1408
A. C. CHATTERJI AND R. N. SINGH
sulfate as required by our interpretation. I n our view, the observed slope depends primarily on the relative conductivities of the monomer and dimer and should increase as the bulkiness of the polar heads makes the dimer less compact and symmetrical. This is confirmed by the facts since the abnormal slopes found by Kraus seem to increase with the bulkiness of the heads, being 137, 139 and 150 for the CIStri-methyl, -ethyl and -propyl, respectively. The 2-1 Onsager slopes, on the other hand, decrease slightly in this series. In the CISseries the slope increases even more markedly from 142 for the trimethyl to 210 for the tributyl head. The comparison of the two series is not simple because the additional factor of different chain length and therefore different dimerization constant comes in, so that a different portion of the S-shaped curve probably is observed. Finally, it may be noted that Kraus, et al., found a discontinuity in tAe limiting conductance values
VOl. 62
of long-chain trimethyl quaternaries a t the same point between C14 and CIS where the slopes became abnormally large. These limiting values were obtained by direct extrapolation using the large experimental slope. In our view, on the other hand, the extrapolation should be conducted along the S-shaped curve which tends to the lower, 1-1 Onsager slope. This leads necessarily to lower limiting conductances and would a t least reduce the reported discontinuity. Acknowledgment.-The author acknowledges gratefully the help and encouragement of Professor Karol J. Mysels throughout the work and during the preparation of the manuscript. This work was supported by the Office of Naval Research under Project NR 356-254 and was presented as part of the 10th technical report of this project. Reproduction in part or in whole for purposes of the United States Government is permitted.
NUCLEATION FROM QUIET SUPERSATURATED SOLUTIONS OF ALKALI HALIDES. PART I. POTASSIUM AND AMMONIUM CHLORIDES, BROMIDES AND IODIDES BY A. C. CHATTERJI AND RAMNARESH SINGH" Department of chemistry, University of ,heknow, India Received January 6 , 1968
The kinetics of precipitation of KC1, KBr, KI, "&I, NH4Br and NHJ from their quiet supersaturated aqueous solutions has been investigated using electrical conductivity measurements at 35.00 f 0.002'. The maximum time 0 required where for the first indication that precipitation has occurred is in fair agreement with the relation log e 0: l!log* (XIX,), X and XOare the mole fractions of solute in supersaturated and saturated salt solutions a t 35", respectively.
Introduction The purpose of our work has been to study nucleation in relatively unstable supersaturated solutions of crystalline substances, in which even if all nuclei are removed the solid phase separates after a limited time. As used in this paper the term "nucleation" includes the deposition of crystalline solids (phase 2) on dusts, metallic surfaces, other surfaces or their spontaneous formation in the bulk of the solution but excludes the deposition on the surfaces of the same material. The start has been made from the aqueous solutions of cubic crystals of alkali halides. The experiments on nucleation of KC1, when none of the foreign nucleating crystals were added, have also been repeated because of the experimental uncertainties in the previous work done by Preckshot and Brown. The waiting time e taken by a nucleus to formin the bulk of solutions is assumed to be a measure of the frequency of nucleus formation. For the case of spontaneous, Le., homogeneous nucleation Preckshot and Brown1 have used the relation log e a 1/ log2 ( X / X o ) ,which applies strictly to isothermal measurements. To obviate this difficulty, ex-
* Radiochemistry Division, Atomic Energy Establishment, Trombay, India. (1) G. W. Preckshot and G. G. Brown, I n d . Ene. Ckem.. 44, 1314 (1951).
periments have been carried out a t a fixed temperature and solutions of different supersaturations have been produced by dissolving calculated quantities of salt in water and bringing the solution t o 35" for observations. Apparatus.-The conductivity bridge set was similar to that of Callendar and GrBith's bridge arrangement. Its sensitivity was 0.0004% when total resistance of the conductivity cell filled with saturated solution ranged in the vicinity of 2000 ohms. All resistances used were calibrated by Callendar and Griffith's Bridge (Type Cambridge L318022 with certificate of test) with respect to Croydon Precision Resistance Box (Type RBA4 No. 1627 with certificate of test) using direct current. The total length of bridge wire was kept 100 cm., the resistance of the wire at 35" being 0.13875 ohm/cm. The minimum could be determined with an accuracy of 0.5 mm. within a few seconds using 1000 c./sec. audio-oscillator (G.E. Cat. 7472242) as a source of current. Conductivity Cells.-The cell I (cell constant a t 35" = 645.21) used for studying nucleation was similar to that of Preckshot and Brown' except a few alterations. The electrodes were made of platinum foil and were fused completely with the walls (Pyrex) of the cel1.z Another simple cell I1 (cell constant at 35' = 91.957) was used for verification of specific conductivities determined by cell I. Before each experiment the cells were cleaned with warm chromic acid, steamed and dried by passing filtered air through them. Temperature Control.-Two thermostats were used. During conductivity measurements cells were housed in thermostat I, in which a bath of transformer oil was main(2) W.B. Campbell, J . Am. Chem. Soc., 61, 2419 (1929).
Nov., 1958
NUCLEATION FROM QUIETSUPERSATURATED SOLUTIONS OF ALKALI HALIDES
tained constant to f0.002' by balancing the heat loss with steady heat input. The internal inhomogeneity was less than 0.004'. Another water thermostat I1 with about 0.5 cm. transformer oil layer was set at 70 k 0.05' and was used for destroying the pre-existing nuclei of phase 2, if any in the supersaturated solutions. Conductivity Water and Chemicals.-As the release of supersaturation is extremely susceptible to dusts and impurities the double distilled water was redistilled in a complete silica apparatus. All alkali halides used were Analar grade except NH4Br (L.R.) and NHJ (L.R.). They were all recrystallized and were reused after repeated crystallizations from triple distilled water. The conductivity of triple distilled water at 35' was 0.8 X 10-6 mho. Experimental Procedure.-The solutions were prepared by weighing a suitable amount of triple distilled water in a weight buret. The amount of alkali halide to be dissolved was calculated before-hand from the relation log X = log XO.+ l/v%, where C was given values at which the velocity of crystallization is conveniently measurable. Filtration of solution was considered unnecessary, since solute and solvent both were obtained in the purest possible state. The cell I filled with saturated solution was housed in the bath I1 for 1.5 hr,a to dissolve the alkali halide nuclei, which if allowed to remain intact would have served as crystallization centers and would have caused a premature crystallization. The cell I then was taken out and transferred to thermostat I. Now bridge readings were noted with respect to time, the latter having been recorded from the moment the cell was housed in thermostat I. The cell did not take more than five minutes to attain the temperature 35". Sensitivity Limitations.-The sensitivity along with the concentration of solutions 5-10 molar and the volume of the cell I, 48 cc., sensitivity X concn. X vol. of system = 4 X X 5 to 10 molar X 0.048 1. = 1 to 2 X 10-6 mole = 6 to 12 X 10lTmolecules, give the amount of salt which has already precipitated to produce minimum detectable change. The total number of solute molecules in the system being 1.5 to 3 X loza,i.e., precipitation of one molecule among every 2 X 106 molecules of solute in solution could only be detected. The geometrjc effect of precipitated salt working as a non-conducting spherical nucleus is more or less of the same order as the concentration depletion. If a single nucleus had formed immediately at time zero it would take of the order of 9 minutes for it to grow to a size where it would have depleted the solution sufficiently to be detected by present method. Visual Observations.-Some visual observations6 were made with KC1 in the stoppered tubes of Pyrex and hard glasses. To eliminate heterogeneities which may serve as nucleation catalysts some of the solid phase was precipitated out from the bulk supersaturated solution. These crystallites will form preferentially on nucleation catalyst. This solution wa.s carefully transferred to previously weighed glass tubes. The tubes were subjected to heat treatment similar to that of cell I and were suspended by a thin thread in a water thermostat at 35 f 0.05" for observations. The tubes were well illuminated by a strong source of light and were swirled frequently by the thread. Gentle swirling should not produce any appreciable nucleation. The time for the first appearance of the crystal was noted. The supersaturation was estimated by weighing the tube with contents and then lastly drying the solution in a long narrow necked flask and weighing the dried KCl. Some of the subcoolings calculated therefrom and the corresponding waiting times are given in Table 11.
1409
70 60
@ 50 m"
M
.Ei 40
3
5 30 M
3 20 w
10 0 0
50 60 70 80 90 100 Time in min. plots of bridge readings a t various [ljlog' ( X / X , ) ] of KC1.
10 20 30 40
Fig. lA.-Time
70 2750
60
50 Qi
M
.t? 40
3
2 30
28 20 p1
10
0
10
Fig. lB.-Time
d
20 301 40 50 60 70 80 90 100 Time in min. plots of bridge readings at various [l/log* ( X / X O ) ]of KBr.
60
93500
Y
I
0
30 40 50 60 70 80 90 100 Time in min. plots of bridge readings at various [l/log2 ( X / X o ) ]of KI.
10 20
Fig. lC.-Time
26, 33, 32, 9, 33, 23, 30 and 32 minutes. More or less similar behavior was shown in other cases too. To overcome this difficulty nearly eight to ten Results experiments were performed a t every particular The observations for waiting time 6, a t a par- concentration. ticular concentration and temperature, were not Out of each set of eight to ten experiments a t a found to be always repeatable. The waiting time particular concentration only one curve represent6 in nine successive experiments in the case of KC1 ing the maximum waiting time 0 a t that concenat Concentration l/log2 ( X I X , ) = 700 were 21, tration has been plotted in Fig. 1-A,B,C,D,E and (3) This time was strictly adhered to in order to avoid the heating F. e is taken to be the time in each case where a effect on the release of supersaturation.' break occurs in these plots of bridge readings (em.) (4) R. Gopal, J . Indian Chsm. Soc., 21, 183 (1943). against time (min.). The break in the case of KI ( 5 ) On the kind suggestion of Dr. W. B. Hillig of General Electric curves was found to be not as defined as with the Research Laboratory, Scheneotady, N. Y.
A. C. CHATTERJI AND R. N. SINGH
1410 70 r
t
60
E' y 50
K800
D .B 40
3
8
1.8
-
1.6
-
1.4
-
Vol. 62
2 1.2 -
30 20
9
-9--4
1.0 -
3000
F4
10 01
I
0
Fig. 1D.-Time
70 60
i4
y 50 D
.B 40
3
I
I
I
I
I
I
1
1
-
0.6
/
400 500 600 700 800 900 1500 1750 2000 2250 2500 2750 3500 4000 4500 5000 5500 6000 %4c1 1000 1500 2000 2500 3000 3500 @ NH4Br 2500 3000 3500 4000 4500 5000 0 "41 30000 40000 50000 60000 70000 l/log* (XIXO). Fig. 2.-Log of waiting time Bplotted against l/log* ( X I X O ) .
KC1 KBr
0 0
r
1
0.8
1
30 40 50 60 70 80 90 100 Time in min. plots of bridge readings at various [l/log* ( X / X o ) ]of NHaCl.
10 20
5:
/ 2 5 0 0
TABLE I
2 30
Solute
KC1
KBr
KI
NHtCl
NHlBr
3 20
l/m
370
1355
3850
2500
2780
8
E9
"41
34480
TABLD I1
10
0 0 10 20 30 40 50 60 70 80 90 100 Fig. lE.-Time plots of bridge readings at various [ l/log* ( X / X a ) ]of NH4Br.
Pyrex glass tube -ATo e, min.
Hard glass tube -AT" e, min.
16.75 16.20 14.84 14.16 12.96
16.85 16.35 15.03 14.07 13.22
9 11 17 26 49
57 65 82 95 >120
The downward trend of the conductivity curves (Fig. 1, D and E) during the waiting period in the case of NH4C1 and NHdBr was observed. With the bridge reading inKC1, KBr, K I and "41 stead of decreasing either remained constant or increased slightly with time. On taking observations under similar conditions with just saturated solutions a t 35" where no crystallization occurred no change in the bridge readiilg, not even of a mm., 0 10 20 30 40 50 60 70 80 90 100 was noticed for nearly an hour. No definite exTime in min. planation could be given for it. Fig. lF.-Time plots of bridge readings at various [l/loga The decrease of specific conductivity with in(x/xo)]Of "41. crease in concentration was noticed in the case of other solutes. I n every plot the increase in bridge NHJ. (in the concentration range of our experiments) and is similar to that observed by Kraus' reading corresponds to increasing resistance. The values of slope "m" as obtained by plotting with KI solutions at 0". Saturated solutions of ",I gradually assumed log 0 against l/log2 ( X / X o )in Fig. 2 are recorded a yellow color during the experiments, presumablys in Table I. Sub-cooling -AT were calculated from these owing to the oxidation from atmospheric oxygen. solubility (8. solute / 100 g. HzO) expressions Discussion of Results The application of equations used by Preckshot SKCI = 0.2882t + 28.528 S K B ~ = 0.47781 3. 57.432 and Brown' to cover the case of homogeneous nuSKI = 0.7920t + 129.58 cleation leads to surface energies (KC1= 2.73, 8NH4C1 = 0.4600.t f 27.40 KBr=l.61, KI=O.99, NH&1=1.51, NH4Br= S N E , B ~ = 0.87331 + 55.134 1.33 and NH41=0.45 ergs/sq. em.) 10 to 20 times S N H ~ I = 0.9100.t 154.10 less than e x p e ~ t e d . ~These low values of surface which were derived, respectively, from their solu- energies calculated on the assumption of homobilitiess in the neighborhood of 35" taking them to (7) C. A. Kraus, J . Am. Chem. Soc.. 36, 35 (1914). be linear function of temperature in that range. (8) J. W. Mellor, "A Comprehensive Treatise on Inorganic and
+
(6) A. Seidell, "Solubilities of Inorganic and Metal Organic Compounds," Vol. 4, D. Van Nostrand Co., Inc., New York, N. Y.,1840.
Theoretical Chemistry." Vol. 2, Longmans, Green & Co., p. 619. (9) Private communication, G. W. Sears.
Nov., 1958
THERBF-ZRF~AND LIF-ZRFI SYSTEMS
geneous nucleation show that the nucleation process in these experiments is not homogeneous. The plots of maximum waiting time 0 against l/log2 ( X / X o ) (Fig. 2) are found to be straight l i e s showing that log 0 is proportional to l/log2 (X/X,) in the ranges of concentrations in which the kinetics is conveniently measurable. Results of Table I1 show that the change of container walls has considerable effect on waiting time, which in turn indicates that the precipitation has been occurring a t the glass (Pyrex) walls of the' cell (may be on electrodes too) by heterogeneous nucleation, the rate of which depends upon the nature of the surface, solvent and solute together with the degree of supersaturation and temperature. Anyhow it cannot be said unequivocally that the
1411
observations are conditioned solely by a nucleation process. It was not possible to give any experimental evidence by the present method that the results may not be the consequence of growth process which follows nucleation. Acknowledgment.-We express our sincere thanks to Prof. G. G. Brown of Michigan University and Prof. G. W. Preckshot of University of Minnesota for sending us valuable information about their nucleation apparatus. We are grateful at the same time t o Dr. W. B. Hillig of General Electric Research Laboratory, Schenectady, N. Y .? for his suggestions leading t o major reorientation in our method of approach to the problem. The financial assistance given to R.N.S. by the U.P. Government was helpful.
VAPOR PRESSURES AND MOLECULAR COMPOSITION OF VAPORS OF THE RbF-ZrF4 AND LiF-ZrF, SYSTEMS1 BY KARLA. SENSE^ AND RICHARD W. STONE Battelle Memorial Institute, Columbus, Ohio Received JGnzlaTy 6 , 1968
The vapor pressures of RbF and LiF were measured over the temperature intervals 584-1059' and 851-1060°, respectively. Thermal analysis showed the melting point of RbF to be 798'. Vapor pressures of the RbF-ZrF4 and LiF-ZrFc systems were measured over the ranges 690-1060° and 670-1060", respectively. On the basis of previously develo ed theory, it was concluded that the complexes RbZrzFeand LiZrtFo exist in the va or phase of the respective systems. qurther work on the NaF-ZrFc system points to the existence of the gaseous compfex NaZrzFo rather than NaZrF8 as previously supposed. A phase diagram of the RbF-ZrF1 system derived from vapor pressure data shows a constant boiling point to exist a t about 33 mole % ' ZrFd for a total pressure of 1 mm. Plots showing the change of total pressure with composition for various temperatures, as well as melting point curves, are given for the various systems.
Introduction This is a further study of the physical properties of fused salt systems. Previous work has dealt with the NaF-ZrF2" and NaF-BeFzab systems. The present work is concerned with the RbF-ZrF4 and LiF-ZrFr systems. Experimental The method and apparatus have been described p r e viously.a-s No changes were made in undertaking the present study. The LiF was J. T. Baker highest grade. The RbF and all fused salt mixtures were supplied by the Oak Ridge National Laboratory a t Oak Ridge, Tennessee.
Results and Discussions The Vapor Pressure of RbF.-Ruff, et aE.,6 and von Wartenberg and Schulz' obtained vapor pressure data on liquid R b F for the 1142-1410° range. On the basis of their data, Kelley* obtained a standard free energy expression which was used to ob(1) Work performed under AEC Contract W-7045-eng-92.
(2) Atomics International, Canoga Park, California. (3) (a) K. A. Sense, C. A. Alexander, R. E. Bowman and R. B. Filbert. Jr.. THISJOURNAL, 61, 337 (1957); (b) K. A. Sense and R. W. Stone, i b i d . , 62, 453 (1958). (4) K. A. Sense, M. J. Snyder and J. W. Clegg, THYE ITOURNAL, 68. 223 (1954). (5) K. A. Sense, M. J. Snyder and R. B. Filbert, Jr., ibid., 68, 995 (1954). (6) 0. Ruff, G. Schmidt and S. Mugdan, 2. anow. alZgem.,Chem., l B S , 83 (1922). (7) H. van Wartenberg and H. Schula, 2. Elektrochem., 27, 568
(1921). (8) K. K. Kelley, U. 8. Bur. Mines, Bull. 383, 1935.
74
76
no
71
82
14
8s
REClPROC4L TEYPfR4TURE 1060
1000
950
900
90
02
$,
h'J. lo*
850
TEYPfRATURf F C I .
Fig. 1.-Vapor
pressures of RbF and LiF over indicat temperature ranges.
tain a vapor pressure curve for the 800-LO6O0 range. A plot of this curve, together with a plot of the datas which were obtained for liquid RbF in
