Nov., 1954
VAPORPRESSURE OF ZIRCONIUMFLUORIDE
where again dT denotes an infinitesimal change in the gel point temperature. This equation is not as useful as eq. 5 for calculating AHo, because the terms b In f/b In M w and b In m , l / b In M , are difficult to evaluate. Nevertheless, we can assign approximate values to these terms and thereby obtain an independent, if rough, estimate of AHO. It should be remarked that the dependence of the equilibrium constant K on M,", and hence a large part of the dependence of the melting point, may actually reflect an unknown variable which happens to parallel the weight-average molecular weight in this particular series but does not in fractionated samples.6b To evaluate b In mCJb in M,, we make use of eq. 1 given in paper I for this series of gelatin samples, namely'
99 5
tive quantity; it is reasonable to suppose that the proportion of cross-links which are non-cyclic will decrease with increasing initial chain length. For want of better information, we suppose that f and M , are inversely proportional, making b I n f / b I n M , = -1
(13)
The quantities b In f / b T and b In m l / d T can be neglected if we assume that cyclic and non-cyclic cross-links have the same heats of reaction, and that the proportion of cross-linking loci combined is always small, respectively. Equation 8 can now be written approximately as (d In M,/dT),
=
- AH0/7RT2
which on integration yields log,, M," = AHo/16RT
+ constant
(14)
(15)
Accordingly, the curves in Fig. 2 should be linear, G'/z/c = 1.22 X io-4(Mw - 3.1 X 1 0 % - 7 ~ ' ~ * )(9) as in fact they are except in the lower molecular where G denotes the rigidity of the gel. Ward9 has weight range. The slopes of the linear sections, pointed out that this relation may be fortuitous combined with eq. 15, give values for AHo of about and that the rigidity, like the melting point, depends -54 kcal. per mole for gels chilled at 0". Because primarily on another unknown variable which of the rough approximations made in deriving eq. happens to parallel the weight-average molecular 15, these-values are not considered as reliable as weight in this particular series. However, the those listed in Table 11. It seems significant, nevequation does hold for this series and so will ertheless, that the values for AHo calculated from suffice for the calculations which follow. Since we independent sets of data (concentration dependassume that G is proportional to the total concen- enoe and molecular weight dependence) agree fairly tration of cross-links, except in the neighborhood well; this fact would seem to support the Table I1 of the melting point and a t higher temperatures,' values and the applicability of eq. 3 to a gelatin solution a t the gel point. lo we may change eq. 9 to read Equation 3 may be applicable to solutions of mcl/cz = k ( M , - 3.1 X 1010e-7~/R*)2 (10) other polymers which yield thermally reversible From this gels. If so, the methods just described could perhaps be used to calculate the heats of reaction for the corresponding cross-linking processes. Because we want the value of b In m c l / d In AfW at Acknowledgment.-This work was supported in the melting point, we choose a value of T as close part by the Research Committee of the Graduate as possible to the melting point without jeopardiz- School of the University of Wisconsin from funds ing the proportionality between G, c2 and hence supplied by the Wisconsin Alumni Research Founm,l. Figure 5 in paper I suggests T = 295, M , = dation. 60,000. Substitution of these values into eq. 11 (10) Data of Pouradier and Venet" on 1.5% gels, prepared from gives fractionated samples (and chilled a t 09, indicate a value of [d log b In ma& In M w = 7.0
(12)
and we assume that the value of this derivative is not far different at the melting temperature. The derivative b In f / b In M, is probably a nega(9) A. G. Ward, reported a t the 2nd International Congress on Rheology, Oxford, 1953, and private communication.
Mw/d(l/T)]a about 2.4 times as high a8 ours, which would indicate a AH0 of 127 kcal./mole if b In mC/b In M , were in this case also 7.0. However, for fractions, i t would appear from the work of Ward and his associates9 t h a t the latter derivative would be considerably smaller, perhaps decreasing - A H 0 to a value comparable with the 54 kcal./mole obtained above. (11) J. Pouradier and A. M. Venet, J . chim. phys., 47, 391 (1950).
-
THE VAPOR PRESSURE OF ZIRCONIURil: FLUORIDE' BY KARLA. SENSE,M. J. SNYDER AND R. B. FILBERT, .JR. BatteUe Memorial Institute, Colurtibzts, Ohio Received February 97, 19K4
Using the transpiration method, the vapor pressures of ZrF, were measured over the temperature range of 616-881' and the pressure range of 0.3-470 mm. The extrapolated sublimation point is 903'.
Introduction This work was undertaken because no experimental data on vapor pressures of ZrFl were available. The transpiration method was found to be a powerful tool in determining vapor pressures since a range greater than loamm* be 'Overed with (1) Work performed under AEC Contract W-7405-eng-92.
good precision and accuracy using a relatively simple apparatus. Experimental The method and apparatus are essentially the same as described previously,* and will be briefly reviewed. An (2) K. A. Sense, M. J. Snyder and J. W. Clegg, THISJOURNAL, 68, 223 (1954).
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I(.A.
Vol. 58
SENSE,M. J. SNYDERAND R. B. FILBERT, JR.
inert gas (nitrogen iq this case) is passed over the salt with which the gas becomes saturated. The saturated inert gas then passes through a condenser where the salt is deposited while the inert gas passes on through and is collected over water. From the moles of nitrogen collected over water, the moles of salt collected in the condenser, and the total pressure of salt and nitrogen in the apparatus, it is easy to calculate the vapor pressure of the salt. The amount of salt depositedjn the condenser due to diffusion alone must be subtracted from the total quantity of salt deposited. The calculations were based on the ideal gas law and Daltons' law of partial pressures. The following changes were made from previous procedure. For ease of operation, the inlet o enings of the condensers were decreased to diameters o?only 1/3g or l/18'. This change decreased the diffusion of the salt into the condenser to such an extent that the correction due to diffusion amounted at most to only 0.3% of the obtained vapor pressure. Because of the low percentage correction, the condenser could be inserted into the apparatus at the beginning of a run while the latter was cold, as well as removed a t the end of a run when the apparatus was cooled down again. Hence, when the desired tem erature was reached it was necessary only to release a $amp (this action permitted the flow of nitrogen) at the exit end of the condenser to start the run. Conversely, at the end of the run, the same clamp was tightened and the 8 paratus was cooled rapidly by a jet of cold air. The confenser could then be removed with ease a t a low temperature. The amount of salt diffusing into the condenser during the heating and cooling-off periods was negligible. Tem eratures were measured with a platinum us. platinum-rgodium thermocouple which was periodically calibrated against the gold point. The temperature was controlled by an electronic controller-recorder in conjunction with a chromel-alumel thermocouple located in the hot zone. Other changes consisted in the use of nickel radiation shields in the apparatus in place of the alundum plugs. The latter were eliminated because porosity of the alundum made purging difficult. The ZrFc was supplied by the Oak Ridge National Laboratories and reDortedlv had the followine imwrities present: 0.19% cadon; 0.01% chlorine; 250 i.p.m. iron; 150 p.p.m. aluminum; 125 p.p.m. nickel; 100 p.p.m. hafnium; the other impurities were less than 100 p.p.m.
Discussion As an outgrowth of the previous study made on BeF2,2efforts were made to establish the maximum rate at which nitrogen would be saturated when passing over the salt. This was particularly important at the low vapor pressures because of the length of time involved in making those runs. Comparison of two runs (see Table I) made at approximately 1 mm. pressure indicates that saturation of the carrier gas was achieved at a flow rate as fast as 51 ~ m . ~ / m i n .The permissible flow rate was therefore much greater than was prevtously supposed and permitted runs to be made much faster than before, the longest run requiring a little less than five hours, At high vapor pressures, it was found that
considerably lower flow rates must be used to assure saturation. For example, a run made a t 876.1' with a flow rate of 7.2 cm.8/min. gave a negative deviation of 5.6% which definitely indicates non-saturation. More runs were made in the high vapor pressure region to establish whether saturation occurred for certain flow rates. It appears that saturation was achieved in every run with the exception of the one made at a flow rate of 7.2 cm.*/ min. Convenience was the only guide in making runs a t various flow rates in the medium vapor pressure range. TABLE I VAPORPRESSURES OF ZrFd Pressure, mm. Calcd.
Temp., OC.
Obsd.
616.6 61.9 652.3 676.4 713.3 757.1 798.0 838.3 856.9 872.0 872.6 873.6 873.9 876.1 880.8
0.310 1.053 1.064 2.29 7.24 24.4 70.0 186.6 284 389 392 413 401 404 470
0.310 1.051 1.065 2.33 7.15 24.4 70.2 184.1 281 392 397 405 408 428 473
Deviation,
% '
Flow rate, nitrogen, om.a/min.
0.0 $0.2 -0.1 -1.7 +1.3 0.0 -0.3 +1.4 +1.1 -0.8 -1.3 +2.0 -1.7 -5.6 -0.6
49.8 50.9 31.5 32.5 25.9 14.5 21.1 6.1 6.5' 4.4 2.8 3.6 2.9 7.2 4.7
Results The standard erroT of estimateais 0.64% when the data listed in Table I (except for the run at 876.1' which is not valid) were fitted to a curve of B / T . The derived results the type log p = A listed at the 66.7% confidence level were
+
+
loglo P,, = A B/T A = 13.3995 i 0.00780 B = -12376.0 i 8 . 1 = 56.63 zk 0.04 kcal./mole Extrapolated sublimation point = 903 O
AHd,limstio.
There was no evidence of dissociation up to the highest temperature studied. Acknowledgment.-The authors wish to acknowledge thcveryhelpfulassistanceof Mr. C. A. Alexander in carrying out the experimental work. (3) See, for example, M. Ezekiel, "Methods of Correlation Analysis," John Wiley and Sons. Inc.. New York. N. Y..1941, Chap. 7.
