edited by ARDENP. Z ~ P P SUNY-CORland Conland. NY 13045
An Evaluation of Drop Counting as a Volume Measurement James Ealy and Mlles Plckerlngl Princeton University Princeton, NJ 08544-1009 In recent years a number of laboratory textbooks (1-4), especially at the bighschool level, have embraced an approach to labs in which counting drops replaces traditional measurement of volume. No comprehensive study of the reproducibility of this method has yet appeared in this Journal. Uncertainty in this technique arises from two sources. First, the drops are discrete, "quantized" units, not a continuous measurement. Second, there may be reproducibility or systematic error problems with the devices used to produce the drops. Theae two sources of uncertainty are very different, and their relative importance must be determined if we are to design good experiments using the new technique of volume measurement. Experimental reproducibili-
Devices used in this study. From top to bonom: Pasteur pipe, Beral Thin Stern, Beral Micro-Tip. Tip Top.
ty measurements are reported in this paper for four representative types of droppers. These will be compared with the uneertainty from drop discreteness to yield overall conclusions. This work should provide important information for curriculum design using the new technique. Experimental Five devices were investigated. The Beral Thin Stem, the Beral Micro Tip pipe, the traditional glass Pasteur pipe, the Tip Top lavailable from Helena Labs. 1530 Lindbergh O r . Hraumont, TX 77304-0732).and the standard glaas-upped buret The pinstimare is shown in the figure. For each device (except the buret) measurements were made with the nozzle of the device at 45and 90' to the horizontal plane to assess whether there was an angle effect. To obtain data an d r m variabilitv. the we~ghtsofdrops of dntilled water from each dewre were measured, uarng a drgltal halance with 10th of milligram readout. Work was done a t a time when the balance was not being used for classes, so that air currents and vibrations were minimized. For buret measurements the buret was mounted above the balance, and the stopcock was set to allow a slow droo rate (less .~~ than one oer second). The first fiw measurements ineacb set were discarded because of the need to saturate the air inside the balance enclosure with moisture. Runs were done of at least 25 individual drops in which weights were recorded after each individual drop. Measurements were also made of 10 sets of 10 drops, since this is more typical of the kind of measurement ~~
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Drop Slre and Varlablllty lor Dmereni Devlces
Device held at 45' that would be done in a student lab. The precision of the balance itaelf was assessed by weighing a nonvolatile object 25 times. The standard deviation of this set of measurements was i0.00003 g. Since t h e weights of the drop and sets of drops were obtained by difference, the inherent balance absolute error far this difference is twice that of the individual measurement, that is iO.OOOO6 e. The results of the study are summarized in thetablc, whichgiveathe weight ofadrop or set of drops, and the standard deviatiun. The relatiwerror show iscomputed as twice the standard deviation divided by the mean value. This is. therefore, the 93% confidence interval. The relative uncertainty includes the uncertainty from the balance weighinga, which is negligible in most cases. The individual devices used to compile the data in the table are believed to be representative samples of their types. Preliminary studies showed that individual droppers differ as much as 5%in the absolute volume of a drop delivered.
min Stem Mcro-Tip Pasteur Tip Top Device held at 90° Thin Stem Micro-Tip Paslew TVPTop Buret 10 h o D sets
Device held at 45' Thin Stem Micro-Tip Pastew Tip Top Device held at DO' Thin Stem Micro-Tip Pasteur
TIP TOP Buret
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Volume 68
Number 5
May 1991
A121
the microtcoie Icrborotory
Discussion The intrinsic precision of any drop-based volume measurement cannot exceed the limit of i 1 drop. If the measurement is of 10 drops, the best that the instrument can possibly do is lo%, even if the drops were perfectly uniform. The drop discreteness becomes less of a problem when the number of drops gets larger, hut there is a practical limit of about 30 drops, beyond which operator fatigue becomes critical. There is a real danger of Losing count! Thus the best possible device with absolutely reproducihle drops has an intrinsic uncertainty of 3.3% in a drop-counting experiment. The uncertainty from drop discreteness has to be combined with measured nonreproducibility of the device if an overall comparison to traditional methods is to he made. Perhaps the most obvious question is: which type of device delivers the most consistently reproducible drops? The relative uncertainty numbers in the tahle give some guidance. The buret is by far the best source of reproducible drops, in all cases producing less than a 1%variahility. The variahility in buret drops is so small as to approach the limits of measurahility in this study (set by the reprodueihility of the balance). The plasticware is not as gwd. Even 10 drop sets show significant variability-the degree to which the drop variation "averages out" is much less than the reader might expect. The possible comparisons of the remaining devices are leas clear. A statistical test of variability, the F test (5, 6) was computed for all possible comparisons. The resultingF values showed the Tip Top and the Beral Micro Tip to he roughly equivalent, and both to he better than the Pasteur pipe and the Berd Thin Stem. A second question is whether the angle at which the dropper is held matters. The size of drop and its reproducibility is displayed in the table for two angles. There is a striking difference in the size of a drop depending on whether the dropper is held vertically or horizontally. Thus how the student holds the device-a variable one might not think to control-is an additional source of drop variability. The devices all display this effect, hut the Tip Top is the least affected by angle. In all cases, the drops are 10-258 smaller fora given device held a t a45- angle. This effect is statistically significant (t values range from 12.7 to 51, all p < 0.001 or better). The values in the tahle also show that there is a difference in intrinsic variability of drops depending on angle. In general, holding the dropper vertically almost alwarj makes the drop size more consistent. There is another source of variability with the Beral Thin Stem pipe that is not present with the other instruments. To use this, the long plastic nozzle is pulled out to form a narrow section, which is then cut. The orifice at the end is not circular, hut an ovalslit. Even if the nozzle is held a t the same angle with respect to the horizontal, axial rotation about the long axis makes a difference in A122
Journal of Chemical Education
drop size of about 15%. The difference is by nomeans as large as the angle effect, hut it is statistically significant (t = 1 1 . 2 , ~< 0.001). Hence there is an additional source of variability to worry about. Even if students hold the pipe so that the tube is a t a fixed angle, drop variahility can he produced by rotating the device about its long axis. In summary, then, our recommendation is that, if uniform drops are required, a buret is the best way to deliver them. The next best is to use the Tip Top held vertically. The Beral Micro Tip or the Pasteur pipe gives reasonably good results if held vertically. Under ideal conditions one can hope for a reproducibility of drop size of about 1.64%, depending on the type of device used. To get an overall uncertainty for the experiment, it is necessary ta comhine the drop discreteness uncertainty and the drop reproducibility. Consider the delivery of 30 drops, for which overall uncertainty will he the sum of uncertainty due to the discreteness of the drop size (30 f 1 drop or 3.3%) and the relative uneertainty due to variability in drop size. (This latter is easy to compute from the tabulated data since it should he the relative error for 10 drops multiplied by JTW3.) Using the best device, the Tip Top dropper held at 90°, the overall precision expected is 4.2%. If a titration is done with two reagents, each of which is measured in this way, the relative uneertainty in the ratio will he multiplied hy 8,and will be about 6%. This is the intrinsic limit on precision in standardization done with plasticware under the best possible conditions. The calculation assumes that the same individual dropper is used for both liquids. Correction may he required if the two liquids do not give drops of the same size or reproducibility (certainly true for concentrated solutions, according to ref 7). This uncertainty is about a n order of magnitude worse than that obtainable with standard glassware. For a gravimetric titration the picture is brighter. Far this, the plastic bulbs are weighed before and after the solution is delivered. This will eliminate the drop variability problems discussed at length in this paper. While the drop discreteness problem still persists, its effect can be made arbitrarily small by the use of larger volumes. To any drop discreteness variability muat be added the uncertainty due to the balance. This is negligible for a good analytical balance with four-decimal-place accuracy hut not if a balance of less precision is used. The density of the solution should also he known, for precise work. The major drawback is that the time needed for weighing destroys at least part of the rationale for drop based experiments--speed and ease of measurement. The reader might also object that some future deviee will produce much less variable drops than any we tested. Nevertheless,
the uncertainty caused by the discrete nature of the drops will persist. For the hest devices we tested, drop discreteness was already the largest contributor to the overall uncertainty. No deuiee, no matter how perfect, can maid the uncertainty due to the discrete nature of the drops. The authors are not trying to condemn the use of drop-based experiments. We realize that different lab instrudors have varied agendas and that the decreased cmt, lah time, and hazards may well counterbalance the loss of precision. We do, however, feel that such dropper-baaed experiments do not illustrate the quantitative side of chemistry very well and that there is an elegance in the precision of traditional analytical chemistry.
Acknowledgement This work was supported hy NSF grant TPE-8751837 as part of a larger study of micro lahoratorv work suitable for hieh school inhoratoriea. This grant is administered by the Institute for Chemical EducaLion at the University of Wisconsin. ~
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Literature Cited
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1. Russo. T . Micro Chemist,":. Kemtec Eduestional: Kenaing&n. MD. 1985. 2. Mieroaeole Chemistry: The Woodrow Wilson National Fellomhip Foundation: Princeton, NJ, 1987. 3. Thompson. S. Chemlrek: Micioacole Experiment8 for General Chemistry; Allyn and Bsean: Needhsm Heights, MA, 1989. 4. Mills. J. L.; Hsmpton, M. D. Mieroseole Laboratory Manual for General Chemistry; Randam House: New
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E&x, ~ England, l98i: ~ p 22.
' Author 10 whom correspondence
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addressed.
~xperimentsfor Organic Chemistry Using the Small-Scale ApHelmuth M. Gllow R h o d e s College
2000 N. Parkway Memphis. TN 38112
Free radical halogenation of hydroearhons is a t o ~ i ecovered durine the first semester of mist introductoryor&ic chemistry courses, although the emphasis on the (Continued on page A124)
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