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Electrochemical study of the thermodynamic properties of mixing of liquid ZnCl2 + NaCl between 593.15 and 683.15 K
M-689 J. Chem. Thermodynamics 1977,9, 333-343
Electrochemical study of the thermodynamic properties of mixing liquid ZnClt + MaCl between 593.15 and 683.15 K a JEAN-BAPTISTE DOUCET
of
LESOURD, YVES ROCCA-SERRA, b and YVES
Laboratoire de Thermodynamique des Sels Fondus Associe’ au C.N.R.S. UniversitP de Provence, Centre de Saint-J&?me, 13397 Marseille Cedex 4, France (Received 8 July 1976; in revised form 11 October 1976) The Gibbs free energy of mixing and the chemical potentials of the components were derived, for ZnClz + NaCl liquid mixtures between 593.15 and 683.15 K, from the study of electrochemical cells of the form: ZnjZnC& + NaCllpyrexlNaN03/AgC1/Ag. The results were interpreted by a statistical model in which departures from ideality were assumed to result from both “pair” interactions on the cation sublattice and “triplet” interactions of the form Na+-Zn2+ -Na+ ; the former were randomly distributed, and the latter non-randomly distributed. The results were satisfactory and in line with information obtained by other methods.
1. Introduction The thermodynamic properties of mixing of ZnCl, + NaCl have been investigated in the electrochemical experiments of Lantratov and Alabyshev.(l) It seems,however, that the few experimental points given by the latter authors, at one temperature (773.15 K), yield only partial information that should be extended and verified. Other works on similar mixtures w-‘) do not include ZnCl, -l- NaCl. It was therefore found desirable to determine the thermodynamic properties of mixing of ZnCl, + NaCI, and in particular their Gibbs free energies, by using an original e.m.f. method, involving the use of an alkali-cation-selective glass-membranecell. Another feature in favour of further investigations of molten salt mixtures containing zinc halide, and similar ones, lies in their particular structural properties. These have been the object of Raman spectroscopic measurements,(6-8)which extend Q Taken from the thesis of J. B. Lesourd, submitted to the University of Provence, Marseille, France, in partial fuhilment of the requirements for the degree of “Docteur d’Etat es-Sciences Physiques” ; some of the experimental work was also carried out by Y. Rocca-Serra and was reported by this author in his thesis, submitted to the University of Provence, Marseille, France, in partial fulfilment of the requirements for the degree of “Docteur de 3eme Cycle en Physique”. b Present address : Ecole Normale Superieure, BP. 47, Yaounde, Cameroon. 24
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J.-B. LESOURD, Y. ROCCA-SERRA,
AND Y. DOUCET
previous work in pure ZnClz. (9-12) We think that the results presented here should complete our understanding of these systems,which, furthermore, have been chosen as solvents for electrochemical kinetic studies.(13*14)
2. Interpretation of the cell potential The cell under investigation may be represented by Zn~ZnCl,+NaCl\pyrex~NaNO,~AgCl~Ag. Inasmuch as the Pyrex glass junction has been shown to be permeable to Na’ ions only 3(15) the diffusion potential reduces itself to a small asymmetry potential. The cell reaction is: NaCl(v) + AgNO,(r) + Zn(v) = NaNO,(r) + Ag(r) +$ZnCl,(v), where v and r refer, respectively, to the variable composition and reference compartments of this cell. According to our previous work(16) the activity of AgNO, in the reference compartment is given by RT ln(a(AgNO,, r)} = -=JIAGeXch+AGf”(NaCl)
-jl{(Ag-Na)NO,}+I{Na(CI-NO,)}], (1) with reference to pure AgN03, where AGexchis the Gibbs free energy for the exchange reaction : AgCl(pure, s) + NaNO,(pure, 1) = AgNO,(pure, 1)+ NaCl(pure, l), AGfUis the Gibbs free energy of solidification; A stands for the W parameter defined by Guggenheim(17*‘*I for “simple” solutions. Therefore, if one defines AG(Ag/Zn) as AG(Ag/Zn) = @‘(Ag)+ &P(ZnCl,) - &‘(Zn) - @(AgCl),
(2)
the following equation for E is readily obtained: E = (1/2F)[AGexch+ AGfU(NaC1)+ n((Ag - Na)NO,) - L{Na(Cl- NO,)]
- (l/F)AG(Ag/Zn) + (RT/2F)ln{a(NaCl)/a(ZnCI,)) = E” + (R T/2F)ln(a(NaCl)/a(ZnC12)],
(3)
where the v’s have been dropped. E” is calculable from standard thermodynamic data and from mixing(‘9P20) data.
3. Experimental The glassware apparatus used was identical to that used previously.(16921--23)The zinc electrode was a 5 mm diameter, 50 mm height zinc rod prepared by melting chemically pure zinc (Riedel-de Ha&n A.G., W. Germany) under fused zinc chloride. Contact to it was achieved by means of a tungsten lead. The Ag/AgCl electrode has already been described.(l@ Temperatures were maintained in the cell and determined as previously;(‘6) however, the cell and thermocouple e.m.f.‘s were, in this work, measured with a
ELECTROCHEMISTRY
OF LIQUID
ZnCl,+NaCl
335
M.E.C.I.-C.C.M.N. 10 (M.E.C.I., France), lo-channel recording potentiometer. The possible instrumental error was about 1 mV for the cell e.m.f. and 10 PV for the thermocouple e.m.f. The components were first heat-dried at 395 K for 48 h, and then weighed to a 0.1 per cent. The mixture was then heated to 625 K and purified according to the method of Maricle and Hume. (24) Similar methods involving the use of NC1 gas instead of Cl,, have been reported. (13-14)Accordingly, the melt was substituted to a Cl, flow (Gazechim, France) for 45 min; Cl, had been previously dehydrated by passagethrough pure HzS04. Argon (Nertal, L’Air Liquide, France) was bubbled through the melt for 6 h to remove the excessof Cl2 ; this argon had been dehydrated by passagethrough anhydrous CaCl,. The efficiency of this procedure was ascertained by titrating the oxygen-ion impurity by linear sweep chronoamperometry at a platinum microelectrode; it was thus proved that this impurity disappeared after the purification operation. Experiments were carried out at constant NaCl mole fraction? for which about 10 to 20 e.m.f. points at temperatures varying from 593.15 to 683.15 K, under a purified argon flow.
4. A Model for the description of the thermodynamics of ZnC12 + NaCl mixtures The thermodynamics of charge-unsymmetrical molten-salt mixtures has been investigated by several authors,@‘925) under the assumption of random mixing of ions of either sign on two independent sublattices. In mixtures such as ZnCl, + NaCl, however, it seems that preferential configurations occur, according to various experimental data,*(6--8)therefore, the random-mixing assumption is certainly not valid for these mixtures. A theoretical approach to such mixtures has already been proposed by Bastos, Fontana, and Winand. tz6) Here we shall develop a model which, in some respects, is close to that of the last authors, but seemsmore adapted to mixtures such as ZnCl, + NaCl for which one can assume the existence of one non-randomly occurring configuration. The phase diagram of ZnCl, + NaCl(“* 28) reveals the existence of a non-congruently melting compound of formula ZnCl, -2NaC1, whereas various spectroscopic data@-‘) are in favour of the existence of independent ZnCli- tetrahedral configurations, especially in NaCl-containing melts. Therefore, configurations involving Na+ and Zn’ f ions as second-nearestneighbours must be considered within such configurations; those with two Na+ ions must be of special importance, since the presence of two Na” ions as second-nearest neighbours of a Zn2+ is necessary to /Cl\ &/Cl\ ,Cl, Zn * * * indefinite chains which account for spectrobreak up the * * *Zn ,C,, scopic data in pure ZnC1,. (9-12) Consequently, it seemslogical to build up a model taking into account the Na+---Zn’+ -Na+ configuration as leading to departures f A small correction to the mass of ZnCIz had to be made, to take into account the fact that about 1 mole per cent of ZnO, which later reacted with Cl, to yield ZnCl,, was present in the unpurified ZllClz.
336
J.-B. LESQURDi Y. ROCCA-SERRA,
AND Y. DOUCET
from random mixing. This configuration is, however, in the model which follows, by no means exclusive and second nearest-neighbour Na+--Znzf “pairs” will also be taken in consideration, but only on a random-mixing basis. Along these lines, configurations involving more than two Naf ions around a given Zn2+ ion will be considered as the mere addition of a non-randomly occurring Na+-Znzf-Na+ “triplet” and one, or several randomly occurring Na+---Zn2+ “pairs”. Let a be the fraction of Na+ ions not involved in the above configurations. To evaluate the configurational partition function, we have to calculate the number of configurations corresponding to the repartition of N,cx Na+ ions, (A5 - (N,/2)(1 -a)> Zn” ions not involved in the above configurations, together with NJ2 Na’-Zn2+---Na” triplets, occupying three cationic sites on the cation sublattice and assumedto be linear. N1 and N2 are the numbers of Na+ and Zn2+ ions present, respectively. The anionic sublattice does not contribute to any degeneracy, since once the above entities have been placed on the cation sublattice, there is only one manner of arranging the Cl- ions. The calculation of the configurational partition function may be carried out according to Guggenheimo7) and leads to 0, = N![(N,a)!{N,-(N,/2)(1-a))!
{(N,/2)(1-ol)}!]-1(Q!/A7!)Z’2p$‘i’2)(1-a),
(4)
where N = N1 + N2, and Q is given by Q = N,v.+N,-(N,/2)(1-cl)+{(32-4)/Z}(N,/2)(1-a),
(5)
where 2 is the mean number of nearest-neighbour cations of a given cation on the assumed cation sublattice, or the number of second-nearest neighbours of a given cation. pT is a constant depending on the geometrical arrangement of the Na+--Zn2+-Na+ “ triplets”, which however need not be further expressed since ln(l/p,) may be lumped with the A, energy of formation of such a “triplet”. The configurational free energy A, may easily be calculated, using Stirling’s approximation. The remaining A, term includes the energetic contributions to A. One can assume that this term is the sum of, on the one hand, the energy of formation of the Na+--Zn2+--Na+ configurations and, on the other hand, the energy of formation of various other, randomly-occurring “pair” configurations. Taking into account the fact that a Naf ion, part of a Na+--Zn’+--Na’ configuration, may only enter (Z- 1) pairs randomly and that, similarly, a Znzf ion part of a Na”-Zn2+ -Na+ configuration may enter only (Z-2) pairs randomly, and defining as A,, the energy of a Na+---Na+ “contact”, Al2 the energy of a Na+---Zn2+ “contact”, and Az2 the energy of a Zn’+---Zn2+ “contact”, we finally find for A,: A, = (~1/2)(1-ol)(A,-x,A,,-x2A22-A12 f(x,/Z)(l-or)(2A,,+A,,+A22))+
x~x~(ZA,~-(Z/~)A,,-(Z/~)A,,).
(6)
The detail of the calculation is available. (23) It is of interest to notice that the latter expression may be derived from a cycle similar to that of Papatheodorou and Kleppa,‘2’ as A, is the sum of the excessfree energy of an hypothetical solution with random mixing of the cations on the cation sublattice (last term) and of the apparent
JiXECTRQCHEMISTRY
OF LI.QIJXD
ZnClc+NaCl
337
energy? of formation of (x,/2)(1 -a) Na+ -Zn2 ‘---Nit+ configurations. Also of interest is that, provided one neglects the term containing (x,/Z)( 1-a), the apparent energy of formation of one Na+--Zn2+ -Na+ configuration is a linear form (xIP,+x2P,), which is the form proposed by Pelton and Thomson(2g) on an empirical basis. We shall follow them by neglecting the term containing (x1/2)(1-~). Let P, = A,-A,,-A12; P2 = AI-A,,-A,,; and P, = .2X,,Taking this approximation into consideration, we obtain for @m4ll -cww22. (pI -,uy), and (,u2-&) the expressions: fir-&
= RT[alnx,+-J(l-a)ln{x,(l-a)/(2-3x,+ax,)}] -~ZRT(1-2(1-a)/Z)ln(l-2x,(1-a)/Z) ~RTx,x2(da/dx,)ln[ax,(x,-~x,(1-~)}1~2{1-~x,(l-a)/Z)~‘(~x,(l-a)~’~2}] t-x~(~(l-a)P,+P,)+~(1-~)(xf+2x,x,)P,-~x,x2(d~/dx,)(x,P2+x2P,),
(7)
and p2-&
= RT ln(l-~x,+~ax,)-)ZRT In{l-2x,(1-a)/Z) -RTx~(d~/dxl)ln[ax,(x,-~x,(l-oc))1~2(1-2x,(1-~))/Z)~1(~xx,(l -x:(+(1 - cc)P1+ P3} - f(1 - cr)xfP,+ $x:(da/dx,)(x,P,
-IIY))-~‘~] + x,P,), (8)
where CImay be obtained by minimizing A, as has been done previously by 0stvold.(30) Taking &4/aa = 0, we obtain CIas the root of the equation: $(l -a#-(2/Z)x,(l
-c#/{(l
-+x1 +&Xx&Zx,}
= K,
(9)
where K = exp[ - (.qP, +x,P,)/RT]. Equation (9) is formally equivalent to the equation derived by applying the equilibrium law to the reaction: ZnCl, + 2NaCl= ZnCl,Na,, the three components forming an athermal solution, as defined by Guggenheim, (I71 and the ZnCl,Na, “complex” occupying three sites on a quasi-lattice; da/dx, may also be calculated from equation (9).
5. Results and discussion Our primary results for E against T are given in figure 1 and for the liquidus of ZnCl,+NaCl in figure 2. Detailed results are available.(23) The difference (E-E”) may be expressed as a function of two variables (x1 = x(NaC1) and T) and three parameters (PI, P,, and P3). Considering the parameters P as adjustable, and applying to @ = F(E-E”) the expression derived from equations (7), (8), and (9), we obtained good agreement between the experimental results and the theoretical expression by a non-linear regression method due to Romanetti;(31) in this calculation, the thermodynamic data were taken from several sources.(“’ 2op32*33) The optimal values for P,, P,, and P3 were P, = -430 Cal,, mol-I; P, = - 18000 Cal,, t This energy is called here “apparent energy of formation” by comparison with the approach of Pelton and Thomson. WI) It is not equal to the energy of formation of (x1/2)(1 - x) such configurations according to our definition.
338
J.-R. LESOURD,
Y. ROCCA-SERRA,
0.8 -
AND
Y. DOUCET I
I A
A A
A$
00
0.6 -
573.15
A
iy; a:;‘;
l *. X0 x0
,,, gA,
A
pg
A A
AAA
m
A
. xx
* . x
9.
x
00
;.
0
04 O x0 8
I 623.15
673.15 T/K
FIGURE 1. Cell e.m.f.s. X, x(NaC1) = 0.012; 0, x(NaC1) = 0.019; 0, x(NaC1) = 0.023; +, x(NaC1) = 0.040; 0, x(NaC1) = 0.070; A, x(NaC1) = 0.120; 0, x(NaC1) = 0.193; V, x(NaC1) = 0.207; n , x(NaC1) = 0.292; A, x(NaC1) = 0.33; +, x(NaC1) = 0.422.
FIGURE
2. Cell e.m.f.‘s along the ZnCla + NaCl liquidus curve.
mol-I; P, = -5650 Cal,,,mol-I.? Table 1 and figure 3 give the experimental and calculated values of Q,at 673.15 K. From the standard deviation of the experimental values of @within a 95 per cent cotidence level, we estimate the uncertainty interval in @ as + 700 caJh mol- r, or f3 x 10m3V in E. This is much lower than the error found in our previous investigation on the Na electrode in the fused LiCl+KCl t Throughout
this paper 1 calth = 4.184 J.
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339
TABLE 1. Values of @ = F(E - E’), at 673.15 K and along the liquidus curve,? as a function of x1 (a) from the interpolation of our experimental lines (figure 1) and (b) from the adjusted @(x1) function at 673.15 K. The comparison of calculated values at 673.15 K with values obtained experimentally along the liquidus, and therefore at temperatures differing from 673.15 K, is practically valid since the temperature variation of @ with temperature is small. In calculating the adjusted parameters, we actually took into account the variations of 0 with both x1 and T (calth = 4.184 J) @/kcal,, mol-1
TIK 0.012 0.019 0.023 0.040 0.070 0.120 0.193 0.207 0.292 0.33 0.422 0.49 t 0.51 t
673.15 673X 673.15 673.15 673.15 673.15 673.15 673.15 673.15 673.15 673.15 612 625
(4
(‘4
-12.0 -11.7 -11.9 -10.0 -8.8 -9.0 -8.6 -8.6 -8.5 -7.8 -8.6 -8.0 -8.4
-12.40 -11.70 -11.42 -10.54 -9.68 -8.85 -8.49 -8.44 -8.25 -8.18 -7.97 -7.70 -7.58
Xl
TIK
0.528 t 0.53 t 0.54 t 0.545 t 0.55 t 0.56 t 0.562 t 0.561 t 0.57 t 0.58 t 0.59 t 0.62 t
629 631 639 643 646 652 653 655 656 633 668 679
I
-5r-
@/kc&, mol-l (4
(b)
-8.1 -7.7 -7.6 -7.9 -7.1 -7.5 -7.2 -7.1 -7.1 -6.7 -6.5 -6.2
-7.47 -7.46 -7.38 -7.34 -7.29 -7.20 -7.18 -7.13 -7.10 -6.98 -6.85 -6.32
I 0 +
+
Id E
2s-10 Qo 2
I
/
+/f--t-+
+/ / ++ I
-15/L 0
0.50
0.25
0.75
x (NaCI) FIGURE 3. Comparison between values of Q, derived from our experimental results and from the @ function adjusted from our model. +, Experimental (673.15 K) (unsaturated); 0, experimental (liquidus); -, model (673.15 K).
340
J.-B. LESOURD, Y. ROCCA.SRI&A,
AND Y. ‘DOUCET
eutectic (22) but higher than the error we found in another previous work.(21) Considering the fact that @ increases very slowly with x(NaC1) in the interval 0.15 < x(NaC1) < 0.5, this uncertainty accounts for the overlapping of some of the e.m.f.‘s in this interval (figure 1). The variations of CIagainst x(NaC1) at 673.15 K, and of the Gibbs free energy of mixing G against x(NaCl), at both 673.15 K and 873.15 K (extrapolated at the latter temperature) are given in figures 4 and 5, and in tables 2 and 3, respectively, as calculated from our adjusted results. For a and G a minimum is found at about
FIGURE 4. Variation of the fraction c( of “free” Na+ ions with x1 at 673.15 K as adjusted from our model. 0
-1
x(NaC1) FIGURE 5. Variation of the Gibbs free energy of mixing G of ZnCl, + NaCI with x1 as fitted from our results according to our model.
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341
ZnClz+NaC1
TABLE 2. Values of the fraction Q of “free” Na+ ions, at 673.15 K, as a function of x1. Calculations from our model. Values between brackets correspond to extrapolated values relating to an unstable liquid mixture
x1 K
01
0.631 0.1
0.2 0.330
(:::46)
0.3 0.168
(::iOO)
(::;77)
(:)
TABLE 3. Values of G, Gibbs free energy of mixing of liquid ZnC1, + NaCl at 673.15 K and 873.15 K as a function of x1, according to our adjusted results. Values between brackets correspond to extrapolated values relating to an unstable liquid mixture (calth = 4.184 J) G/caltb mol-1 873.15 K 673.15 K
Xl
673.15 K
0 0.1
0 -1060
0 -1190
0.6 0.7
-4979 (-5284)
0.3 0.2 0.4 0.5
-2743 -1923 -3539 -4300
-2948 -2110 -3733 -4456
0.9 0.8 1
(-2603) (-4379) (0)
G/caltl, mol-1 873.15 K -5114 -5322 :z::; (0)
x(NaC1) = 2/3, in agreement with the existenceof the Z&l, *2NaCI compound.(27,28) Finally, we calculated the values of ~xs(ZnC12) against x(NaC1) from our adjusted results at both 673.15 K and 873.15K (table 4). The extrapolated values of pxS(ZnCI,) at 873.15 K have been plotted against x(NaC1) in figure 6 for comparison with the data of Robertson and Kucharski(4) concerning similar systems at 873.15 K. We seethat our results are in good agreement with the trend that may be deduced from the data of Robertson and Kucharski: the excesschemical potentials become more negative as the size of the alkali ion increases. On the other hand, the data of TABLE 4. Variations of @a(ZnClz) with x1, at 673.15 and 873.15 K, as calculated from our adjusted results. Values between brackets correspond to extrapolated values relating to an unstable liquid mixture (~11th = 4.184 J) Xl 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35
~Xs(ZnCl,)/cal,, mol-l 673.15 K
0 -7.1 -11.0 4.1 41.1 94.5 157.4 220.9
873.15 K
0 -7.1 -14.9 -0.9
13.9 53.1
101.3 149.4
Xl 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
.S”(ZnCl,)/cal,, mol - 1 673.15 K 873.15 K 274.9 305.2 288.3 178.6 -141.7
(-1190.3) (-5908.1) (-10083)
186.4 195.0 146.8 -12.1 408.6 -1449.8 -4626.0 -8956.8
342
J.-B. LESOURD, Y. ROCCA-SERRA,
AND Y. DOUCET
Lantratov and Alabyshev, (‘) which we also plotted in figure 6, do not agree with that trend. As those data comprise only a few points, the comparison with the data of Robertson and Kucharski(4) seemto be in our favour.
FIGURE 6. Comparison of the variations of $s(ZnCl,) with x(MCl), in several ZnCl, + MCI mixtures. Robertson and Kucharski (*) at 873.15 K: 1, ZnClz + CsCl; 2, ZnClz + RbCl; 3, ZnClz + KCl. Lantratov and Alabyshev w at 773.15 K: +, ZnCiz + NaCI. 4, Extrapolation of our results at 873.15 K according to our model.
6. Conclusion Our experimental results are well described by a lattice model, and insert favourably into the trend observed by Robertson and Kucharski,‘4) as a function of size of the alkali ion. It might be interesting to obtain further thermodynamic results on this mixture at higher temperatures, and to carry out electrochemical kinetic investigations in ZnCl,-containing mixtures, so as to complete our understanding of the structure of such mixtures. The validity of the model proposed here should be tested with other similar mixtures; in a slightly modified version it has already been applied successfully to CdCI, f KC1.(34) The authors wish to thank Professor A. Peneloux for helpful criticism and discussion of the manuscript. REFERENCES 1. Lantratov, M. F.; Alabyshev, A. F. J. Appl. Chem. U.S.S.R. 1953,26, 235; 1953,26, 321. 2. Papatheodorou, G. N.; Kleppa, 0. J. 2. Anorg. AN. Chem. 1973,401, 132. 3. Dijkhuis, C.; Dijkhuis, R.; Jam. G. Chem. Rev. 1968,68, 253. 4. Robertson, R. J.; Kucharski, A. S. Can. J. Chem. 1973, 51, 3114. 5. Markov, B. F.; Volkov. S. V. Ukr. Khim. Zh. 1964, 30, 545; 1964, 30, 906.
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Smith, G. P.; Boston, C. R.; Brynestad, J. J. Chem. Phys. 1966, 45, 829. Gruen, D. M.; McBeth, R. L. Appl. Chem. 1963, 6, 23. Angell, C. A.; Gruen, D. M. J. Am. Chem. Sot. 1966, 88, 5192. Irish, D. E.; Young, T. F. J. Chem. Phys. 1965,43, 1765. Mayer, J. R. ; Evans, J. C. ; Lo. G. V.-S. J. Electrochem. Sot. 1966, 113, 158. Ellis, R. B. J. Electrochem. Sot. 1966, 113, 485. Bues, W. Z. Anorg. Allg. Chem. 1955, 279, 104. Rubel, G.; Gross, M. Corros. Sci. 1975, 15, 261. :% Deanhardt, M. L.; Hanck, K. W. J. Electrochem. Sot. 1975, 122, 1627. 15. Bartlett, H. E. ; Crowther, P. Electrochim. Actu. 1970, 1.5,681. 16. Lesourd, J. B.; Vailet, C. ; Doucet, Y. J. Electroanal. Chem. 1973, 48, 99. 17. Guggenheim, E. A. Mixtures. Clarendon Press: Oxford. 1952. Guggenheim, E. A. Thermodynamics. 5th Edition. North Holland: Amsterdam. 1967. :t Boxall, L. G.; Johnson, K. E. Trans. Fauaday. Sot. 1971, 67, 1433. 20: Saboungi, M. L.: Valiet, C.; Doucet, Y. J. Phys. Chem. 1973, 77. 1699. 21. Lesourd; J. B.; Flambeck, J; A. Can: J. Chem. 1969, 47, 3387. Pean, H.; Lesourd, J. B.; Doucet, Y. C. R. Acad. Sci. (Paris), SQ.C. 1973, 277, 541. u”: Lesourd, J. B. These de Doctorat d’Etat &s-SciencesPhysiques, Universite de Provence: Marseille. 1975. 24. Maricle, D. L.; Hume, D. N. J. Electrochem. Sot. 1960, 107, 354. 25. Forland, T. Thermodynamic properties of fused salts, in Fused salts. Sundheim, B. R. : editor. McGraw Hill: New York. 1964. Bastes, H.; Fontana, A.; Winand, R. Silicates Industriels 1976, 31, 129. Evseeva, N. N.; Bergman, A. G. Izv. Sektora Fiz. Khin. Anal. Inst. Obshch. Neorg. Khim., Akad. Nauk. SSSR. 1952,21, 212. 28. Levin, E. M.; Robins, C. R.; McMurdie, H. F. Phase Diagrams for Ceramists. Supal. Amer. Chem. Sot. : Columbus, Ohio. U.S.A. 304, 1969. 29. Pelton. A. D.: Thomson. W. T. Can. J. Chem. 1970. 48. 1585. 30. OstvoId, T. Doctoral Thesis, Technical University of Norway, Trondheim. 1971. 31. Romanetti, R. These de Doctorat d’Etat es-Sciences Physiques, Universite de Provence, Marseille. 1973. 32. Rossini, F. D.; Wagman, D. D.; Evans, W. H.; Levine, S.; Jaffe, I. Nut. But-. Stand. U.S. Circ. Nr. 500. U.S. Government Printing O&e: Washington, D.C. 1952. 33. Kelley, K. K. U.S. Bur. Mines, Bull. 584. U.S. Government Printing Office: Washington, D.C. 1960. 34. Cristol, B.; Houriez, J.; Baiesdent, D. Communication, JournCe d’Etudes sur les Sels Fondus, Mavseile May 1976. Cristol, B. These de Doctorat d’Etat es-Sciences Physiques. Institut National Polytechnique, Nancy. 1976. 6. 7. 8. 9. 10. 11. 12.
Electrochemical study of the thermodynamic properties of mixing liquid ZnClt + MaCl between 593.15 and 683.15 K a JEAN-BAPTISTE DOUCET
of
LESOURD, YVES ROCCA-SERRA, b and YVES
Laboratoire de Thermodynamique des Sels Fondus Associe’ au C.N.R.S. UniversitP de Provence, Centre de Saint-J&?me, 13397 Marseille Cedex 4, France (Received 8 July 1976; in revised form 11 October 1976) The Gibbs free energy of mixing and the chemical potentials of the components were derived, for ZnClz + NaCl liquid mixtures between 593.15 and 683.15 K, from the study of electrochemical cells of the form: ZnjZnC& + NaCllpyrexlNaN03/AgC1/Ag. The results were interpreted by a statistical model in which departures from ideality were assumed to result from both “pair” interactions on the cation sublattice and “triplet” interactions of the form Na+-Zn2+ -Na+ ; the former were randomly distributed, and the latter non-randomly distributed. The results were satisfactory and in line with information obtained by other methods.
1. Introduction The thermodynamic properties of mixing of ZnCl, + NaCl have been investigated in the electrochemical experiments of Lantratov and Alabyshev.(l) It seems,however, that the few experimental points given by the latter authors, at one temperature (773.15 K), yield only partial information that should be extended and verified. Other works on similar mixtures w-‘) do not include ZnCl, -l- NaCl. It was therefore found desirable to determine the thermodynamic properties of mixing of ZnCl, + NaCI, and in particular their Gibbs free energies, by using an original e.m.f. method, involving the use of an alkali-cation-selective glass-membranecell. Another feature in favour of further investigations of molten salt mixtures containing zinc halide, and similar ones, lies in their particular structural properties. These have been the object of Raman spectroscopic measurements,(6-8)which extend Q Taken from the thesis of J. B. Lesourd, submitted to the University of Provence, Marseille, France, in partial fuhilment of the requirements for the degree of “Docteur d’Etat es-Sciences Physiques” ; some of the experimental work was also carried out by Y. Rocca-Serra and was reported by this author in his thesis, submitted to the University of Provence, Marseille, France, in partial fulfilment of the requirements for the degree of “Docteur de 3eme Cycle en Physique”. b Present address : Ecole Normale Superieure, BP. 47, Yaounde, Cameroon. 24
334
J.-B. LESOURD, Y. ROCCA-SERRA,
AND Y. DOUCET
previous work in pure ZnClz. (9-12) We think that the results presented here should complete our understanding of these systems,which, furthermore, have been chosen as solvents for electrochemical kinetic studies.(13*14)
2. Interpretation of the cell potential The cell under investigation may be represented by Zn~ZnCl,+NaCl\pyrex~NaNO,~AgCl~Ag. Inasmuch as the Pyrex glass junction has been shown to be permeable to Na’ ions only 3(15) the diffusion potential reduces itself to a small asymmetry potential. The cell reaction is: NaCl(v) + AgNO,(r) + Zn(v) = NaNO,(r) + Ag(r) +$ZnCl,(v), where v and r refer, respectively, to the variable composition and reference compartments of this cell. According to our previous work(16) the activity of AgNO, in the reference compartment is given by RT ln(a(AgNO,, r)} = -=JIAGeXch+AGf”(NaCl)
-jl{(Ag-Na)NO,}+I{Na(CI-NO,)}], (1) with reference to pure AgN03, where AGexchis the Gibbs free energy for the exchange reaction : AgCl(pure, s) + NaNO,(pure, 1) = AgNO,(pure, 1)+ NaCl(pure, l), AGfUis the Gibbs free energy of solidification; A stands for the W parameter defined by Guggenheim(17*‘*I for “simple” solutions. Therefore, if one defines AG(Ag/Zn) as AG(Ag/Zn) = @‘(Ag)+ &P(ZnCl,) - &‘(Zn) - @(AgCl),
(2)
the following equation for E is readily obtained: E = (1/2F)[AGexch+ AGfU(NaC1)+ n((Ag - Na)NO,) - L{Na(Cl- NO,)]
- (l/F)AG(Ag/Zn) + (RT/2F)ln{a(NaCl)/a(ZnCI,)) = E” + (R T/2F)ln(a(NaCl)/a(ZnC12)],
(3)
where the v’s have been dropped. E” is calculable from standard thermodynamic data and from mixing(‘9P20) data.
3. Experimental The glassware apparatus used was identical to that used previously.(16921--23)The zinc electrode was a 5 mm diameter, 50 mm height zinc rod prepared by melting chemically pure zinc (Riedel-de Ha&n A.G., W. Germany) under fused zinc chloride. Contact to it was achieved by means of a tungsten lead. The Ag/AgCl electrode has already been described.(l@ Temperatures were maintained in the cell and determined as previously;(‘6) however, the cell and thermocouple e.m.f.‘s were, in this work, measured with a
ELECTROCHEMISTRY
OF LIQUID
ZnCl,+NaCl
335
M.E.C.I.-C.C.M.N. 10 (M.E.C.I., France), lo-channel recording potentiometer. The possible instrumental error was about 1 mV for the cell e.m.f. and 10 PV for the thermocouple e.m.f. The components were first heat-dried at 395 K for 48 h, and then weighed to a 0.1 per cent. The mixture was then heated to 625 K and purified according to the method of Maricle and Hume. (24) Similar methods involving the use of NC1 gas instead of Cl,, have been reported. (13-14)Accordingly, the melt was substituted to a Cl, flow (Gazechim, France) for 45 min; Cl, had been previously dehydrated by passagethrough pure HzS04. Argon (Nertal, L’Air Liquide, France) was bubbled through the melt for 6 h to remove the excessof Cl2 ; this argon had been dehydrated by passagethrough anhydrous CaCl,. The efficiency of this procedure was ascertained by titrating the oxygen-ion impurity by linear sweep chronoamperometry at a platinum microelectrode; it was thus proved that this impurity disappeared after the purification operation. Experiments were carried out at constant NaCl mole fraction? for which about 10 to 20 e.m.f. points at temperatures varying from 593.15 to 683.15 K, under a purified argon flow.
4. A Model for the description of the thermodynamics of ZnC12 + NaCl mixtures The thermodynamics of charge-unsymmetrical molten-salt mixtures has been investigated by several authors,@‘925) under the assumption of random mixing of ions of either sign on two independent sublattices. In mixtures such as ZnCl, + NaCl, however, it seems that preferential configurations occur, according to various experimental data,*(6--8)therefore, the random-mixing assumption is certainly not valid for these mixtures. A theoretical approach to such mixtures has already been proposed by Bastos, Fontana, and Winand. tz6) Here we shall develop a model which, in some respects, is close to that of the last authors, but seemsmore adapted to mixtures such as ZnCl, + NaCl for which one can assume the existence of one non-randomly occurring configuration. The phase diagram of ZnCl, + NaCl(“* 28) reveals the existence of a non-congruently melting compound of formula ZnCl, -2NaC1, whereas various spectroscopic data@-‘) are in favour of the existence of independent ZnCli- tetrahedral configurations, especially in NaCl-containing melts. Therefore, configurations involving Na+ and Zn’ f ions as second-nearestneighbours must be considered within such configurations; those with two Na+ ions must be of special importance, since the presence of two Na” ions as second-nearest neighbours of a Zn2+ is necessary to /Cl\ &/Cl\ ,Cl, Zn * * * indefinite chains which account for spectrobreak up the * * *Zn ,C,, scopic data in pure ZnC1,. (9-12) Consequently, it seemslogical to build up a model taking into account the Na+---Zn’+ -Na+ configuration as leading to departures f A small correction to the mass of ZnCIz had to be made, to take into account the fact that about 1 mole per cent of ZnO, which later reacted with Cl, to yield ZnCl,, was present in the unpurified ZllClz.
336
J.-B. LESQURDi Y. ROCCA-SERRA,
AND Y. DOUCET
from random mixing. This configuration is, however, in the model which follows, by no means exclusive and second nearest-neighbour Na+--Znzf “pairs” will also be taken in consideration, but only on a random-mixing basis. Along these lines, configurations involving more than two Naf ions around a given Zn2+ ion will be considered as the mere addition of a non-randomly occurring Na+-Znzf-Na+ “triplet” and one, or several randomly occurring Na+---Zn2+ “pairs”. Let a be the fraction of Na+ ions not involved in the above configurations. To evaluate the configurational partition function, we have to calculate the number of configurations corresponding to the repartition of N,cx Na+ ions, (A5 - (N,/2)(1 -a)> Zn” ions not involved in the above configurations, together with NJ2 Na’-Zn2+---Na” triplets, occupying three cationic sites on the cation sublattice and assumedto be linear. N1 and N2 are the numbers of Na+ and Zn2+ ions present, respectively. The anionic sublattice does not contribute to any degeneracy, since once the above entities have been placed on the cation sublattice, there is only one manner of arranging the Cl- ions. The calculation of the configurational partition function may be carried out according to Guggenheimo7) and leads to 0, = N![(N,a)!{N,-(N,/2)(1-a))!
{(N,/2)(1-ol)}!]-1(Q!/A7!)Z’2p$‘i’2)(1-a),
(4)
where N = N1 + N2, and Q is given by Q = N,v.+N,-(N,/2)(1-cl)+{(32-4)/Z}(N,/2)(1-a),
(5)
where 2 is the mean number of nearest-neighbour cations of a given cation on the assumed cation sublattice, or the number of second-nearest neighbours of a given cation. pT is a constant depending on the geometrical arrangement of the Na+--Zn2+-Na+ “ triplets”, which however need not be further expressed since ln(l/p,) may be lumped with the A, energy of formation of such a “triplet”. The configurational free energy A, may easily be calculated, using Stirling’s approximation. The remaining A, term includes the energetic contributions to A. One can assume that this term is the sum of, on the one hand, the energy of formation of the Na+--Zn2+--Na+ configurations and, on the other hand, the energy of formation of various other, randomly-occurring “pair” configurations. Taking into account the fact that a Naf ion, part of a Na+--Zn’+--Na’ configuration, may only enter (Z- 1) pairs randomly and that, similarly, a Znzf ion part of a Na”-Zn2+ -Na+ configuration may enter only (Z-2) pairs randomly, and defining as A,, the energy of a Na+---Na+ “contact”, Al2 the energy of a Na+---Zn2+ “contact”, and Az2 the energy of a Zn’+---Zn2+ “contact”, we finally find for A,: A, = (~1/2)(1-ol)(A,-x,A,,-x2A22-A12 f(x,/Z)(l-or)(2A,,+A,,+A22))+
x~x~(ZA,~-(Z/~)A,,-(Z/~)A,,).
(6)
The detail of the calculation is available. (23) It is of interest to notice that the latter expression may be derived from a cycle similar to that of Papatheodorou and Kleppa,‘2’ as A, is the sum of the excessfree energy of an hypothetical solution with random mixing of the cations on the cation sublattice (last term) and of the apparent
JiXECTRQCHEMISTRY
OF LI.QIJXD
ZnClc+NaCl
337
energy? of formation of (x,/2)(1 -a) Na+ -Zn2 ‘---Nit+ configurations. Also of interest is that, provided one neglects the term containing (x,/Z)( 1-a), the apparent energy of formation of one Na+--Zn2+ -Na+ configuration is a linear form (xIP,+x2P,), which is the form proposed by Pelton and Thomson(2g) on an empirical basis. We shall follow them by neglecting the term containing (x1/2)(1-~). Let P, = A,-A,,-A12; P2 = AI-A,,-A,,; and P, = .2X,,Taking this approximation into consideration, we obtain for @m4ll -cww22. (pI -,uy), and (,u2-&) the expressions: fir-&
= RT[alnx,+-J(l-a)ln{x,(l-a)/(2-3x,+ax,)}] -~ZRT(1-2(1-a)/Z)ln(l-2x,(1-a)/Z) ~RTx,x2(da/dx,)ln[ax,(x,-~x,(1-~)}1~2{1-~x,(l-a)/Z)~‘(~x,(l-a)~’~2}] t-x~(~(l-a)P,+P,)+~(1-~)(xf+2x,x,)P,-~x,x2(d~/dx,)(x,P2+x2P,),
(7)
and p2-&
= RT ln(l-~x,+~ax,)-)ZRT In{l-2x,(1-a)/Z) -RTx~(d~/dxl)ln[ax,(x,-~x,(l-oc))1~2(1-2x,(1-~))/Z)~1(~xx,(l -x:(+(1 - cc)P1+ P3} - f(1 - cr)xfP,+ $x:(da/dx,)(x,P,
-IIY))-~‘~] + x,P,), (8)
where CImay be obtained by minimizing A, as has been done previously by 0stvold.(30) Taking &4/aa = 0, we obtain CIas the root of the equation: $(l -a#-(2/Z)x,(l
-c#/{(l
-+x1 +&Xx&Zx,}
= K,
(9)
where K = exp[ - (.qP, +x,P,)/RT]. Equation (9) is formally equivalent to the equation derived by applying the equilibrium law to the reaction: ZnCl, + 2NaCl= ZnCl,Na,, the three components forming an athermal solution, as defined by Guggenheim, (I71 and the ZnCl,Na, “complex” occupying three sites on a quasi-lattice; da/dx, may also be calculated from equation (9).
5. Results and discussion Our primary results for E against T are given in figure 1 and for the liquidus of ZnCl,+NaCl in figure 2. Detailed results are available.(23) The difference (E-E”) may be expressed as a function of two variables (x1 = x(NaC1) and T) and three parameters (PI, P,, and P3). Considering the parameters P as adjustable, and applying to @ = F(E-E”) the expression derived from equations (7), (8), and (9), we obtained good agreement between the experimental results and the theoretical expression by a non-linear regression method due to Romanetti;(31) in this calculation, the thermodynamic data were taken from several sources.(“’ 2op32*33) The optimal values for P,, P,, and P3 were P, = -430 Cal,, mol-I; P, = - 18000 Cal,, t This energy is called here “apparent energy of formation” by comparison with the approach of Pelton and Thomson. WI) It is not equal to the energy of formation of (x1/2)(1 - x) such configurations according to our definition.
338
J.-R. LESOURD,
Y. ROCCA-SERRA,
0.8 -
AND
Y. DOUCET I
I A
A A
A$
00
0.6 -
573.15
A
iy; a:;‘;
l *. X0 x0
,,, gA,
A
pg
A A
AAA
m
A
. xx
* . x
9.
x
00
;.
0
04 O x0 8
I 623.15
673.15 T/K
FIGURE 1. Cell e.m.f.s. X, x(NaC1) = 0.012; 0, x(NaC1) = 0.019; 0, x(NaC1) = 0.023; +, x(NaC1) = 0.040; 0, x(NaC1) = 0.070; A, x(NaC1) = 0.120; 0, x(NaC1) = 0.193; V, x(NaC1) = 0.207; n , x(NaC1) = 0.292; A, x(NaC1) = 0.33; +, x(NaC1) = 0.422.
FIGURE
2. Cell e.m.f.‘s along the ZnCla + NaCl liquidus curve.
mol-I; P, = -5650 Cal,,,mol-I.? Table 1 and figure 3 give the experimental and calculated values of Q,at 673.15 K. From the standard deviation of the experimental values of @within a 95 per cent cotidence level, we estimate the uncertainty interval in @ as + 700 caJh mol- r, or f3 x 10m3V in E. This is much lower than the error found in our previous investigation on the Na electrode in the fused LiCl+KCl t Throughout
this paper 1 calth = 4.184 J.
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339
TABLE 1. Values of @ = F(E - E’), at 673.15 K and along the liquidus curve,? as a function of x1 (a) from the interpolation of our experimental lines (figure 1) and (b) from the adjusted @(x1) function at 673.15 K. The comparison of calculated values at 673.15 K with values obtained experimentally along the liquidus, and therefore at temperatures differing from 673.15 K, is practically valid since the temperature variation of @ with temperature is small. In calculating the adjusted parameters, we actually took into account the variations of 0 with both x1 and T (calth = 4.184 J) @/kcal,, mol-1
TIK 0.012 0.019 0.023 0.040 0.070 0.120 0.193 0.207 0.292 0.33 0.422 0.49 t 0.51 t
673.15 673X 673.15 673.15 673.15 673.15 673.15 673.15 673.15 673.15 673.15 612 625
(4
(‘4
-12.0 -11.7 -11.9 -10.0 -8.8 -9.0 -8.6 -8.6 -8.5 -7.8 -8.6 -8.0 -8.4
-12.40 -11.70 -11.42 -10.54 -9.68 -8.85 -8.49 -8.44 -8.25 -8.18 -7.97 -7.70 -7.58
Xl
TIK
0.528 t 0.53 t 0.54 t 0.545 t 0.55 t 0.56 t 0.562 t 0.561 t 0.57 t 0.58 t 0.59 t 0.62 t
629 631 639 643 646 652 653 655 656 633 668 679
I
-5r-
@/kc&, mol-l (4
(b)
-8.1 -7.7 -7.6 -7.9 -7.1 -7.5 -7.2 -7.1 -7.1 -6.7 -6.5 -6.2
-7.47 -7.46 -7.38 -7.34 -7.29 -7.20 -7.18 -7.13 -7.10 -6.98 -6.85 -6.32
I 0 +
+
Id E
2s-10 Qo 2
I
/
+/f--t-+
+/ / ++ I
-15/L 0
0.50
0.25
0.75
x (NaCI) FIGURE 3. Comparison between values of Q, derived from our experimental results and from the @ function adjusted from our model. +, Experimental (673.15 K) (unsaturated); 0, experimental (liquidus); -, model (673.15 K).
340
J.-B. LESOURD, Y. ROCCA.SRI&A,
AND Y. ‘DOUCET
eutectic (22) but higher than the error we found in another previous work.(21) Considering the fact that @ increases very slowly with x(NaC1) in the interval 0.15 < x(NaC1) < 0.5, this uncertainty accounts for the overlapping of some of the e.m.f.‘s in this interval (figure 1). The variations of CIagainst x(NaC1) at 673.15 K, and of the Gibbs free energy of mixing G against x(NaCl), at both 673.15 K and 873.15 K (extrapolated at the latter temperature) are given in figures 4 and 5, and in tables 2 and 3, respectively, as calculated from our adjusted results. For a and G a minimum is found at about
FIGURE 4. Variation of the fraction c( of “free” Na+ ions with x1 at 673.15 K as adjusted from our model. 0
-1
x(NaC1) FIGURE 5. Variation of the Gibbs free energy of mixing G of ZnCl, + NaCI with x1 as fitted from our results according to our model.
ELECTROCHEMISTRY
OF LIQUID
341
ZnClz+NaC1
TABLE 2. Values of the fraction Q of “free” Na+ ions, at 673.15 K, as a function of x1. Calculations from our model. Values between brackets correspond to extrapolated values relating to an unstable liquid mixture
x1 K
01
0.631 0.1
0.2 0.330
(:::46)
0.3 0.168
(::iOO)
(::;77)
(:)
TABLE 3. Values of G, Gibbs free energy of mixing of liquid ZnC1, + NaCl at 673.15 K and 873.15 K as a function of x1, according to our adjusted results. Values between brackets correspond to extrapolated values relating to an unstable liquid mixture (calth = 4.184 J) G/caltb mol-1 873.15 K 673.15 K
Xl
673.15 K
0 0.1
0 -1060
0 -1190
0.6 0.7
-4979 (-5284)
0.3 0.2 0.4 0.5
-2743 -1923 -3539 -4300
-2948 -2110 -3733 -4456
0.9 0.8 1
(-2603) (-4379) (0)
G/caltl, mol-1 873.15 K -5114 -5322 :z::; (0)
x(NaC1) = 2/3, in agreement with the existenceof the Z&l, *2NaCI compound.(27,28) Finally, we calculated the values of ~xs(ZnC12) against x(NaC1) from our adjusted results at both 673.15 K and 873.15K (table 4). The extrapolated values of pxS(ZnCI,) at 873.15 K have been plotted against x(NaC1) in figure 6 for comparison with the data of Robertson and Kucharski(4) concerning similar systems at 873.15 K. We seethat our results are in good agreement with the trend that may be deduced from the data of Robertson and Kucharski: the excesschemical potentials become more negative as the size of the alkali ion increases. On the other hand, the data of TABLE 4. Variations of @a(ZnClz) with x1, at 673.15 and 873.15 K, as calculated from our adjusted results. Values between brackets correspond to extrapolated values relating to an unstable liquid mixture (~11th = 4.184 J) Xl 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35
~Xs(ZnCl,)/cal,, mol-l 673.15 K
0 -7.1 -11.0 4.1 41.1 94.5 157.4 220.9
873.15 K
0 -7.1 -14.9 -0.9
13.9 53.1
101.3 149.4
Xl 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
.S”(ZnCl,)/cal,, mol - 1 673.15 K 873.15 K 274.9 305.2 288.3 178.6 -141.7
(-1190.3) (-5908.1) (-10083)
186.4 195.0 146.8 -12.1 408.6 -1449.8 -4626.0 -8956.8
342
J.-B. LESOURD, Y. ROCCA-SERRA,
AND Y. DOUCET
Lantratov and Alabyshev, (‘) which we also plotted in figure 6, do not agree with that trend. As those data comprise only a few points, the comparison with the data of Robertson and Kucharski(4) seemto be in our favour.
FIGURE 6. Comparison of the variations of $s(ZnCl,) with x(MCl), in several ZnCl, + MCI mixtures. Robertson and Kucharski (*) at 873.15 K: 1, ZnClz + CsCl; 2, ZnClz + RbCl; 3, ZnClz + KCl. Lantratov and Alabyshev w at 773.15 K: +, ZnCiz + NaCI. 4, Extrapolation of our results at 873.15 K according to our model.
6. Conclusion Our experimental results are well described by a lattice model, and insert favourably into the trend observed by Robertson and Kucharski,‘4) as a function of size of the alkali ion. It might be interesting to obtain further thermodynamic results on this mixture at higher temperatures, and to carry out electrochemical kinetic investigations in ZnCl,-containing mixtures, so as to complete our understanding of the structure of such mixtures. The validity of the model proposed here should be tested with other similar mixtures; in a slightly modified version it has already been applied successfully to CdCI, f KC1.(34) The authors wish to thank Professor A. Peneloux for helpful criticism and discussion of the manuscript. REFERENCES 1. Lantratov, M. F.; Alabyshev, A. F. J. Appl. Chem. U.S.S.R. 1953,26, 235; 1953,26, 321. 2. Papatheodorou, G. N.; Kleppa, 0. J. 2. Anorg. AN. Chem. 1973,401, 132. 3. Dijkhuis, C.; Dijkhuis, R.; Jam. G. Chem. Rev. 1968,68, 253. 4. Robertson, R. J.; Kucharski, A. S. Can. J. Chem. 1973, 51, 3114. 5. Markov, B. F.; Volkov. S. V. Ukr. Khim. Zh. 1964, 30, 545; 1964, 30, 906.
ELECTROCHEMISTRY
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ZnCl, +NaCl
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Smith, G. P.; Boston, C. R.; Brynestad, J. J. Chem. Phys. 1966, 45, 829. Gruen, D. M.; McBeth, R. L. Appl. Chem. 1963, 6, 23. Angell, C. A.; Gruen, D. M. J. Am. Chem. Sot. 1966, 88, 5192. Irish, D. E.; Young, T. F. J. Chem. Phys. 1965,43, 1765. Mayer, J. R. ; Evans, J. C. ; Lo. G. V.-S. J. Electrochem. Sot. 1966, 113, 158. Ellis, R. B. J. Electrochem. Sot. 1966, 113, 485. Bues, W. Z. Anorg. Allg. Chem. 1955, 279, 104. Rubel, G.; Gross, M. Corros. Sci. 1975, 15, 261. :% Deanhardt, M. L.; Hanck, K. W. J. Electrochem. Sot. 1975, 122, 1627. 15. Bartlett, H. E. ; Crowther, P. Electrochim. Actu. 1970, 1.5,681. 16. Lesourd, J. B.; Vailet, C. ; Doucet, Y. J. Electroanal. Chem. 1973, 48, 99. 17. Guggenheim, E. A. Mixtures. Clarendon Press: Oxford. 1952. Guggenheim, E. A. Thermodynamics. 5th Edition. North Holland: Amsterdam. 1967. :t Boxall, L. G.; Johnson, K. E. Trans. Fauaday. Sot. 1971, 67, 1433. 20: Saboungi, M. L.: Valiet, C.; Doucet, Y. J. Phys. Chem. 1973, 77. 1699. 21. Lesourd; J. B.; Flambeck, J; A. Can: J. Chem. 1969, 47, 3387. Pean, H.; Lesourd, J. B.; Doucet, Y. C. R. Acad. Sci. (Paris), SQ.C. 1973, 277, 541. u”: Lesourd, J. B. These de Doctorat d’Etat &s-SciencesPhysiques, Universite de Provence: Marseille. 1975. 24. Maricle, D. L.; Hume, D. N. J. Electrochem. Sot. 1960, 107, 354. 25. Forland, T. Thermodynamic properties of fused salts, in Fused salts. Sundheim, B. R. : editor. McGraw Hill: New York. 1964. Bastes, H.; Fontana, A.; Winand, R. Silicates Industriels 1976, 31, 129. Evseeva, N. N.; Bergman, A. G. Izv. Sektora Fiz. Khin. Anal. Inst. Obshch. Neorg. Khim., Akad. Nauk. SSSR. 1952,21, 212. 28. Levin, E. M.; Robins, C. R.; McMurdie, H. F. Phase Diagrams for Ceramists. Supal. Amer. Chem. Sot. : Columbus, Ohio. U.S.A. 304, 1969. 29. Pelton. A. D.: Thomson. W. T. Can. J. Chem. 1970. 48. 1585. 30. OstvoId, T. Doctoral Thesis, Technical University of Norway, Trondheim. 1971. 31. Romanetti, R. These de Doctorat d’Etat es-Sciences Physiques, Universite de Provence, Marseille. 1973. 32. Rossini, F. D.; Wagman, D. D.; Evans, W. H.; Levine, S.; Jaffe, I. Nut. But-. Stand. U.S. Circ. Nr. 500. U.S. Government Printing O&e: Washington, D.C. 1952. 33. Kelley, K. K. U.S. Bur. Mines, Bull. 584. U.S. Government Printing Office: Washington, D.C. 1960. 34. Cristol, B.; Houriez, J.; Baiesdent, D. Communication, JournCe d’Etudes sur les Sels Fondus, Mavseile May 1976. Cristol, B. These de Doctorat d’Etat es-Sciences Physiques. Institut National Polytechnique, Nancy. 1976. 6. 7. 8. 9. 10. 11. 12.