Monoprotic or Diprotic?
To the Editor: I n the April issue of THIS JOURNAL [45, 259 (1968)], Peter E. Sturrock concluded that when K 1 = 4K2 for a diprotic acid, the numerical difference in p H , between the points on the titration curve a t 25 and 75% titrated, is identical to the corresponding pH difference for a monohasic acid. The purpose of this communication is to explicitly demonstrate that this result is not altogether unexpected and to furthermore briefly discuss its consequences. Into Sturrock's eqn. (6)
we may substitute 4K2 for Kl wherever it appears, to obtain
where the latter form of the expression is recognized as the equation for a monoprotic weak acid with K . = 2K2, because for such an acid, li
=
[HAI/([HAI
+ [A-I)
=
[H+I/([Hf1
+Kd
I t is evident that whereas a ri value of 1.50 corresponds to the 25% titrated point for a diprotic acid, the value of ri' would he 0.75 for a monoprotic acid a t 25% titrated. Similarly, at the 75% titrated point, li is equal to 0.50 for a diprotic acid whereas n' is equal to 0.25 for a monoprotic acid. From eqn. (1) it is readily possible to write ApH = logl(l/?i' - 1)75%/(1/fi - l)zs%l = log[(2/7il) -75%/(2/fi
- 1)25%1
which explicitly demonstrates that the pH difference, ApH, is numerically the same for the two cases under consideration when the constraint upon the value of K 1 / K 2= 4 is imposed. I t should be noted that in general, we may express K l as kKp, which upon substitution into Sturrock's eqn. (6) results in
so that and it then can he seen that only when k
=
4 does it
Volume 46, Number 2, February 1969
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become possible to express il by a n equation which is of those who go no further than high school it appears that t,he first degree in [H+] instead of one which is quafor over 90% of our graduates the high school chemistry dratically dependent upon [H+]. That this situation is course is a terminal one. unique has been recognized before.' Using a city directory which gave the names, adWhen K 1 I 16K2, the curve for a dibasic acid posdresses, and occupations of over 20,000 residents of the sesses no inflection point a t the first equivalence p ~ i n t , ~ , city ~ in which my high school is located I made a check of and according to R i c ~ i consequently: ,~ ". . .the dia randomly selected 7y0 sample. I t appears that for basic acid appeals to behave like a monobasic acid.. . about 3% of the group the occupations require a college but the shape of the curve is not necessarily that of a major in some field of science, for about 2% of the group monobasic acid." From Ricci's, Sturrock's, and the the occupations require some science beyond high present discussion it is evident that the only condition school, and for 95% of the group the occupations refor which "not necessarily" could be deleted from this quire no science background. Ricci statement is when K I = 4 K z . Furthermore, The high school chemistry course which is terminal "if K I # 4K2 the two curves [diabasic compared to for 90% of the students and which is not needed in the monobasic] differ in shape whether or not there is an occupations of some 95% of the employed must be inflection" a t the first equivalence point.' quite different from a course intended for those who just I n summary we may then conclude that when K1 = happen to be destined to become professors of science. 4K1, although no inflection point exists in the region of Textbook writers of earlier years recognized the the first equivalence point, the curve for a dihasic acid problem. Why must modern writers ignore the wisis indistinguishable from a monobasic one; when 4K2 < dom shown years ago? I n the preface to a text K , I16K2,no inflection point exists in the region of the ["Steele's New Chemistry," A. S. Barnes & Co., 1876.1 first equivalence point for a dibasic acid but the ApH published about 90 years ago we find, "There is a large between two given points is greater for a dibasic acid class of pupils who can pursue chemistry only a single than it is for a monobasic one; and when K 1 > 16K,, an year. They do not intend to become chemists nor even inflection point does exist in the region of the first professional students. If they wander through a large textbook they become confused by the multiplicity of strange terms which they cannot tarry to master, and as a result too often only 'see men as trees walking."' I n choosing the materials for his book the author has ". . . omitted that which could not be long retained in the memory and that which is essential only to the chemist." L R ~ c ~J r. ,E., "Hydrogen Ion Concentration," Princeton If the older textbook writers found the college preUniversity P~.ess,Princeton, 1952, p. 252. paratory courses of their day unsuitable for the students =SMITH, T. B., "Analytical Processes," Arnold Publishers, going no further than high school, I feel they would find Ltd, London, 1940, pp. 194-5. "ICCI, o p . cil., p. 2.51. the college preparatory courses of today even less suitable for those students. Dr. Davenport expressed concern about the "bottom 90%" of entering college students and the chemical fare available for them. I am equally concerned about the 90% of high school graduates who Chemistry for the High School Student will have no further chemical fare. The current textbooks rush to the scientific frontiers, and the urge to T o the Editor: teach too much too soon is hardly making for scientific I n the dune issue of THIS JOURNAL,Dr. Davenport literacy among those who will not be scientists. and Dr. Gehrke raise [45, 419, 441 (1968)l issues conI feel that it is more than high time to "Elevate them cerning general chemistry texts and courses for beginguns a little lower," to try to substitute some underning college students. As a high school teacher of standing and comprehension of a fcw chemical topics, chemistry with considerable graduate study; industrial rather than to add to the tremendous number of topics analytical and research experience; several years of about which the students are as confused as ever, to college teaching of general chemistry, qualitative, and teach what we can make interesting, vivid, and of some quant,itative analysis; and years of teaching high school service-and be content to omit the rest. This may chemistry I view with ever increasing concern the curresult in college freshmen who have not been exposed to rent trend in high school texts. the complete treatment of some new "approach," or The curriculum reforms which are trying to make the some new "study" and in unevenness of preparation. teaching of high school chemistry more logical, more Rut if it also results in freshmen with enthusiasm and rigorous, and more abstract are resulting in texts that whetted appetites, and if it results in a better compreare going far afield from the needs and abilities of the hension of chemistry and some of its implications for greater number of high school students. everyday life by that large group of citizens who do not Three years ago I made a study of the college course become scientists, it will be more advantageous than elections of 219 graduates of the school where I teach the creation of a multitude of chemical wanderers who who were then enrolled in 29 colleges. About 20Yc of saw "men as trees walking." this group were majoring in some field of science. The others were electing only the minimum number of science courses to meet college distribution requirements. More than 75% of this group did not elect chemistry. When to this group is added the number of 124
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