Allen C. West'
Lawrence University Appleton, Wisconsin 5491 1
I
I I
The Effects of Chloride Ion and Temperature on Lead Chloride Solubility A versatile quantitative experirnenf
The study of ionic equilibrium has been the traditional subject of courses in elementary quantitative analysis. As the range and sophistication of subject matter in the undergraduate curriculum increases, this course is being either absorbed into introductory chemistry or asked to incorporate a growing variety of topics. In either case, the time available in the laboratory for quantitative experiments involving ionic equilibria is decreasing, and we must reexamine closely the kinds of experiments we choose to fit into this limited time. Another reason for such a reexamination is the complexity of most ionic equilibrium systems and our desire to give students as realistic a picture of this complexity as possible (1-4). One way of utilizing the time more efficientlyis to use group experiments, which let the students work with a statistically significant set of data, collected under a range of conditions, without spending weeks repeating the same operation. A second way is t o use the results of a quantitative experiment involving ionic equilibria to illustrate fundamental chemical concepts, rather than simply to determine the percentage of something in a manufactured unknown. Chemical kinetics (5), the solubility product principle (1, 8, 4, 6-9) and chemical equilibria of other kinds (4, 8, 10-14, the concept of activity: all can be the subject of quantitative experiments incorporating gravimetric, volumetric, or instrumental techniques. Thermodynamics can be introduced via such experiments (I/+),and the study of systems involving complex-ion equilibria is particularly fruitful. The experiment described in this paper attempts to implement the ideas mentioned above. Quantitative technique is emphasized. The student is introduced to several concepts: complexometric titrations, elementary statistics describing precision and its measurement, ion activities and activity coefficients, free energy and equilihrium, a thermodynamic picture of the solution process, and the solubility product principle and its limitations.
orange as the indicator. He then determines the solubility of lead chloride in two systems using the same procedure: in distilled water a t one of three temperatures and in a solution of specified chloride concentration a t fixed ionic strength. From his data, each student calculates and reports an average NazHzY molarity, the molar solubility of lead chloride in the two systems, and both concentration and activity soluhility product constants for the distilled water system.? When results are in from the whole class, each student uses them to calculate the relative standard deviation and 95% confidence limit of the set of NazHaYmolarities. He plots molar solubility versus [GI-] to show the common ion effect and makes a log-log plot of the same data. A comparison of the log-log plot with a theoretical common-ion plot using the most relevant K,' value demonstrates clearly the deviations from ideality that occur. Each student also plots the average log K,' for each temperature against 1 / T and calculates the standard heat of solution (AH,') of lead chloride. I n his report each student is asked to discuss the precision and accuracy of titrations, and factors that may affect them. He is asked to compare the two log-log plots and discuss possible explanations for the discrepancies between them, and to outline possible additional experiments that might resolve ambiguities in the class results. Discussion
An examination of results obtained in 1967 will show how well the experiment worked in practice. There were 33 students in the class. A histogram of NazHzY molarities calculated from each individual titration is given in Figure 1. The mean of this data is 0.01200 M.
The Experiment
The experiment occupies three three-hour laboratory periods. Each student standardizes the common solution of disodium dihydrogen ethylenediaminetetraacetic acid (Na2H2Y)against weighcd samples of lead nitrate, using an acetic acid-acetate buffer and xylenol Copies of the experimental write-up can be obtained from the author. We use K, for the concentration constant and K,' for the activity constant at any temperature, ignoring the effeot of temperature on activity coefficients.
Figure 1.
Histogram of rerultr of individual student titrotionr
Volume 46, Number 1 I, November
1969
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The solution used was made up, as quantitatively as possible, to be 0.01200 M, so there appears to be no significant bias in the titration. The relative standard deviation of all these results .is l.lojo. However, this precision includes several values that clearly involve non-random errors, and the relative standard deviation is 0.5% neglecting these values. An error curve constructed using 0.50jo fib the bulk of the data well, and the relative standard deviation of the mean, assuming triplicate analyses, id 0.3%. This agrees very well with 0.250j0 calculated from the reported student means. The 95y0 confidence limit for these student means is O.lyO,The titration is, therefore, precise as well as accurate. Table 1.
K.' x 106
774
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Figure 3.
a2
0.2
,om,CllOslDr
a.
05
CONCSNTR.,lON
Com~orativeK.' Values
-
Temuerature. "C
Table 1 gives mean values of K,' at the three temperatures used, and a comparison of interpolated and literature data for 2 5 T . The mean values are calculated from K , data using activity coefficients obtained from the Debye-Hiickel equation with size parameters from IGelland. The K , values are calculated directly from the solubility data, assuming that all the lead chloride is in solution as Pb2+ and CI- ions. K, = 1.56 X at 21°C. This compares with textbook values varying from to 2.4 X A look a t these data will give students a healthy skepticism about tabulated equilibrium constants. Figure 2 is a plot of log K,' versus 1/T. From the slope, AH,' is calculated to be +9.4 kcal/mole. This compares with +6.4 kcal/mole calculated from N.B.S. data (17). Figure 3 is a plot of molar solubility versus total concentration of chloride ion, with the ionic strength fixed a t 0.5. M using NaN03. The data in
Figure 2.
&I
Effect of added chloride on the solubility of PbCI2.
Determination of standard heot of solution.
Journal of Chemical Education
-1.5
-1.0
-as
-0.2
roo Figure 4. Comparison of experimental and theoretical common ion plots. The line represents the theoreticol common ion plot for K,' = 3.3 X 10-8.
this figure were taken a t lQ°C. Each point represents the average of two student means. The data are replotted on a log-log scale in Figure 4, together with a theoretical common-ion plot using K,' for 21°C and the simple solubility product expression. There are several ways to change the emphasis of this experiment or, if there is time, to make it openended. The variation of K, with ionic strength can be investigated and K,' obtained by extrapolation. The common-ion study can he extended to higher [CI-1 and the data used to estimate numerical values for stability constants of complexes involved in the Ph2+-Cl- system. Fleck (id) describes very well the problems and possibilities of such an approach. A computer program to obtain these constants would be a challenging problem for students prepared to tackle it. An effective way to extend the experiment is to investigate sources of error in the procedure or calculations. One source of error in the common-ion study was introduced by the use of NaN03 to fix the ionic strength. The ion pair PbN03+ has an appreciable stability constant (15.4 a t 25°C and zero ionic strength) (S), and the formation of this species would make the measured solubility of PbCh too high a t low C1concentrations. Another reason why the PbC1, solubility is high a t low C1- concentrations is that the ionic
strength approaches 0.6 M as the NaNOs concentration approaches 0.5 M. The effect of PbN03+ formation can be eliminated by using NaC104 instead of NaNO* and the constancy of the ionic strength can be improved either by using a higher concentration of inert electrolyte or by correcting for the contribution of P b and C1 species to the ionic strength. Without considerable calculation, the common ion study gives only a general picture of the effect of added Cl-; the picture is further complicated by the presence of NOs-. However, the other half of the experiment gives K, and K,' values and a AH,', which can be compared with literature values, and discrepancies can he checked for sources of error in this experiment. The average K,' values appear to be too high. This indicates that perhaps small solid particles of PbCL passed through the glass wool filters that were used on the pipet tips. However, any error in AH,' must be the result of a change in the slope of the log K,' versus 1/T plot, and in fact, if the same amount of solid passed through the filters a t all temperatures, the experimental slope would be less negative, and AH,' smaller, than if no solid passed. The errors in K,' and AH,' can be accounted for qualitatively by considering the formation of lead chloride complexes. For simplicity we will neglect all but PbClt, in which case the relevant equilibria are K, = [PbZ+][C1-1' PbCl.(s) Pb2+ + 2CI-
=
K, appears to stay relatively constant as the temperature changes from -3 to 25'C, and it only decreases by a factor of about two as the ionic strength increases from 0 to 2 M (16). If we assume, then, that Kl is constant for the conditions of this experiment we find that if the value of K1 is increased, the slope of the log K,' versus 1/T plot becomes less negative and, therefore, AH,' becomes smaller. Figure 5 shows several -do
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111 x 103
Figure 5. Effect of complex-ion formation on stmdord hoot of solution. Ill KI = 0, I21 Kr = 5; I31 KI = 7.6; I41 KI = 10; 151 KI = 15; 161 KL = 25.
such plots with K, varied from 0 to 25. AH0, = f6.4 kcal/mole for K1 = 10. This value falls in the range of reported KI values. However, K,' = 1.1 X 10-5, if Kl = 10, and this seems low. The important point is not that the data can be treated to give quantitative corrections, hut that a clear picture can be obtained of the way in which complex ion formation will affect the AH,' and K,' values calculated from this experiment. The procedure followed for including the effect of Kl was to use the experimentally measured solubility of PbClp,Kl, and mass and charge balances to calculate [Pb2+], [PbCl+], and [Cl-1. From these results K , values and ionic strengths were determined, and then K,' values were calculated as previously described. Table 2 lists AH," and K," (interpolated) for each K, used in Figure 5 . Table 2.
K, 0 5 7.6 10 15 25
Data for Figure - 5 AH." (kcal/mole)
KaD ( X 10s) 4.1 1.9 1.5 1.1 .77 .41
9.4 7.6 7.4 6.4 5.9 5.2
Conclusion
This experiment is based on a simple accurate volumetric method. By using all the student results a significant amount of data can be collected in a short time. The lead chloride system lends itself to study and interpretation a t several levels of sophistication, so that the experiment can be adapted to the background of the students and the time available. It demonstrates some of the false simplifications involved in a rudimentary treatment of solubility equilibria and the common ion effect, and i t can also be made openended in a variety of ways. Literature Cited (1) MCALPINE, R. K., J. CHEM.EDUC.23,28 (1946). R . W., J. CHEM.EDUC.37,348 (1960). (2) RAMETTE, (3) MEITES, L., PODE,J. 8. F., THOMAS,H. C., J. CHEM. Enuc. 43, 667 (1966). R. W., J. CHEM.EDUC.43,299 (1966). (4) RAMETTE, H. F., J. CHEM.EDUC.44,577 (1967). (5) SHURVELL, (6) GOODMAN, R. c., PETHUCCI,R . H., J. CHEM.EDUC.42, 104 (1965). (7) NEIDIG,H. A,, YINGLING,R. T., J. CHBM.EDUC.42, 475 (1965). D. A,, LATHAM,J. L., J. CHEM.EDUC.43, 82 (8) . . JENKINS, (1966j. (9) MARSHALL, J. C., BLANCHARD, D. P., Atomic Absorption Newsletter, 6, 109 (1967). (10) PEACOCKE, T. A. H., Sch. Sc. Rev. 45, No. 157,597 (1964). (11) FLECK,G. M., J . CHEM.EDUC.42, 106 (1965). (12) FLECK,G. M., "Equilibria in Solution," Halt, Rinehart and Winston, Inc., New York, 1966, pp. 154-158. R. W., J. CHEM.E ~ u c . 4 4 , 6 4 7(1967). (13) RAMETTE, R. T., J. CHEM. (14) NEIDIG,IT. A,, TEATES,T. G., YINGLING, EDUC.45,57 (1968). (15) LATIMER,W. M., "Oxidation Potentials," ( h ~ ded.) Prentiee-Hall, Inc., Englewood Cliffs, N. J., 1952, p. 153. L. G., "Stability Constants of Metal(16) MAETELL,A., SILLEN, Ion Complexes," Special Publication No. 17, The Cbemical Society, London, 1964, pp. 297-298. (17) "Selected Values of Chemical Therrnodynttrnie Properties," Circular 500, National Bureau of Standards, Washington, D. C., 1952. Volume46, Number 1 1 , November 1969
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