TRANSPIRATION VAPORPRESSURE MEASUREMENTS
2361
lated values are of the right order of magnitude for small particle concentrations. The descrepancy between the experimental and calculated values is not
considered serious because of the ideality of the doublelayer model assumed, uix., point charges, infinitely large flat plates, and uniform surface charge.
Transpiration Vapor Pressure Measurements for the Molten Salt Systems PbCl,
+ CsCl and CdCI, + CsCl
by H. Bloom and J. W. Hastie Chemistry Department, The Unaversity of Tasmania, Hobart, Australia (Received October 16, 1967)
A transpiration method has been used to obtain partial pressure data over a range of compositions for molten PbClz CsCl and CdClz CsCl mixtures. The data have been interpreted to indicate the formation of complex ions in the melts. Vapors in equilibrium with the molten PbClz CsCl mixtures contain the complex molecule CsPbCls as well as CsCl and PbClZ while in the CdClz CsCl system there is the complex molecule CsCdC13 together, probably, with CsCdzCls, in equilibrium with the components.
+
+
+
Introduction For all the PbC12 AC1 and CdC12 AC1 systems (where A is Na, K, Rb, or Cs), none yet forms simple ionic mixtures in any phase, with the exception of solid mixtures of PbC12 NaCI. Thermodynamic activities for the two components of each binary system, calculated from transpiration measurements, are not consistent with the Gibbs-Duhem relationship,6if the vapors are assumed to be the simple unassociated components. In these systems, the activities of AC1 deviate in a positive sense from the Raoult and Henry laws, while large negative deviations are found for PbCl2 or CdC12. Previous workers have attributed these to vapor association equilibria, e.g., for the PbClz CsCl system
+
+
+
+
+
PbCl2 CSCl+ CsPbCla (1) Hagemark, Hengstenberg, and Blander’ have recently inferred, by measuring pressure-temperature relations, the presence of KPbC13 and RbPbCla in the vapor systems KC1 PbClz and RbCl PbC12, respectively. In a comprehensive study of a number of systems by mass spectrometry, Bloom and Hastie* have directly verified the existence of complex molecules over molten PbC12 salt mixtures, including CsPbC4 in the CsCl system and CsCdC4 in t h e CsCl CdC12system.
+
+
+
+
Experimental Section The transpiration apparatus and method which were used have been described by other The carrier gas was purified argon and flow rates were
+
kept within ranges for which it had been verified that derived partial pressures of the components were independent of flow rate. For example, for the equimolar mixture PbCl2 CsCl a t 700°, the various partial pressures were found to be independent of the rate of flow of argon over the range 0-60 ml/min. Errors due to thermal diffusion (significant only a t very low flow rates or at high pressures) were shown to be mostly absent under the selected conditions of measurement, but corrections where made where necessary by making duplicate runs a t zero flow rate. Temperature was measured by 13% Rh-Pt-Pt thermocouples calibrated a t the melting points of metals and sodium chloride. Salts were of analytical reagent quality and, except for Cs, standard chemical methods of analysis were
+
(1) H. H. Landolt and R. Bornstein, “Zahlenwerte und Funktionen,” Vol. 11, Part 3, Springer-Verlag, Berlin, 1956. (2) F. G. McCarty and 0. J. Kleppa, J . Phys. Chem., 68, 3846 (1964). (3) A. G . Bergman and Zh. V. Misler, Russ. J . Inorg. Chem., 10, 696 (1965). (4) B. F. Markov, Iu. K. Delimarskii, and I. D. Panohenko, Zh. Fiz. Khim., 28, 1987 (1954). (5) I. I. Il’yasov, A . G. Bergman, and N. I. Chaurskii, Russ. J . Inorg. Chem., 10, 679 (1965). (6) J. L. Barton and H. Bloom, Trans. Faraday Soc., 55, 1792 (1959). (7) K. Hagenmark, D. Hengstenberg, and M. Blander, J . Phys. Chem., 71, 1819 (1967). (8) H. Bloom and J. W. Hastie, Aust. J . Chem., 19, 1003 (1966). (9) C. Beusman, “Activities in the KC1-FeCla and LiCl-FeCla Systems,” ORNL Report 2323, Oak Ridge, Tenn., 1957.
Volume 72,Number 7 July 1968
H. BLOOM AND J. W HASTIE
2362
used. For Cs, which often had to be determined in small amounts, the y-active 13'Cs isotope was used to label the CsCl and its concentration was determined by standard procedure using a Geiger liquid counter.
Results and Discussion I n this article, only the measurements at 650" will be discussed, as this was the only temperature a t which all the salt-mixture compositions were investigated. Isothermal (660") Properties of the PbC& CsCl System. Values of apparent and corrected partial pressures obtained by transpiration (at mole fraction 2 ) are listed in Table I.
PCsPbCla
Composition (zpbclJ, mol fraotion
0.000 0.299 0.503 0,507 0.598 0.690 0.796 0.891 1.000
Cor partial True --Transpiration results-pressures activities Ppbci2(trans), Pcsci(trans), (PPbcie(true)), of PbClz mm mm mm (4
0 0.550 2.320 2.360 3.470 5.240 6.850 7.830 9.860
0 0.182 1.559 1.559 2.901 4.710 6.600 7.680 9.860
0.126 0.368 0.761 0.801 0.569 0.530 0.250 0.150 0
0 0.018 0.158 0.158 0.294 0.478 0.669 0.779 1.000
I t will be noticed that the transpiration partial pressures of PbClz deviate from the Raoult-law values in a negative sense, but those of CsCl are all much higher than the ideal values; e.g., for the mixture 0.507 mol fraction of PbClz 0.493 mol fraction of CsC1, the apparent partial pressure of CsCl was found to be 0.801 mm by analysis of Cs instead of 0.0621 mm, which would be expected if the system were to behave as ideal mixtures of Cs+, C1-, and Pb2+,according to the model of molten salt mixtures devised by Temkin.lO It has been shown6J1that for each component of the ACl, the activities, binary molten salt system PbCh u (Le,, Pi/Pio,where Pi is the partial pressure of component i, of the mixture] and Pio is the total vapor pressure of the pure salt at the same temperature) are very much smaller over a considerable part of the composition range than the Temkin activities. The latter for an ideal binary mixture would be the same as the mole fraction. Thus the true partial pressures of CsCl over the liquid mixtures are actually very small over most of the composition range, in contrast to the transpiration values which are the combined pressures of CsCl and CsPbC13. This has been confirmed by the mass spectrometry results.* Since
+
+
The Journal of Physical Chemistry
- Pcscl(true)
(2)
and Pc,cl(trans)
>> Pcscl(true)
(3)
the values of Pc,cl(trans) for the mixtures in Table I can be regarded as being the actual vapor pressures of CsPbC18 in the vapor. The true vapor pressures of PbClzabove the mixtures are thus given by
+
Table I: Partial Pressures and Activities for the System PbCh f CsCl at 650"
= Pc,cl(trans)
- PCsPbCla
PpbCl,(true) = PpbCl&ans)
(4) Ppbcl,(true) = Ppbcl,(trans) - Pc,cl(trans) These values of true partial pressures of PbClz above the liquid mixtures are shown also in Table I, together with the activities of PbClz calculated from corrected vapor pressures. Activity coefficients of PbCI2 (YPbCla = aPbCl%/$PbCle) are plotted as a function of melt composition in Figure 1. This figure illustrates the errors in activity coefficient which would be caused by neglecting compound formation in the vapor phase in these transpiration measurements. For ideal mixing, e.g., of AX with BX2, the Temkin model would allow the calculation of activities of components of a binary molten salt system as follows
aAX = NAtNx-
(5)
and
aBXn = N B ~ C N X - ' (6) where the ionic fractions N At )etc., are given in terms of mole fractions of ions by the equations NAt =
$At/(ZA+
2gzt)
etc. This simple behavior has been confirmed for several molten salt systems. 1.0
0.8
-, 0.8
eV
0.4 0.2 0
0
0.2
0.4
0.6
0.8
1.0
Z P ~ C mol ~ ~ , fraction.
-+
Figure 1. Activity coefficients for PbClz in the PbClz CsCl system at 650': 0 , uncorrected for compound formation in vapor; 0, corrected for compound formation in vapor.
(IO) M. Temkin, Acta Physicochirn. URSS,20,411 (1946). (11) H.Bloom, Pure AppZ. Chem., 7, 389 (1963).
TRANSPIRATION VAPOR PRESSURE n'IEASUREMENTS
2363
+
BrediglZ has shown that for the systems CdC12 KC1 and CdBrz KBr, the activities can be calculated using the Temkin model only if allowance is made for complex ions in the mixtures, e.g., C d C l P in the chloride system. Perfect curve fitting could not, in any case, be achieved by Bredig without assuming equilibria between complexed and uncomplexed ions rather than reactions to completion. I n order to calculate activities and hence activity coefficients of CsCl and PbC12, we use Temkin equations, analogous to eq 5 and 6 putting the ionic fractions
+
Ncs+ =
ZCS+/(ZCS+
+
ZPb*+)
and
0
+
N C l - = ZCl-/(XPbCls-
Z P ~ O I mol ~,
%I-)
If PbC13- is the only complex ion present in the system and if it mixes ideally with the ions from PbClz and CsC1, the activity of PbC12 can be shown by the use of the Temkin equation to be given by aPbC12
=
kxPbCl2
- 2 + 2[1
-
~~P~CIZ~CSCI]"~
kxPbC12
where the constant IC = 4 K / ( K librium constant is given by
K
(7)
+ l), and the equi-
= aCsPbCL/aCsCl~PbC12
(8)
Through iteration it was found that a value of K = 30 fits the experimental activity and activity coefficient (Figure 1) curves within the estimated uncertainty of ~ 4 % over the whole of the composition range. Similar calculations were made for other complex species, such as PbC12- or PbClG4-, but none of these agreed with the experimental curve. Hence it seems reasonable to postulate that PbC13- is the major species in the mixtures responsible for the nonideal behavior. Additional information on complex-ion formation in this system can be drawn from a consideration of the partial molar excess entropies of PbClz (SEpbc12) in these mixtures. These values, obtained from a combination of R'IcCarty and Kleppa's2 partial molar excess enthalpy data with our partial molar excess free energy (from activity) data, are plotted in Figure 2. As was found by Kleppa and McCarty13for the MgClz KC1 system, the partial excess entropies of MClz vary from positive to negative values, and this trend parallels that of the partial excess molar volumes. Formation of complex ions would be expected to lead to negative values of the partial molar excess entropies. This is reflected in a minimum in the integral entropy at the equimolar composition accompanying the formation of PbCla-, owing to the high relative degree of local order at the equimolar composition. The formation of CsPbCla in the vapor state is most likely related to the ability of Pb2+ to form PbC13- in the liquid state. It is suggested that the vapor-phase
+
0.4
0.2
0.6 fraction.
0.8
1.0
Figure 2. Partial molar excess entropies of PbClt in the PbCls CsCl system a t 650'.
+
CsPbC13 molecule is essentially Cs+PbCla- and that the structure of PbCla- is similar in both the liquid and the vapor states. The structure of PbCh- in PbClz KC1 melts has been found from Raman spectra to be pyramidal (point group CaV).l4 We suggest a similar structure for the CsPbC13 molecule, Cs forming three Cs-C1 bridges to Pb. The recent identification of the pyramidal SnC13complex ion in SnClz KC1 mixtures suggests that the formation of complex ions and possibly complex molecules (in the vapor state) could be general for all group IVa metal-halide systems.ls The CdClz CsCl System. I n this system the partial pressures of CdC1, were found to be very much larger than those of the vapor compound CsCdCL, hence the transpiration vapor pressures of CdClz are also the true vapor pressures. The carrier-gas flow rates used for this system were ca. 10 ml/min. The results for 650" together with the activities of CdCl2 calculated using the vapor pressure of pure CdClz at this temperature, measured by Bloom and Welch,16are shown in Table 11. For this system, the equilibrium constant for the formation of CsCdCla (~CdCls/(~CCdCIt~CsCl))required to give a good fit of the experimental activity coefficient curve at 650" was K = 130. The experimental and calculated results are shown in Figure 3, where the broken lines show deviations of the calculated values at the extremes of composition. The assumption that CdCb- is the only complex ion formed in this system is thus inadequate over parts of the composition range,
+
+
+
(12) M. A. Bredig, J . Chem. Phys., 37, 451 (1962). (13) 0. J. Kleppa and F. G. McCarty, J . Phys. Chem., 70, 1249
(1966). (14) K.Balasubrahmanyam and L. Nanis, J . Chem. Phus., 40, 2657 (1964). (15) J. H.R. Clarke and C. Solomons, Abstracts, 153rd National Meeting of the American Chemical Society, Miami Beach, Fla., April 1967. (16) H. Bloom and B. J. Welch, J . Phus. Chem., 62, 1594 (1958). Volume 79,Number 7 July 1968
*
H. BLOOM AND J. W. HASTIE
2364
Table 11: Partial Pressures and Activities for the System CdClz CsCl at 650"
+
Composition
-Transpiration Pcdcidtrana), mm
(ZCdCIz) I
mol fraction
0.000 0.226 0.279 0.388 0.398 0.489 0.500 0.512 0.540 0.562 0.591 0.610 0.662 0.690 0.705 0.725 0.738 0.770 0.780 1,000
vapor pressuresPcm(trans), mm
.*. 0.0925
...
(Q)
0.000
...
0.009
...
g 0.10 n
3
2 0.04
...
...
0.355
0.033
0.02
0.123
...
0.96
... .,.
*..
...
0.090
0.138 0.154 0.169
... ...
...
0,222
2.38
...
0.180
...
3.80
...
...
I
. . I
* .
.. ... ...
I
.
I
...
...
6.87 10.72
0.01 0.2
0
A 8
-
0.6
-
0.4
-
0.2
0.2
0
0.640 1.000
0
0.4
0.6
0.8
1.0
Z C ~ C mol ~ ~ , fraction.
Figure 3. Activity coefficients for CdClz in the CdCl, CsCl system a t 650".
+
A possible explanation of these deviations may be due to other complex ions, e.g., CdC12- and CdCla4-, being present also in these liquid mixtures. Vapor Pressures of the Compounds at 660'. From Table I the vapor pressures of CsPbCla, i.e., PcScl (trans), a t 650" are known as a function of composition. The values are symmetrical about the equimolar composition. This is thermodynamically consistent with the formation of CsPbCla as the sole vapor-phase compound in this system. For the CdC12 CsCl system, the vapor pressures of CsCdCla at various compositions can be calculated as follows: Pcdcl,(trans) is very much greater than PcGc(trans) over most of the composition range (Table II), hence the true values of PCdClg can be regarded as the same as the transpiration values. From the ac-
+
The Journal of Physical Chemistry
0.6
0.8
mol fraotion.
Figure 4. Partial pressures of CsCdCla in the CdCla system a t 650", calculated from eq 9.
1.0
+ CsCl
tivities of CdCI2, true activities of CsCl are calculated by graphical integration of the Gibbs-Duhem equation. From these values for the mixtures and the partial pressure of pure CsCl at the same temperature, the true partial pressures of CsCl are calculated. The values of PCsCdC18 can then be obtained from the equation PCsCdCla
0.8
0.4 ZCdClz,
0.354
0 109 0.094 0 071 0 066 0.022
... .
Activities of CdClz
0.126 0.0455 0.0354 0.067
0
I
0.40 0.20
= Pc,cl(trans)
- Pc,cl(true)
(9)
These PCsCdCla results at 650" are shown plotted against molar composition in Figure 4. The curve is not symmetrical about the equimolar composition, hence there is at least one other vapor-phase compound containing more than one molecule of CdClz for each molecule of CsCl. The formation of some dinuclear compound CsCdzC16a t mole fractions of CdClz greater than 0.5 mol fraction could lead to the observed results. It is estimated from Figure 4 that the partial pressure of CsCd2Cls would reach a maximum of ca. 0.03 mm at 0.66 mol fraction of CdClz. Unfortunately no mass spectrometric evidence is available to prove the existence of the CsCd2Clbspecies. Previous mass spectrometric measurements* were made over the composition range 0.3 mol fraction < XCdClz < 0.5 mol fraction, in which the pressure of CsCd2C&would be very small and difficult to detect in mass spectrometric experiments. . It is significant that the transpiration dataaJ1for the NaCl system are exactly analogous to the CdClz present data. I n particular, the apparent P N ~ C Ius. XCdClz curve shows similar dissymmetry about the XCdClz = 0.5 mol fraction composition, hence the vapors above CdClz NaCl mixtures could also be considered to contain the complex species NaCdzCls as well as NaCdCla. The data of Schrier and Clark" for the MgC12 KC1 system also indicate an unsymmetrical P K M ~ Cus.~ ~ m&lZ curve, which may be regarded as the superposition of two curves: one due to KMgCls and one due to E(Mg2CL in the vapor at compositions greater than
+
+
+
(17) E.E.Schrier and H.M. Clark, S.Phys. Chem,., 67, 1269 (1963).
A MULTILAYER MODELFOR
THE
SURFACE TRANSPORT OF ADSORBED GASES
= 0.6 mol fraction. The maximum pressure of KMg2C15would be about 3 mm, compared with a value of 21 mm for KMgCL. The absence of corresponding species such as CsPb2C16 and KPb2C15 from both transpiration and mass spectrometrics evidence is possibly related to the inability of PbC12 to dimerize, in contrast to niIgClz and extent in the latter CdC1z Only to a case17J8). ZMgCla
2365
Acknowledgment. This work was supported by a grant from the Australian Research Grants Committee. J. W. H. was the recipient of a Titan Products Research Fellowship. The specially selected cadmium rods used for preparing cadmium chloride were donated by the Electrolytic Zinc Co. of Australasia, Ltd. (18) F. J. Keneshea and D. D. Cubiciotti, J . Chem. Phys., 40, 1778 (1964).
A Multilayer Model for the Surface Transport of Adsorbed Gases by Weldon K. Bell and Lee F. Brown Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80506
(Received October 60, 1967)
A model for the multilayer flow of adsorbed gases is developed and its application to surface migration in microporous media is investigated. Transport within an individual layer is viewed as resulting from a twodimensional spreading-pressure gradient, and momentum exchange between adjacent layers is represented by a simplified law. Equations for the concentration of each layer are developed within the framework of BET adsorption theory. Employing a circular-pore geometry, a two-parameter relation results which describes the adsorbed flux. The model is applied to published experimental data. The values obtained for the two parameters exhibited concentration dependence, temperature dependence, and relationship with each other in agreement with physical expectations. The quantitative values of the parameters are dependent upon the assumed number of adsorbed layers, however, and this represents a weakness of the model.
Introduction Previous investigators of the surface transport of adsorbed gases have described it by a single-phase flow utilizing a spreading pressure or with models based on random molecular movement between adsorbed sites. These models do not consider the possible multilayer nature of adsorption nor do they allow for the diluteliquid behavior of these adsorbed layers. This article presents a multilayer model for the flow of adsorbed gases and investigates its application to surface transport in microporous media. For many years the transport of adsorbed gases has been generally accepted and has come to be known as “surface migration” or ‘(surface diffusion.” A recent review of the surface diffusion of adsorbed molecules is that by Dacey.’ Hayward and Trapnel12 provide a fairly complete discussion of the surface mobility of chemisorbed species. I n Dacey’s review, four regions for surface flow in porous solids are considered. The first region occurs at very low pressures where surface coverages are very small. At somewhat higher surface concentrations, a region of less-than-monolayer coverage occurs. Multilayer coverage is significant in the third region, while capillary condensation exists in the fourth.
To explain the surface flow in these regions, several models have been p r o p o ~ e d . ~ -While ~ none correlates the data in all regions, the models proposed by Smith and I v l e t ~ n e rand ~~~ by Gilliland, et a1.,4t5have had fair success. Smith and Metzner’s equation for surface flow was derived from a basis of random molecular motion between adsorbed sites and fits data well at low coverage. Gilliland, et al., proposed a single-phase flow resulting from a spreading pressure and obtained the best results at low- and intermediate-adsorbed concentrations. Both assumed only a single surface layer. Since multilayer coverage begins to assume significant (1) J. R. Dacey, Ind. Eng. Chem., 57, 27 (1965). (2) D.0.Hayward and B. M. W. Trapnell, “Chemisorption,” 2nd ed, Butterworths and Co. Ltd., Washington, D. C., 1964. (3) 5. Kruyer, Koninkl. Ned. Akad. Wentenschap. Proc., 56B, 274 (1952). (4) J. 8. Russell, 8c.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1963. (6) E. R. Gilliland, R. F. Baddour, and J. S. Russell, A.I.Ch.E. (Amer. Inst. Chem. Eng.) J., 4 (1958). (6) R. K.Smith, M.Ch.E. Thesis, University of Delaware, Newark, Del., 1963. (7) R. K.Smith and A. B. Metsner, J. Phgs. Chem., 68,2741 (1964). (8) J. A. Weaver and A. B. Metsner, A.I.Ch.E. (Amer. Inst. Chem. Eng.) J . , 12, 656 (1966). Volume 78, Number 7
July 1968
