Example
Determination of pH for c = 0.01 moWL (NH&HP04. From comparison of charge and concentration balances one obtains (7) [HI + 2[H3P0,1 + IH2PO41= IOHI + [PO,] + [NHsI
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ular formula. The better students in the class easily come up with a dozen for a molecule such as C6H6.I n fact, a recent enumeration (3)lists 217 possible topological (structural) isomers. Although many of these are unlikely to be stable entities, some are a t least a s stable as the ones cited in this article.
(see eq 5 a t q = n = 3). The preliminary evaluation (see figure) gives pH 8 for the point P of intersection of the corresponding resultant functions. At the point P, eq 7 can be simplified into the form = [NHd (8) [HzPO~I
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pH 8 lies close to the pk2 =log (KdKJ = 7.2 value and the expression for Z (eq 1) ought be reduced into the form
z = K,[HI + K ~ [ H I ~ Moreover we see also that IogK,' = pk,' = 9.35 for TQL' lies close to the evaluated pH value. I t is then advisable to write
Then we get, in turn, C.K~[HI~ 2~ KJHI + K ~ [ H=IK< ~ [HI + 1
Tadeusz Michalowski Faculty of Chemistry Jagiellonian University 30-060 Krakow, Poland To the Editor:
Obviously, there is more than one way to solve acid-base problems. The purpose of my paper was to point out that in this kind of chemical problem we have chemistry involved, rather than a cross point in a logarithmic plot or a n exact number coming from the use of purely mathematical techniques. Even though a method may include some extra algebraic manipulation, it may also include more chemistry. As a chemist, one may prefer not to do simply what can be done chemically. Aleiandro Olivieri Depanamento oe OJ mlca Anal llca F a c ~tad de C enc as Bloq~rnlcas y Farmace~tcas Suipacha 531 Rosario (2000),Argentina
Benzene Isomers? To the Editor:
After mentioning benzene ( I ) , Dewar benzene (2), benzvalene (3),and prismane (41, the recent essay on "The Diverse Nature of the CsH6 Molecule" (I)states that "the only remaining isomers of C6H6 t h a t are possible are the ...bicyclopropenyls" of which "there are three isomers, namely 1,l-, 1,2-, 2,2-." Again in referring to the synthesis of the latter two ofthese compounds (2)they are characterized a s "the last of the remaining benzene isomers". What about fulvene ( 5 ) and trimethylidenecyclopropane (6)to name just a couple? As a n introduction to the structural theory of organic chemistry I routinely ask students to draw a s many isomers as possible for a particular molec-
The author may have misread the statement of Billups and Haley (2)that 2,2-bicyclopropenyl(7) is the last of the remaining (CHI6 isomers. In fact, six (1-4,7,8) of the 217 C6H6isomers are composed solely of CH groups (4),but the 1,2-(9) and 1,l-bicyclopropenyls (10) mentioned in reference 1do not fit into this category Literature Cited 1. Patgieter,J.H. J. Chem. Ed., 1981,68,280. 2. Billuos. W. E.: Halev. M. M . A m u Cham Int. Ed. Enel.. - . 1963. 28.. 1711 3. ~ m k H.A"& : ~ h e n Int. z ~ d y ~ n g 1988,Z8,1627. l., 4. Bslaban.A.TRm Rournn. Chim l9BB.11, 1097:Warren,D. S.;Oimare,B.M. J.Am. Ckam Soc 1992,114,5378.
Manfred G. Reinecke Texas Christian University Fort Worth, TX 76129 To the Editor:
I want to thank Professor Reinecke for pointing out that the CfHf molecule is indeed much more diverse than the contentiof my article suggests. The phrase "last of the remaining benzene isomers" was perhaps a poor choice of words when one considers the contents of the article, but a t the same time it also indicates the main thrust of the article, and that is to discuss some of the less well-known benzene isomers. I t was never my intention to discuss the whole spectrum or even the well-known C6H6isomers, because, a s was pointed out by Professor Reinecke, it would be a n immense task, but to concentrate on the ones most closely related to benzene. A better choice of title and clearer explanation in the introductory part of the article Volume 69 Number 10 October 1992
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