VISCOSITY OF FUSED SODIUMNITRATE
1205
Effects of High-pressure Helium, Argon, and Nitrogen on the Viscosity of Fused Sodium Nitratel by James L. Copeland and James R. Christie Department of Chemistry, Kansas State University, Manhattan, Kansas
66508
(Received June 5 , 1968)
The viscosity of molten NaN03 has been measured by a capillary flow technique, from 328 to 444', while pressurized with He, Ar, and Nz at pressures from 1 to 414 bars. Increasing the pressure of He resulted in diminishing the fluidity, 4, to nearly the same extent at each temperature. Use of Ar, however, actually increased 4 with increasing pressure at each temperature, although the effect became less and less pronounced with increasing temperature, being almost nonexistent at 444'. A similar trend was observed with N2, although this gas increased $J only slightly at 328' and decreased 4 to an ever-increasing extent with increasing temperature. The results are interpreted in terms of the Ar and Nz molecules diluting the melt, tending to make it less viscous in competition with the effect of pressure alone. The different extents of the effects of Ar and IY2 are attributed to the degrees of the ion-gas molecule interactions, as reflected by the heats and entropies of solution of these gases in fused NaN08. If the dilution effect by the very small, virtually nonpolarizable He atoms is negligible, an activation volume for viscous flow at 400' is calculated as AVq* = -RT(d In $/dP)T = 8.79 em3 mol-l, and the activation energies at constant pressure, E p , and at constant volume, Ev,evaluated at 400' (1 atm) result as 3.93 and 1.50 kcal, respectively.
Introduction In recent years this laboratory has reported results of studies of the dependence of electrical conductance of simple fused salts on inert-gas pressures and solubilities2Jand the thermodynamics of some of these gas-salt s0lutions.~*6 Within the past year Barton, Cleaver, and Hills6 have reported on the effect of pressure alone on electrical conductance of simple fused salts, without the complicating dissolution of a gas, and have thereby succeeded in measuring constant-volume characteristics of this property. In the present work we report our findings in a recent investigation of the viscosity of molten NaN03 while pressurized with He, Ar, and NZ over significant ranges of temperature and pressure.
Experimental Section Apparatus and Materials. A capillary flow system, illustrated in Figure 1, was constructed of Pyrex and was somewhat similar to that of Bloom, Harrap, and Heymann' with an internal subreservoir as suggested by Kellner.* It was built into a Pyrex liner, and the entire assembly was contained within a Parr Instrument Co. A243HC5 Inconel metal autoclave provided with Conax lava-packed glands. The viscometer tube was filled by tilting the entire apparatus, consisting of furnace, autoclave, and viscometer, to 90' from the upright position. Upon restoration to the vertical position, the liquid NaNOs drained by gravity through the trumpet-ended capillary into the subreservoir, which assured a constant lower liquid level.* The flow time was transduced from successive interruptions, by the fused-salt meniscus, of 1000 Hz, cu. 50-mV signals, impressed across the two sets of Pt probes
(of 24-gauge Pt wire). Gases could be admitted into the system to any desired pressure below a safety limit dependent on the temperature. Two chromel-alumel thermocouples in Pyrex sheaths, one at the upper end of the viscometer tube and one a t its lower end, served for temperature measurements. The resistance furnace was provided with independently controlled upper and lower windings, allowing the elimination of the temperature gradient. Viscosity measurements were performed only when the two thermocouples indicated identical temperatures. Fisher Scientific Co. reagent grade NaNOa was employed. Prior to being placed in the viscometer assembly, the salt was dried for over 50 hr a t 135". The gases He, Ar, and N2 were from the National Cylinder Gas Co. and had stated purities of better than 99.98%. Procedure. A 74.700-g sample of the dried NaNOa (calculated for the molten salt to fill the viscometer adequately while the liquid surface was still slightly below the rim of the subreservoir) was placed in the viscometer assembly. The latter was installed in the autoclave, which was in turn placed in the furnace, (1) This work was presented at the 156th National Meeting of the American Chemical Society, Atlantic City, N . J.,Sept 9, 1968. (2) (a) J. L. Copeland and W. C. Zybko. J . Phys. Chem., 7 0 , 181 (1966); (b) J. L. Copeland and S. Radak, (bid., 70, 3356 (1966). (3) J. L. Copeland and 9. Radak, ibid., 71, 4360 (1967). (4) J. L. Copeland and L. Seibles, ibid., 70, 1811 (1966). (5) J. L. Copeland and L. Seibles, ibid., 72, 603 (1968). (6) A. F. M. Barton, B . Cleaver, and G. J. Hills, Trans. Faraday Soc., 64, 208 (1968). (7) H. Bloom, B . J. Harrap, and E. Heymann, Proe. Roy. SOC. (London), A194, 237 (1948). (8) J. D. Kellner, J . Phys. Chem., 71, 3254 (1967).
Volume 73,Number 6 May 1060
1206
JAMES L. COPELAND AND JAMES R. CHRISTIE 2500, 1500, and 500 psig, yielding average flow time measurements at 13 different pressures (including 1 atm) at the temperature in question. Such runs were performed at temperatures of 328, 350, 379, 401, 420, and 444". In calcuhting the viscosity, the gas densities a t such pressures could not be ignored. Thus, the relationship employed to find q (in cP) was
L
77 = K(Pl -
Figure 1. Viscometer assembly for measurement of fused-salt viscosity under gas pressure. The viscometer tube is fixed in Pyrex liner, L, by braces, B. The liquid meniscus is m. The capillary, C, has a trumpet-end and empties into the subreservoir, T, which ensures a constant lower liquid level. Pt indicates platinum probes. The entire assembly is located within the high-pressure autoclave, The drawing is to scale.
While being heated and fused, the salt was kept under vacuum by constant pumping on the system with a mechanical vacuum pump. The viscometer was calibrated a t eight temperatures from 328 to 444" and a t atmospheric pressure using the NaN03 viscosity data of Protsenko and Ra~umovskaya.~ An effective viscometer constant, K , was obtained a t each temperature from the relationship
K
(1)
= q/pit
where q is the coefficient of viscosity of NaNOalgp1 is the density of liquid NaNOa, and t is the flow time. The density, p1 (in g cmdS),was obtained from the empirical relation10 pi =
2.134
- (7.03 X
10-4)T
(2)
where T is temperature ("C). Typical flow times (throughout the entire investigation) were of the order of 20 sec and were reproducible to within h0.05 sec. At least five measurements of the flow time at each temperature were made, and an average time was taken at each temperature. The calculated K values (in CPcm3 g-l sec-l) were linear with temperature with a least-squares equation of
K
=
(7.297 f 0.021) X
lo-*
- (4.556 f 0.054)
X 10-'jT
(4)
where p g is the gas density a t the appropriate temperature and pressure. Values of the latter density were obtained from computer solutions to the BeattieBridgeman equation, which has demonstrated its value and acceptable accuracy in earlier work.5 The liquid density a t a temperature T (in "C) and pressure P (in atm) was found from pi
= 2.134
- (7.03 X
10-4)T
+ (3.9 X lO-')P
(5)
where the temperature coefficient is as beforello and the pressure coefficient is derived from the work of Owens.11
Results A table (too extensive for inclusion here, but copies of which may be obtained by writing directly to the authors) summarizes the results obtained for the viscosity of NaN03 pressurized with He, Ar, and N2 a t pressures from 1 to 414 bars and temperatures from 328 to 444". It has already been established that the viscosity of this salt follows Arrhenius behavior in this temperature range at 1 atm,gand this seems to be true a t the other pressures as well, but to different extents with the different gases. Figure 2 shows plots of In cp ( 4 is fluidity; l/v, in reciprocal poise) us. P (in bars) with the three gases employed at each of the six temperatures. A distinct effect of gas solubility on the transport property is noted. The major points can be seen from Figure 2 and the summary in Table I.
Discussion As in conductivity, two factors affect the viscosity a t a given temperature: (a) pressure and (b) gas solubility, I n general, the effect of pressure alone should be to increase the viscosity (decrease the fluidity). This is the direct result of decrease in free volume available for the necessary configurational changes of the ions undergoing fluid flow. For example, in the theory of Macedo and LitovitzI2
(3)
where the errors are probable errors. For runs with gases, starting with 1 atm pressure in the system at a given temperature, a gas (He, Ar, or Nz) was admitted to 1000 psig and the flow time was determined (at least five times for averaging) in the manner described. The procedure was continued with increasing gas pressures of 2000, 3000, 4000, 5000, and 6000 psig and was then reversed to 5500, 4500, 3500, The Journal of Physical Chemistry
Pdt
A is a temperature-dependent preexponential factor,
Ev (the so-called activation energy for viscous flow a t (9) P. I. Protsenko and 0 . N. Razumovskaya, Zh. Prikl. Khim., 3 8 , 2355 (1965). (10) H.Bloom, I. W. Knaggs, J. J. Molloy, and D . Welch, Trans. Faraday Sac., 49, 1458 (1953). (11) B. B. Owens, J. Chem. Phys., 4 4 , 3918 (1966). (12) P.B. Macedo and T.A. Litovitz, ibid., 42, 245 (1965).
1207
VISCOSITY OF FUSED SODIUMNITRATE
3
i o '
4
b
I
IbO'
do'iw'
240 I
I
280 I
I
'
3#J
I
360 I I 400 I
'
440 I
'
Pressure, P (bars) Figure 2. Plots of In 9 (+ is the fluidity in P-1) US. gas-saturating pressure, P (in bars), for molten NaN03 under He, Ar, and NZgases, a t various temperatures.
where AB,* is the viscosity activation volume
constant volume) is given by
EY = -R[d In d / d ( l / T ) ] ~
(7)
-y is a factor between 0.5 and 1, Vo is the close-packed volume, and Bt is the free volume. Thus, any factor tending to diminish V f ,such as pressure, should tend to diminish 4. The isobaric activation energy for viscous flow, Ep, is the more usual Arrhenius coefficient
EP = -R[d In +/d(l/T)]p
(8)
From eq 7 and 8 one can obtain
EP = EV
+ (a/P)TAV,*
(9)
Table I: Summary of Ln C#J us. P D a t a for Fluidity of Molten NaNOs a t Various Temperatures under Helium, Argon, and Nitrogen Pressures In C/dP)T, cma dyn-1 He0 Arc Nz*
lOlO(d
Temp,
328 350 379 40 1 420 444
O 0
-1,146 -1.293 -1.465 -1.569 -1.695 -1.814
1.759 1.422 1.063 0.736 0.531 0.241
0.105 -0.194 -0.542 -0.751 -0.991 -1.241
Ab',* [ = - R T X (d In 6 l d P ) TI. cma
mol-' (for He only)
5.73 6.70 7.94 8.79 9.77 10.8
The slopes of the curves for He are all negative and comparatively constant. The slopes of the curves for Nz begin slightly positive a t the lowest temperature of 328" and become increasingly negative a t higher temperatures, approaching the curve for He a t the highest temperature of 444'. 0 The slopes of the curves for Ar are all positive, being greatest a t 328" but decreasing markedly a t an almost horizontal plot a t 444' (in this sense following the same trend as the Nz curves).
AB,"
=
(10)
-RT(dIn $J/dP)T
and a and p are the thermal coefficient of expansion and the isothermal compressibility of the fluid, respectively. Thus, eq 9 indicates E p t o consist of two parts: (a) Ev, the energy required for a particle to move, and (b) the energy necessary for the formation of a "hole" into which the particle m o v e ~ . ~ For ~ J ~relatively nonassociated liquids, EV is generally much smaller than Ep but becomes nearer the latter value as the particles become much more highly a~sociated.'~There are, of course, many current theories of viscous flow of liquids, and none appear as yet t o be able to be completely adequate. However they do all seem to agree on at least one point, namely, that any factor tending to diminish free volume should increase the viscosity at any given temperature. In our present studies, therefore, we find it reasonable t o assume that pressure alone acts in the normal fashion of tending to decrease 4, this in turn tending to produce negative slopes of In + us. P isotherms. The observed effects of solubility on tend to support our earlier hypothesis concerning these effects on conductance; ie., the effect is primarily one of dilution.2a If gas molecules were to dissolve predominantly by occupying existing liquid free volume, fluidity should decrease more than it would with pressure alone, in view of the additional removal of
+
(13) J. D. MacKenzie, J. Chem. Phys., 2 8 , 1037 (1958). (14)A. Jobling and A. S. 0.Lawrence, Proc. Roy. 9oc. (London), A206, 257 (1951). Volume Y.9, Number 6 May 1069
1208 free volume from the transport mechanism. Such is certainly not the case for Ar in NaNOa, at least a t 444" and below, and for Nzin NaNOa at lower temperatures, since these gases actually increase the fluidity with increasing saturating pressures, as seen in Figure 2 and Table I. On the other hand, if gas molecules dissolve mainly by creation of their own holes in the melt, then the existing free volume is essentially unaltered (except for the pressure effect, of course) and its contribution to the flow mechanism should remain about the same. However, the effect of the inserted neutral gas particles should be to break up to some extent some of the interionic forces, leading to a slight lowering (on the average) of the potential energy barrier to viscous flow as a result of this dilution. Thus, if the dilution effect tending to increase fluidity is greater than the pressure effect tending to decrease this property, the result would be a net increase in 4 with increasing gassaturating pressure. That dilution of NaNOs by Ar should apparently have the greatest effect on increasing cp is not surprising, since this gas also had the greatest effect on decreasing the specific conductance of the melt presumably by the same mechanjsm.' The fact that this net effect with Ar becomes less pronounced at higher temperatures (Figure 2 and Table I) [(d In rj/dP) T being almost zero a t 444" and probably reversing sign above this temperature] is probably attributable to the slightly exothermic heat of solution of Ar in NaNOa (ca. -1.84 kcal mol-') .5 Thus, at higher temperatures, less Ar dissolves at a given pressure, allowing the effect of pressure (tending to diminish 4 ) to be more strongly felt. The same argument may be advanced for the NZ study. Here, too, since Nz has an exothermic heat of solution (ca. -2.69 kcal mol-') ,4 the decreasing solubility of the gas a t higher temperatures should result in less dilution effect and a decreasing trend in the slope of In cp vs. P, as is again the case. Although this latter trend is of about the same extent as that experienced with Ar (Table I), the actual values of the slopes a t the various temperatures are markedly smaller than those for Ar, in spite of the slightly greater solubility of N2,4 However, since N2 is considerably more exothermic in its solution heat than is Ar, there may be a greater "associating" effect of ions with NZ molecules than with Ar as B result of stronger ioninduced dipole forces. This phenomenon should serve to increase slightly the average size of a flow unit in the melt, resulting in a tendency to decrease 4 in competition with the ordinary dilution effect. On the other hand, Nz had the least effect of all on depressing the specific conductance of NaNOa.2 If one adopts the reasonable approximation of FrenkeP that the viscosity of a fused salt is controlled mainly by large anions and its conductance is due primarily to small cations, then one would conclude that Nz is predominantly interThe Journal of Physical Chemistry
JAMESL. COPELAND AND
JAMES R. CHRISTIE
Table 11: Comparison of Transport Parameters for Viscosity (Using Gas-Saturated Melt) and Equivalent Conductance (Using Pressure Alone) for Molten NaNOa
EP, koa1 AV*, oma mol-' E V, kcal
Viscosity (this work)
Equiv conds
3.93 8.79 1.50
3.21 3.8 2.10
acting with the large NOS- ions to produce larger viscous flow units, while leaving the Naf ions not so extensively perturbed and still relatively free to continue to contribute to the conductance mechanism. Some support for this concept is given by the large entropy decrease of N2 undergoing solution in this melt.4 This entropy decrease may well indicate a t least partial tie-up of the rotational degrees of freedom of Nz by interactions in the m e k 4 The most likely candidate responsible for this mild rotational arrestment i s the NOa- ion, since its own rotation in fused NaNOa is not completely free.10 As regards the viscosity results using He as the pressurizing medium, this gas obviously has the greatest and most relatively constant effect on depressing fluidity. One would anticipate that the tiny molecules of He would produce minimal dilution, effects, and certainly ion-molecule interactions should be negligible in view of the nearly zero polarizability of this gas. Thus, the results indicate that the net effect of He may be quite close to the effect of pressure alone. On this assumption the activation volumes for viscous flow, using He, have been calculated and tabulated in the last column of Table I. At 1 atm, EP for the viscosity of NaNOa is calculated from eq 8 as 3.93 kcal, deg-l and and at 400" and 1 atm, a = 3.84 X 0 = 2.16 X lo-'' cmz dyn-I for this liquid." Thus, use of our AV,* = 8.79 cma mol-' at 401", from Table I, together with eq 9 yields EV = 1.50 kcal at 400' and 1 atm. These values may be compared to corresponding values for equivalent conductance for NaNOa found by Barton, et aZ.,@in Table 11. It is apparent that AV* for viscosity, from the direct pressurization of the melt with He gas, is larger than the AV* for equivalent conductance of the same salt, found by the pressurealone studies. Here, however, this is not unreasonable if one accepts Frenkel's view of the large Nos- ions controlling viscosity and the small Na+ ions dominating conductance. The foregoing concepts are still tenuous. We feel, (15) J. Frenkel, "Kinetic Theory of Liquids," Dover Publications, Inc., New York, N . Y . , 1955, pp 439-445. (16) K.Furukawa, Discussions Faraday BOG.,3 2 , 53 (1961). (17) G. J. Janz, "Molten Salts Handbook," Academic Press, Inc., New York, N . Y.,1967, pp 250, 252.
1209
CATALYTIC EFFECT OF METALOXIDES
Acknowledgments. The authors express their appreciation to the National Science Foundation for support of this work by Grant No. GP-7012. Dr. Kenneth Conrow of this department graciously provided PL-1 computer programs for treatment of the data.
however, that these viscosity results, together with the conductance data, overwhelmingly support the dilution hypothesis to the virtual exclusion of any process involving gas molecules taking up existing liquid free volume (at least for Ar and Nz in NaN03).
The Catalytic Effect of Metal Oxides on Thermal-DecompositionReactions. I. The Mechanism of the Molten-Phase Thermal Decomposition of Potassium Chlorate and of Potassium Chlorate in Mixtures with Potassium Chloride and Potassium Perchlorate by Winfried K. Rudloff and Eli S. Freeman I I T Research Institute, Chicago, Illinois
60616
(Received June 1 7 , 1 9 6 8 )
The thermal decomposition of potassium chlorate was investigated by means of differential thermal analysis (dta) , thermogravimetric analysis (tga) , and differential thermogravimetric analysis (dtga) Nonisothermal decomposition to the final decomposition products occurred via an intermediate disproportionation reaction 2KC103--+ KC104 KC1 02. The reaction was verified by isothermal experiments at low temperatures and stepwise analysis of the thermogravimetric analysis residues. Addition of potassium chloride, one of the final reaction products, decelerated the reaction at low temperatures and high potassium chloride concentrations but accelerated the reaction at high temperatures and intermediate potassium chloride concentrations. Addition of potassium perchlorate did not catalyze the thermal decomposition. There is indication, however, that a eutectic is formed.
.
+
+
Introduction Solid-molten- and solid-solid-phase reactions are generally difficult to investigate and present problems in interpretation, particularly if they involve interaction between a solid catalyst surface and molten or solid reactants. Reasons for the problems are: contact surfaces between the catalyst and the reactant are difficult to define and evaluate, reaction products in the molten or solid phase are frequently complex, and models of solid-liquid or solid-solid interactions are more complex than those of solid-gas interactions. Work indicating that there is a relationship between electronic properties of metal oxides and their catalytic activity has been reported in the 1iterature.l Much of the work involves the decomposition of gases such as nitrous oxide? Experimental procedures and mechanistic interpretation of gaseous phases are, however, simpler than those of condensed phases. Several investigators have studied the catalyzed decomposition of chloratess-l1 and perchlorates.l*al However, no systematic investigation has clearly related defect structure of solid oxide catalysts t o their activity with respect to the thermal decomposition of solid and molten phases of chlorates and perchlorates.
This paper is the first in a series that is aimed a t elucidating the mechanisms of catalyzed decomposition (1) W. E. Garner, “Chemistry of the Solid State,” Butterworth and Co. Ltd., London, 1955. (2) K. Hauffe, Advan. Catal., 7, 213 (1956);9, 187 (1957),and references cited therein. (3) S. 8. Bhatnagar, P. Brahm, and J. Singh, J . Indian Chem. SOC., 17, 125 (1940). (4) F. E. Brown, J. A. Burrows, and H. M. McLaughlin, J. Amer. Chem. SOC.,45, 1343 (1923). See also references cited therein. ( 6 ) F. E. Brown and J. D. Woods, Proc. Iowa Acad. Sci., 6 3 , 410 (1956). (6) J. A. Burrows and F. E. Brown, J . Amer. Chem. SOC.,48, 1790 (1926). (7) J. M. Gaidis and E. G. Rochow, J . Chem. Educ., 40, 78 (1963). (8) H. M. McLaughlin and F. E. Brown, J . Amer. Chem. Soc., 5 0 , 782 (1928). (9) M. Meyer, J . Chem. Educ., 17, 494 (1940). (IO) H.A. Neville, J . Amer. Chem. SOC.,45, 2330 (1923). (11) F. Solymosi, and N. Krix, Acta Chim. Acad. Sci. Hung., 34, 241 (1962). (12) A. K. Galway and P. W. M . Jacobs, Trans. Faraday Soc., 55, 1165 (1959). (13) E. 9. Freeman and D. A. Anderson, Nature, 206, 378 (1965). (14) A. E . Harvey, Jr., M. T . Edmison, E. D. Jones, R. A. Seybert, and K. A. Catto, J . Amer. Chem. &c., 7 6 , 3270 (1954). (15) A. Hermoni and A. Salmon, Bull. Res. Council Israel, A , 9, 206 (1960). (16) 0.E. Otto and H. 8 . Fry, J . Amer. Chem. Soc., 4 5 , 1134 (1923). (17) M. M. Markowite and D. A. Boryta, J . Phys. Chem., 69, 1114 (1965). Volume 73,Number 6 May 196s
