letters Equations for Potentiometric Titration
To the Editor: We have used the potentiometric titration experiment and the criteria suggested by Professor Sturrock [J. CHEX.EDUC.,45, 258 (1968)l with good success in an undergraduate course in analytical chemistry. Some difficulties arising from certain tacit assumptions in the derivation of the pHal, - pHil, criterion and in the treatment of the data to obtain the pKa of the weak acid deserve clarification, however. The rigorous equation for the hydrogen ion concentration during a titration of a monoprotic acid with a strong base, neglecting dilution, is [H+18 (Ka -t jCa)lH+l2 - lKX*I.l - f )
+
+
K.] [H+] - K,K.
=
0 (1)
where Ca is the analytical concentration of the acid and f is the fraction of the acid titrated The linear equation usually given for the titration and employed by Sturrock
is obtained by making several approximations in eqn. (I), namely that the first and last terms in the cubic equation are very small compared to the other terms, that K.C.(l - J) >> K., and that jC. >> K.. This last approximation causes deviations from the behavior predictedby eqn. (2) whenever K a becomes large compared to Ca, or when the ratio of Ca/Ka becomes small. Under these conditions the monoprotic acid criterion ApH = pH,,. - pH,,! = 0954 breaks down. The table below shows solutions of the rigorous eqn. (1) for ApH values for various values of Ca/Ka. ApH CJK.
= pHij, pH*/. 0 954
ApH = Ho 3 P& 0 954
-
Note that the linear approximation only holds with reasonable accuracy for CJK. > lo2. Note also that because the approximation involves j, that the portion of the titration curve past the half-titration point is more accurately described by the linear approximation than the first half, and a criterion based on this portion, e.g., ApH = pHo 9 - pHsl2 or ApH = pHo pHo 8, holds over a wider range of CJK. values. The same reasoning also applies to the determination of pKa-values. For example, for salicylic acid, p K a = 2.98, at a C. = 0 01 M, the least squares line of pH versus log (f/1 - j) for 0.1 < j< 0 9 gives a slope of 0.708 (instead of the one expected from eqn. (2)) and a p K a = 3.18 The least squares line of the region 0.5 < J < 0 9 has aslopeof 0.918 and a pK. = 3.09, This experiment and the useful criterion suggested by Sturrock provide then the opportunity for allowing
the students to gain experience in using chemical equilibrium data to make decisions about chemical structure and to obtain useful thermodynamic data. The students should be aware, however, of the approximate nature of the derivation, and might be encouraged to devise alternate procedures for treatment of the data which =ill hold over a nider range of experimental conditions.
To the Editor: The ApH criterion was suggested as a simple way to distinguish between a monoprotic acid and a polyprotic acid. Under the conditions described by Lomax and Bard (C./Ka < lo2), the titration curve for a monoprotic acid is flattened and a ApH value of less than 0.95 is found. Thus the difference in ApH between such a monoprotic acid and a polyprotic acid is increased. The ApH criterion is still valid since no monoprotic acid will have a ApH greater than 0 95 and a volyprotic acid will not have a AÈ value less .. than 0.95 For obtaining the p K a value for a monoprotic acid, the method suggested by Lomax and Bard is clearly sunerior to simulv " takine the n H at the half titration point. Similar considerations apply to polyprotic acids as was pointed out in the original paper. Thus the suggestions, made by Lomax and Bard, undoubtedly lead to a closer agreement between theory and experiment. Still closer agreement could be obtained if activity effects were considered. However, it seems questionable whether or not the improvement is worth the additional complexity when teaching at the introductory level. s
-
"Relating Science to People"
To the Editor: I n your editorial, "A Summons for Scientists" [J. CHEM.EDUC., 45, 4 (1968)l you stated; "It (this country) needs teachers who will show students how to use science and how to live with its by-products." In her letter to the editor [C. & 13. News, May 20, 19681 under the heading, "Science needs new perspectives" Elizabeth A. Eipper stated that, "The true crossroad, the one in most urgent need of thoughtful consideration, is that one which concerns the relationship of Volume 45, Number 9, September 1968
/ 621
chemistry and a chemical education to the world around u s ' The entire letter by Miss Eipper, also the further comments by other students (C. & E. News, May 20, p. 48-57, 1968) should be carefully road by all teachers of chemistry both in the secondary schools and colleges. With the increasing emphasis upon theory in the newer textbooks and syllabi of general chemistry there appears to he a decrease in the so-called applications of chemistry-topics which should be of great interest to the student, e.g., role of various oxides in air pollution, use of pesticides as related to health and conservation of natural resources, etc. In short, "the challenge is to relate science to people."
I treasure a story going back many years when a final examination question read: Draw a cross-section of a blast furnace and label all the parts One student's drawing was beautiful. At the bottom of the blast furnace there was an arrow pointing to a little blob. It was marked, TADPOLE. But how about the teachers? The son of a friend attended a course in organic chemistry in which the average grade on the final examination was 25. Nothing wrong with the students. The teacher's psychological need is involved. He wants students to know how brilliant he is (he ain't) and he leaves the befuddled students to acquire their own psychological frustrations. "It was all over my head,'" say the students, ' h u t gee, he sure knows his stuff !" The king ain't got no clothes on in many areas of the teaching profession. Do we have the courage to be responsible to our obligations?
A Closer Look at the King's New Clothes
T o the Edztor: My compliments to Professors Davenport[ J. CHEM. EDUC.,45, 419(1968)] and Gehrke [J. CHEM.EDUC., 45,441 (1968)l for having the courage to say, "Look ma, the king ain't got no clothes on." I should like to add a few experiences of my own. A class in Freshman Chemistry. A young lady who had had a year of chemistry in a New York City high school, and in which course she had a grade of 92 on the New York State Regents examination, came to me with the pleas that (1) something was wrong with her thermometer because she could not shake it down, and therefore it had been used; (2) she wanted a new thermometer, brand new, that is. I gave her a "new" thermometer without making any comment. In a few moments she came back with a puzzled expression on her face. The experiment dealt with the gas laws. "Where do you put the thermometer to take the temperature of the room?" she asked!! A class in Organic Chemistry. A detailed demonstration for the detection of nitrogen is given. It is pointed out that the water in the test tube should be boiled t o get rid of the oxygen before adding ferrous sulfate to it. Of course the reason for this is emphasized. At the end of the demonstration, twenty witnesses are asked, 'How could you detect dissolved oxygen in water?" Silence. A student volunteers, "Heat the water and put a glowing splint above it." When it is pointed out that the distillation of liquid air is not involved, a gloomy silence descends on the students. After a while the hand of a premedic is raised. "Put a fish in the water. If it lives there is oxygen present." A class in Freshman Chemistry. In a recitation class we were reviewing chemical equilibrium. At the end of the period I said, "As you know, all this is summed up by the equation: Concentration of C times the concentration of D divided by the concentration of A times the concentration of B equals K. And Mr. Smith, what is K?" "Potassium," replied the scholar. 622
/
Journol of Chemical Education
Mole Fraction versus Molality
T o the Editor: In a recent article [SACKS,L. J., .J. CHEM.Eouc., 45, 183 (1968)1, the use of mole fractions in place of molalities is strongly advocated While I fully support the use of mole fractions, on the grounds that they are less arbitrary and more immediately informative than molalities, I feel that it should he emphasized that they are not always unambiguous when used in the context of ionic solutions. As an illustration, consider a solution of 1 mole of potassium chloride in 9 moles of water. If we regard the solution as KC1 9H20, the mole fraction of water is 0.9; on the other hand, if we assert that the solution is K+ Cl9H20, the mole fraction of water is 0.818. Which of these alternatives is correct? (Interestingly, there is no ambiguity if the molality scale is used.) Thermodynamics provides no guidance, except by way of experimental measurement; in this special case of a completely ionized salt, experiment obliges us to choose the second alternative. But if we consider a solution in which the solute is only partially ionized, the same criterion forces us to the conclusion that neither answer is appropriate, and that the mole fractions in the solution are dependent on the degree of ionization of the solute. This situation can be turned to pedagogical advantage by using it to focus attention on the importance of the extent of ionization of the solute. It is nevertheless markedly inconvenient for routine practical use, and I would be interested to hear of any (preferably) simple way of circumventing these complications
+
+
+
