of Q may be spontaneous (3), which is based on the equation:

∆G = ∆G° + RTln Q.

That is, I agree with Lederer and Silverstein that Q is a valuable concept. The value of not using Q to solve equilibrium problems was to simplify its solution and not to imply that Q is not valuable.

I agree with Silverstein’s comment that solving for “exact” equilibrium concentrations is not a good use of class time owing to the complexity of the calculations (4). While my paper simplifies the calculations to determine the equilibrium concentrations of chemicals in a reaction compared to the traditional algorithm, it does not affect the “accuracy” of the results. I agree with Silverstein’s point that class time is better spent on learning chemistry on a semi-rigorous (or more qualitative) level rather than at a more rigorous (or quantitative or tedious) level, especially at the high-school level. For example, (i) solving buffer problems using the Henderson–Hasselbalch equation (2, 3), despite its limitations (5), is preferable to using the traditional “ICE” table (2), (ii) using a graphing calculator is preferable to solve equilibrium problems than to do calculations “by hand”, and (iii) solving for pH as “–log [H⁺]” (2) is preferable to using “–log a(H⁺)” (7).

Lederer’s interesting demonstration shows that an understanding of Q may be used to explain an unexpected observation. An alternative explanation of the demonstration would be that a decrease in the (initial) concentration of a weak acid, increases the percent ionization (I) of the acid (2), which may be rationalized as follows. The dissociation of a weak acid is

where

(1)

while

(2)

Solving for [H⁺]_e in eq 2 and substituting into eq 1 followed by rearrangement yields,

which may be solved using the quadratic formula

(3)

Using L’Hôpital’s rule to evaluate eq 3,

shows that as the concentration of HA decreases, there is an increase in percent ionization.

Literature Cited

1. Matsumoto, P. S. J. Chem. Educ. 2005, 82, 406–407.
2. Brown, T. L.; LeMay, H. E.; Bursten, B. E. Chemistry, The Central Science, 7th ed.; Prentice Hall: Upper Saddle River, NJ, 1997.
3. Lenhinger, A. L. Biochemistry, 2nd ed.; Worth Publ.: New York, NY, 1975.
4. Clark, R. W.; Bonicamp, J. M. J. Chem. Educ. 1998, 75, 1182–1185. Hawkes, S. J. J. Chem. Educ. 1998, 75, 1179–1181. Silverstein, T. P. J. Chem. Educ. 2000, 77, 1120. Stolzberg, R. J. J. Chem. Educ. 1999, 76, 640–641.
5. Po, H. N.; Senozan, N. M. J. Chem. Educ. 2001, 78, 1499–1503.
6. Donato, H. J. Chem. Educ. 1999, 76, 632–634.
7. Levine, I. N. Physical Chemistry; McGraw-Hill: New York, NY 1978.