NOTES
Nov., 1959 reaction rate correctly as given in equation 4, but made the same error as Temkin and Pyzhev in evaluating r by the contact time method. Emmett and Kummer obtained equation 1 with n = 3. Bokhovens obtained an equation similar to that of Emmett and Kummer, except that it is multiplied by RT/r$. We will now show that equation 3 also results from a correct derivation in terms of contact time. The differential of contact time may be given as
1983
A generally applicable form of the equation of Hougen and Watsons is ~i
= dzi/d(W/Fi)
(9)
where x i is the fractional conversion of reactant or reactants i, Fi is the feed rate of components designated by i in moles, S.T.P. volumes, or weight per unit time, and W is the bulk volume of catalyst or weight of catalyst. The units of are those of the quantity F i / W . The only requirement is that the components i provide an adequate measure dt = (+/&')dV (5) of the forward progress of the process. Equation where V is the volume of catalyst bed, r$ the frac- 9 can be used in diverse systems such as those tion of voids, and Q' the gas flow rate (volumes involving liquid phases and ill-defined reactants per unit time) in the increment dV a t the tempera- such as broad distillation fractions of hydrocarbons. ture and pressure of the system. Volume dV The equation is equally applicable to homomay be taken as the catalyst space swept out in geneous reactions where W is the volume of the time dt by a plane that is normal to the mean reactor. flow direction and moving at the mean velocity of Appendix.-A precise definition of differential the gas. Then8 reaction rate in terms of time may be obtained by writing equation 4 as dt = +(273P/T&)dV = +(&0/&)(273P/T&o)dV = +(l/z)(273p/T)d(l/so)
(6)
where Q and Q0 are the gas flow rates under standard (S.T.P.) conditions in volume element dV and at the inlet of the bed, respectively, P i s the system pressure in atmospheres, and z = Q/Qo. We now will follow a volume element of gas, occupying a volume of catalyst space dVo at the inlet of the bed, through the catalyst bed. If a volume change occurs, the volume of catalyst space occupied by the gaseous volume element will be xdVo after a conversion of feed 2 has occurred. The problem is then analogous to a variablevolume batch reactor operated a t constant pressure, and the rate must be evaluated per unit volume of reactor space that is occupied. As conversion x is defined in terms of feed consumed, the change in number of moles dni is dni = +NidVoda: = +(P/RT)dVo&
(7)
where Ni is the moles of component i per unit volume of feed. The volume of the catalyst, z dVo (which is V,), and the expressions for d a and dt are introduced into equation 4 to give T
= (l/Vo)dni/dt = (1/273R)da:/d(I/So)
+
(8)
T
= +lim AV-o
1 d(CiAV) AV
dt
where Ci is the concentration of species i in the free space of bulk volume of catalyst AV. Replacing AV by zAVo yields T
=
(+/z)d(Ciz)/dt
(11)
Acknowledgment.-The authors are grateful t o Professor P. H. Emmett for a helpful discussion and encouragement to publish this material. Professor Theodore Vermeulen also made valuable suggestions. PHASE EQUILIBRIA OF THE BINARY SYSTEM PuC13-KCl' B Y ROBERTB E N Z MILTON ,~ K A H N S AND
J. A.
LEARY'
Contribution from the University of New Mexico, Albuquerque New Mexico, and the Loa Alamos Scientific Laboratory, Los Alamos: New Mexico Received May 1, l06g
Interests in pyrometallurgical processing of reactor fuels have stimulated the need for physical properties of certain fused salt systems. I n this paper the results of an analysis of cooling curves for PuCla-KC1 solutions a t various compositions are reported.
where T is expressed as moles Hz Nz consumed per unit volume per unit time. This expression leads directly t o equations 2 and 3. Materials.-Plutonium( 111) chloride was prepared from For other systems a more serious error that has plutonium (99.9% pure) by reaction with hydrogen been made occasionally with the contact-time gas at 150"metal to form plutonium hydride; the hydride was approach involves using r = dx/dt, an expression subsequently converted to the chloride by reaction with hythat has the dimension time-'. This definition drogen chloride a t 350'. The product, plutonium(II1) chloride, was vacuum distilled, cooled as large crystals and does not agree with equation 4 and, when the then stored in a vacuum desiccator. An analysis of the system pressure is varied, has the effect of de- product yielded 69.14 f 0.2% plutonium (theoretical, creasing the dependence of rate on total pressure by 69.22%) and 30.85 f 0.5% chloride (theoretical, 30.78%). Granular potassium chloride (Mallinckrodt Analytical a power of one. Reagent Grade) was dried, melted in a quartz container Although when one considers kinetics in flowing under an atmosphere of hydrogen chloride, cast into a stick systems for the first time the contact time approach seems familiar and obvious, the concept is (1) Taken from a dissertation by R. Benz submitted in partial difficult to formulate in terms of experimental fulfillment of the requirements for the Degree of Doctor of Philosophy parameters, even for relatively simple systems in Chemistry a t the University of New Mexico. (2) Presently on leave of absence from the Los Alamos Scientific involving gaseous reactants and products. Laboratory as a fellow a t the Max Planck Institut fiir phyaikalische (7) P. H. Emmett and J. T. Eummer, Ind. Eng. Chern., 85, 677 (1943). ( 8 ) In these and subsequent transformations reactants and products are assumed to be ideal gages and the pressure drop through the bed is assumed to he negligible.
Chemie, GGttingen, Germany. (a) Chemistry Department, University of New Mexico, Albuquerque, New Mexico. (4) Loa Alamos Scientific Laboratory, P. 0. Box 1663, Los Alamos, New Mesiao.
1984
NOTES
Vol. 63
the sotationary arrest points was estimated to be within f2 The compositions in mole fractions are based upon the weights of the added salts.
.
800 6
700
P.. 600
500
0.4 0.6 0.8 PL I PuCls, mole fraction. Fig. 1.-Phase diagram of the binary system PuCL-KC1 as d e t e r e d by thermal analysis: (1) PuC13melting point, 769 j = 2 ; (2) eutectic point, 486 f 3" at PuC13 mole fraction 0.57; (3) peritectic point for the compound KzPuC15, 611 f 3" a t Pu$& mole fraction 0.35; (4) K3PuCls melting point, 685 f 3 . (5) eutectic point, 621 f. 3' at PuC13 mole fraction O.l$'; (6) KCl melting point, 771 f 2'.
KC1
0.2
form by transferring the melt under vacuum into a Pyrex mold and stored in a vacuum desiccator. The melting point of the potassium chloride was determined to be 771 =k 2' in agreement with the reported value.6 Hydrogen chloride (Matheson Co.) and argon (Linde Air Products) were dried with phosphorus entoxide. Apparatus.-The mezing chamber consisted of a 32 cm. long, 22 mm. diameter quartz test-tube with a Teflon stopper in which was mounted a 35 cm. long, 5 mm. quartz tube for the gas inlet and 35 cm. long, 3 mm. diameter quartz thermocouple well. The lower 20 cm. of the melting chamber was surrounded by graphite to ensure uniform temperatures. A Pt-lO% R h thermocouple which checked within f 0 . 4 " with the melting points of zinc and aluminum was employed for the temperature determinations. The thermocouple was provided with a plug-and-jack connection for the purpose of switching from a Honeywell 0-1650° recorder used to indicate the liquidns points to another thermocouple a t 0' and a K-2 potentiometer used t o measure the temperature a t the stationary arrest points. Procedure .-To begin an experiment the desired quantities (20 to 80 g. total) of salts in the melting chamber were melted and stirred with a stream of hydrogen chloride or argon gas. The thermocouple well projected to within 5 mm. of the bottom of the melting chamber and the volume of the solution was such that the thermocouple was immersed to a depth of 2.5 to 6.0 cm. After 0.5 hr. of stirring with the melt approximately 70" above the liquidus, the cooling curve was begun. Although hydrogen chloride was employed in most of the experiments, identical cooling curves were obtained with argon. The accuracy of the temperature measurements a t ( 5 ) National Bureau of Standards Circular, Number 500, 1952. p.
804.
Results The experimental results are summarized in Fig. 1. These data indicate the existence of the compound K3PuClG (melting point, 685 & 3") and a second compound (peritectic point, 611 f 3" a t the plutonium(II1) chloride mole fraction 0.35), possibly KzPuC16. The composition of the latter compound was chosen on the basis that it is the simplest compound consistent with the experimental data. The two eutectic points occur at the mole fractions 0.17 and 0.57 and the respective temperatures 621 f 3 and 489 f 3". An attempt was made to isolate each of the two compounds by crystallization from the appropriate liquid melts. An optical study of the samples obtained in this manner indicated the presence of two different phases distinct from pure potassium chloride and pure plutonium(II1) chloride. Acknowledgments.-We wish to thank W. J. Maraman and It. D. Baker of the Los Alamos Scientific Laboratory for discussions and encouraging interests. This work was done in the Los Alamos Scientific Laboratory. We are indebted to A. N. Morgan for the metallic plutonium, J. W. Anderson for the fabrication of the plutonium metal, C. F. Metz, G. R. Waterbury, C. T. Ape1 and L. A. Pulliam for chemical analyses and R. M. Douglas for inspection (optical and powder diffraction techniques) of crystals of the PuC13-KC1 compounds. THE SOLUBILITY OF SILVER SULFATE IN ELECTROLYTE SOLUTIONS. PART 5 . SOLUBILITY I N MAGNESIUM SULFATE SOLUTIONS BY M. H. LIETZKEAND R. W. STOUGHTON COntribUtiOn from the Chemistry Division. Oak Ridge National Laboratory, Oak Ridge, Tenn. Received June 18, 1969
Previous papers in this series have described the solubility of AgzS04 in KN03,2 K2S04,*HPso44and "035 solutions. It was shown in these papers that expressions of the Debye-Huckel type could be used to describe the solubility data in each system over a wide range of temperature and ionic strength. Since it seemed to be a logical extension of this solubility program to determine whether similar expressions could be used to describe the solubilit,y of Ag2S04in polyvalent electrolyte solutions, a study has been made of the solubility of Ag2SO4in 0.1, 0.5 and 1.0 m MgS04 solutions to above 150". Again a high speed digital computer has been used in making the calculations. (1) This paper is based upon work performed for the United States Atomic Energy Commission a t the Oak Ridge National Laboratory operated by Union Carbide Corporation. (2) M. H. Lietzke and R. W. Stoughton, THIBJOURNAL,63, 1188 (1959). (3) M. H. Lietzke and R. W. Stoughton, ibid., 63, 1186 (1959). (4) M. H.Lietzke and R. W. Stoughton, iMd., 63, 1188 (1959). (5) M. H.Lietzke and R. W. Stoughton, ibid., 63, 1190 (1959).
