NOTES
4320
Vz is maintained down to this concentration and the limiting-law slopes are approached just below the limit of significance of differential density balance measurements, so that r#+ - 1.868M”2 then becomes parallel with the M axis. The isotope effect in P can therefore safely be expected to be maintained down to infinite dilution with almost the same values as observed at the low but finite concentrations. I n the case of (n-C4H&NBr, the curves of q h 1.868M1’2are seen to cross around 0.1 mol l.-l, and this may be because of a structure-breaking effect (e.g., due to Br-) becoming relatively more important at the higher concentrations of this salt. Within the confines of this brief note it will not be possible to present any detailed theory or speculations on the origin of the effects observed. However, it will be useful to note that since HzO and DzO molecules are approximately the same size (@., the bond lengths are identical4 to within 0.001 A) differences in must reflect the degree to which the solute affects the structure of the solvent. The isotope effect AVD,O-H~O can be regarded therefore as the difference between the electrostrictions in HzO and DzO or the corresponding positive structural volume changes. It might be expected that A V D ~ O - would H ~ ~ be related to the field strength in the first solvent coordination layer at the ion in the same way as is the electrostricted We have made estimates of the field acting on the water in the first hydration layer, and an approximately linear relation results, the isotope effect becoming less negative and eventually positive with increasing radiusz1of the cation. The present results and the work referred to above lead to the conclusion that both structure making and structure breaking are more extensive in DzO than in HzO. Solutes such as the ones dealt with here can cause a shift in the structural temperatures of the solvents. Worley and KlotzZ2have measured the structural temperature of solutions of structure-making and structure-breaking ions and found, for example, that a 0.641 M (Bu)iNBr solution in DzO causes a shift of -3” in the structural temperature. This means that in order for the same shift in structural temperature to occur for HzO and DzO the cluster size would increase relatively more in DzO than in HzO and hence the partial molar volume would tend to be higher. The converse of this argument would apply to an electrostricting NaF solution, thus accounting for the negative isotope effect in V2in that case. If the significance of the present results is further considered, it is also of interest (a) to note that DZO has a higher heat capacity than H20,20 which could be interpreted as being due to its having structured regions which are more susceptible to “melting” (the higher compressibility3 would also support these conclusions) and (b) to compare the molar volume change upon freezing, AVf, in the case of DzO and HzO. From
rzo
The Journal of Physical Chemistry
Kell’s tabulation23and assuming that the molar volumes of HzO and DzO ices are almost identical (the OH and OD bond lengths differ by only ca. 0.001 AV~,D,O= 1.530 ml mol-’ and AVf,HzO= 1.633 ml mol-’; interpolated at the same temperature as for water ( O O ) , AV~,D,O would be 1.518 ml mol-l, from the data on the density of supercooled DzO. Evidently, on forming icelike regions in water, a larger positive volume change than that in DzO would tend t o occur and this is consistent with general views about the relative degrees of structure in HzOand DzO. This implies that whatever effect the R4N+ salts have on the structures of HzO and DzO, it is not quite the same as that which would arise if formation of local icelike structures were assisted by the “hydrophobic” ions. A similar conclusion regarding the properties of ((structure-enhanced’’ water was reached for other reasons by Everett.24 It is clear that whatever the local solvent structures formed in the proximity of hydrophobic ions are, the water in such regions must exist in a relatively narrow, spherical annular envelope and its extension may simply not be sufficient for any approximation to true “icelike” behavior to be manifested in measurements of macroscopic properties. In conclusion, the present results support the suggestion we have proposed: a useful indication of whether or not ionic organic solutes cause structureenhancing effects in water can be given by the sign and magnitude of the solvent isotope effect in the partial molal volumes.
A4),
Acknowledgments. Grateful acknowledgment is made to the National Research Council for support of this work. L. H. L. acknowledges award of a National Research Council Scholarship. (21) (22) (23) (24)
K. Wirtl;, Angew. Chem., A59, 138 (1947). J. D. Worley and I. M. Klotz, J . Chern. Phys., 45, 2868 (1966). G. S. Kell, J . Chem. Eng. Data, 12, 66 (1967). D. H. Everett, Discussions Faraday Soc., 24, 216 (1957).
An Analysis of the Particle Size Distribution of Ammonium Chloride Formed by Rhythmic Precipitation of Ammonia and Hydrogen Chloride by G. A. Davies, A. B. Ponter, and 5. Singh Department of Chemical Engineering, Faculty of Technology, University of Manchester, Manchester, England (Received April 26, 1968)
Observations made under controlled conditions show that some gaseous and liquid systems are capable of reacting to produce a solid product which forms in
4321
NOTES
PHERE
J
Figure 1.
rhythmic cycles producing so-called “Liesegang rings.” A comprehensive review of investigations into this phenomenon has been presented by Stern. A successful theory to account for ring formation was first proposed by Ostwald.2 This assumed that nucleation and deposition of the product can only occur when conditions of supersaturation exist, that is, when the concentration products of the reactants greatly exceeds the solubility product of the solid. By using this concept Wagner3 has developed a mathematical model which can account for the formation, frequency, and distance of separation between successive rings. Confirmation of this theory for reaction between ammonia and hydrogen chloride has been reported by Singh.4 For this particular system some uncertainty has arisen as t o the importance of the presence of water vapor in the iiucleation and formation of the rings. Hedges5 stated that rings could be formed in the absence of water vapor, while Johnson and hiIanno6 expressed a contrary opinion. Spotz and Hirschfelder’ generated the ammonia and hydrogen chloride from the aqueous solutions and postulated that nuclei were formed in the gas by clusters of reactant molecules of not less than a certain critical size, approximately 100 molecules. The reaction between the molecules and the Using was assumed to occur similar experimental coditions Twomeys m€%hSured the rate of nucleation and demonstrated that classical nucleation theory@may be applied quantitatively $0 the formation Of the ‘‘lid particles* Davies, and SinghlO have shown that rings can only be formed if a certain critical moisture content is present in the system. the mechanism Of ring ring tion, and frequency has received considerable attention,
no data have been reported on the particle size of the product formed or on how physical conditions affect particle size. A series of experiments have been carried out to determine this and the results are presented here. A diagram of the apparatus is given in Figure 1. Essentially, this consisted of two large reservoirs, A and B, connected by a reaction tube, length 3 ft X 0.394 in i.d. All the glassware was carefully cleaned and dried at 200” for 3-4 hr before each experiment. During the drying period the apparatus was continuously flushed with dry nitrogen. The moisture content of the gas leaving the apparatus was measured using a Consolidated Electrodynamics moisture monitor. .This was capable of measuring moisture contents down to 0.5 ppm. This was continued until the moisture level of the gas leaving the apparatus was below the level of sensitivity of the moisture meter. The reactants, anhydrous HC1 and ammonia, were supplied from cylinders S1 and 52. The reservoir, A, was charged with a mixture of HC1 and nitrogen to the required concentra(1) K. H. Stern, Chem. Rev., 54, 79 (1954). (2) w. Ostwald, Kozzoid z., 36, 380 (1925). (3) c. Wagner, J. Colloid Sei., 5, 85 (1950). (4) 5. Singh, M.So. Thesis, University of Manchester, 1966. (5) E. 8. Hedges, “Liesegang Rings and Other Periodic Structures,” Chapman and Hall, London, 1932. (6) W. H. Johnson and P. J. Manno, 2nd. Eng. Chem., 44, 1304 (1952). (7) E. L. Spotz, and J. 0. Hirschfelder, J. Chem. Phys., 19, 1215 (1951). (8) S. Twomey, ibid., 31, 1684 (1959). (9) M. Volmer, “Kinetic der Phasenbildung,” Th. Steinkopk, Leipzig, 1939. (10) G. A. Davies, A. B. Ponter, and S. Singh, Nature, 213, 279 (1967). Volume 72,Number 1.9 November 1968
4322
NOTES
10/o
4%
N HI
NHa
L
1.5 PARTICLE
2.5
2.0 DIAMETER
(A)
3.0
-
-
3.5
Figure 2.
PARTICLE
DIAMETER
(A)
Figure 4.
16.0
2%
5% NH,
H,
i
PARTICLE
DIAMETER
-
(A)
12.0-
L 2.0
-
PARTICLE
Figure 3.
DIAMETER
25
(A)
30
3.5
-
Figure 5.
tion by first evacuating A using the vacuum pump, D, and then allowing the desired flow of nitrogen, from cylinder S, and HC1, monitored by flow meters A2 and A5, to flow through the reservoir. After 30 min, valves A6 and A l l were closed. A similar procedure was adopted to charge reservoir B with a mixture of nitrogen and ammonia. Water vapor in the nitrogen stream was controlled by passing the gas through selected The Journal of Physical Chemistry
drying agents (molecular sieves (BDH Type 5A), Pz05,CaC12,Ca(OH)2),contained in G, and was monitored by the moisture meter. The pressure in the reservoirs was equalbed using taps A l l and B11. The apparatus was enclosed in a constant-temperature cabinet controlled to =t0.5". The concentration of the ammonia-nitrogen mixture in the reservoir was
NOTES checked using a Zeiss interferometer. When all conditions had reached equilibrium, taps A12 and B12 were opened, and ammonia and hydrogen chloride were allowed to counterdiffuse into the reaction tube. Measuremente of the rate of ring formation and ring separation were recorded. At the end of each experiment the reaction tube was carefully removed from the apparatus and was sectioned, and the ammonium chloride from a section was carefully transferred onto a microscope slide for examination. Photomicrographs were taken of each sample a t a total magnification of 1000. Particle size analyses of the product over a range of reactant compositions 1-5% at two temperatures, 25 and 30’, were obtained. Examples of the distribution of sizes of the particles as a percentage frequency vs. size in microns are shown in Figures 2-5. The majority of particles were between 0.25-2.5 p mean diameter. Comparison of the sample populations obtained from experiments over the full range of concentrations studied showed no significant difference at the 5% level. Furthermore, (comparing samples between rings formed after 5 and 601min showed again no significant difference at the 5% level, suggesting that subsequent agglomeration of the particles does not take place. Above the critical moisture content for ring formation, we conclude that the concentration of the reactants does not effect the particle size distribution of the product formed and that no significant agglomeration of the particles takes place after nucleation and growth.
Possible Error in the Calibration of Knudsen Cells by Mercury Effusion’
by David A. Northrop Sandia Laboratory, Albuquerque, New Mexico (Received M a y 2, 1968)
The purpose of this note is to illustrate a possible experimental error in the calibration of Knudsen cells by mercury effusion. This error is particularly insidious in that it results in effective orifice areas that are quite different from the expected Clausing-corrected orifice areas but which produce coincident vapor pressure curves when applied to rate-temperature data obtained from different cells. This error does not affect the linearity or the slope of the usual log P ws. 1/T plot. It does affect the consistency and magnitude of the derived vapor pressures. This effect was encountered in the course of an investigation of vaporization in telluride systems where graphite is a convenient cell material. This graphite was porous and this porosity is the direct cause of the
4323
1.’
I
,001
I
I
I
.OM CLAUSINC - CORRECTEDAREA (cm2) .002
,003
I
*
I
005
Figure 1. Comparison of the Clausing-corrected orifice areas and effective orifice areas determined by mercury (0)and lead ( 0 )effusion.
crossover and nonzero intercept in Figure 1 and the separate but parallel lines of set A, Figure 2. Similar effects could be noted for other types of nonorifice losses. As no further attempts were made to illustrate the error, the cell porosity is an unfortunate but necessary parameter. The error to be described is independent of cell material and is not limited to porous graphite cells. Four graphite cells were calibrated at the same time by mercury effusion. The cells were contained in a flask attached to a liquid nitrogen trapped vacuum system. The flask was immersed in a water bath maintained at 25.00 0.05’. Effusion times and weight loss were sufficiently great to make the temperature uncertainty the largest source of error in the calibration procedure. The vapor pressure of mercury was taken as 1.998 X t ~ r r . ~Four ! ~ separate calibrations were reproducible to better than 1%. The orifice areas were also measured from photomicrographs of the orifices and corrected for channel length by conventional Clausing correction^.^ The effective orifice areas determined by mercury effusion and the measured Clausing-corrected areas are compared in Figure 1 ; the dashed line represents agreement between the two methods.
*
(1) This work was supported by the U. S. Atomic Energy Commission. (2) K. D. Carlson, P. W. Gilles, and R. J. Thorn, J . Chem. Phys., 38, 2725 (1963). (3) R. H. Busey and W. F. Giauque, J . Amer. Chem. Soe., 75, 806 (1953). (4) S. Dushman, “Scientific Foundations of Vacuum Techniques,” John Wiley & Sons, Inc., New York, N. Y., 1962, p 95.
Volume 72, Number 12 November 1968
