MEANINGFUL SOLUBILITY STUDIES IN ELEMENTARY QUANTITATIVE ANALYSIS' R. W. RAMETTE Carleton College, Northfield, Minnesota
ALTHOUGH most chemists will admit that elementary quantitative analysis is at least an important course, they are not so likely to agree that it is also a very stimulating and interesting course, especially in its lahoratory work' why this be? After ''quant'' marks the transition from the impractical, poorly performed experiments with unrealistic apparatus in the unscientific atmos~hereof the crowded freshman lab, to the relatively peaceful conditions under which the student learns t o do work of a quality high enough t o satisfy most research chemists. Further, with the background gained in the general and qualitative analysis courses he is in position to understand the fundamentals of his work. Quantitative analysis lends itself perfectly to a treatment showing the close correlation between theory and practice. The answer to the question posed above may be given in two parts. First, many typical analytical experiments involve long periods of boredom and tedium, such as slow evaporations, long ignitions with subsequent cooling, and double precipitations. These operations consume a great deal of laboratory time, but it is doubtful whether the student learns any new fundamentals during such work. The proposal that he use the waiting times for the preparation of more work is seldom practical and is irrelevant anyway, for it adds no interest. The second part of the answer is the more important one. The typical quantitative experiment offers no scientificincentive to the student. He has been handed a small sample by the instructor and told to "do copper." He knows that this is just another examination, that the exact composition of the sample is neatly filed away. There is t o be no probing into the new or unknown. The only practical application of the analytical result is to help the instructor assign a grade, the one thing which counts least in the long run. The chemistry involved in the experiment, the skill gained in doing the work, the intrinsic value of precise workall these become of secondary importance because the experiment has no purpose. Kolthoff2 expressed this problem when he wrote: The aims and objectives of analytical chemistry are to determine the composition of any simple or complex compound or mixture of compounds. Academically, the question arises im-
'
mediately, why should anyone have a desire to know such oomposition? What satisfaction does one derive from the determination of such composition? Frankly speaking, I believe none.
Later in the same paper he wrote: M y thesis is that the progress and advance of analytical chemistry depend t o a. great extent upon an intelligent apflication of the fundamentals of physical chemistry and the close relation between physical and analytical chemistry.
It is the purpose of this paper to describe three experiments, designed for the elementary course in quantitative analysis a t Carleton College. These use the corollary of Kolthoff's thesis as a guide, allowing the intelligent application of analytical methods to fundamental problems of physical chemistry. There is ample opportunity for teachers to design more experiments with the same goal: placing the established techniques of analytical chemistry in the proper perspective by using them as tools rather than as ends in themselves. This does not imply that the science of analytical chemistry is merely a handmaiden, for indeed it is often impossible to distinguish the type of work done by research analytical chemists from that performed by the physical, organic and inorganic chemists. Solubility of Silver Bromate in Potassium Bromate Solutions. This experiment is designed to acquaint the student with the Volhard titration, to give reality to the law of chemical equilibrium, to allow the determination of a quite reliable value for the solubility product, and to give training in scientific writing. The procedure is as follows: The instructor prepares a series of solutions of potassium bromate and potassium nitrate in varying proportions hut with constant ionic strength. Solid silver bromate is added in excess and the solutions are stirred mechanically for several days in the view of the students. A lecture is devoted to the principles of the experiment. When the day for the laboratory work arrives the solutions are filtered and the temperature is noted. The student determines the concentration of silver in each solution by titrating an aliquot with standard potassium thiocyanate, using ferric alum as indicator. Knowing the amount of potassium bromate originally present and the amount of silver bromate due t o solubility, he can calculate the solubility product for each solution. He also prepares a plot of the silver ion concentration, versus the the reciprocal of the total bromate concentration. This straight line has a slope equal to the solubility product. An example of student results is shown in Figure 1. The student is asked to try for concise
Presented before the Division of Chomicsl Education a t the 129th Meeting of the American Chemical Society, Dallas, April, 1956. KOLTAOFF,I. M., Chem. Eng. News, 28,2882 (1950). 610
VOLUME 33, NO. 12, DECEMBER, 1956
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and clear expression in writing his report, so that a chemist who is not familiar with the particular experiment will understand what was done. The report covers the purpose of the experiment, the underlying theory and principles, procedure, observed data, calculated results, comparison with literature values, conclusions and suggestions for improvements and variations. Solubility of Calcium Sulfate in Potassium Nitrate Sol~tions.~Here the concept of activity and activity coefficient and the Debye-Hiickel theory are brought to reality in the laboratoly. The instructor prepares a series of solutions of potassium nitrate of varying concentration, and solid calcium sulfate diiydrate is equilibrated with each by mechanical stirring. The students determine the concentration of dissolved calcium by titration with versene (ethylenediaminetetraSlope = K = 6.5 X lod. Temperature = 23°C. Ionic strength = acetic acid, disodium salt) using murexide as indicator. 0.050. Dsta of Willism P. Brown. The classical solubility product is simply the square of the calcium ion concentration, since no common ion Taking logarithms of equation (4)and inserting equawas originally present. I n lecture, the concept of tion (6) : activity is reviewed and the principles of the experiment are discussed as follows: The 'true' or thermodynamic solubility product is This predicts a straight line with a slope of -4.08 and defined by the equation an intercept of pK, if the experimental values of K C = ac.*+ asor-- = a true constant (1) pK, are plotted versus the complex ionic strength where the a's represent the activities of the ions. How- function taken as a simple variable. One valuable ever, each activity can be considered as the product of aspect of this plot is the wedding of the purely theomolarity and an activity coefficientso that: retical with the experimental results. That this works K , = (Ca++)(SO,--lfc.*+f~o,-(2) well in practice is shown by Figure 2,which is taken from the reports of students. The value thus obtained for The product of the concentrations of the ions is the familiar classical solubility product, Kc. The mean activity coefficientis defined as: kt& 4.33
-
f = (fc.++fso*--)" to give the relationship Kt
=
K,fZ
K , can be determined for a particular ionic strength simply by calculation from titration results. What is desired is a method for determining K cso that the mean activity coefficient may be calculated in turn. The principle involved in extrapolation of the values of K , obtained in the experiment to zero ionic strength is discussed. It is pointed out that plots of K c or pK, versus ionic strength are not satisfactory for the extrapolation because they are curved, and a large error in the intercept can be easily made. The Debye-Hiickel equation, its form and history, is introduced. It is presented first as
It is shown that for calcium sulfate a t 25' C. this becomes:
F i m e 2.
logf=
-
Determination of Thsrmod-ic
Solubility Rodvct of
Clldum Sulfate ='"-P-'-
1
+ 1.25,"/'
See aleo: NOYES, A. A., J. Am. Chem. Sac. 46, 1098 (1924).
Temperature = 25'C. Open circles, data of Robert Stewart, using POtassium chloride as inert salt. Solid oircles, data of Thomas Blackburn using potassium nitrate as inert
612
pK, is used with values of pK, taken from the graph to calculate the experimental values of the mean activity coefficient as a function of ionic strength. These are compared with the theoretical values obtained by using the Debye-Hiickel equation, a procedure which gives somewhat different results because the slope of the plot does not check with the theoretical slope, even though linearity is apparent. The student report is written in the same general pattern as described for the silver bromate experiment. The reader can sum up the numerous important fuudamentals which the student can learn from this experiment in comparison with those from the mere use of versene for determining the hardness of a syuthetically prepared sample of water. Objection may be made to the philosophy of teaching activities, ionic strength, etc., in the analytical course because the material 'properly' belongs in the physical chemistry course. Sometimes the erroneous notion is held that sharp boundaries exist between fields and especially between courses. The view is untenable when one considers the virtues and advantages of teaching reality as early as possible. The great body of evidence, including this calcium sulfate experiment, which shows how greatly the classical constants vary with 'inert' salt concentration, makes it impossible for one t o teach with intellectual integrity the thoroughly disproven notion that "for our purposes we are justified in using the simplified treatment, leaving out activity coefficients." One problem which must be recognized is that most textbooks for quantitative analysis do not contain a treatment of activities which is truly instructive. Those who are interested in seeing how the subject can be introduced to the sophomore in a thorough, realistic and completely understandable manner may examine the book by Rieman, Neuss, and Naimm.& These authors have made a splendid contribution by showing how the sophomore can learn not only about activities, but also how to use the concept consistently in regular practical work. Of particular value are the charts in the appendix showing the variation of most of the common equilibrium constants with ionic strength. The student not only understands this treatment, he appreciates it. Finally, the addition of a laboratory experiment similar to the above will clinch his acceptance, understanding and appreciation of activities quite thoroughly. Solubility of Lead Sulfate as a Function of Acidity. For this third experiment the instructor prepares a series of solutions of perchloric acid and sodium perchlorate, in varying proportions but with constant ionic strength. Solid lead sulfate is equilibrated with each. The student takes a portion of each of the saturated solutions, adjusts the pH t o about 5 by the addition of a quantity (calculated by the student) of sodium acetate, and precipitates the lead quantitatively by the addition of potassium chromate. After a brief aging period, the precipitate is filtered and RIEMAN, 111, W., J. D. NEUSS,and B. NAIMAN, "Quantitative Analysis." 3rd ed., McGraw-Hill Book Co., Inc., 1951.
JOURNAL OF CHEMICAL EDUCATION
washed. A portion of 1 M hydrochloric acid saturated with sodium chloride is used t o dissolve the lead chromate and transfer i t t o a titration flask. Potassium iodide is added in excess, and the lead is determined volumetrically by titration of the liberated iodine with standard thiosulfate solution. The following principles are set forth in lecture: The solubility of lead sulfate increases with acidity due t o the formation of the hydrogen sulfate ion. The total solubility in a given case may be expressed as: S = (Ph++) = (SO,--)
+ (HS04-)
(8)
By rearranging the expression for Kz, the second ionization of sulfuric acid, we obtain (HSO,-) = (H +)(SOI--)/KI
(9)
and from the solubility product expression we have: (SO.--) = K./(Pht+)
(10)
Upon substitution and rearrangement the result is: (Ph++)l = SB= Kc
+ K.(H+)/Ks
(11)
By this time the student is willing to concede that almost any equation can be plotted as a straight line, and he can see that a plot of his experimental values of 8%versus the known acidity should be linear with a slope of K J K 2 and an intercept of K,. Thus, both constants may be determined from the same graph. The results of one student are shown in Figure 3.5 The fact that an occasional point does not fall on the expected line does not detract from the experiment, for any research worker knows how realistic such a discrepancy is in practice. The usual written report is prepared, and by this time there is at least a small improvement in the student's ability to state with clearness and conciseness what he has accomplished. As outlined here, these experiments certainly are not without some difficulties. I n the silver bromate and calcium sulfate experiments it is necessary to use only 0.01 M solutions of titrants in order to use appreciable volumes. This means that the end points are not as sharp as might be desired. Also, in the Volhard titration of silver, the presence of bromate is troublesome because it will oxidize thiocyanate in acid solution, and the acidity must be kept a t the minimum value required to eliminate the color of the hydroxyiron(II1) ions. In the lead sulfate experiment, such a small amount of lead sulfate dissolves that areat care must The experiment was carried out using potassium nitratenitric acid mixtures, before the existence of the ion PbNO.+ was appreH. M., M. E. SMITH, ciated. (See, for example, HERSHENLION, AND D. N . H u m , J . Am. Chem. Soe., 75,507(1953)). Therefore the datado not obey the relationship derived above. I t can be shown that the values obtained for Pare higher than they 'should' he by the constant fact,or(1 K,-(NO1-)) where K j is the formation constant for the PhNOat ion, and (NOa-) is constant at 1 M. Thus, even though K, is unknown for our particular conditions, the ratio of the intercept to the slope still yields the value of Kz. In the example presented, K* is found to be 0.093 which is in agreement with E~CHLER, E., AND S. RABIOEIU, J. Am. Chem. Soc., 77, 5501 (1955) who found Kg = 0.084 == ! 0.012 at an ionic strength of one by means of potentiometric studies in this acidity range.
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VOLUME 33, NO. 12, DECEMBER, 1956
he taken in transferring and washing to avoid relatively 14 large errors. With a small class it would he preferable to dissolve the lead chromate and determine it spectrophotometrically at 370 mp in alkaline solution, thus 12 avoiding the errors in the titration of small amounts. The important point of this paper is that such experi10 ments are possible and desirable in the elementary quantitative course. Professors can modify these s experiments or devise new ones to teach principles, 8 X and they can enjoy doing it. For example, the solu6 ,,,, ,,,/ bility of silver bromate can be studied as a function of 6, ionic strength, using the iodometric determination of dissolved bromate; the solubility of calcium sulfate 4 C as a function of acidity, using versene as before; and the solubility of lead chloride as a function of lead perchlorate cmcentration, using one of the standard 2 methods for determining dissolved chloride. There seems to be some feeling that these experiments I I are best used as optional experiments in advanced 0.05 0.10 0.15 0.20 courses for the better students. I think that such (H+) feelings underrate both the capabilities of the average riwm 3. O r a p h i d 1 n t q m t r t i o n of L..d S~1f.t. S.L"bi1'tgD.t. sophomore and the desirability of giving him an increased understanding of principles a t an early stage Temperature = 23.5%. Ionio strength = 1.0. Data of William Stocker. in his career. All of the more typical quantitative experiments, i.e., unknowns, should not he discarded. students a healthy skepticism of figures which are not The inclusion of just two or three of the type described backed up in some way, and this attitude alone is an in this paper is enough to improve the student opinion important step forward in their thinking. As for the of the hboratory work considerably. report writing, they find it painful at first and easier The reactions to these experiments, especially from later on. Reading of the early reports makes it clear the best students, have been most satisfying. These to the instructor how badly they need this kind of students enjoy the research nature of the experiments training. and the close connection made between lecture and The quantitative analysis course comes a t a crucial laboratory work. They like to mull over their results time in the curriculum, when many students with exand talk them over. Several have chosen to come in cellent scientific ability are wavering between careers on their own time to do extra related experiments. in mathematics, physics, medicine, and chemistry. One encouraging aspect is the interest taken by the If we are concerned with attracting good people into students in their constant values, graphs, etc., com- the profession we must pay more attention to ways in pared with literature values. It is stimulating for which the stimulating aspects of chemistry can be them to learn that their values are actually better made available t o the student. We should design our than many in the literature, for often the latter are courses so that they grow up with him. As his thinkgiven without reference to temperature, ionic strength, ing ability improves, so should the opportunity for or the method of determination. This instills in the advanced thinking appear more regularly.
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