Dec., 1960
DIFFUSION COEFFICIENTS OF LEADAND CHLORINE IN MOLTEN P B C L KCL ~.
1911
THE DIFFUSION COEFFICIENTS OF Pb2l0AND C13‘ I N MOLTEN PbC12-KCI MIXTURES I N THE VICINITY OF THE COMPOSITION 2PbClyKCl’ BYGERALDPERKINS, JR.,R. B. ESCUE, JAMES F. LAMB,^ TROY H. TIDWELL* AND J. WAYNE WIMBERLEY~ Department of Chemistry, North Texas Stale College, Denton, Texas Received J u n e 16, 1060
The diffusion coefficients of Pbela and C P were measured for three compositions of PbC1,-KCI mixtures: 25.2, 33.3 and 37.0 mole % KC1. The measurements were made over a temperature range of about 100’ from within about 10” of the melting point. The diffusion of CISa seems to be independent of composition. The diffusion coefficient of Pb*lo, on the other hand, varies with composition and the diffusion of this isotope seems to be particularly hindered a t the composition, 2PbClyKCl.
According to many authors, the system, molten PbC12-KC1, is considered to show ambiguities in physical properties. Duke and Fleming3 studied transport phenomena in this system and concluded that the lead is not part of a negative ion but that negative deviations in the value of the cation transference number observed in passing from pure lead chloride through progressive, intermediate compositions to pure potassium chloride are due to decreased conductance on the part of the potassium. Transference experiments by Tubandt and Reinhold4 and X-ray crystal structure determinations by Mehmel and Nespita16 suggest the absence of complex ions in solid PbClzKCl mixtures. Tubandt and Reinhold found the transference number of chlorine to be equal to one in solid 2PbC12.KC1. The phase diagram for the systems shows a congruently melting compound at the composition, 2PbClyKCl. Harrap and Heymann7 observed no anomalous behavior in the viscosity of the system. In order to reconcile viscosity and conductance data these authors postulated the operation of a different mechanism for viscous flow which would be Iess sensitive to association of the ions into small complexes. On the other hand, Loren2 and his co-workers* also studied transport phenomena in these mixtures and found, for some compositions, that the lead migrated out of the cathode compartment. The significance of their “transference numbers” is not clear, but their results have been taken to indicate the presence of complex ions in the melt. Bloom and Heymanng observed negative deviations in the value of the equivalent conductance of this system as the composition was changed. A minimum was observed in the conductance at about 50 mole % KCl for all temperatures investigated and this was attributed to the presence of the complex ion [PbClaI-. A further, sharp minimum was observed a t about 80 mole yo KC1 a t temperatures below (1) The work reported in this paper is part of a continuing project initiated under a Frederick G. Cottrell grant and continued under a seriea of grants from the Robert A. Welch Foundation. (2) Robert A. Welch Foundation Research Fellow. (3) F. R. Duke and R. A. Fleming, J. Electrochem. SOC.,106, 130 (1959). (4) C. Tubandt and H. Reinhold, 2. Elektrochem., 29, 213 (1923). ( 5 ) M, Mehmel and W . Nespital, Z. R+laZZogr., 88, 345 (1934). (6) K. Treis, Jahtb. Min. BeiZ-Bd., 57, 766 (1914). 81, 268 (7) B. 8. Harrap and E. Heymann, Trans. Faraaday SOC., (1955). (8) (a) R. Lorenz and G. Fausti, Z. Elektrochem., 10, 630 (1904): (b) R. Lorenz and W. Ruckstuhl, 2. anorg. Chem., 62, 41 (1907). (9) H. Bloom and E. Heymann, Proc. Roll. SOC.(London). AlS8, 392 (1943).
650’. This second minimum did not occur above that temperature. The complex ion [PbCl& was postulated to explain the second minimum. Bloom and Heymann considered as anomalous the absence of a conductance minimum for the melt a t the composition 2PbClyKC1 (33.3 mole yo KC1). It would appear, in the light of such conflicting evidence, that the case for complex ions in this system is in considerable doubt. In order to help resolve this question an additional insight into the structure of the melt should be provided by a knowledge of the behavior of the diffusion coefficients of the lead and chlorine in the PbC12-KCl mixture in the vicinity of the composition 2PbC12.KC1. This is the region in which Bloom and Heymann indicated anomalous behavior. Supplementary evidence might determine whether the observed properties should be attributed to the influence of complex aggregates and whether these are actually complex ions involving the lead and chlorine or whether they represent instead the involvement of lead along with potassium in some restriction to cation mobility. Earlier work in this Laboratory10 showed the possibility of a restricted movement for the cation in molten PbClz and it is possible that some similar cation interaction might restrict the movement of the potassium in PbCl2-KCl mixtures. To establish this evidence the following measurements were made. The necessary data were collected by the “capillary method” of Anderson and Saddington.11 Active material contained within a Pyrex capillary was allowed to diffuse for a measured time into a large volume of inactive material of identical chemical composition. Conditions of the experiment were such thah the solution of Fick’s law for this particular case reduces to
E
=(~CO/R exp( ~ )- aZDt/4l2)
where = average concn. of active material remaining in the
capillary at time t
CO= initial concn. of active material within the capillary
D = diffusion coefficient, cm.* sec.-1 t = time, sec. 1 = length of capiIIary, cm.
The particular conditions which lead to this simplification are discussed by Carslaw and Jaeger12 and Anderson and Saddington.” The ratio C/Co (10) G. Perkina, Jr., R. B. Escue, J. F. Lamb and T. H. Tidwell, THISJ O U ~ N A L64, , 496 (1960). (11) K. Baddington and J. 9. Anderson, J. Chem. Soc., 9381 (1949). (12) H. 8. Carslaw and J. C. Jaeger. “Conduction of Heat in Solidr,” Oxford univ. Press, London, 1947. p. 79.
1912
G. lJERKINS, JR., R. B. ESCUE, J. E'. LAMB,T. a.TIDWELL -4SD J.
w.WIMBERLEY
v01. 64
TABLE I THEDIFFUSION COEFFICIENTS OF ,--
Temp., OC.
448 449 450 470 473 475 490 500 505 520 524 530 539 550 555 570 575
25.2 mole % KC1 -
C-
0.53
I
ClSb
Pb210
* 0.06
AND
0 . 3 4 z!z 0 . 0 5
.04
mole % KC1-
-37.0
Pb"0 0.58 f 0.02
CIS6
1.51 f 0.03
1.49 rt 0.03
.04 .6l
.05
-
1.40 i0 . 0 4 1.56
0.76
C L IN~ MOLTEN ~ PBCLZ-KCL
B(cm.* see.-') X 105 33.3 mole % KClPb2lO CP
1.57
.10
1.98
.06
0.99 1.19
.02
2.42 2.54
.11 .04
1.23 1.38
.23 .15
2.40 2.78
.02 .09
.03
1.69
.02
.80
.12
1.97
.02
.82
.08
1.95
.29
1.10
.02
2.60
.02
1.50
-05
3.01
.04
represents the fraction of active material remaining in the capillary at the end of the experiment and is equal to the ratio of final count to initial count. This value, together with the appropriate values of t and 1, will allow the calculation of D. The mechanics of the operations involved in making these various measurements, including a description of the apparatus employed, has been described in an earlier paper.1° Experimental Preparation of the Mixtures.-The mixtures were made from reagent grade materials without further purification except for the removal of water. This was accomplished bv heating the salts under vacuum to about 400" for a period of several hours. In the case of lead chloride the vessel was periodically flooded with hydrogen chloride to minimize hydrolysis of the salt. After melting an appropriate quantity of the lead chloride (ca. 2 kg.), potassium chloride in pre-calculated quantity was dissolved in the melt. A sample of the homogeneous mixture was withdrawn for the determination of system composition and for activation. In the case of the composition 2PbClssKCl the sample was not removed for activation until repeated analysis and readjustment of the potassium chloride content gave the desired composition. The samples were treated a~ follows. Analysis of System Composition.-A sample of the molten mixture was withdrawn b pipet and transferred to an alundum mortar while still fquid. Upon solidification, the entire sample was pulverized and homogenized. Separate portions of this were removed for replicate analyses. For the first composition, the proportions of all three species, Pb++,C1- and IC+, were determined and the mole per cent. KC1 calculated from the results. I n subsequent mixtures only a potassium analysis was performed, since this value allowed the most precise determination of the composition. The potassium was separated as the sulfate after precipitation of lead sulfate and was subsequently ignited and weighed as the sulfate. Lead was determined by precipitation as the molybdate according to &ott13 and the chloride ion was titrated with silver nitrate. Activation.-A portion of the material from which the final system analysis was made was transferred to a reflux flask. Water was added to dissolve the mixture and Pb2lD and C136were introduced into the flask in the form of crushed radon needles and HCl, respectively. Reflux was maintained until the exchange had reached equilibrium. At this point the solution was filtered while hot in order to remove the crushed glass and was then evaporated to dryness to recover the original PbClrKCl mixture. This mixture was dried under vacuum exactly as was the pure lead chloride, (13) W. W. Scott, "Standard Methods of Chemical Analysis," Vol. I, D. Van Nostrand C o . , New York, N. Y., 1939, p. 506.
.67
.02
1.70
.04
.76
.03
2.10
.05
.94
.04
2.56
.04
1.27
.09
2.64
.12
2.86
.04
1.28
.02
then pulverized, homogenized and stored under an argon atmosphere for later use in filling the capillaries. A t such time, pnly the amount needed for filling a particular group of capillaries was introduced into the fillin furnace. This procedure was employed to minimize cfanges in composition which might otherwise be brought about by evaporation. Separation and Recovery of the Isotopes.-When the capillaries were withdrawn from the immersion bath they were first allowed to cool, after which the surface was carefully scraped and cleaned of all external traces of salt. The individual capillaries were crushed and quantitatively removed to a small flask containing an aqueous mixture of nitric acid and silver nitrate. This system was refluxed for several hours until the chlorine was quhtitatively precipitated as silver chloride and the lead was discharged into solution in soluble form. The mixture was filtered and washed and the filtrate diluted t o a volume of 50 ml. This solution contained all the lead and was counted by standard techniques. The residue of silver chloride was next dissolved with several portions of a solution of sodium thiosulfate and the filtrate collected as i t came through the filter. This solution contained all of the chloride ion. After collecting the washings, the solution was diluted to 50 ml. and counted in the same manner as the lead. The procedure for the separation of the isotopes was carefully checked for efficiency of separation and shown to give no measurable activity of unwanted isotope in either fraction and no measurable activity in the filter after the separation.
Results The diffusion coefficients of Pb2l0and Cl38 were measured at three compositions of the PbC12-KCl mixture and at several temperatures for each composition. The results are shown in Table I. The values of the diffusion coefficient are averages gathered from four trials. The average deviation is calculated from the individual values for each trial. The value given for the composition of each mixture is an average value obtained from at least three analyses. In Fig. 1 the logarithms of these data have been plotted as a function of the reciprocal of the absolute temperature. The straight lines in the figure have been fitted to the data by the method of least squares. The equations of the lines, with standard errors indicated in parentheses, are given in Table 11. Figs. 2a and 2b present a family of isotherms whose points have been calculated from the equations of Table 11, while Fig. 2c gives the variation of activation energy with composition. The pertinent
DIFFUSIONCOEFFICIENTS OF LEADAND CHLORINE IN MOLTEN PBCL~. KCL
Dec., 1960
1913
area of the phase diagram has been appended to Fig. 2 for convenience. TABLE I1 EQUATIONS FOR
DIFFUSION COEFFICIENT OF C1" AT EACHCOMPOSITION THE
Compn (mole 70 KC1)
Pb210 AND
DPb
25.2 33.3 37.0
D = 5.03 X D = 2.92 X D = 1.96 X
25.2 33.3 37.0
D D
exp(-9864 f 242/RT) exp(-l2796 i 1092/RT) exp(-8405 f 566/RT) Dei
2.34 X exp(-7403 f 541/RT) = 1.44 X 10- expl-6608 f 573/RT) D = 1.31 X 10-3exp(-6443 i 4 1 7 / R T ) =
\ m v.3
I
Discussion 120 As in the case of pure lead chloride'O these data show the diffusion coefficient of C13ato be greater Fig. 1.-Diffusion than that of Pb2lo. Unlike pure lead chloride, the (lower) in molten activation energy for diffusion is greater for lead KC1; m, 33.3 mole than for chlorine. It is expected that the diffusion coefficient will be given by an equation of the form ,
D
=
I
I
I
I
125
130 135 140 106/T,"A. coefficients of C1s (upper) and Pb210 PbC12-KC1 mixtures ( 0 ,25.2 mole % % KC1; A, 37.0 mole % KCl).
\
A exp(B/RT)
in which D = the diffusion coefficient B = an activation energy for diffusion T = absolute temperature -4 = a constant
The straight line relationship between log D and 1/T indicated by this equation was borne out well by the data. The results a t a given temperature show changes a t each composition for both the chlorine and lead. These changes seem to be progressive in the case of Cl36 and the activation energy shows a steady decrease as the amount of KC1 in the mixture increases. This decrease may be illusory, however. The error in the data is of the order of 10% and an almost horizontal line can be drawn through the points. The range of standard error calculated by the method of least squares has been indicated by the vertical bars on the figure. In the case of Pb2l0 the data indicate unique fluctuations in the vicinity of the composition 2PbCl2.KC1. Taking into account the standard error, or even increasing the range of error to lo%, the diffusion coefficients of the lead are significantly lower and the activation energy for diffusion is significantly higher at the compound composition. For both the activation energy and the diffusion coefficient the change is more pronounced on that side of the compound composition having the lower melting eutectic. While it is possible that the results could be explained by precipitation of lead chloride and potassium chloride from the melt a t the lower temperatures, the measurements were made a t least ten degrees above the melting point so that no change in composition of the melt should occur due to accidental solidification of one component. The isotherms of Fig. 2 show a progressive shift toward horizontal lines. If the equations given in Table I1 are used to extrapolate isotherms a t higher temperatures, this trend is reversed. However, in view of the conductance data gathered bv Bloom u
I
I
I
I
25
30
35
40
Mole % KCI. Fig. 2.-Diffusion in the system PbC12-KC1: (a) isotherms of D vs. composition for Pb*"J; (b) isotherms of D vs. composition for Cl36; (c) activation energy €or diffusion vs. composition (upper curve) Pb2lO; (lower curve) Cl36; (d) phase diagram for region investigated.
and Heymanng and the viscosity data of Harrap and Heymann,' anomalous behavior is not expected a t temDeratures higher than about 550' so that one would expect the curves shown in Fig. 1to approach identical slopes in the vicinity of that temperature. The limitations of the glass apparatus made measurements a t temperatures above about
1914
L. G. LONGSWORTH
T'ol. 64
575' impractical, and extensions to higher temperaApparently the disparity in conductance behavtures were not possible. We infer from Fig. 1 that ior at the compositions 2PbC12.KC1 and PbC13. the two sets of curves would resolve themselves into 4KC1 reported by Bloom and Heymanns was due to single lines a t the upper limits of the temperature the relative differences between the melting points range investigated. of the compounds and the temperatures a t which This work was primarily concerned with those the measurements were made. It is likely that a temperatures between the melting point and the conductance minimum would also be observed at lowest temperatures used by Bloom and H e ~ m a n n . ~the composition 2PbCl2-KC1 a t temperatures In this range, it seems that the lead encounters nearer the melting point. However, the relatively some hindrance to diffusion while the chlorine is low diffusion coefficient of the lead, with its attendunaffected. The lead is increasingly hindered in ant low transference number, would probably its diffusion as the composition approaches that of moderate the decrease in conductance. Thus, the the compound 2PbCl2-KC1,but this hindrance be- minimum a t the composition 2PbC12.KC1 should comes less as the temperature is raised. not be so pronounced as that a t the composition In order to explain the inapplicability of the PbC12.4KCl. Stokes-Einstein equation to the pure, molten PbCl, More interesting here is the lack of any evidence system it was postulated that the lead was held that changes in composition influence the diffusion more immobile than the chlorine.1° This might be of the chlorine. Heretofore, explanations of the due to the greater mass, the influence of the greater various types of behavior encountered in this syscharge in electrostatic interactions, or to other tem have always assumed the presence of one or factors. It would seem that the same mechanism more complex ions involving both the chlorine and is operative here, since the diffusion coefficient of lead. It would appear that any complexes or other the lead remains smaller than that of the chlorine in PbC12-KC1 mixtures. On the other hand, for the aggregations which might be present a t these temthree compositions investigated, the activation peratures have little or no influence on the difenergy of diffusion is greater for the lead than for fusion of the chlorine but mainly involve the lead. the chlorine. This is contrary to the behavior of It may be that close to the melting point the bepure lead chloride. Since the activation energy of havior is influenced more by the presence of some Pb2l0varies with composition and is a maximum cation aggregation, while at higher temperatures, a t that potassium content corresponding to 2PbC12. these cation structures may vanish and the behavior KC1, it would appear that the potassium ion has an may become dependent upon the presence of the adverse influence upon the mobility of the lead in complex ions previously postulated. The trends the vicinity of the compound composition. It is to shown by these data, however, would indicate that, be expected that this influence is mutual and that the potassium ion also encounters a hindrance to its at the higher temperatures, the behavior of the diffusion. Such an effect has been indicated in the lead and the chlorine becomes independent of comresults of Duke and Fleming3 and Tubandt and position and this would rule out the presence of complex ions involving the lead and chlorine. Reinh~ld.~
THE MUTUAL DIFFUSION OF LIGHT AND HEAVY WATER BY L. G. LONGSWORTH Rockefeller Institute, New Y o r k , N . Y . Received June 9.8, I960
With the aid of a new diffusion cell and Rayleigh interferometry the mutual diffusion of light and heavy water has been measured at 5,25 and 45' over the entire range of composition. Paralleling rather closely the fluidity of HzO-DzO mixtures, and also the chloride ion mobility therein, the diffusion coefficient exhibits small negative departures from a linear decrease with increasing mole fraction of DzO. The effect of temperature on diffusion in this system is compared with that of large solutes in aqueous solution.
Using a diaphragm cell Adamson and Iranil observed a pronounced minimum in the diffusion of light and heavy water at a mole ratio near unity. With the aid of a porous frit Baur, Garland and Stockmayer2 were unable to confirm this result but their measurements did not indicate the slight dependence on the mole fraction that had been observed3 with an optical method in H20(1) A. W. Adamson and R. R. Irani, J. Am. Chrm. Soc., 79, 2967 (1967). (2) M. E. Baur, C. W. Garland and W. H. Stookmsyer,
