1328
JTJIH.
[CONTRIBUTION NO. 1190 FROM
THE
WANG
Vol. 76
DEPARTMENT O F CHEMISTRY O F YALE UNIVERSITY]
On the Theory of the Polarographic Diffusion Current. I. Diffusion of Small Amounts of Lead and Zinc Ions in Solutions of Various Supporting Electrolytes BY JTJIH. WANG RECEIVED NOVEMBER 19, 1953 The tracer-diffusion coefficients' of Pb(I1) ion in aqueous potassium chloride solutions of concentration from 0.02 to 4.0 F and in 0.1 Fpotassium chloride 0.1 F hydrochloric acid solution were determined. Preliminary examination of the effect of gelatin on the tracer-diffusion coefFicient of Pb(I1) ion was made. Similar results were obtained on the diffusion of small amounts of Zn(I1) ion in aqueous potassium chloride and nitrate solutions of different concentrations and in 1.0 F "40H 41.0 F S H & l solution. The variation of the tracer-diffusion coefficient of Zn(I1) ion with concentration of the supporting electrolyte in dilute solutions was compared with that predicted from the Onsager theory. The rapid increase of the tracerdiffusion coefficient of Zn(I1) ion in potassium chloride solution with increasing salt concentration was interpreted on the basis of complex ion formation. The effect of gelatin on the tracer-diffusion coefficient of Zn(I1) ion in 1 F "4OH f 1F NHdCl solution was investigated. Finally, theoretical values of the "diffusion current constant" were calculated from the IlkoviE, Strehlow-von Stackelberg and Lingane-Loveridge equations, and compared with experimental data.
+
During the last decade considerable amount of of an "enrichment effect," More definite evievidences has been accumulated to show that a t dences for the validity or invalidity of von Stackelleast in solutions containing gelatin the "diffusion berg's arguments are yet to be established. Furcurrent constant", 1 = id/(cm2/atL/a), increases with thermore since equation l was obtained by taking t 1 ' 6 nz-l/3 when the latter is above a certain "critiinto consideration the effect of curvature of the cal value.?" By taking into account the curvature dropping electrode surface, its validity should not of the electrode surface, Lingane and Loveridge,? be affected by the presence or absence of gelatin. and independently, Strehlow and von Stackelberg? Contrary to this expectation, Meites5 has shown 110th arrived a t the following modified IlkoviE equa- that in the absence of gelatin the values of i d ' tion ( ~ m ~ / for ~ t several ~ / ~ ) depolarizer ions remain c o w stant and independent of the drop time. Needless to say that before the theory of the poLingane and Loveridge assigned to the constant A larographic diffusion current is more successfully the value of 39, whereas Strehlow and von Stackel- worked out, we should be cautious in accepting berg estimated i t to be 17. Both groups of investi- tracer-diffusion coefficients evaluated from polarogators claimed that their own polarographic data graphic measurements. agreed with their own value of the constant A betExperimental ter than the value estimated by the other group. Preparation of Tracer.-Radioactive lead (Pb2'0) prepared Sctually since the tracer-diffusion coefficient of the the active deposit of aged radon tubes was used as depolarizer ion is unknown in most cases, the agree- from tracer for Pb(I1) ions. The radon tubes used were made of ment or disagreement found between the calcu- gold and were cut into small segments and leached with 1 lated and experimental values of id/(6?%'/'t1/') is ml. of 1 F nitric acid for 24 hr. T o prepare the radioactive quite uncertain. The purpose of the present re- solution for diffusion measurements, a measured volume of leach liquor was evaporated to dryness in a platinum search program is to determine the tracer-diffusion this crucible, the invisible residue was dissolved in aqueous pocoefficient of several depolarizer ions in different tassium chloride solution of the desired concentration. All solutions of supporting electrolytes, and to com- potassium chloride solutions used in the present work were pare the values of id/(cmZ/gt1/6)computed from made 0.002 F in Pb(I1) to avoid adsorption errors and 0.0005 F in HCl (except those solutions containing gelatin) them by means of different theories with the ex- to prevent the hydrolysis of lead ion in dilute solutions. perimental values. It is the hope of this investiga- Zna5was used as tracer for Zn(I1) ions. This wa? obtained tor that the tracer-diffusion coefficients reported in from the isotopes division of the U. S. Atomic Energy Comthe present and subsequent articles of this series mission a t Oak Ridge, Tennessee. Diffusion Measurement.-The improved capillary will be found useful in future studies on the theory method6 was used in the present work. The diffusion of the polarographic diffusion current. period of the present measurements varied from 3 to 4 days. Apparently the theory of the polarographic dif- For the measurements with Zn(I1) ions, all the GO- and fusion current is still in its early stage of develop- samples mere dried over anhydrous calcium chloride for a t 24 hours before being counted with a thin micament. For example, Koutecky has recently3 de- least window counter. For the measurements with Pb(I1) ions, rived the new diffusion current equation the c,,-samples obtained after each diffusion experiment ('By-
i,i =
607nD1/%m'/d1/6(1
+ 34% f
1 0 0 ~ ' ) (2)
where x = DL/?t1/6m-'/3 But according to von Stackelberg,4 the term i o 0 2 in equation 2 is negligible, the constant 31 should be changed to 17 because of what he called a "depletion effect," and the constant GO7 should be changed to 619 because ( 1 ) For t h e definition of tracer-diffusion coefficient, see
J. H . Wang,
THISJ O U R K A L , 7 4 , 1182. 6317 (1952). (2) See I. A I . Kolthoff and J. J. Lingane, "Polarographv." science Publ., Inc., S e w York, N. Y., 1952, Chap. IV. (3) J. Kouteckj., Ccskoslowcnsky Em, f y s . , I,117 (1952). (4) M. von Stockelberg, 2 . Blrklrochsm., 67, 338 (1963).
Inter-
were kept in a desiccator together with the co-samples foia t least 40 days and then counted together. This waiting period is necessary for the lead samples for two reasons. Firstly, the 8-radiation from Pb2IO is too weak for direct counting and consequently we determine the amount of Pb*IO by waiting until transient equilibrium is attained and then counting its daughter Biz1o (half-life = 5 days) which emits 1 . 2 MeV. 8-radiation. The second and even more important reason is that the radioactive solution prepared nccording to the procedure described above actually contained both PbZ1Oand BiZ1*(Po was not detected by the present (5) L. hleites, THIS J O U R N A L , 73, 1581 (1951). (6) J. H. Wang, C. V. Robinson and I . S. Edelman, i b i d . , 76, 466 (1953).
bIar. 20, 1954
D I F F U S I O N O F L E A 4 D AND Z I N C I O N S IN S U P P O R T I N G
counting set-up and hence need not be considered here). In order t o measure the tracer-difision of Pbz10alone, it was thus necessary to wait for a t least 40 days (8 times the halflife of Bizlo) when practically all the B P o originally present in the samples had decayed into the harmless Po2" before counting. The assumption that the a-particles from PoZl0 were not detected by the present counting set-up was confinned by the counting of these samples covered with aluminum absorbezs. All the measurements were carried out at 25.00 4-0.01 . Adsorption Error and Its Elimination.-Although the concentration of the supporting electrolyte is above 0.02 F i n all cases of the present work, there is the possibility that the P b + + or Z n + + ions may be preferentially adsorbed from the electrolytic solution by the glass surface of the capillaries and consequently exhibit an "anomalous" tracer-diffusion coefficient. In fact it was found that when carrier-free Pb2'0 was used for the measurements, erroneous diffusion coefficients were obtained which cannot be reproduced with capillaries of different cross-sectional area and length. Even for the same capillary the measured diffusion coefficient varied with the length of diffusion time and previous treatment of the glass surface of the capillary. In the present work, this type of adsorption error was eliminated by adding enough inert lead salt in the solutions (both inside the capillaries and in the diffusion bath) to make the latter 0.002 F in Pb(I1). Apparently when the concentration of Pb(I1) in these solutions is 0.002 F or more, the fraction of Pb(I1) adsorbed to the glass surface of each capillary is negligibly small as compared to that in the bulk of the solution. It was found that with these solutions containing inert Pb(I1) the measured tracer-diffusion coefficients are reproducible and independent of the characteristics of the capillary, the diffusion time, and the concentration of Pb(I1) provided th:it the latter is small as compared to that of the supporting electrolyte. For the same reason all solutions for the measurement o f the diffusion of Zn(I1) ions were made 0.005 F i n Zn(I1).
Results and Discussion Diffusion of Small Amount of Pb(I1) Ion in Aqueous KCl Solutions.-The results of these measurements are summarized in Table I. Each value listed in Table I is the average result of 6 TABLE I TRACER n I F F U S I O N COEFFICIENTS OF Pb(I1) IONIN KCl (AQ.) AT 26" Concn. (formular wt./l.)
0.00 .02 .10 .25 .70
X 10s (cm.2/sec.)
Dpb(lr:
(0.940) ,941 & 0.009 ,970 f ,012 ,988 f ,010 1.025 =t ,012
Concn. (formular wt./l.)
1.00 2.00 3.00 4.00
X 105 (cm.2/sec.)
Dpb(I1)
1.001 0.005 0.937 h ,012 ,859 =I= ,016 ,794 f ,018
measurements. A11 solutions listed in Table I are 0.009 F in Pb(I1) and 0.0005 F i n HCl and contain no gelatin. The temperature was kept a t 25.00 0.01' for all the measurements. These values of D in Table I are plotted z's. .\/G of KCl in Fig. 1. The value of D a t infinite dilution in Table I was calculated from conductive data with = 147.0 given by Korman and Garrett, and the accepted value of A; - = ' T ( j . X by means of Nernst's formula. Figure 1 shows clearly that as the concentration of the supporting electrolyte decreases indefinitely, our measured value of the tracer-diffusion coefficient for Pb(I1) ion approaches a value which is in agreement with Nernst's limiting value from conductmce data. This agreement is an independent check on the reliability of the present results. The change of D DS. .\/Z of the supporting electro-
*
(7) J. W. Norman and A. B. Garrett, THISJOTTRNAL, 6 0 , 110 (1947).
1.10
-.0 x 3
ELECTROLYTE SOLUTIONS
r---
1529
1.00
h
u
P
-2 Ej 0.90 V
v
Q
0.80
0.70
1
0.0
I
0.5
I
I
I
1.0
1.5
2.0
2.5
4; Fig. 1.-Tracer-diffusion coefficient of Pb( 11) ion iii aqueous potassium chloride solutions a t 25". The shaded point represents D0pb.t + a t infinite dilution calculated from conductance data.
lyte as depicted in Fig. 1 is considerably different from those found for Na+, C1- and Ca++.137g Fromherz,lO in his study of the absorption spectra of lead halide solutions, has shown the existence of relatively high concentrations of PbCl+ ions. There are also evidences" that in concentrated chloride solutions complex ions such as PbC13- exist. I n view of the existence of these complex ions, we may take Fig. 1 as suggesting that ions such as PbCI+ have higher tracer-diffusion coefficient than the simple hydrated Pb++ ion in solutions of moderate concentrations. Similar observations have been made by von Stackelberg4in his studies with a linear stationary electrode on the diffusion of Pb(I1) ion in KCl solutions containing 0.01% by weight of gelatin. However, von Stackelberg's diffusion coefficients may not be directly comparable to the present values because of the possible complications due to the presence of gelatin described in the following section. Discussion on the Effect of Gelatin.-Since the majority of accurate data in the literature of polarography are for solutions containing 0.01% by weight of gelatin, it is necessary for us to examine the effect of gelatin on the measured tracer-diffusion coefficient. Determinations of the tracer-diffusion coefficient of Pb(I1) ion in 1.0 F KC1 solutions containing gelatin have been made in the present work. The results indicate that there is an appreciable decrease in the tracer-diffusion coefficient of Pb(I1) ion in 1.0 F KCI solution as the gelatin content or the fiH of the solution or both are raised. But since only a small portion of published polarographic diffusion current data have been reported for solutions of specific PH and since the nature of the gelatinelectrode surface interaction is not yet fully understood, there is a t the moment little hope of making ( 8 ) J. H. Wang and 9.Miller. ibid., 1 4 , 1611 (1952). (9) J. H. W a g , i b i d . , 74, 1612 (1962); ibid., 76, 1769 (1953). (10) H. Fromherz, Z. p h y s i k . Chem., 163, 321 (1931); i b i d . , 382 (1931). (11) L. M . Koreman, J . Gen. Chcm, U.S.S.R., 16, 157 (1946).
I530
JUI
H. WANG
42
4.2
..
h
Y
+
*
2 4.0 -,
6)
.$
II
3.9
3.8
bound to bovine serum albumin decreases rapidly when the p H of the solution is lowered from 7 to 4, and that below pH 3 the “diffusion current constant” is independent of PH and is equal to that in the absence of albumin. Likewise if we assume that the fraction of Pb(I1) bound to gelatin in 0.1 F KCl 0.1 F HCl 0.009% gelatin solution is negligible, we may use the above-measured tracerdiffusion coefficient of Pb(I1) ion (DX lo5 = 0.936 0.011 cm.*/sec.) in this solution to calculate i d l ( c m ‘ 4 ’ by means of equation 1. The results are illustrated in Fig. 2 where the three straight lines represent equation 1 with the constant A equal to 0, 17 and 39, respectively. In contrast to earlier statements,2 Fig. 2 shows clearly that the deviations of the values of I = i d / ( c m ’ / ~ t ‘ /calculated ~) by means of equation 2 with A = 39 are much larger than those with A = 17. However the agreement between the latter values and experimental data cannot be considered as satisfactory. Further work in this direction is necessary before definite conclusions can be drawn. Moreover, according to Meitesl6 the “diffusion current constant” of Pb(I1) ion in 0.1 F KC1 0.1 F HC1 solution in the absence of gelatin is independent of drop time and remains a t the constant value of 3.992 f 0.013 from t = 2 t o t = 10 sec. But if we compute the “diffusion current constant” from the measured value of D by means of equation 1 with A = 0 we get I = 3.77 f- 0.02 which is 5.5% lower than his experimental value. This discrepancy also seems to deserve further investigation. Results on the D i h s i o n of Small Amount of Zn(I1) Ion in Aqueous Solutions.-The tracerdiffusion coefficients of Zn(I1) ion in aqueous potassium chloride solutions determined in the present work are listed in Table 11. A11 solutions listed in Table I1 were made 0.005 F i n Zn(I1) and 0.0005 F in HC1. Each value of D listed in Table I11 is the average result of 6 measurements. The value
+
4.1
cE
c,
Vol. 76
6
0
3.7
0.0
I
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1.2
t’/am-
VI.
Fig. 2.-Comparison of equation ( 2 ) with polarographic diffusion current data for Pb(I1) ion in 0.1 F HCl 0.1 F KCl solution containing 0.009% by wt. of gelatin.16
+
+
quantitative application of this kind of data to polarography. However, these data do indicate that in salt solutions of unspecified pH the effect of gelatin on the tracer-diffusion coefficient of Pb(I1) ion may not always be negligible. Diffusion of Pb(I1) Ion in 0.1 F KCl 0.1 F HC1 Solution.-For the purpose of comparison with the polarographic diffusion current data of Pb(I1) in 0.1 F KCI 0.1 F HCI solution reported by hfeites,12 the tracer-diffusion coefficient of Pb(I1) in 0.1 F KC1 0.1 F HCl solution without gelatin has been determined. The average result of nine such measurements is D X lo5 = 0.963 i 0.011 TABLE I1 Comparison of the Tracer-diffusion Coefficients TRACER-DIFFUSION COEFFICIENTS OF Zn(I1) ION IY KCl of Pb(I1) Ion with Polarographic Diffusion Current (AQ.) AT 25’ Data.-The variation of the “diffusion current Concn. Concn. Dz.(II) X 106 (formular D z ~ ( I I )X loa l ~ ~ )t’/em-’/a , for Pb(I1) (formular constant,,’ & / ( c m z ~ ~ twith wt./l.) (cm.Z/sec.) wt./l.) (cm.Z/sec.) in 1F KC1 O . O l ~ ogelatin solution has been stud0.00 (0.71) 1.00 0.818 f 0.00s ied by Lingane and Loveridge.2 Strehlow, hfad.05 ,714 f 0.010 1.40 ,878 f .010 rich and von Stackelberg6 have made similar stud$10 .729 f .010 2.00 ,940 f ,010 ies for Pb(I1) in 0.1 F 0.01% gelatin solution. .28 .736 f .010 3.00 ,971 f .010 Unfortunately neither group of workers used solu.60 .751 i .013 4.00 .P51 f .015 tions of controlled PH. Thus because of the possi.70 ,788 f .013 ble enrichment of gelatin due to adsorption near the electrode surface and because of the uncertainty of D a t infinite dilution in Table I was calcuin the pH of their solutions, i t seems difficult for us lated from conductance data by means of Nernst’s to decide what values of D should be used for theo- formula with A & + + = 53.1.14 retical computation. On the other hand, the diffuThe tracer-diffusion coefficients of Zn(I1) ion in sion current data of Pb(I1) ion in 0.1 F KCl aqueous potassium nitrate solutions are listed in 0.1 F HC1 0.009% gelatin solution obtained by Table IV. All solutions listed in Table I V were Meitesl6 should be useful for comparison with theo- made 0.005 F in Zn(I1) and 0.0005 F in hydrogen retical calculations based on the present measured ion concentration. Since these tracer-diffusion value of D in the absence of gelatin, because in such coefficients of Zn(I1) ion in potassium nitrate highly acid solution we may assume that the frac- solutions were determined merely for comparison tion of Pb(I1) bound to gelatin is negligible. I n - with those in the chloride solutions instead of for deed, T n n f o r ~ l ’found ~ that the fraction of Ph(1T) (14) H. S. Harned and B. B. Owen, “Physical Chemistry of Irlec-
+
+
+
+
+
+
(12) I, V r i t e s , THISJ O I J H N A L , 73, 3724 (lq51). ( 1 < ) (‘ I . i t i f < d i h r d 74, d l 1 (1952).
+
trolytic Solutions,” 2nd F X , Reinhold PuhI. Corp., N e w York, N. Y . , 1950, Appendix A.
DIFFUSION OF LEADAND ZINC IONS IN SUPPORTING ELECTROLYTE SOLUTIONS 1j31
Mar. 20, 1954
direct use in polarography, only three measurements were made for each solution listed in 111. Consequently these tracer-diffusion coefficients are in general less accurate than those listed in Table 11. TABLE 111 TRACER-DIFFUSION COEFFICIENTS OF Zn(I1) ION IN KNOs (AQ.) AT 25' Concn. (formular wt./l.)
Dzn(rr, X 106
Coacn. (formular wt./l.)
0.00 .05 .20 .50
(0.71) .69 i 0.014 .69 i: .009 .70 i ,015
1.00 1.50 2.00 2.50
icm
sec)
DZn(I1)
X 106
(cm.Z/sec.)
0.730 =t0.005 .75 .01 .74 3~ ,015 .OF) i .015
1.00
+
Results of the measurements on the tracer-diffusion of Zn(I1) ion in aqueous 1.0 F NHlOH 1.0 F NH4CI solutions with and without gelatin are listed in Table IV.
+
TABLE IV TRACER-DIFFUSION COEFFICIENTS OF Zn(I1) IONIN 1.0 ",OH 1.0 F "4Cl SOLUTXONS AT 25'
+
Concn. of gelatin (% by wt.)
No. of measurements
0 .oo
9 6 6
.01 -10
F
1.03 f 0 . 0 1 5 1 . 0 2 f .015 1 . 0 2 2 ~ .015
For the diffusion of tracer amount of ions of species 1 in salt solution containing ions of species 2 and 3, we have ~ 2 1 2 2 1=
calZal
(5)
and hence (4)can be written as
For the tracer-diffusion of Zn(I1) ion in aqueous solutions, if we take X o Z n + + = 53.1, X a ~ += 73.52, ANO,= 71.4414 we obtain from equations 3 and 6 " 0 3
0.71
- 0.32
