letters Hydrolysis of Salts To the Editor
I would like to make a couple of comments about papers (1, 2) that use and discuss my simplified approach (3) for the hydrolysis of a salt from both monoprotic acid and base: 1. Malinowski ( I ) describes the same computer method I used to calculate exact pH values. He stresses a very important practical point, which I recognize I did not even mention in my paper, and that is the use of my farmula as a f ~ sapproximation t for the iterative pmeedure. 2. Cardinali et al. (2) make a very careful and valuable mathematical analysis, hut in my opinion, it has little chemical feeling. Areasonable concentration range for the analysis should he lo4 < c < 10" and not 0 < e < =a. I would summarize my own "chemicalfeeling contribution" with the aid of the accompanyingfigure:My approximate
lo4 < c < lo-', we have to point out that no explicit indication was given in his article a s regards the range where his approximate formula (eq 10) yields almost exact results. However, the important points in our analysis remain the statements that: 1. a solution of a salt of the kind under discussion has a [HI]
value that must lie within the range between Kwm and ( K , . K. I K ~ )and ~ ,not between K, and Kb, the actual value depending on the analytical concentratioif; 2 a not.negligible portion of the corren range cannot ror can only grossly hr repmducrd by Agu~rrr-Ode'sformula, unKt, >> K,I2 are satisless b f h conditions K, >> KmL1and licd As for the '%hemica1feeling contribution" provided by the figure in Aguirre-Ode's letter, it would confirm graphically the numerical results in Table 2 of our article, but there is a n important point to be made. For any given salt concentration, the upper and lower curves in the figure, which should mark the beeinnine of sienificant errors. though being symmetrical &h respect todiagonal D, are not svmmetrical to the other diagonal D' (crossing - D a t DK* = 7, $ C b = 7 and not shown in the figure), contrary to what the shape of the curves seems to suggest. Actually, beyond D', where K.. Kt,< K,, the errors hecome larger and larger, since, a s Amirre-Ode himself implicitly admits, his formula cannot give accurate results Lnde; these conditions; on the other hand, in our Table 2, K& is always larger than K,. I n the accompanying figure, relative to a lo3 M concentration of salt, the percent error in [H+l (upper number) a n d t h e ApH (lower number) involved i n employing Armirre-Ode's formula versus the exact values. are shown for several (pK., pKb) points, each of them having its symD'. The asvmmetrical oattern of the metrical ~ o i n across t errors o n t h e two sides of D' is evident. A
-
V%
expression gives exact results along diagonal D. Errors increase maduallv mine.. from D toward the onnosite , .. .. corners Both upper rU. and lowcr (I., curves mark symmet. L' and I. ncally the hrpnnmg of rl~m~ficanr errors l.~m~rs change thew poscrlon drpcndmg upon the mnemtratwn r , becoming closer to the comer for large values of c and closer to diagonal D for small values of c. Fernando Aguine-Ode Depanamento de Quimica Universidad TFSanta Maria Valpariso, Chile
Literature Cited
To the Editor: Although we agree with Aguirre-Ode's statement, in his letter of comments to Malinowski's (1) and to our paper (21, that a chemically reasonable concentration range range is 690
Journal of Chemical Education
Error lnvolved In uslng Agu rre-Ode's(3form~la for the hydrolys s of salts, mapped as a f~nc11on of the plCs of the acd and the oase from w h c h the salt der ves, the concentrat on of the salt 1s 1 M Uwer number: per cent error in [Hi] ; lower number: ApH.
Literature Cited 1. Malinowslu, E . R . J. Chrm.Educ. IM, 61.502406. 2. Cerdinali, M. E.; Giomini, C.; Mamsu, G. J Chem. Educ. 1990,67,221-223. 3. Aguirre-Ode. F. J. Chem. Educ. 1981.64.957-958,
M. E. Cardinali Deparlment of Inorganic Chemistry The University via Elce di Sotto 10 06100 Perugia, Italy
C. ~iomini' G. Marrosu ICMMPM Department "La Sapienza" University via del Castro Laurenziano 7 00161 Rome, Italy
To the Editor: The statement in the letter-to-the-editor written by Aguirre-Ode "Malinowski (1)describes the same computer method I used to calculate exact pH values" is inwrrect. Aguirre-Ode's method does not yield 'exact pH values." I t yields approximate values that are correct in certain ranees of DK. and DKLbut incorrect in other ranees. The iterative method k a t i described corrects for thisinaccuracy, but was neither recognized nor used by Aguirre-Ode. Edmund R. Mallnowski Stevens Institute of Technology Hoboken, NJ 07030 Assigning Oxidation Numbers To the Editor Packer and Woodgate's formal oxidation numbers for sulfurs in thiosulfate and tetrathionate ions (1)e m ~ h a sizes our warning that assignments should not'be treked a s purely numerical exercises divorced from chemical reality (2). Thus S2032-is made from Sm03?aud SaOby oxidative addition without interchange of sulfurs as shown by radioactive tagging. In addition S(Ka) X-ray shifts from the elemental value show the central sulfur equivalent to that in sulfate and the outer sulfur to that in sulfide. Hence a zero oxidation number in S2032-or SqOs2-,corresponding to unchanged sulfur, is hardly realistic. The difficulty is avoided if one recognizes the difference between sulfurs and assigns the bonding electrons to the much more negative peripheral or bridging sulfurs instead of sharing them equally in all the sulfur-sulfur bonds. Then both Lewis structures become [S"SVIO"$L and the outer sulfur is oxidized to S-on forming S4OS2-. Literature Cited 1.Packer, J. E.; Woodgate. S. D. J Chrm. Educ 2. Woolf, A.A. J. Chom. Educ. 1988.65, 45.
1991,68,456. A. A. Woolf Bristol Polytechnic Coldharbour Lane, Frenchay Bristol, England BS16 IQY
To the Editor: Oxidation number is essentiallv a '%ookkee~ine" . ., w n c e ~ t vew useful for classification in many areas of'chemistry It is ~ r o ~ eintroduced rl~ as ~reciselvthis at a relativelv carlv s t i g e i n d a s such students do need a set of purely nume;ical rules to assign them in the first instance. That there are limitations 6the chemical reality of the numbers derived from our rules (our oxidation rules are essentiallv 'To whom any further correspondence should be addressed.
those proposed by K a u f i a n (1)) is clearly shown by the fact that one can arrive a t different formal charges and oxidation numbers from different resonance Lewis structures of the same species (e.g., NzO). While fully agreeing with Woolf that the assignment of +6 and -2 to the central and peripheral sulfur atoms respectively of Sz03'- is chemically preferable we would not advocate the introduction of a second rule to cover ~- cases such as NzO and S203'-, which wntain one element in two different environments. This problem does not arise for most important inorganic species covered, even in first year university chemistry. At this foundation level rules should be kept as straightforward and simple as possible. In further study one soon learns of the frailties of the oxidation number concept and of Lewis structures themselves. ~
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Literature Cited 1. Kaufiman, J.M. J. Chem. Edue. 198B.63. 474.
J. E. Packer and Sheila D. Woodgate
University of Auckland Auckland. New Zealand Standard Relative Electrode Potentials: Conceptually and Pedagogically the Right Name To the Editor: A recent article in this Journal (1990,67,403) describes an effectiveapproach to teaching electrochemistry in order to clear up the most important problems that students are likely to enwunter. I agree very much with this approach and I consider making electrochemistry teaching more consistent with the facts a valid effort. However, the authors of this article fail to name adequately the standard electrode potential, Eo, measured with respect to the standard hydrogen electrode. They call it mistakenly 'standard reduction potential" based (I suppose) on the fact that in the potential table the reactions are written by convention in the direction of reduction. This name, besides being erroneous, is a source of wnfusion for students. I t is erroneous because the wnstruction of the ~otential table implies that the potential difference (in the electrochemical equilibrium condition) is measured in cells formed between each electrode and the standard hydrogen electrode. In other words, the potential table reports the behavior of each electrode with respect to the standard hydrogen electrode. This behavior can be of two different types: reduction or oxidation (implies different signs) with respect to the standard hydrogen electrode, that is, the Li+/Li electrode with an E' value of 3 . 0 4 5 V is oxidized with respect to the Hz electrode, and the Ag+/Agelectrode with an E" value of 0.779 V is reduced with resnect to the Hz electrode. In conclusion, we cannot assign the same name. "standard reductron ~otential"to these two different behaAors. The wrrect n&e is "standard relatiue potential". Furthermore, the name "standard reduction potential" is a strong source of confusion for the students because it induces the bad practice of reversing the sign of the potential in electrode reactions that are written as oxidation reactions. Finally, I am of the opinion that the name "standard relative potential electrode" instead of "standard reduction potential electrode" is better both conceptually and pedagogically J. A. Squella Universidad de Chile P.O.B. 233 Santiago I , Chde
Volume 70 Number 8 August 1993
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