SOLUBILITY OF LEAD SULFATE AND LEAD OXALATE
56 1
2. An equation is given for calculating the limiting value of h/r”’ and h’/rl’* at infinite dilution. 3. The Debye-Huckel limiting slopes of the curves h’/r’’* vs. TI’* and h/r”’ vs.
d’’ are zero and 3, respectively. REFERENCES
(1) FALKENHAGEN, H . : Electrolytes. Oxford University Press, London (1934). (2) LEWIS,G. N., AND RANDALL, M . : Thermodynamics and the Free Energy of Chemical Substances. McGraw-Hill Book Company, Inc., New York (1923). (3) RANDALL, M., LIRRY,W. F . , AND LONGTIN, B . : J. Phys. Chem. 44, 313 (1940). (4) RANDALL, M . , AND LONOTIN, B . : J. Phys. Chem. 44, 306 (1940).
T H E SOLUBILITY OF LEAD SULFATE AND OF LEAD OXALATE IN VARIOUS MEDIA’ I. M. KOLTHOFF, R . W. PERLICH,
AND
D. WEIBLEN
School of Chemistry, Institute of Technology, University of Minnesota, Minneapolis, J4innesota Received January 31, 194.8
Diphenylthiocarbazone (dithizone) has been found to be a very suitable reagent for the quantitative determination of traces of metal ions dissolved in aqueous media (4). It should have great advantages over other methods in the determination of the solubility of various slightly soluble metal salts in different media. Most of the other chemical methods require the use of large volumes of solvent, and the saturated solutions have to be evaporated to small volumes before the analyses can be made. As the dithizone method can be applied directly at extremely great dilutions, evaporation is not necessary, and the solubility can be determined using small volumes of solvent. It has great advantages over the electrometric methods, as the total amount of dissolved (ionized and un-ionized) metal is determined. The electrical conductance method is limited in its application and allows only the determination of the ionized part of the solution. The potentiometric method has a wider range of application than the conductometric one, but it allows only the determination of the activity of the metal ion of the dissolved salt. The activity coefficient of the dissolved metal ion has to be known in order to find the concentration of the latter. Moreover, the concentrations of undissociated salt or of complex metal ions are not determined by the potentiometric method. In the present study the solubilities of lead sulfate and lead oxalate have been determined in various media. The dissolved lead was determined colorimetri1 This article is based upon a thesis submitted by R . W. Perlich to the Faculty of the Graduate School of the University of Minnesota in partial fulfillment of the requirements for the degree of Master of Science, 1938.
562
I. M. KOLTHOFF, R. W. PERLICH AND D. WEIBLEN
cally, using a slightly modified procedure given by Fischer and coworkers (5, 6). ,MATERIALS USED
Lead sulfate. This was prepared by slowly adding, with constant stirring, hot 0.05 N reagent quality sulfuric acid to boiling 0.05 N lead nitrate solution, until a slight excess of sulfuric acid was present. The precipitate was digested for about 2 hr. n.hile the solution was near the boiling point; it was decanted, washed several times with water, and then aged for 24 hr. in 0.01 N nitric acid on the sand bath. The precipitate was filtered, washed thoroughly with water, washed with alcohol and ether, and then air-dried. Lead oxalate. This was prepared by adding, with vigorous stirring, 1 liter of boiling 0.1 M C.P. lead nitrate containing 20 ml. of glacial acetic acid to 1 liter of boiling 0.014 df C.P. ammonium oxalate. After digestion for 1 to 2 hr. on the steam brtth, the solution was decanted and the product washed several times by decantation and then transferred to a Buchner funnel. It was further washed with water, alcohol, and ether, and then air-dried. Ammonium hydroxide. Reagent quality ammonium hydroxide was redistilled and dissolved in lead-free distilled water. A 1 N solution was used and stored in a paraffin-lined bottle. Potassium cyanide. A 0.5 per cent solution of Mallinckrodt’s reagent potassium cyanide was prepared in lead-free water. Immediately after making up this solution, a test with dithisone showed the presence of a trace of lead. After a few days of standing in a glass bottle, this trace of lead was completely taken up by the glass and the solution gave no test for lead with dithisone. Water. Lead-free water was obtained by redistilling ordinary distilled water to which a small amount of sodium carbonate had been added in an all-glass Pyrex distillation apparatus. Sodium hydroxide. A 0.5 N sodium hydroxide solution w~tsmade by dissolving reagent quality sodium hydroxide in lead-free water and shaking with reagent quality calcium oxide. The solution was then centrifuged, decanted, and stored in a Pyrex flask. It was free from lead. Lead standards. A stock solution was made up which was about 0.0015 M in lead by dissolving the corresponding amount of C.P. lead nitrate in 0.01.V lead-free hydrochloric acid. This solution was diluted with 0.01 N hydrochloric acid to give standard solutions of the required concentrations. The acid is necessary to prevent adsorption of lead by the glass. All other chemicals used were lead-free. Dithizone. A 0.01 per cent stock solution of dithisone was prepared in carbon tetrachloride and kept in a dark bottle. It was diluted with the same solvent to give 0.001 per cent solutions, which were used in the colorimetric determination of the lead. The 0.001 per cent solution of the reagent was made fresh each day. If necessary, the oxidation products present in the solid dithizone were removed by the method of Wichmann et al. (14). Preparation of saturated solutions. One-gram samples of lead sulfate or lead
SOLUBILITY OF LEAD SULFATE AXD LEAD 0X.kL.iTE
563
oxalate were added to 100 ml. of solvent in paraffined bottles which were closed with paraffined corks. The. bottles were placed on a mechanical shaker and shaken at room temperature (25OC. Z!Z 2') for 80 hr. or more to insure complete saturation. The suspensions were then centrifuged and samples of the clear supernatant liquid were withdrawn with a paraffined pipet. All of the shaking experiments were carried out at least in duplicate, over such periods of time that longer shaking did not show any change in concentration. METHOD OF ANALYSIS
By using the following procedure, difficulties caused by the distribution of the lead dithizonate and also of the dithizone were eliminated (1). The lead content of the saturated solutions was determined approximately by the colorimetric method described below. Then a suitable volume of the saturated solution, containing about 15 micrograms of lead, was placed in a Pyrex test tube with a ground-glass stopper. An amount of standard lead solution containing approximately the same amount of lead was added to a second test tube. One milliliter of 0.5 per cent cyanide, 1 ml. of 1 N ammonia, and 10 ml. of 0.001 per cent dithizone in carbon tetrachloride were added and the test tubes shaken for 1 min. A yellow color in the aqueous layer indicated an excess of dithizone. The cherry-red layers of carbon tetrachloride were transferred to colorimeter cups and the intensities of both compared in a Duboscq colorimeter. Four determinations were run for each particular solution, two samples from each bottle, the average being reported in the tables and graphs. For a given solution the results agreed within 5 per cent except in the case of very low lead concentrations, when they varied by as much as 10 per cent. The samples from the alcohol solutions were evaporated to dryness and redissolved in dilute acid. The accuracy of the determinations in 50 per cent ethanol was of the order of 50 per cent. EXPERIMENTAL RESULTS
Solubility of lead sulfate in sodium sulfate solutzons By adding known amounts of lead to sodium sulfate solutions, it was shown that the sulfate does not interfere with the lead determination. The results obtained are given in table 1. The results are plotted in figure 1, together with those of Huybrechts and Delangeron (9), which were obtained at 25°C. The latter authors concentrated the saturated solutions by evaporation, precipitated the lead as the sulfide, and determined the amount colorimetrically. Considering the inaccuracies of both methods, the agreement is satisfactory. I t is seen that the solubility decreases very markedly in going from water to 0.001 M sodium sulfate. This is to be expected from the law of mass action. The solubility reaches a very flat minimum in about 0.05 J4 sulfate solution and increases only very slightly with increasing sulfate concentration. I t was shown that the solid body in equilibrium with 0.5 M sodium sulfate consisted of lead sulfate and not of a double salt. No indication is obtained that the lead forms a complex ion with sulfate at higher sulfate concentrations. The flat minimum and the slight
564
I. M. EOLTHOFF, R. W. PERLICH AND I). WEIBLEN
increase of the solubility with higher concentrations of sulfate are explained by the fact that the activity coefficient of the lead and sulfate ions decremes markedly with increasing ionic strength of the solution: cpb++ =
S.P.
1
-a-
C S O i - fPbt+f80i-
TABLE 1 Solubility of lead sulfate in sodium sulfate soZu2ions at M"C. i 9' SOLWILlTY OF LBAD S U U A T E
mouaxn
OF NarSOd
Milligrams of Pb per liter
0.08 0.100 0.200 0.350
0.500
0
I
Moles of PbSOa per liter X
0.10
azo aw Molarity of NqS04
FIG.1. Solubility of lead sulfate in sodium sulfate solutions. Weiblen; 0 , Huybrechts and Delangeron.
106
15.2 2.4 1.6 1.4 1.3 1.3 1.6 1.9 2.3 2.3
31.5 4.8 3.3 2.9 2.7 2.7 3.4 3.9 4.8 4.8
0 0.001 0.01 0.02 0.04
a40
1 io
0 , Kolthoff,
Perlich, and
In this equation C p p and Csoc- denote the concentrations of the lead and sulfate ions, S.P. the solubility product of lead sulfate, and f p b + + and fsor- the activity coefficients of the lead and sulfate ions. As both the lead and sulfate
565
SOLUBILITY OF LEAD SULFATE AND LEAD OXALATE
ions are divalent, the effect of the ionic strength upon the activity coefficient is very pronounced. The large effect of the ionic strength upon the solubility of lead sulfate was demonstrated by determining the solubility in 0.01 M sodium sulfate solutions containing various amounts of sodium nitrate. The results are given in table 2.
Solubili!y of lead sulfate i n sulfuric acid solutions The determinations were made in the same way as described before, except that the acid wv&9 neutralized with the lead-free sodium hydroxide solution. TABLE 2 Solubility of lead sulfate i n 0.01 M sodium sulfate i n the presence of varying amounts of sodium nitrate at 36°C. SOLUBILITY 01 LEAD SUL?ATE YoLAPIrY OF
NaNOi Milligrams of Pb per liter
0 0.0500 0.100 0.500 1 .OO
I
Moles of PbSOa per liter X 100
3.0 5.2 7.9 34.0 96
1.5 2.6 3.9 17 47
TABLE 3 Solubility of lead sulfate i n s d f u r i c acid at 36°C. SOLUBILITY 01 LEAD SULFATE MOLARITY OF
HrSOd Milligrams of
0.001 0.005 0.0075 0.010 0.025 0.050 0.100 0.250 0.500
Pb per liter
7.2 4.5 4.4 3.6 3.6 3.4 3.2 3.6 4.2
Mola of PbSOc pu liter X l(r
3.6 2.2 2.2 1.8 1.8 1.7 1.6 1.8 2.1
After this work had been completed, Craig and Vinal ( 2 ) reported the results of an extensive investigation of the solubility of lead sulfate at 0°C. and 25OC. over a wide range of concentrations of sulfuric acid. They also employed the dithizone method, using a photronic cell in making the measurements. By their procedure they obtained an accuracy of 1 per cent. Our results (at 25OC.) are in good agreement with theirs, although the accuracy attained by Craig and Vinal is much greater than ours, Huybrechts and Ramelot (10) determined the solubility a t 30°C. over a relatively wide range of sulfuric acid concentrations, and Purdum and Rutherford (13) at 20°C. over a small range of acid concentra-
566
I. M. ROLTHOFF, R. W. PERLICH AND D. WEIBLEN
tions. All these authors used the iodometric chromate method on the analysis for lead. When corrected for the difference in temperature, all the results are in satisfactory agreement. Our results are given in table 3. The results of Crockford and Brawley (3), obtained by the chromate method a t 25OC., are lower than those reported above.
Solubility of lead sulfate in ethanol-water mixtures In these experiments, unparafied bottles were used in general, as at the higher alcohol concentrations the dissolved paraffin interfered somewhat with
TABLE 4 Solubility of lead sulfate in water-ethanol mixtures SOLWILIIY 01 LEAD SULFATE
CONCENTRATION OF EIEANOL I N VOLUYE PEP C E N I
Moles of PbSOA rxr liter X 106
Milligrams of Pb per liter
15 5.4 2.1
30 11.0 4.2 1.5 0.51 0.32 0.20 0.06
0 10 20 30 40 50
60 70
I
0
I
10
1
20
I
30
0.76 0.25 0.16 0.10 0.03
I
40
Percent Alcohol
I
so
I 60
I
FIG. 2. Solubility of lead sulfate in water-ethanol mixtures
the lead determination. Blank experiments showed that, within the experimental error, the same results were obtained in paraffined bottles as in unparaffined bottles. The samples taken for analysis were larger than in the previous determinations, 50-ml. samples being taken when the alcohol concentration was over 40 per cent. If paraffined bottles were used, 1ml. of 1 N hydrochloric acid
SOLUBILITY OF LEAD SULFTAE AND LEAD OXALATE
567
was added to the solution and the alcohol removed by evaporation. This was done to eliminate the paraffin dissolved by the alcohol. When unparaffined bottles were used, the alcohol was not removed, as the lead could be extracted quantitatively from the alcohol-containing mixtures. If the solutions contained some dissolved paraffin, emulsions were formed upon shaking with carbon tetrachloride and the above evaporation procedure was necessary. The results are given in table 4 and shown graphically in figure 2. The concentration of alcohol is given in volume per cent. The solubility decreases rapidly with increasing alcohol concentration. It is seen that the solubility product of lead sulfate in 50 per cent ethanol is about 2.5 X 1O-I2, Le., more than 10,000 times smaller than in water. The effect of the presence of sodium sulfate up to a concentration of 0.1 M in 50 per cent ethanol was found to be very small. Some data are reported in table 5. A minimum solubility was found at sodium sulfate concentrations between 0.01 and 0.1 hl comparable to the results in aqueous sodium sulfate solutions.
SOLUTBILIIY OF LEAD SULFATE CONCENTPATION OF
NanSO4 Milligrams of
Pb per liter
Moles of
PbSO, per liter
X I@
M
O.OO0 0.001 0.005 0.010 0.100
0.24 0.17
0.82
0.25
1.22
Apparently, the effect of the ionic strength in the medium of 50 per cent ethanol is much greater than that in water, as the dielectric constant of the former is much smaller. Solubility oj lead oxalate in water and in potassium oxalate solutions The solubility of lead oxalate was determined in water and inaqueous solutions of potassium oxalate a t 26°C. The results are found in table 6 and graphically represented in figure 3. The solubility attains a minimum value a t a potassium oxalate concentration of about 0.005 M . With increasing oxalate concentration the solubility increases almost linearly with the oxalate concentration (see figure 3), indicating the formation of the complex Pb(Cz04)2-- ion. From the results it can be calculated that in systems saturated with lead oxalate the value of the constant (average of values calculated a t [CzOd--] = 0.025 and higher) is
568
I. M. KOLTHOFF, R:W.
PERLICH AND D. WEIBLEN
Considering the saturated solution of lead oxalate in water aa being completely ionized and taking the concentrations equal to the solubilities, a solubility product of lead oxalate
TABLE 6 Solubility of lead ozalate i n potassium ozalate solutions at W C . coNfPrrP*noN P-
or & G O 4 unm
G0LTII)ILITY 01 L u n 0XALAm
IN MOL-
Milligrams of Pb per liter
0 0.001
I
.4.5 3.7 3.0 4.3 8.4 17.4
0.005 0.01 0.025 0.050 0.075 0.100
24
0.500
x IOI
2.2 1.8 1.5 2.2 4.1 8.5 12 16 35
32 72 135 175
0.200 0.400
Moles of PbCtOI peer liter
66 85
FIG.3. Solubility of lead oxalate in potassium oxalate solutions a t
26°C.
is calculated at 26°C. From the above data we calculate the complex constant of the reaction Pb*
+ 2C2OT-
Pb(CzO&-
SOLUBILITY OF LEAD SITLFATE AND LEAD OXALATE
569
Solubility of lead oxalate in ethanol-water mixtures The solubility was found to decrease with increasing alcohol concentration, a behavior which is in qualitative agreement with that of lead sulfate. In 10 per cent alcohol the solubility was found to be equal to 8.2 X JI (1.7 mg. Pb per liter); in 20 per cent alcohol 4.2 X M (0.85 mg. Pb per liter); in 30 per cent alcohol 1.2 X 10+ M (0.24 mg. Pb per liter). Solubility o j lead chromate in water Finally, it may be st,ated that the dithixone method was also useful in the determination of t,he solubility of lead cliromatc. A very pure product of the latter, prepared by Mr. F. T. Eggortsen in this lal)oratory, was used. After saturation the lead was determined in 50 ml. of thc clear centrifugatr. The solubility found was 5.3 X lo-' 111, in good agrerment with thc data of liohlrausch and Rose (12) (6.2 X lo-' ill) and of Iiolilrausch (11) (3.1 X 111). There authors used the conductance method. IIcvesy and Pancth (7), -using a radioactive method, found a solubility of 3.7 X lo-* AI, mhilc Hevesy and Rona (8), using a similar method, reported a solubility of 2 X 10-7 M . Our value of 5 x JI seems to be a fair average of thc more reliable data reported in the literature. SUMMARY
1. Dithizone was found to bc a suitable reagent for the detcrrninntion of the solubility of slightly soluble lead salts in various media. 2. The solubilities of lead sulfate in ayucous solutions of sodium sulfate and sulfuric acid were in good :tgreement, with data rcported by other authors. The effect of the ionic strength of sodium nitrate upon the solubility of lead sulfate in 0.01 M sodium sulfate has been found to be very large. 3. .&oh01 decreases the solubility of lead sulfate very markedly. Tlic solubility has been determinetl in water-cthanol misturrs with an alrohol rontent up to 70 per cent. 4. The solubility product of lead oxalatr in wttrr JVW found rqual to 5 x 10-10; thr constant of tlir following rrwtion, "'+
+2
was calculated fi.om the rrsults,
c204--
a3
e Pb(C!20n)2--
follow:
5. The solubility of lead oxalatr has l)ccn determined in water-ethanol mixtures with an alcohol content up to 30 per cent G . The solubility of lead rhromatc in wntcr was found t u bc 5 X loMimoles per liter.
570
E. S. FETCHER, JR.
IZEFERESCES (1) (2) (3) (4) (5) (6) (7) (8) (9)
(10) (11) (12) (13) (14)
CLIFFORD, P . A , , AND WICHMANN, H. J . : ,J. Assoc. Official Agr. Cheni. 19, 130 (1936). CRAIO,D. Pi., AND VINAL,G. W . : J. Research Piatl. Bur. Standards 22, 55 (1939). CROCKFORD, H . D., AND BRAWLEY, D. J.: J. Am. Chem. Soc. 68, 2600 (1931). FISCHER, H . : Angew. Chem. 42, 1025 (1929). FISCHER, H . : Angew. Chem. 47, 685 (1934). FISCHER, H . , AND LEOPOLDI, G . : Angen. Chem. 47, 90 (1931). HEYESY,G . v., AND PASETH,I?.: Z.anorg. allgem. Chem. 8'2, 323 (1913). HEVESY,G . v . , A N D RONA,E.: 2 . physik. Chem. 89, 305 (1916). HUYBRECHTS, M . , A N D DELANQERON, Pi. A , : Bull. soc. chim. Belg. 36, 13 (1930). HUYBRECHTS, M., AND RAMELOT, H . : Brill. soc. chim. Belg. 36, 219 (1927). KOHLRAUSCH, F.: Z . physik. Chem. 44, 197 (1903). KOHLRACSCH, F., A N D ROSE,F . : 2 . physik. Chem. 12, 241 (1893). R. B., AND RUTHERFORD, €1. A . , J R . : J . Am. Chem. 8oc. 66, 3221 (1933). PURDUM, WICHMANN, H . .J., MURRAY, C. W . , HARRIS, M . , CLIFFORD, P. A , , I~OIJOHREY,J. H., AND VORHES, F. A . : J. .4ssoc. Official Agr. Chem. 17, 117 (19.34).
A CRITICISM O F T H E TEORELL-MEYER-SIEVERS MEMBRANE PERMEABILITY
THEORY OF
E . S. FETCHER, JR.
Department of Physiology, University of Minnesota, Minneapolis, Minnesota
Received J a n u a r y 16, 19.48
The publication of the similar theories of membrane permeability of Teorell (6) and of Meyer and Sievers (3, 4, 5) has been considered as marking an epoch in the study of ionic permeability. These theories have been widely discussed (see, for example, references 1, 2, 7 ) , and there have been some attempts to interpret data by means of them. I t is the purpose of this communication to analyze the data presented by hieyer and Sievers in support of their theory; the analysis was deemed necessary because Meyer and Sievers (4) do not discuss all of the data which they give. The author has determined by the graphical techniques described by Meyer and Sievers (3, 4) the two parametcrs which, according to thc theory, are necessary to characterize a membrane-clcctrolytc system. In several cases the values obtained by the author for these parametcrs do not agree with those given by JIeyer and Sievers, owing probably to the difficulty of matching the experimental and theoretical curves in those cases. In figure 1 all the data of Meyer and Sievers for simple syst,ems (4) are, plotted. 0rdinat)es are niillivolts; abscissae are log l / c l ; c1 is the ion concentration of the less concentrated electrolyte of the pair in which cp equals twice cI. The family of theoretical curves from Meyer and Sievers (3) is given also, plotted on the same scale as the experimental curves. The sign of the potentials of Curves F and G has been reversed for convenience.
