S. B. TRICKLEBANK, L. NANIS,A N D J. O’M. BOCKRIS
58
Diffusion in the System Molten Sadibm Iodide-Potassium Chloride
by S. B. Tricklebank, L. Nanis, and J. O’hl.Bockris The Electrochemistr~Laboratory The Universily of Pennsylvania, Philadelphicr 4, Pennsylvania (Received July 3, f 9 W )
The difTusion coefficients of NaZ2in NaI, 50 mole % XaI-50 mole yo KC1, and KC1, and of into NaI have been measured as a function of temperature. Although special attention to end errors was paid, deviations from the Nernst-Einstein equation are confirmed to be of the same order as those previously measured. The energy of activation for paired diffusion is approxitnstely twice that for the individual ions. The energies of activation for Naf and 1- in pure NaI are not equal. The energy of activation for Na2* In the system NaI-KC1 is greater a t the FjO-EiO composition than for pure NaI or in KC1 and AEdiffU8ionw AEcol,ductance R T . The difference in the energies of activation of Na+ aild I- is interpreted in terms of a significant jump energy arising when the ion concerned is larger than the average hole size. The maximum of the energy of activation of ?Jazz in the mixture is interpreted in terms of trimer formation.
+
From self-diffusion results for simple fused salts and the hole theory for liquids, it appears that the energy of activation (Ah’) for diffusion of the ions is equal to the energy to form a hole, which is equal to 3.74RTT,,1 where IZ is the gas constant and TI”the melting point of the salt in dogrccs absolute. (‘l’hc singular fact that AI3 depcinds only on thc melting point, Le.,, lattice energy of the entire salt, raises the question of how AI3 would behave as a function (if interactions in a mixture.) The simplest method of approach is met by the diffusion of M’X into RIX (cf. Ihckris, et a1.,2where the diffusion of thc alkali mctal ions into molten sodium chloride has been measurctd). In the present paper an examination has bocn niadc of thc offoct of diffusion in the reciprocal salt system NaI-KCI, chosen to contain ions of widely differing size. Of the mottiods used to determine self-diffusion cocfficients in niolten s a l t ~ l # ~the . - ~most convenient metliod is that of I3ocki.i~arid Hooper,’ where the diffusion takes place from a radioactive bulk into an inactive capillary. rPtic advantage of their method is that it avoids tho ticccwity of capillary tube filling in a second vucuurn furnace. ‘I’hcreiore, the Bockris and Hopper rriothod was uscd in the present work.
Experimental The apparatus and method uscd were similar to those of Ihckris and Ilooper. With the measurement
of diffusion of Xa22into the 50 mole % NaI-50 mole % KCl mixture, difficulty in obtaining a constant D was experienced. This was found to be due to the lower melting point salt (NaI) melting first and forming a layer of liquid NaI under solid KC1. The KC1 then melted and, being less dense than NaI, formed an upper layer, in spite of the absence of evidence concerning immiscibility from phase diagram studies.* (Similar behavior has been noticed in the preparation of PbC12KCI mixture^.^) Hence in the cap of the dihsiori cell, an extra hollow slip joint was placed parallel to that carrying the silica capillary holder. A silica capillary was joined to this slip joint through which prepurified J. O’M. Bockris and G . W. Hooper, Diacusswna Faraday Soc., 32, 218 (1962).
J. O’hl. Bockrin, 8. Yosliikawa, L. Nanis, and 5. R. Richards, to be published. E. R. Van Artsdalen, D. Brown, A. 9. Dworkin, and 1‘. J. Miller, J . A m . Chem. Sac., 78, 1772 (1956). A. 2. Borucka, J. O’M. Bockris, and J. A. Kitchencr, Proc. Roy. SOC.(London), A241, 554 (1957). C. A. Angcll and J. O’,M. Bockriu, J. Sci. Instr., 3 5 , 458 (1958). 9. Djordjcvic and 0. J. Hills, 7’rans. Faraday Soc., 5 6 , 269 (1960). See also L. Yarig and hI. T. Simnad, “Physico-Chemical Measurements a t High Temperatures,” J. O’M. Bockris, J. L. White, and J. D. Rlackerieie, Ed., Buttcrworths, London, 1959, Chapter 14, p. 295. Landolt-Bornstcin, 11, 3, 158 (1956). K.Balasubrahmanyam, private communication.
DIFFUSIOXI N MOLTENSODIUM IODIDE-POTASSIUM CHLORIDE
nitrogen was passed to stir the melt. The melt was mixed both before filling the capillaries and after adding the radioactive pellets. During the work, silica capillaries were rcplaced by those of platinum. This eliminated any errors associated with corrosion of the capillaries by the melt. Radioactive analyses were made with a Cosmic Radiation Labs., Inc., scintillation counter . Diffusion coefficients may be calculated for appropriate values of time arid tube length by measurement of the total diffusate Q, from the equationlo Q
=
2cd1/Dl/lr
(1)
where co is the concentration of the radioactive species in the bulk, A is the cross-sectional area of the capillary, and 1 is the time. I t was thought by Bockris and Hooper that their method required certain end corrections due to (a) gasphase transfer of radioactive salt from the bulk to the nonactive salt in the capillaries during equilibration of the tracer with the nonactive material, and (b) adherence of active salt to the mouth of the capillary when the run was terminated. nlechanism (a) was eliminated by holding the mouths of the capillaries 10 cm. above the melt during equilibration, and (b) was corrected for by “zero-time” experiments (runs of J-sec. duration). Their correction was found to be independent of ion and temperature. Dependence on bath concentration was not examined. D was found to be independent of stirring rate between 4 and 55 r.p.m. Rorucka, Bockris, and Kitchener4 suggested that in diffusion measurements by capillary techniques, when the liquid is swept past the mouth of the capillary, some of the liquid in the capillary is “dragged out” and replaced by the surrounding liquid. This gives a positive error to I) values in which no account is made for this effect. They established by dye experiments that, this “Al-effect” increased with increasing flow rate across the mouth of the capillary (6) and depended upon the capillary diameter (d). By making experiments a t different times, A1 was eliminated. The correction factor reduced the D value in NaCl in the temperature range 825-942O by 10-30%. Berne and Rerggrenll confirmed the existence of this Al-effect. A I i l l ~recognized ’~ the existence of a possible dependence of an uncorrected D on e and stated that it was possible to find an r.p.m. which gave a 8 a t which the effect of end errors was zero. Dworkin, et al.,laused approximately the same r.p.m. values as AIills and. as their D values did not change with changes in length of capillaries or in length of diffusion time, assumed that their r.p.m. gave a negligible Al. Bockris and Hooper confirmed that A1 effects exist
59
and that for values of 8 of approximately 0-2 mm.i set.-', an apparent dependence of the measured D value upon 8 existed. However, their D values were apparently independent of 8 over the range 2-30 mm. sec. - I for NaCl a t 928’. They concluded that they had reached the e which Mills had found for “zero end error.” The observed dependence of D on a in the 0-2 mm. set.-' region was interpreted in terms of a breakdown of the boundary conditions assumed in ( l ) ,due to depletion of the radioactive concentration a t the mouth of the capillary. An alternative explanation, however, is that the change of D with 8 in the region 0-2 mm. sec.-I is not due to the latter effect, but to the existence of the ALeffect, changing rapidly with 8 in the lower region and rFlatively slowly in the upper region (2-30 mm. sec.-’), and that the end-error-free region postulated by Mills is not present. I t would then be necessary to subtract from apparent D values an amount corresponding to the counts per minute which accrue from the melt by means of the Al-effect. A detailed re-study of a dye system,“ similar to that performed by Borucka, Bockris, and Kitchener, confirmed the existence of the Al-effect suggested by these authors, together with a dependence there noted upon a and d. An empirical relation has been established between 8 and A l / d . Dimensional analysis suggests (see also Thom and Apelt15) that Al/d = f ( d d p / q ) = f (Reynolds number)
(2)
where p is the density and n the viscosity. In the present study, Reynolds numbers have been calculated for the conditions of the experiment, and from the empirical relation established by Richards, A1 was calculated. The corrected value of Q was calculated by subtraction of an amount coAA1 from the total observed counts in the capillary. This amount, coAAl, corresponds to the radioactivity swept into the capillary by the Aleffect. Thus the diffusion coefficients were calculated on the basis of the equation = 2coA d
Dt/~
(3) If a constant end correction of 200 counts/min. is taken instead of the A1 correction used in this work, it &corrected
J. Crank, “Mathematics of Diffusion,” Oxford University Press, 1957. pp. 18, 31. (11) E. Berne and J. Berggren. Ac& Chem. Scand., 14, 428 (1980). (12) 11. llills. J . A m . Chem. Soc., 7 7 , 6116 (1955). (13) A. S. Dworkin, R. B.&cue. and E. R. Van Artsdalen, J . Phya. Chem., 64, 872 (1980). (14) 9. It. Ilichardu, 1’h.D. Theaia. Universit.y of Pennsylvania. (15) A. Thoni and C. J. .Apelt, Aeronautical Research Council, R. & .?I. No. 3090. Her Majesty’s S t d o n e r y Ofice. London, 1958. (10)
Volume 68,Number 1 January, 1964
S. B. TRICKLEBANK, L. NANIS,AND J. O'M. BOCKRIS
60
has been calculated that the energy of activation does not change significantly but D values may be increased by some 10%. The errors in the measurement have been assessed as : Qoorrected *3.2%, Co, f 1.6%, A , *0.5%, and t, *0.2%, making the total possible error in D for any one capillary *10.8~o,with the average deviation from the mean in this work being *7%.
0
0
0
Results The results are expressed in terms of
D
=
A exp [ - A E / R T ]
(4) where D is the diffusion coefficient, AI3 is the energy of activation, R is the gas constant, T is the absolute temperature, and A is a term independent of temperature. Table I gives D values for individual capillaries and Fig. 1-3 show plots of log D as a function of l / T . Table I1 gives values of A and Ah' calculated by the
Figure 2. Log D N ~ in Z Z50 mole yo NaI-50% KCl against 1/T.
method of least squares together with the standard deviation of AE in each case.
5.8
8.3
8.5
8.7
89
9.1
9.3
9.5
I~~/TOK
Figure 3. Log DNazl in KC1 against 1/T.
Discussion Previous Work, The only previous self-diffusion
Figure 1. Log D N ~and % ~log Drlal in NaI against l / T : 0, Nazz; 0 , 1 1 3 1 .
The Journal of Phyeical C h m i e t r y
measurements on NaI have been made by Rockris and Hooper,' who found that the energies of activation for diffusion of cation and anion differed by 0.4 kcal. mole-'. Results of the paired vacancy diffusion treatment were inconsistent with those for other alkali
DIFFUSION IN MOLTEN SODIUM IODIDE-POTASSIUM CHLLORIDE
~~~
~
~
Table 1 : Average Diffusion Coefficients in the System NaI-KCl Temp., ‘C.
S1
D x 104,
D x 104, cm.2 aec.3
Temp., ‘C.
Na22 in NaI
1181
vacancy; and (ii) the diffusion of two oppositely charged ions (by rotation), D,, into a paired vacancy, leading to the equations
cm.l8ec.-1
D+* = D+
in NaI
675 692 720 722 738 750 763 782
0.75 .79 .91 .81 .91 .90 .95 .99
673 700 711 730 751 767 785
01.42 .44 .47 .54 .57 .58 .60
655 669 676 694 758 765 803 831 833
0.62 .62 .58 .70 .86 .83 .87 1.06 1.09
791 831 880 914
01.79 .86 .94 1.00
D-*
=
D-
+ D, + D,
(6)
(7)
For mechanism (ii) it is not necessary to postulate the existence of “long-lived” paired entities, but it is only necessary that they have a lifetime greater than thle time required for a rotational movement of the ion pair into a paired vacancy. Values of the diffusion coefficients, D;ua+,DI -, and D N ~have I been calculated from simultaneous solution of eq. 5, 6, and 7, using conductance data of Yaffe and Van Artsdalen.16 These are given in Table I11 together with the activation energy for each diffusion process, as calculated from plots of log D i as a function of 1/T. Figure 4 shows the plot of
~~
Table 11: Constants of the Equation D = A exp[- AEIRT] System
Tracer
A X 103
NaI
Na22
50q;b Na1-r5070 KCl KCl
Na22 NaZ2
1.09 1.88 2.08 0.73
AE, kcal. mole-’
5.02 i 0.77 7.21 f .76 6.59 f .38 4.70 f 1.14
Temp. range, “C.
675-782 673-785 655-833 791-914
halides reported in the same paper, where the calculated energy of activation for I- was greater than that for Ka+. (The energy of activation for KaI pair was not constant, as distinct from the other salts.) The dis-. crepancies in the AE values between the present and the former work may be due to some decomposition of NaI which is very sensitive to traces of water and oxygen. Application o
