provocative opinion On Pet Peeves and Sacred Cows Jack L. Hedrick Elizabethtown College, One Alpha Drive, Elizabethtown. PA 17022 While perusing a recent issue of this Journal, something caused me to stop reading in my tracks and, as they say, gave me pause for thought. Two papers ironically or, perhaps, purposely placed consecutively described some new applications for some old methods. The first dealt with spectrophotometric titrations ( I ) , the second (2)with the use of the socalled Gran method (3) in plotting potentiometric data. A casual glance may have resulted in the reader wondering if the plots included with these articles had not been reversed by some vindictive editor or typesetter. Allow me to exnlain hv considerine first the article on spectrophotometric titrations. I doubt that it is an exaggeration to state that spectrophotometric titrations are old hat. A review of the theory and practical considerations appeared in the literature (4) more than three decades ago, a sure sign that the method had matured. Now, I don't mind uncovering new applications for old methods in these pages. In fact, I seek them out. Who hasn't quested for fresh ideas when revising an old course, instituting a new one, or simply wanting a change in experiments thatstudents are performing? I occasionally submit such papers to this Journal, the most recent d e ~ ~ r i h i nthe g determination of calcium in eggshells via a potentiometric titration utilizing a calcium ion selective electrode. What caueht mv . eve . in the article under discussion was a plot of absorbance vs. volume that looked for all the world like a typical S-shaped potentiometric titration curve. This was quite a jolt to my stodgy, preconceived notion that one of the great advantaees of photometric titrations is the ease of endboint determination since it is usually found a t the intersection of two straight lines, one of which may he the abscissa. Upon closer examination, of course, I found the anticipated straight lines as extrapolations of the experimental data. I t was, thus, in a somewhat startled and preoccupied frame of mind that I paged quickly through the next paper, the one involving potentiometric titrations. A few pages later I thought, wait a minute, those plots weren't S-shaped, that article probably dealt with Gran plots. Sure enough, as my fingers retraced their hurried steps, there they were, Gran plots. A new experiment for an old method. Good, I said to mvself. . . let's see what's here. But. as I was reading the paper, I was reminded why I long ago gave up on having my students perform this kind of plot. Sure, it's a nifty idea and doesn't involve calculations that are all that difficult. But, mv students seem to find it an unnecessarily confusing concept. ?!I ~dvanlngeo r (:ran ph11i that is l'rtquentl) emphat sized is t hnt rhr strairhr lines pnxlu~i,dare e a ~ i e1r ~ p l 0and produce more accurate end point values. But, shucks, if it's straight lines that I want for data ordinarily collected by students, I'll have them do the variation of the first derivative plot suggested by Cohen (5) or the first of Gran's plotting suggestions ( 6 ) ,which is nothing more than a plot of the reciprocal of the first derivative vs. volume. In both of these methods, straight lines are produced from calculations that 614
Journal of Chemical Education
Table 1.
potentiornetricTitration Data for Fez+-Ce4+
Volume, mL
E mV
Volume, mL
E, mV
21.00 22.00 23.00 24.00 25.00 25.10 25.20 25.30 25.40 25.50 25.60 25.70 25.80 25.90 26.00
474 482 490 501 520 523 527 530 535 540 546 553 564 572 600
26.10 26.20 26.30 26.40 26.50 26.60 26.70 26.80 26.90 27.00 27.50 28.00 29.00 30.00 31.00
944 1005 1035 1057 1070 1078 1065 1091 1095 1099 1112 1120 1131 1139 1145
are relatively easy for students to comprehend and result in accurate end point values. What more could a lazy -plotter of points hope for? While rummaging through my mind and reflecting on all of this, I foundmiself hecoming more and more anxious, irritated even. Then it dawned on me. By association, I had fallen into the midst of one of my pet peeves, the insistence of some textbook authors that first and second derivative plots of potentiometric data produce more accurate end point values than simple E or p X vs. volume plots. This despite the considerable imagination that is frequently forced upon the plotter in constructing and extrapolating lines through the derivative points. (I'm, of course, considering here plots that are done hy hand rather than by a recorder or computer program.) Have these authors worked through a derivative plot lately? Have you? In case you haven't, I have shown in Table 1 the data I obtained quite a few years ago for the potentiometric titration of Fe(I1) with Ce(1V) as the titrant utilizing a P t wire indicator electrode and a SCE as reference. This narticular titration appears as an example in many textbooks. It is ideal for relatine Nernst eauation theory and calculations mesented in t i e classroom to potentialimeasured in the labbratory since there is almost exact agreement between the two. The data was obtained using a Leeds and Northrup Type K3 potentiometer and represents the last time I used such an instrument for this kind of work, having long ago switched to pH meters for routine potential measurements in the laboratory. Granted the data could have been more precise. I could have recorded E values in the vicinity of the equivalence point every 0.05 mL or less rather than every 0.10 mL. But, the additions are constant so that differences in Evalues can ~
Figure 1. Potential as a function of volurna for the Fe(l1)-Cs(lV) titration
Figure 3.Secondderivative of potential asa function of volume for the Fe(i1)Ce(lV)titration.
Table 2.
End Point Volumes Determlned by Various Plotting Methods Method
End paint, mL
Evs. Volume First Derivative Second Derivative Cohen Gran's First
,.........:
25.00
....-
26.M
V~LUHE C.,IV,
27.00
L.
Figure 2. First derivative of potential as a function of volume for the Fe(l1)Ce(1V) titration.
be used directly in derivative plots without the need to divide by the volume differences. And, given that I am more experienced than the students in collecting data of this kind, it would seem that this data is a t least as good as they would collect in their first attempts. Figures i-3 show the data points for E as well as the first and second derivative values as a function of volume. For simplicity, only those values in the neighborhood of the equivalence point are displayed. Now, I ask you, for which one of these three would you feel most comfortable in constructing the line($ and having confidence in the end ooint value obtained? Going one step fGrther, Table 2 lists the end point volumes determined utilizing five d o t t i n g methods mentioned above. The values range from 26.02io 26.07 mL. No matter how the data is plotted, in effect, the same number is ohtained. Certainly many principles are demonstrated and students should learn a great deal from duplicating this exercise. But, they will also question why they can't plot the data in just one way, the way they perceive to he the simplest and easiest. Will they accept such answers as they need to be
26.06 26.07 26.05 26.06 26.02
exposed to these methods to learn how to use them, to he able to evaluate them, to examine critically what textbook bibles proclaim, or i t is good for their academic soul? I hope so, but sometimes I wonder. Here's another one of mv oet oeeves. Manv. mavhe most. analytical textbook authors in di'scussing theibpicd of determination of best value, standard deviation, and Student's t test insist on spending page after page describing methods that are applicable to large sets of data. These methods are fine for playing around with major league batting averages or the averace number of eallons of milk produced by dairy cows in ~ennsylvania.~ ; t ,in the academic world, students usually report the results of only three to five trials. Except for the usk of the rejection quotient, Q, the paper by Dean and Dixon (7) describing the rapid and simple processing of small sets of data is largely ignored. Somewhere in here there's a point I'm trying to make. Mavbe it's this. How manv- oracticallv useless skills and . techniques are we introducing to our students, methods that mav not demonstrate anvthine worthwhile? How often do . we as teachers take a critical look a t those sacred cows we oresent simnlv . "because we are comfortable with them, have always included them in our courses, and student grasp of them is readilv measured and iudged in examinations? We ask our students to have open a i d inquiring minds and to be critical in their thinking. Yet, many of us insist that our teaching cannot be accurately evaluated because the ability to teach or inspire critical thinking cannot he measured. Are we really involved in the process of critical thinking? Do we as teachers serve as shining examples of critical thinking in the classroom? I suspect that the answers all too often are, no. Perhaps if the answers more often were yes, there would be fewer commissions, accrediting agencies, and government Volume 64
Number
7
July
1987
615
officials oroclaimine that we are doina a lousy ioh as teachers. perhaps ifmore.bfus applied the &tical thinking we use in our research efforts and demand of our students in the classroom, we'd all have a lot more pet peeves. Then, perhaps, there would he far fewer sacred cows in academe.
616
Journal of Chemical Education
Literature Cited I . Fulton,R.;Ross, M.:Schroeder, K r l Chern.Edur. 1986,63,721
i:~ ~ ~ ~ ~ yF.; ,":~$2~$;~Q:,,,63,7u~ N 4. 5. 6. 7.
Galdu.R. H u m e , ~ . A ~ ~ ! . C 1954.26,1740. ~ * ~ . C0hen.S. R. A n d Chem. 1966.38, 158. Gran. G. A d a Chern. Scond. 1950.1.559. Dean. R. B.;Diion, Chem. 1951,23,636.
W.J.Ana1.
