2066
NOTES
Vol. 63
tions were diluted while maintaining the pH at the original value of the 0.8 M solution by addition of hydrochloric acid, and then aged, diffusion was much more rapid. The rate of diffusion is dependent less on the zirconium concentration than on acidity.
General Discussion.-A complete theoretical treatment of the relation between diffusion coefficient in liquid systems and ionic or molecular weight is lacking.8 Approximate values of particle weight can be calculated from the SutherlandEinstein equation and the equation expressing radius in terms of particle weight and partial TABLE I1 specific volume.14 Although these values are no VARIATIONS IN THE DIFFUSION COEFFICIENT OF ZIRCONIUM more than approximate, it is interesting to examine OXYCHLORIDE WITH CONCENTRATION OF SOLUTION the effect of various solution conditions on the Supporting electrolyte 1.O M sodium nitrate; solutions particle size of zirconium, even if the results are aged 5-6 weeks; c in moles/l., b in cm.2 sec.-l. regarded as only qualitatively correct. The partiNo pH adjustment pH adjusted to 0 2 8 cle weight of 730, calculated from the diffusion C pH X 108 C pH D X 106 coeficients of 0.5 M zirconium in acid solutions of 0.856 0.38 3.86 0.856 0.38 3.86 1.0 to 5.0 M , indicate a degree of polymerization -558 .47 3.84 in the region of 3.7 (particle weight of the mono.494 .50 3.84 mer15is taken to be 196). This is in close agree.281 .65 3.71 ment with the values of 3 to 4 obtained by other .280 .65 3.71 methods.la-l8 In connection with the above, .236 .72 3.65 .200 .38 4.01 aggregation of zirconium particles by oxygen .185 .86 3.69 bridge@ to give asymmetric linear polymers im,110 1 00 3.47 .110 .38 4.17 poses severe limitations on the validity of particle ,097 1 08 3.48 weights calculated from diffusion data, partic.052 1.32 3.27 .055 .38 4.40 ularly when the diffusion coefficients are small. Diffusion Coefficient as a Function of Acidity.Acknowledgment.-The author wishes to thank Diffusion coefficients obtained in hydrochloric Dr. R. L. Sykes for useful suggestions and conacid solutions are given in Table 111together with structive criticism during the course of this work. coefficients for zirconium particles in solutions to (14) Ref. 13, p. 259. which alkali had been added. The presence of acid (15) Ref. 9,p. 124. increases the diffusion coeficient of zirconium but (16) .(I A. Kraus and J. S. Johnson, J . A m . Chem. Soc., 76, 5769 a limiting value is reached quickly. This value (1953). (17) J. S. Johnson and K. A. Kraus, ibid., 78, 3937 (1956). is attained when the acid concentration is 1 M or (18) A. J. Zielen and R. E. Connick, ibid., 78, 5785 (1056). greater. By comparison, the results found by (19) W. B. Blumenthal, I n d . Eng. Chem., 46,528 (1954). Lister and McDonald3 in nitric acid solution show no limiting value. The addition of alkali on the other hand rapidly reduces the rate of diffusion. THE SLOW EVOLUTION OF HEAT IN HEAT OF IMMERSION CALORIMETRY1 These results are probably in agreement with the formation of highly aggregated hydrolysis products. BY C. A. GUDERJAHN,D. A. PAYNT&R, P. E. BEROHAUSLN The highly basic solutions, particularly those that AND R. J. GOOD^ are faintly opalescent, contain particles that are University of Cincinnati, Department of Applied Science, Cincinnati probably markedly asymmetric and of high moOhio lecular weight, in which case the calibration of Received May $8, 1969 the cell by low molecular weight substances is Since the time of Pouillet* thermal data in not necessarily valid. l3 studies of heats of immersion have been analyzed assuming that the “heat of immersion” is released TABLE I11 all a t once, and that effects of appreciable duration VARIATIONS IN THE DIFFUSION COEFFICIENT OF 0 0 5 M are due to thermal transients of the s y ~ t e m . ~ ! ~ ZIRCONIUMOXYCHLORIDE WITH ACIDITY OF SOLUTION During measurements of the heat of immersion Solutions aged 8 weeks; c in moles/l., b in cm.2 see.+ of alumina in water, heat release was observed for Added supporting a period of several hours-a time far greater than electrolyte Acid that required for thermal transients to die out. NaNOs, M C 6 x 108 This note reports our efforts to analyze this phe... 5.00 4.63 nomenon. ... 2.00 4.63
...
0.5 .63 .8 .9 1.0
1.00 0.50 .37 .20 .10 00
.
4.59 4.57 4.49 4.46 4.30 3.27
Alkali 0
1 .o 1 .o 1.0
0.02 .04 .05
2.75 2.44 2.21
(13) A. E. Alexander and P. Johnson, “Colloid Science,” Oxford University Press, Oxford, 1950, p. 242.
Experimental Our twin calorimeter has been described elsewhere6; it was run adiabatically. All runs stretched over periods of several hours. Results are reported for immersion at 20”. The solids were extracted with distilled water and acti~
(1) From the Ph.D. theses of C. A. Guderjahn (1955) and D . A. Paynter (1954). (2) Convair Scientific Research Laboratory, 5001 Kearney Villa Road, San Diego 11, California. (3) M. Pouillet, Ann. chim. phys., 10, 141 (1822). (4) G. E. Boyd and W. D. Harkins, J . A m . Chem. Soc., 64, 1190, 1195 (1942). (5) P. E. Berghausen, in “Adhesion and Adhesives,” F. Clark, J. E. Rutzler and R. L. Savage, editors, John Wiley and Sons, Inc., New York, N. Y.,1954, p. 225.
I
I
NOTES
Dec., 1959
2067
vated under vacuum. Fifteen-ml. sample bulbs were used. Correction for heat of bulb breaking was made.6 Heat of stirring was measured separately for each run. Areas were measured by NZadsorption .7 J. T. Baker and Co. A1203 was activated a t 150 to 300’, commercial Davidson Co. SiOz was activated a t 250°, du Pont “Ti-Pure’’ anatase and rutile were activated a t 150 to 350” and Godfrey L. Cabot Co. Graphon was activated a t 300’. Of t,he five solids, only the Si02 was porous as indicated by a Type 4 adsorption isotherm.7
Analysis of Data.-To facilitate estimation of slow heat from time-temperature curves, we assumed the rate of release of slow heat decayed exponentially with time. With this hypothesis, the expression for total heat evolved up to time t takes the form Y
= hi
+ h,(l - e + t ) +
L
m A T dt
(1)
total slow heat total immediate heat ~ ( t =) total heat released up to time t m = heat leakage coefficient (measured se arately, as a function of differential temp.). T i e last term on the right is the cumulative heat leakage A T = absolute temp. difference between flask and bath A = time constant for the process h, hi
= =
A typical graph of raw data for alumina (a sample activated at 150’) is given in Fig. 1; also shown are the raw data corrected for heat leakage. (In the absence of slow heat, the curve for the open circles would approach a straight line after about 5 minutes.) Figure 2 shows result of the treatment eq. 1, rearranged to the form (hi
+ h.) - r + SA m A T dt = h,e-ht
100
200 300 400 500 Minutes. Fig. 1.-Calorimeter differential temperature us. time for immersion of alumina in wat.er: 0,raw data; 0 , data corrected for heat leakage; A1208 activated a t 150’. 150 100 80 60 40 N.
d9
\
20
a
(2) 10
Extrapolation to t = 0 yields 105 ergs/cm.2 for e 8 h,, and the half-life for the slow heat t11, is 67 6 minutes. The satisfactory fit to a straight line is evident, indicating that over the intervals employed 4 the analysis is valid. 50 100 150 200 250 When the slow heat is known as a function of Minutes. time, its contribution to the temperature rise Fig. 2.-Semilog plot of total heat minus heat evolved may be deducted. The resulting curve resembles up to time t vs. time; & 0 3 activated a t 150”. temperature traces obtained when there is no It may be seen that for alumina, the slow heat slow heat, and the usual extrapolation to zero time was very appreciable, of long duration, and incan be made accurately. Results.-Table I summarizes our results. Prob- creased with activation temperature. There was able errors (50% confidence limits for mean values) no sensible dependence of slow heat, or of its halfare reported where five or more runs under constant life, on immersion temperature. For a series of A1z03 samples activated simultaneously at 300°, experimental conditions were made. it appeared that t i / , increased linearly with h,. TABLE r For silica gel, slow heat also was evolved over EL HEATSOF IMMERSION IN WATER long period of time, but the magnitude of the heat, Half-life per cm.2, was much smaller than with alumina. of slow Act. Surface Imrned. (Since the area was very large, a small heat per temp area, heat, Slow heat, heat, OC. m.Z/g. erg/cm.Z erg/cm.z min. Substance cm.z represented a large total heat.) ti/, appeared AlnOa 150 7.16 427 86 70 to be independent of the magnitude of the slow 3 10 51 250 7.94 582 heat. 300 8 . 3 679 i 7 3323Z39 139 f 2 7 With rutile and anatase, no slow heat was SiOz 250 701 1 6 5 i 0 . 3 6.33Z0.1 3 4 f 4 observed. If any was present, its time constant Ti02 was less than the time for thermal transients to Anatase 300 11.06 441 f 14 < 5
