KOTES
Sept., 1963 CONCElWING THE CRITICAI, CONSTZWTS OF SODIUM CHLORIDE A N I POTASSIUM CHLORIDE I BY 1’. J.
>fCaONIGAL
Research Institute of Temple Cninersity, Philadelphia
44,Pa.
Received March 25, 1903
Recently several sets of values for the critical constants of KaC1 arid KCl have bcen published. It is the purpose of this notc to compare these values and to present some observations upon the methods by which they were obtained. Carlson, Eyriiig, and nee2 (CER) applied the well known method of significant structures to KaCl, KCl, KaBr, and KBr and calculated values for melting point and boiling point propcrties as well as the critical constants. The agreement between experiment and calculation for the melting point and boiling point properties is very good and tends to give confidence in this method of approach. While no experimental values are available for the critical constants of NaCl and KC1, the success of the significant structure method iii predicting critical constants for the rare gases,a chlorine,4 and several othcr liquids6 is impressive. An interesting comparison of Eyring’s fluid vacancy model with two othcr current theories has appeared recently. A second approach to the problcni of calculating the critical constants of NaC1 and KCl (and all the other alkali halides cxcept those of cesium) has been proposed by RlcQuarric.’ He niadc a straightforward application of the Lennard-Jones and Devoiishire theory modified to account for a two-component system and to include interactions from ions in all the spherical shells surrounding .a given ion. I n this trcatmeiit it was assumed that all lattice sites are occupied and that the Madelung constant for the fuscd salt is the same as that for the crystal. Calculated entropies of vaporization are about twice as large ae those observed experimentally. Critical consta1it.s iverc obtaiiicd from %he equation of state of the model using the reduced variables of Reiss, Maycr, and Katz.8 A third method for the estimation of the critical coiistarits of NaC1 and KCl has bccii used by Kirshenbaum, Cahill, McGonigal, and (’Jrosse9 (KCRG). I n this work the rectiliiicar diameters for the liquid salt,s were constructed from density data which were obtained ovcr the entire rangc from the melting point to the boiling point. The upper limits of the critical temperatures were established by the intersection of the calculated vapor dcnsity curw with the rectilinear diameter and the final values of critical temperatures were estimated from careful study of the liquid range diagrams. The three scts of critical constants are shown in Table I. (1) (a) A report of this work will constitute a portion of a dissertation to
be submitted by the author t o the Graduate Board of Temple University in partial fulfillment of the requirements for the dagree of Doctor of Pl>ilosoplly; (b) presonted before the Division of Physical Chemistry, 145th National Mooting of the American Chemical Society, New York, N. Y,, Sept.. 1963. (2) C. M. Carlson, H. E y i n g , and T. Ree, Proc. iVafl. h a d . Sci. L‘,S., 46, 833 (1960). (3) H. Eyring, T. Ree, and N. Hirai, ibid., 44, 683 ( 1 9 5 8 ) . (4) T. R. Thomson, H. Eyring, and T. Ree, ibid., 46, 3 % (19130). ( 5 ) E. J. Fuller, T. Ree, and H. Eyring, ibid.. 46, 1594 (1959). (6) €1. Eyring, J. Hildebrand, and ‘8. Itice, Intern. Sci. Tech., No. 15, 80 (March, 1963). Phys. Chem., 66, 1508 (19132). ( 8 ) H. Reiss, S. W. &layer, and J. L. Katz, J . Chem. Phys., S I , 820 (1961). (9) A. D . Kirslieribanm, J. A. Cahill, P. .J. M c ( ~ o ~ i y sand l , A . T’. Grosse. J . Inoru. N w l . Chem.. 24, 1287 (J9GZ).
1031 TABJ,E: I CRITICAL C O A ~ T A FOR N T ~NaCl
--
-
NaCl
KCI
NaCl
KCI
NaCl
KCI
3600 4340 3400
3092 4060 3200
293 333
431 464 415
235 5 240 350
135 5 154 220
--To,
Inbestigators
CER hf(3Qusrrie
KClIG
OK
Vc. cm
2(i6
A ~ KC1 D
8-
-Pet
ah--
The significance of the data in ‘I’ablc I may not be inimcdiatcly apparent. Thew is good agrccment betilceii the data of CER and KCJIG for TC, fair a g r w nient among all iiivestigators for V ? ,arid good agreement hetween CElt and AIcQuarrie for 1’‘. (It should be noted that t n o of the eiitrics in Table 1111 of ref. 9 are in error: the correct V, for KCl is 415 cm.8and the correct l’,V,/RT, is 0.348.) Thc high l’, values obtained by KCAIG arc due to thc cxtrapolation procedure used: their 7’, and V , values are, of course, consistent, based on rrctiliiiear diameter considerations. The Tc and Vc values obtained by Eyring are within the error limits assigncd to the values of KCAIG. The very high values for T , obtained by NcQuarrie, however, arc not coiisistent n i t h his values for Vr. Indeed, extrapolation of the rectiliiicar diameter for NaC1 indicates that the density would be zero a t 4320°K., z.e., ne11 belon McQuarric’s Ye of 424OOK. The fact that McQuariic’s Y’? values arc so high is undoubtedly due to thc artificial orderliiicss and rigidity of his modrl. There is an additional factor to be coiisidcrcd in regard to the choice of model and critical constants of SaCl and KC1 and other salts M hich may be regarded as having a realg critical tcmperaturc. Since AHvap must bc zero at Yr, the liquid phase must be composed of molcculcs in the limit of close approach to Yc. It may be assumed that the change from thc fully ioiiized form to the molecular form takes place gradually over a. fairly lorig temperature range. Such a proccss would in all likelihood tend to decrease the density and cause thc rectilinear diamcter to curve downward. This behavior would tcnd to lower l’,, incrcascV,, or both. Thus, the straight line extrapolation used by KCMG may be regarded as the upper limiting form. Acknowledgment.-The author gratefully acknowledges the guidance and counsel of Dr. A. Fr. Grosse. This work was supported by the U. S. Atomic Energy Commission under Contract AT(?dl-1)-2082. _---
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QUANTUM CORRECTIONS FOR THE AIISORPTIOK OF NEON ON (;ItAPHT’TIt’ CARBON’ BY JOIIN 12. S A N S , JR.,*A h l )
ROBhlf‘l’ Y
ARI~~
Department of Chemastry, Unzversity of Washington, Seattle 6, Washzngton Received March 29, 1963
We recently have presented a quantum treatment of physical a d s o r p t i ~ i iand ~ have employed ithe theory to explain the observed5 interactions of isotopic species with the highly graphitized carbon black P33 (2700’) (1) Thls research was supported i n part b y the [J. S.Air Force through the W O S R , a n d in p a r t by the American Petroleum Institute (2) Department of Physical Chemistry, Imperial Collegp uf Solexice, London, S W. 7, England. (8) SchooL of Chemistry, University of Minnesota, M i n n e a p o h 14, Minnesota T o whom reprint requests should be sent (4) R. Y a m a n d B R B a r n , J r ,J . Chem Phys , 3 T , 671 (1962). (5) G. Constabaris, J R Barns, J r , a n d G D Halsey, Jr., J . Phys Chem., 66, 367 (1961)
