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 curve 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.
1031 TABJ,E: I CRITICAL C O A ~ T A FOR N T ~NaCl
Inbestigators
CER
-
NaCl
KCI
NaCl
KCI
NaCl
KCI
3600
3092 4060 3200
293 333
431 464 415
235 5 240 350
135 5 154 220
hf(3Qusrrie
4340
KClIG
3400
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
(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).
--
--To,
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)
SOTES
1932
in the IIe~ii~y’slaw regioii. Similar experimental measurements for the rare gases on this surfacee have not been correctcd for quantum statistical mass effects, and we preseiit such corrections here. Por argon, krypton, and xenon, tlie data were obtained at temperatures siifficieiitly high so that quantum deviations are totally iiegligible. 111 the case of neoii, the data were takeii a t fairly low temperatures (5(3-1)4OK.), and although the deviations from classical behavior are not largc, it is felt that the data are sufhiently accurate so that corrcctioiis larger than the experimental uncertaiiities should not be neglected. Wc present only a brief outline of the theory, which has beeii published ill dctail else~vhere.~The second gas-surface virial coefficieiit, iiicludiiig quantum terms to order of h4, may be written as
B,] = AsJ,] -
BAS
+ B,‘*’
=
(la)
( l l S ” K / ~ ’ ) ~ q ( l )f (ASJ/Y’z)Zq(2)
(lb) The integrals Z are functions only of the reduced gassurface interaction tcmperaturc, k7’/eI8*. Their exact form, of C O I I ~ S P , dcpctitls iipoli tlie modcl chosen to rcprcscnt the gas-solid iiiteractioiis. A is the area of the solid and s;, the apparent separatioii of a gas atom arid the plane surface at zero iiet iiiteractioii. The constants K and X are given by K =
x
=
h’/24pkSo2
’ih‘/576op*/i2s”4
(2)
(8
VOl. 67
teiitial well tlian is tlie classical configuration integral, the nature of the fit in this case should be a more stringent test of the potential model chosen. Consequciitly, we have refitted the quantum corrected neon results using three different models for the interaction poteiitial, all based on the Lennard-Jones (12-6) fuiiction. These are: (a) a (8-3) law which results from a threefold iiitegratioii of the (12-6) over the three dimensions of the semi-infinite solid; (b) a (10-4) potential, resulting from intcgratioii of the (12-6) over a single iiifiriite plane: (c) a (12-3) law, which correspoiids to a tlireefold iiitcgration of the attractive part of the potential alone. Values of IC],Z q ( l ) , and 1cL(2) for these three models, and a more complete discussion of quaiiturn effects iii physical absorption, have been published elsewliere. The quaritum correctcd values of the interaction energies are given in columns 3 and 4 of Table I, and the classical values are listed for comparison in column 2 . As expected, the correctioiis are small, amounting a t most to about 2.3yo,but considerably larger than the experimental errors of the measurements. The differences between the values in thc third and fourth columns arise solely from the different methods of estimating so. TABLE I CLASSICAL A N D QUANTUM VALUESOF &./k
FOR
Ne (OK.)
Model
CI
QL
QKM
10-4 9-3 12-3
367 382 383
372 390 393
369 384 386
where h is l’laiick’s constant divided by 2n, k the Boltzmann constant, and p the mass of the gas atom. TABLE I1 I n the original analysis,6 data for H A S as a function of AREASA N D STANDARD DEVIATIONS FOR QUANTUM FIT temperature were fitted only to the classical part of AL [Std. dev. X 1061 the configuration integral (Le., to ZcJ by adjusting the Model (m.2 g. AKM L KJI two parameters qs*/k and As0, thus obtaining best-fit 0.42 0.34 13.23 8.37 10-4 values for these parameters. E’rom (lb) it is apparent .93 1.24 14.34 9-3 7.94 that these results can be used to calculate the two .66 1.11 12-3 15.31 8.52 quantum corrections to BAS to a first approximation. I n Table I1 revised values of the surface area of the These corrected B A Svalues can then be refitted to IC!, adsorbent are given. These were calculated from the giving new values of qs*/k arid Aso. This procedure As0 values obtained from fitting the quantum corrected is iterated until tlie results become self-consistent. data, together with so’s calculated through either the l h e quantity so, which appears in K and X, cannot London or Kirkwood-Muller formula. As with the be obtained directly from the model. However, if one classical rcsults,‘j the London formula is found to give identifies the gassurface attractive potential with the coiisidcrably larger values for the area than does the London forces attraction of two isolated systems, then Kirkwod-Muller formula. This is partly due to the from the experimental elsd and any one of the familiar approximation of using ionization potentials in the formulas which have been proposed for the constant of proportionality in the London expression, a value for SO London formula. For many-elcctron systems, as I’itzer has pointed the off-diagonal matrix elecan be caculated. ‘l’\vo such formulas, those of meiits in the dispersion ericrgy expression make a subKirkwood and Muller and of‘ Tmdon, have been staiitial contrihutioli. I t has bccn suggested7* that used here. These represent the upper arid lower for a typical many-electron atom, the value for the bounds, respectively, of values obtained for so by characteristic eiiergy in thc Lolidon formda may the five formulas which have been discussed elsewhere.6 be about twice the ionization potential. Although one E’ort.unately in this case, since the quantum deviations does not kiiow what "effective characteristic energy” are small, the energy is quite insensitive to the exact to assume for the solid, if just two times thc ionization choice of so: a 40% variation of this latter parameter encrgy is used for both solid and adatom, then the affects the energy by no more than 2%. Values of the valucs for the Loiidoii area will be reduced by the mulpolarizabilities, ionizatioii energies, and diamagnetic tiplicative factor 2-‘Ia [or 2-‘14 in the case of the susceptibilities used in these calculations are tabulated (10-4) potential]. This, then, would bring areas comin ref. 6. puted by this formula into closer agreement with the Owing to the fact that the quantum effects are more Kirkwood-filuller areas. Similar considerations apply strongly dependent on the depth and shape of the po-1)
r7
(6) J. R. Sama, Jr., G . Constabaria, a n d G . D . Halsey, Jr., J . Phm. Chem., 64, 1689 (1960).
(7) I
