THERMODYNAMIC CONSIDERATIONS IN METAL-METAL SALTSOLUTIONS
values of 01 are chosen (as described previously for the saturated solution) at selected concentrations in the range covered by our measurements and the quantity (1 - a) is plotted against the left-hand side of eq. 4, a straight line can be fitted through the points. The intercept, 4140 h 50 cal./mole, and slope, -1.5 f 0.3 kcal./mole, correspond to AHl’ and AH1’, respectively. The accord between the experimental value for AHIO and that estimated previously on the assumption of a “weak” second ionization step is excellent and substantiates that assumption. Additional evidence that a second process occurs concomitantly with solution and ionization of silver sulfate is the over-all concentration dependence of the heat of solution. When compared to ‘hormal” electrolytes of the same valence type (alkali sulfates and alkaline earth halides) the slope of A H o h s d against 4% is nearly twice as steep for silver sulfate as for the others.
11
The estimated equilibrium constant for eq. 2 is 0.05, from the work of Righellato and Davies.? The standard free energy is then AGzo = -RT In 0.05 = 1.8 kcal./mole, and the standard entropy increment for eq. 2 is (-1.5 - 1.8)/0.298 = -11 cal./(mole O K . ) . This last datum combined with the ionic entropies for the aqueous silver and sulfate ions can be used to estimate the entropy of the aqueous AgSOi- ion as 33 cal./ (mole OK.). This value is consistent with those of other univalent oxy anions. Acknowledgment.-The authors are grateful to Professor Loren G. Hepler for the use of his laboratory and its facilities and to Professor Clark C. Stephenson, of the Massachusetts Institute of Technology, for his helpful discussion. The partial financial support of the Xational Science Foundation is gratefully acknowledged.
Thermodynamic Considerations in Molten Metal-Metal Salt Solutions’”
by L. E. Topollb Atomics International, A Division of North American Aviation, Canoga Park, California (Received September 16, 1963)
The standard free energies of solution of isolated metal atoms with the molten chloride of that metal were calculated from vapor pressure and solubility data for 34 systems. Based on the values of these standard free energies of dissolution, a useful correlation is obtained. This correlation allows one to classify systems in terms of the magnitude of the energies and to estimate solubilities in some systems where experimental data are not available.
Introduction Solutions of various metals in their respective molten salts have been tjhe subject of numerous investigations.2 It is the purpose Of this paper to the standard free energies of dissolutiorl iIlvolved in the equilibrium between isolated g&SeOUSnletal atollls and nletal atoms dissolved in molten salts from solubility and vapor pressure data and t o correlate these values. The results of this study suggest that the dissolution energy
may be employed as a measure of the interaction energy of isolated metal atoms with the solvent. A classi(1) (a) This work was supported by the Research Division of the E. S. Atomic Energy Commission. It has been presented before the Division of Physical Chemistry a t the 145th National Meeting of the Ameficarl Chemical Society, New York, N. T.,sept. 1963. (b) North American Aviation Science Center, Thousand Oaks, Calif. (2) See, for example, M. Bredig in “Molten Salt Chemistry,” M. Blander, Ed., Interscience Publishers, Inc., New York, N T., 1964,p.
367.
Volume 69,.Vumber 1
.7anuary 1965
L. E. TOPOL
12
fication of these systems, based on the magnitude of these energies, appears to be more meaningful and useful (for the estimation of solubilities in unknown systems) than a correlation based on a nonquantitative property, e.g., subhalide formation. To calculate the solution energy of isolated metal atoms with a fused salt, one may consider the dissolution of a metal as the removal of metal atoms from the bulk metal to the gas phase followed by interaction of the atJoms with the solvent to yield a solution of concentration C. (The process requires the formation of holes in the solvent to accommodate the metal atoms.) The work required to overcome the cohesive binding energy of the metal in the first step is equal to the standard free energy of sublimation or vaporization of the metal to a monatomic gas. This work (along with that involved in the formation of holes) is then compensated by the interaction energy arising in the second step. A similar approach was suggested by Blander3 and used to calculate the interaction energy of a hypothetical alkali-alkali halide melt.
Thermodynamic Considerations To calculate the standard chemical potential or free Of ‘pD* for a consider a solution of a metal M in a molten salt RIX, in equilibrium with metal atoms in the gas at a T’ phase above the is then given by the relation ‘Iemperature
where pM*(g), fM(g), and YM(g) are the standard state chemical potential, fugacity, and activity coefficient, respectively, of the metal in the vapor phase, and p M *(soln), U M (soh), and Y M (soln) are the standard chemical potential, activity, and activity coefficient of the metal in solution. The standard state for the components is taken as the hypothetical solution with a concentration of 1 mole/l. The equilibrium concentration CMof metal in the two phases should be taken in similar units, such as moles/l., in order to eliminate a physically unimportant contribution to the free energy arising from the choice of two different standard states. [n the application of eq. 1 to calculate the change in the standard free energy of a mole of isolated metal atoms going from the gas phase into solution, the concentration or partial pressure of the nietal as monomer atonis in the vapor phase above the solution must be known. Since these values are usually available only for solutions in equilibrium with a pure metal phase, Tht, Journal of Physiral Chemistry
one is restricted to the consideration of such saturated solutions. ’ Then CM(g) can be calculated from the vapor pressure data4 for the pure metal with the aid of the perfect gas relation. Even if an appreciable amount of the gas consists of metal polymers, no error is involved, as long as the concentration of monomer cM(g) is known. The CM(so1n) values used were calculated from the data (given in mole yo) cited in the references in Table I and the densities of the solutions. When no density data for the solutions were available, the densities were estimated from those of the pure components. Even if these estimates were to be wrong by as much as a factor of two, the error in the resulting solution energy would be of the order of only 1 kcal. The activity coefficients also are not available for most of the systems. However, if cM(g) is taken as the concentration of metal monomer atoms, then, at the low metal vapor pressures that prevail at the temperatures under consideration, Y M (g) is unity. For the metal dissolved in the molten salt the standard state has been chosen so that -yM(soln) is unity a t infinite dilution. Consequently, -yM (soln) represents the deviation from Henry’s law, and for the majority of the systems considered its contribution can be assumed to be small, relative to the magnitude of the energies calculated. (Estimates of RT In yM(soln) in typical solutions can be shown to be about 2 to 3 kcal./mole for metal concentrations of as much as 20 mole yo.) For those systems where the saturating phase is not the pure metal, ie., where there is either some salt solubility in the metal or where a solid subhalide is formed, additional corrections must be applied. The solubility of salts in metals is negligible in all but a few systems. In these systems, Raoult’s law was applied to calculate the vapor pressure of the metal above the solution. For systems in which a reaction occurs and a lower valent compound is the separating phase, a more detailed correction is necessary. For example, in the case of the reaction Hg(U
+ HgCM1)
=
HgzClds)
(2)
it can be shown (see Appendix) that AMD* = m*(soln) - m*(g) = RT In aM(g)/
aM(so1n)
+ RT In aMx,(l)/adsoln) + A p 0
(3)
where UMXJ) is the activity of the pure divalent salt and Ar0 is the standard free energy of formation of the (3) M . Blander, as quoted in ref. 2. D. Stull and G . Sinke, “Thermodynamic Properties of the Elements,” American Chemical Society, Waahington, D. .C., 1956. (4)
THERMODYNAMIC COSSIDERATIONS I N
RIETAL-JIETAL
13
SALT SOLCTIONS
Table I : Dissolution Energies of Metal-Metal Salt Systems -AND*,
-APD*,
Vapor pressure of metal,“ atm
T,
System Li-LiCI’ Eia-NaCId K-KCIC Rb-RbCl’ Ag-AgCla Ag-AgCP TI-TICI’
OK
1 64 x 10-4
913 1068 1025
0 344 0 70 0 57
969
Cu-CuCLh
1000
I 23 X lo-”
l\Zg-MgC1zt Ca-CaCIzJ’k Sr-SrClzhaL Ba-BaClP
1073 1093 1112 1151
0 034 I 52 x 10-3 7 I O x 10-3 I 60 x 10-3
Au-.4uChh
1000
0 50 2 1 10 5
1 49 1 56 1 53 2 05
x 10-13 x 10-9 x 10-5
1 1 I 81 3 62
973 973 553 973
psoln,*
18
763 973 923
Zn-ZnClzn Cd-CdClz’ Hg-HgClzP Hg-HgCP
Sletal soly., mole 90
0 076 0 44 0 184
509 2 0 X 10-12
0 03 0 06 0 009 50h
g /cc.
0 30
1 66
2 io 55 15 0
2 06 2 75
System A1-A1IsQ Ga-GazCI@ Ga-GaCla‘ In-InChh TI-TIChh La-LaCl? Ce-CeClsL Nd-NdC1xU
10
11 12
4 80 4 60 5 23
44 40 15 ~
6
6 12 11 17
3 23
1 64 18 0 5.0
3.60 4.55
55 0
7.0
2 35
13.0
11 13 11 7
Vapor pressure of metal,a atm.
T,
20
55
66.ih
koa1 / mole
5
~u-UClS“
OK.
X 10-18 X 10-26
696 453 453 900 923 1193 1050
6.8 4.1 4.1 6.9 3 52 1.5 2.5
1128
7 1
x 10-11 x 10-10 x
X 10-26 x 10-g
x 10-5 X 10-12
1093
1 2
Ni-NiClzw
1250
Fe-FeCla‘
1000
x 10-10 1.2 x 10-14
Sn-SnClzQ Pb-PbCW Pb-PbIz”
Cr-CrClzz Cr-CrClr‘ Mn-JInC1z2
773 973 973 1191 1191 925
10-16
1.0
2.1
x
I 5 1 5
X 10-5
10-15 X 10-5
Metal soly., mole Yo 03 1 92 35 2’ 66 i h 66 ih 11 0 93 30 5
kcal./ mole
P d * ?
g./cc.
55
2 5
2 2 5 5
55
41 41
23 3 20 3 60
57’ -47h 32h 65 61
4 0
-60
5
4 1
4 1
88
91 33 3’
26
io -777
3 2 x 10-4 0 052 0 41
1.7 X 10-10 1.7 X 10-10 2.5 X 10-Q
1.9 35.3r 0 8
4.8 X 10-1Q X 10-18 2 3 X 10-5
35 0 35.0
5 0
5 5
46 21 25
2.2 22 23
61 68‘ 41
2.1 4 65E 3 752
43 38 32
3 09 4 65
-6gh
Sb-SbCIP Bi-BiClsb’ Bi-BiCP
546 553 973
5 7
0 018
* See A. Klemm in “Molten Salt Chemistry,” M. Blander, Ed., Interscience Publishers, Inc., New York, N. Y., a See ref. 4. A. S. Dworkin, H. R. Bronstein, and &I. A. Bredig, J . Phys. Chem., 66, 572 (1962). hI. A. Bredig and H. R. 1964, p. 535. Bronstein, ibid., 64, 64 (1960). e J. W. Johnson rind M. A. Bredig, ibid., 62, 604 (1958). 11.A. Bredig and J. W. Johnson, ibid., 64, 1899 (1960). a J. D. Corbett and S. von Winbush, J . -4m. Chem. Soc., 77, 3964 (1955). Calculated for monovalent
’
‘
salt formation. P. S. Rogers, J. W. Tomlinson, and F. D. Richardson, International Symposium on the Physical Chemistry of Process Metallurgy, Pittsburgh, Pa., 1959, Yol. 8, G. R. St. Pierre, Ed., Interscience Publishers, Inc., Xew York, N. Y., I>. T. Peterson and J. A. Hinkebein, J. Phys. Cheni., 63, 1360 (1959). A. S. Dworkin, H. R . Bronstein, and M. A. 1961, p. 909. Bredig, Discussions Faraday SOC.,32, 188 (1962). L. E. Staffansson, Ph.D. Thesis, London, Dec. 1959. H. Schafer and A. Niklas, Angew. Chem., 64, 611 (1952). J. D. Corbett, S.von Winbush, and F. C. Albers, J . Am. Chem. Soc., 79, 3020 (1957). ’ L. E. Topol and A. L. Landis, ibid., 82, 6291 (1960). S. J. Yosini and S. W. Mayer, J . Phys. Chem., 64, 909 (1960). ‘ N. A. Lange, “Handbook of Chemistry,” XIcGraw-Hill Book Co., Inc., New York, N. Y., 1961. ’ Calculated for divalent salt formation. ’ F. J. Keneshea, Jr., and 11. Cubicciotti, J . Chem. Eng. Data, 6, 507 (1961). t G. W. Mellors and 8. Senderoff, J . Phys. Chem., 63, 1110 (1!359). ’L. F. Druding and J. D. Corbett, J. A m . Chem. SOC.,83, 2462 (1961). ’ D. Cubicciotti, “High Temperature Equilibria in I\Ietal-Metal Halide Systems,” MDDC-1058 (1946). J. W. Johnson, D. Cubicciotti, and C. M.Kelley, J . Phys. Chem., 62, 1107 (1!358). ’ J. D. Corbett, R. J. Clark, and T. F. Munday, J . Inorg. ,VucZ. Chem., 25, 1287 (1963). S. J. 1-osim, A. J. Darnell, W. G. Gehman, and S.W. &layer, J . Phys. Chem., 63, 230 (1959). F. J. Keneshea, Jr., and D. Cubicciotti, ihzd., 62,843 (1958).
solid subhalide from the metal and normal halide. For reacbions of the type 2RI(S,l)
+ JIXa(1) = 3RIX(S)
(4)
2Bi(s,l)
+ BiCl,(l)
(5)
e.g. =
3BiCl(s)
a similar treatment yields pbf*(soln) - m*(g)
=
+
+ ’/zApa
(6)
and for a reaction such as
+
> I ( S , ~ ) 211x3(1) = 311IX*(s) e.y., Sd-SdCI,, one finds
=
RT In ahr(g)/ahf(soln)
+
+
2RT In a ~ ~ ~ ( l ) / a ~ ~ , ( s oApo l n ) (8) From the above relations (eq. 3, 6, and 8) involving subhalide formation and eq. 1, it can be seen that, for dilut,e solutions where a solid subhalide is the separating phase, the magnitude of the standard free energy of dissolution is essentially increased by a quantity proportional to AI”. E‘or the calomel reaction (2), Ap” at 280” is -5.7 kcaL5 F o r the Bi-BiCla system reaction 5, with all three coniponerits in the solid stat,e, has a Ap0 of -2.1 kcal.6 at 45O0K. Correcting ,
RT In aM(g)/aM(soln)
‘/2RT In a>rx3(1) /asm(soln)
pnr*(soln) - pM*(g)
(7)
( 5 ) L. Brewer, “Chemistry and Metallurgy of Miscellaneous Materials: Thermodynamics,” L. L. Quill. Ed., 1IcGraw-Hill Book Co., Inc., New l-ork, N . T., 1950. (6) A. J. Darnell and 9. 3.Tosim. J . Phys. Chem.. 63, 1813 (1959).
Volume 69, Number 1
January 1BfX
14
to the hypothetical liquid for Bi and BiCl, using 5.68' and 2.604 kcal./mole for the heats of fusion of BiCL and Bi, respectively, we obtain a Apo of -2.7 kcal. for reaction 5 at 553'K. For the Au-AuCL, CuCuC12, TI-TICl3, Ga-GaCl3, In-InCL, Cr-CrCL, and Fe-FeCL systems no solid subhalides exist at the temperatures considered in this study. For the Nd-NdC13 system, unfortunately, the value of Abo for subhalide formation is unknown.
L. E. TOPOL
sented here, the values should be correlated a t a common reference temperature such as the temperature where the metal vapor pressures are equal. Unfortunately, such a tabulation is impossible because of the widely different temperature ranges at which the various solutions exist. This being the case, the energies were calculated at approximately 10OO0K. wherever data were available. For most metals the free energy of sublimation or vaporization decreases about 2 to 4 kcal./g.-atom per 100' increase in temperature, Results whereas the change in the solution free energy for metalIn Table I are listed the pertinent data and A ~ D * salt systems for a AT of 100' is generally about 1 to values calculated from eq. 1 , 3 , 6 ,or 8 for various metal2 kcal./mole. Thus, a decrease in the negative partial metal halide systems with the assumption that the molar free energy of dissolution of 1-2 kcal. for a 100' activities can be replaced by concentrations, ie., increase in temperature should occur. The typical that Henry's law and ideal gas behavior hold. The effects of temperature on some of these systems are results indicate that all the energies of dissolution are illustrated by Bi-BiC13 and Hg-HgCl2 at 553 and appreciable, and they illustrate, with a few exceptions, 973OK. and by Ag-AgC1 at 763 and 973'K. some interesting relations between the energies and the The dependence upon the anion is shown by the periodicity of the metals. For the alkali metal sysincrease in magnitude of the dissolution energy as one tems, with the exception of Li, the values of A ~ D * goes from chloride to iodide in the lead system and this a t T 'v 1000'K. are all approximately equal and behavior is typical of most of the cations listed in exhibit only a slight trend if any. The anomalous Table I (with the exception of the Cd system). This behavior of Li is probably related to its small size and variation is due to the increase in solubility of the metal its presence largely as atom dimers2 Liz in the melt. in its halide in the order I > Br > C1. Since the The alkaline earths have dissolution energies of similar solubility of A1 in AlC13 is not known but appears to magnitude, but the energies become increasingly negabe about five orders of magnitude smallerg than in tive with increasing atomic number. Dissolution Al13, a less negative value of A ~ D *of about -40 to energies similar to those for groups I-A and 11-A are - 45 kcal./mole appears likely for the chloride. observed for systems containing the group 11-B metals, The Interaction Energy Zn, Cd, and Hg, and also for TI (in TIC1) and Pb. In the calculation of AMD* values, Henry's law and Much larger energies are observed with the Ag, Sn, ideal gas behavior were assumed. In those cases TI (in TIC&), In (in InCL), Sb, Bi, and Mn solutions, where departure from Henry's law occurs, the corand still larger values are evident with Cu (in CuC12), rections should not be more and in most instances are Au (in AuC13), Al, Ga, the lanthanides, Cr, Fe (in much less than 3 4 kcal., and these corrections will FeCL), S i , and U. (Recent solubility measurementss usually make the dissolution energy less negative. of U in UBr3 and in u13yield virtually identical values (Again the reader is reminded that the standard state of A ~ D *as in U-UC13.) The high energy value for is not the pure metal but a hypothetical solution of the the silver system and the large difference between the 1 mole/l.) metal at tin and lead systems cannot be explained. However, In those systems where salt solubility in the metal the chemical similarity of the lanthanides is again occurs, the solubility is usually extremely small, and shown in the almost identical solution energy values. the extent of departure of the vapor pressure from that Further, since the actinides are also expected to show of the pure metal should also be correspondingly small. mutually similar dissolution energies (about - 90 However, even in those systems where the salt aolukcal./mole as for U-UC13), one would expect a large bility in the metal is appreciable, e.g., K-KCl, Rb-RbC1, * one goes from the lanthanides to increase in A ~ D as the errors involved in the use of Raoult's law should the actinides. Thus, although the values of the dis1-2 kcal., and the correction to not be greater than solution energies in Table I may be somewhat in error, all the systems considered can be categorized arbitrarily in ternis of weak (say, less negative than -25 (7) L. E. Topol, S. W. Mayer, and L. D. Ransom, J . Phys. Chem.. kcal.) or strong (more negative than -35 kcal.) 64,862 (1960). solution energies. (8) See ref. x , Table I. In a compilation of energy values, such as that pre(9) See ref. n, Table I. Thc JouTnd of Physical Chemistry
THERMODYSAMIC COXSIDERATIONS IN METAL-METAL SALTSOLUTIOXS
ApD* tends to cancel that due to the Henry’s law correction. Thus, it should be stated that, although errors in the calculation are apparent, the magnitude of the errors is undoubtedly not large enough to mask the correlations we wish to illustrate. The free energy of dissolution can be considered to consist of two parts: first, the free energy of formation of holes in the solvent large enough to accommodate the metal atoms and, second, the free energy of interaction of the atoms with the molten salt environment. An estimate of the free energy of hole formation leads to a value of +6 k ~ a l . / m o l e ” J -and ~ ~ does not vary by more than =k3 kcal./mole for a wide range of possible hole sizes. This approximate constancy of the free energy of hole formation indicates that the relative values of A ~ D *are essentially in the same order as the relative values of the free energy of interaction of metal atoms with the salt. A delineation of metal-salt systems in terms of solution or interaction energies as a measure of the strength of metal-salt interactions appears to be more meaningful than the use of a nonquantitative property such as subhalide or nonsubhalide formation. As is evident from Table I, there are many systems containing no known solid subhalide that have solution energies as large as or larger than systenis, such as Hg and Bi, with a solid subhalide present. (If A ~ D *for Nd-NdC13 is about the same as that for the other lanthanide systems, it appears likely that the A p o for subhalide formation here is of the order of -1 to -4 kcal.) It should be understood that the existence of a solid subhalide cannot be taken as confirmation that a stable subhalide species exists in the liquid; conversely, the nonoccurrence of a solid subhalide does not preclude the existence of a lower valent cation species in solution. It is interesting to note that the transition metals and all the metals with three or more valence electrons exhibit large dissolution or interaction energies. In addition, many of these latter metals are known to exist in their m e h a s lowervalent cations, e.g., Sb +, Bi +, Ga+,13-15 T1+, In+, Cr+2,Fe+2. (Although the data in Sb-SbIa are consistent with the species Sbf, Corbett and Albers13 assumed S b A entities because these melts are diamagnetic. However. in analogy with Bi-Bi13 solutions Sb+ would be expected to be diamagnetic16 also.) It thus appears that lower oxidation states containing fully paired electrons are favored, and the large energies in the trivalent metal solutions are probably associated with the shift of electrons from a metal atom (or pair of atoms) to localized orbitals around the trivalent cation as depicted in reactions 4 and 7 . For the normal divalent metals, the dimerization reaction (2) is consistent with the tendency for the s-electrons to remain paired.
15
Although there is no evidence a t present for the existence of monovalent monomeric cations of normal or transition divalent metals,l’ except for Ni,l*llgno distinction can be made from existing evidence between entities of the type lM2+2 and metal atoms. Actually, the difference is a subtle one since metal atoms, being very polarizable, would presumably exist in these melts as strongly solvated species of the type M-M+2. The difference between such a solvate and the entity M2+2 is then mainly due to a difference in the degree of interaction between the metal atom and cation. With the monovalent metals, such as the alkali metals, silver, and thallium, the formation of fully paired electronic structures does not appear feasible except by dimerization of the atoms, and it is difficult to postulate a subhalide species although solvated species may exist. (10) The expression for the work involved in the formation of an Avogadro’s number N of holes derived by Reiss, et al.,” is given by Aph*
= p(‘/a)~r*
-/- 4urzuN(1
- 26/r)
where p is the pressure of the fluid, u is the interfacial tension between the fluid and the hole, 6 is a distance of the order of the thickness of the inhomogeneous layer near the hole-fluid interface, and r equals the sum of the radius of the metal atom plus the average radius of the solvent ions. Since the p-V term is negligible (of the order of 1 cal.) for the systems under consideration, the above expression can be approximated by Aph*
E 18.1r2u(1 - 2 6 / r )
where r is expressed in A. and Arb* is given in cal. Taking average radii of 1.5 A. for both metal atoms and salt ions and substituting typical values of r , 26/r, and u of 3.0 A., 0.64,” and 100 dynes/cm.,l* respectively, into the above equation, we find a &h* of approximately 6 kcal. (11) H.Reiss, H.L. Frisch, E. Helfand, and J. L. Lebowitr, J . Chem. Phys., 32, 119 (1960). (12) H. Bloom and J. O’,M. Bockris, “Modern Aspects of Electrochemistry No. 2,” J. O’M.Bockris, Ed., Academic Press Inc., New York, N. Y., 1959, Chapter 3. (13) J. D. Corbett and F. C. Albers, J . Am. Chem. Soc., 82, 533 (1960). (14) L.E. Topol, S. J. Yosim, and R. A. Osteryoung, J . Phys. Chem., 65, 1511 (1961). (15) L. A. Woodward, G. Garton, and H. L. Roberts, J . Chem. S o c . , 3723 (1956). (16) L. E. Topol and L. D. Ransom, J . Chem. Phys., 3 8 , 1663 (1963). (17) L. E.Topol, J . Phys. Chem., 67,2222 (1963) (18) See ref. w , Table I. (19) The evidence for the apparent anomaly with Xi in NiCh results from a cryoscopic study which favors the species Xi+. These results are based on a heat of fusion20 of 18.45 kcal./mole for NiClz, but this value, together with the melting point of the salt, 1282’K.,’8 yields an entropy of fusion of 14.4 e.u. or 4.8. e.u./g.-ion. Virtually all ionic salts have entropies of fusion of 2.5-3.5 e.u./g.-ion, and FeClz and CoClz have values5 of 3.6 and 2.5 e.u./g.-ion, respectively. If the measured heat of fusion of NiCL is in error and a more normal value of 10 kcal./mole is taken, Le., an entropy o f fusion of 3.0e.u./ g.-ion is assumed, then the cryoscopy results are in accord with N1 atoms or Niz+2. Although the removal of an electron to form Niis consistent with the high dissolution energy found in Ni-NiClz, it is difficult to see why Ni- should be more stable than Xi*+*.and a redetermination of the heat of fusion of NiC12 seems warranted. (20) J. P.Coughlin, J . Am. Chem. SOC.,73, 5314 (1951)
Volume 69, 1Vumber 1
January 1966
16
Predictions Since the dissolution or interaction energies of many of the systems discussed previously display a regularity which is not apparent from the solubility data alone, it appears that reasonable estimates of A ~ D *and, thus, the solubility of some unmeasured systems are feasible. Several systems for which solubility predictions can be made are Fe-FeC12, Co-CoCl2, and the rare earth metals in their chlorides. It is interesting to note that the dissolution or interaction energies of the systems composed of the divalent metals (Ca, Cr, Mn, Ni, Cu, and Zn) of the fourth period, which comprises mainly the first transition series, closely parallel the lattice energies for the respective metal chlorides.21s22 The Zn-ZnCl2 dissolution energy appears to be an exception here since its value, - 11 kcal., is much smaller than would be expected, -60 to -70 kcal., from the lattice energy or ligand field correlation. However, if an approximately parallel behavior between the lattice energies and dissolution or interaction energies is assumed for the other metals in this series, ie., if the shielding by the 4s-electrons does not alter the ligand field effect on the 3d-electrons appreciably, estimates of the solubilities of iron and cobalt in their molten chlorides can be made. The Fe-FeC12 system should be especially amenable to a solubility prediction since the number of d-electrons, as well as the ligand field effect, increases continuously as one goes from A h to Co or Ni. (A mrixinium effect should be found for nickel or cobalt, respectively, depending on the environment, ie., whether octahedral- or tetrahedral-like coordinationz2 is present.) In any case, the energy of dissolution for Fe in FeC12 at 1000’K. would be expected to be about - ,54 kcal., and a solubility of approximately lo-* mole % is calculated. For Co in C0C12a t 1000OK. the A ~ D * could vary from about -62 kcal. for octahedral-like coordination to approximately - 70 kcal. for tetrahedral-like coordination. These energies result in maximum solubilities of and 1 mole %, respectively. Although the solubility of neither the iron nor cobalt system has been measured accurately, it is known that the values are very lows and thus are in accard with the probable estimates given above. In the case of the rare earth metal systems all the measured data yield dissolution energies of -62 f 3 kcal. (The Pr-PrC13 system, the solubility in which is 17.8 mole yo metal at l100°K.,23was not included in Table I since the vapor pressure of Pr is not known. However, if a reasonable value of about atm. is assumed for Pr at llOOoIlo mole %) for Tb, Dy, Ho, and Er, and exceedingly high solubilities (possibly complete solution) for Sm, Eu, Tm, Yb, and Lu in their respective chlorides near the melting point of the salt. In these systems of high solubility, large deviations from ideality would be expected to occur and complicate calculations based on the simple method used above. The agreement between the estimated and measured values for the GdGdCls system and the apparent accord for Fe-FeC12 and Co-CoC4 illustrate the value of the compilation of dissolution energies. The Fe-FeC12 case is especially interesting since Fe and Ni, which have approximately equal free energies of vaporization, are shown to have widely different solubilities in their respective salts.
Conclusions On the basis of the magnitude of the standard free energies of dissolution between individual atoms of metals and their molten chlorides, two chief classifications of metal-salt systems can be made. In the first category are systems which exhibit relatively weak solution energies (arbitrarily set as less negative than - 25 kcal.) , and these consist primarily of the mono- and divalent metals. The second category includes the transition metals and the trivalent metals, systems which are characterized by relatively strong solution energies (more negative than -35 kcal.). This classification of metal-salt systems in terms of dissolution energies appears to be a more reasonable and useful delineation than one based on a nonquantitative property such as solid subhalide formation since predictions of solubility from reasonable estimates of solution energies are feasible for many unmeasured systems.
Acknowledgment. The author expresses his gratitude to Dr. M. Blander for his many helpful comments and suggestions. Appendix Designate Hg,C12, HgC12, and the metal in reaction 2 by the subscripts 1, 2, and 11,respectively. Then for the solid phase in equilibrium with the solut,ion (21) T. C. Waddington, “Advances in Inorganic Chemistry and Radiochemistry,” H . J. Emelbus and A. G. Sharpe, Ed., Vol. 1, Academic Press Inc., New York, N . Y., 1959. (22) L. E . Orgel, “An Introduction t o Transition-Metal Chemistry: Ligand Field Theory,” John Wiley and Sons Inc.. New York, N. Y., 1960. (23) A. S. Dworkin, H . R. Bronstein, and M. A. Bredig, J . Phys. Chem., 66, 1201 (1962). (24) J. D. Corbett has recently measured the solubility to be 2.0 mole % at 943’K., private communication.
THERMODYNAMICS OF ADSORPTION OF CARBON DIOXIDE ON ZINC OXIDE
pi" =
pM(so1n)
+ b(so1n)
(1-4)
and
17
we obtain
+
+
+
~ ~ ( s o l n )d s o l n ) = P M * ( g ) RT In aM(g) cc2*(1) RT In az(l) Ap"
where po refers to the pure condensed phase, and Apo is the standard free energy change of reaction 2. Equating eq. 1A and 2A and substituting for ~ M O PM"
:=
m*(g)
+ RT In aM(g)
(34
and for pzo PZ" =
+
PZ*(~) RT In a2(U
+
+
(5A)
Now substituting pt(soln) = pl*(soln)
+ RT In at(soln)
(6A)
into (5a) for ~ ~ ( s o l nand ) p2(soln), recognizing that p2*(1) = pz*(soln), and rearranging terms, we find pM*(soln) - C(M*(g) = RT In aM(g)/aM(soln)
RT In aMx,(l)/aMx,(soln)
(44
+ Apo
+ (7A)
Thermodynamics of Adsorption of Carbon Dioxide on Zinc Oxide
by R. J. Kokes and Rimantas Glemza Department of Chemistry, The Johns Hopkins Univereity, Baltimore, Maryland (Received December 69, 1969)
81618
Chemisorption of carbon dioxide on zinc oxide has been studied between 473 and 588'K. for pressures ranging from lo-' to 1 atm. Partial molal enthalpies and entropies of adsorption were computed by application of the Clausius-Clapeyron equation at fixed coverage; corresponding molar thermodynamic quantities were computed by application of the Clausius-Clapeyron equation at fixed spreading pressure. Experimental data show that the isosteric heat of adsorption a t low coverage is about 25 kcal. ; at coverages above half a monolayer, the isosteric heat is approximately equal to that for the formation of bulk zinc carbonate even though the bulk phase is thermodynamically unstable. Analysis of the data suggests that adsorption of carbon dioxide on zinc oxide results in the formation of surface carbonate groups.
Introduction Although a large number of studies of adsorption on semiconductor oxides have been carried out, very few of these deal with equilibrium adsorption. In this paper we present such data for the ZnO-CO2 system. This system was chosen for three reasons. (a) It yields reproducible data. (b) Bulk zinc carbonate (which is unstable under the conditions of our measurements) is a well-known compound, and it is possible to conipare the properties of the bulk phase with those of the
adsorbed phase. (c) Recent infrared studies' suggest the mode in which carbon dioxide is bound to the surface. Adsorption data for this system have been reported in the past12tabut these data are in conflict.
(1) J. H. Taylor and C. H. Amberg, Can. J . Chem., 39, 535 (1961). (2) P. M. G . Hart and F. Sebba, Trans. Faraday Soc., 5 6 , 557 (1960). (3) T . Kwan, T . Kinuyama, and I;. Fuiita, J . Res. Inst. Catalysis, Hokkaido Uniu., 3 , 31 (1953).
Volume 69,Number 1
January 1906
