B. G. Kraiochvil, T. J. Bydalek, and w. J. Blaedel
University of Wisconsin Madison
Closely Spaced Samples for Teaching Quantitative Analysis
Qne of the disadvantages of conventional quantitative analysis experiments that involve unknown samples is that correct sample percentages cannot be disclosed. This restriction deprives the student of an opportunity to evaluate his laboratory work constructively on the basis of the direction and magnitude of the error in his reported values. One approach to this problem is to replace analysis of unknowns with quantitative measurements of physical properties, such as determination of the solubility product of an insoluble salt or the dissociation constant of a weak acid. Complete elimination of unknown samples is undesirable, however, for unknowns are the best device for encouraging the achievement of maximum accuracy in the laboratory. A second approach is to issue samples in liquid form. Since an unlimited number of sample sizes can be selected by variations in volume of sample issued, a student can be given his sample size a t the time that he is given his grade on the experiment. Liquid samples have several drawbacks, however. These in-
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clude the necessity of frequent preparation and standardization of stock solutions, the possibility of errors during dispensing of samples (more serious than with solid bottled samples where crosschecking is simple), and, the lack of opportunity for student experience in the handling and dissolution of solid unknowns. A third approach of this problem has rcccntly been introduced at the University of Wisconsin. A series of solid samples has been prepared in which the amount of sought-for component varies between samples by small, unifonnlyspaced increments of 0.2-0.3% relative. For example, the chloride unknown series consists of 21 samples ranging from 47.7 to 50.3y0 chloride, adjacent samples in the series differing by about 0.13y0 chloride. Even if the correct values of the series become known to the students, they are of no help in the identification of individual samples. Thus, a student must have a result within 0.06% chloride of the correct value (or within 0.1% relative) if he is to "improve" his grade by arbitrarily reporting the lrnown sample value closest to his experimental result.
Student Results for Individual Chloride Sam~les
Sample
-Gravimetric--Faiana 7VolhardNumber Number Number of Median of Median of Median student error student error student error reports in % Cl reports in % C l reports in % CL
Weighted average of the medians. Student errors in chloride anolyrir Ail errors above 1.00% CI and below -1.00% CI are grouped a t 1.05% and -1.05%, respectively. Gravimetris method; median, 0.0O7% Cl; standard deviation, 0.1 3% CI. Fajonr method; medion, 0.02a% Ci; stondwd deviation,0.25%CI. Valhord method; medion, -0.07r%CI; rtondord deviation. 0.28%Cl.
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The preparation of a sample set of this kind is not difficult. Reagent-grade batches of powdered sodium and potassium chlorides were dried a t 150-160°C for several hours, sieved to pass 100 mesh, and redried. Portions of each salt were weighed accurately into a two-quart stainless steel V-blender to give a 750-g lot of the desired chloride content. Each lot was mixed thoroughly for about 45 min, then distributed immediately in 2-g portions into glass screw-capped sample vials. Careful titration of one of the samples with standard AgNO, showed that the sample was homogeneous, and that the chloride content agreed with the theoretical composition within 0.01%. Student results with these samples have been compiled over a two year period. The figure shows the distribution of values reported. The majority of these are averages of three determinations, but some are based on only one or two. Results for all 21 samples for each method are shown on a single histogram because analysis of the data showed no significant differences among samples. Distributions of student results are shown for the gravirnetric chloride determination and for the Fajans titration with standard silver nitrate using dichlorofluorescein adsorption indicator. In addition, some students who took an extra credit of laboratory did a Volhard titration, in which a measured excess of standard silver nitrate is added and the excess titrated with standard KSCN after inactivation of the AgCl precipitate with nitrobenzene, using iron(II1) as indicator. The laboratory procedures have been described.' Standard deviations for each method were obtained by finding the range that included 68% of all reports, the assumption being made that the distribution of results followed the normal error curve, which is only ~BLAEDEL, W. J., AND MELOCHE, V. W., ''Elementary Qumtitative Analysis," 2nd ed., Harper and Row, h e . , New York, 1963.
approximately true. This procedure was considered more reliable than calculation from the squared individual deviations, which gives unwarranted weight to the highly divergent values associated with gross errors. Standard deviation values found were 0.13% chloride for the gravimetric method, 0.25% chloride for the Fajans volumetric method, and 0.28y0 chloride for the Volhard volumetric method. It is interesting to note that 42% of the students doing the gravimetric experiment reported a result that was within O.lyorelative of the true value. Park2 has reported a standard deviation for the Fajans method of 0.31% chloride for 454 results, which compares favorably with the value of 0.25% chloride calculated here. He also reported a standard deviation of 0.30% chloride for the gravimetric method for 453 results, which compares with the value of 0.35% chloride found by Daugherty and Robinson3 for 2570 determinations, but which is considerably higher than the value of 0.13% chloride found here for 864 students. The table lists the median student errors by sample for each of the three methods. Median errors for the gravimetric method are small for all the samples, indicating no bias in any sample and confirming the accuracy of the previously described method of sample preparation. The larger median errors for the Fajans and Volhard procedures indicate a lower precision for these methods, a conclusion drawn from the figure. Other samples either prepared or being prepared in a similar manner include carbonate, dichromate, barium chloride dihydrate, and iron ore. Giving the correct percentage for unknowns a t the time that the experiment grade is returned has resulted in considerable student interest in searching for errors in their laboratory work. The only dissatisfaction expressed by students has been that correct sample values cannot be released for other experiments for which closely spaced samples are not available. The assistance of Jean Armstrong in compiling a portion of the data is gratefully aclmowledged. $PARK, B., J. CHEM.EDUC.,35, 516 (1958). 3 D ~K. E.,~ AND ROBINSON, ~ ~ R.~ J., J.~CHEM. ~EDUC., , 41, 51 (1964).
Volume 42, Number 8, August 1965
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