Ethalpies of mixing in some binary molten akali fluoride mixtures

J. Chem. Thertnodynatnics 1975, 7, 103-l 18

Enthalpies of mixing molten alkali fluoride A. C. MACLEOD

in some binary mixtures

and J. CLELAND

Department of Metallurgy, Glasgow CI, U.K.

University of Strathrlyde,

(Received 27 July 1973; in revised form 18 March 1974) Excess enthalpies H,” of mixing at constant pressure have been determined as a function of composition and temperature for the molten fluoride mixtures NaF + LiF, NaF + KF, NaF + RbF, and NaF + CsF by a combination of adiabatic drop calorimetry and solution calorimetry. In all cases it was found that H,” was strongly temperature-dependent.

1. Introduction The experimental determination of thermodynamic properties for molten salt mixtures has been vigorously pursued in recent years. Of the many techniques employed, those involving studies of vapour pressure, electrochemical cells, and direct reaction calorimetry are perhaps the most important. The last technique should yield reliable excessenthalpies H;, while the experimental uncertainty involved in the other two methods is such that only excessfree energies can be determined with sufficient accuracy. Most of the existing values of H,” for binary molten salt mixtures have been determined by Kleppa and co-workers using a modified twin Calvet reaction calorimeter operating at temperatures up to 1100 K. In this manner H,” was measured for binary mixtures of alkali nitrates,(‘) chlorides, bromides, and iodides.@)However, due to volatalization of the molten salt mixtures the highest temperature at which Kleppa’s method yields accurate results can be considerably less than the upper operating temperature of the calorimeter. This limitation, in conjunction with the fact that some binary salt systems melt above 1100 K, meant that the theoretically interesting alkali fluoride mixtures could not be studied by Kleppa’s technique. This was the position when the present determinations of H,” for molten fluorides by drop calorimetry were initiated. Previously, Gilbertc3) had shown the feasibility of the method which involves taking the difference between the enthalpy of the mixture measured directly and the sum of the enthalpies of the pure components all measured at the same temperature in the same apparatus. In the operating temperature range where the drop method and Kleppa’s direct method overlap the former should be less precise at the lower temperatures but is probably more precise at the higher end of the temperature range. In addition it has the significant advantage of yielding results over a temperature range which may be as much as 1000 K and 8

104

A. (.‘. MACLEOTI

AND J. t.‘l.FL.ANI)

this enables the temperature dependence of N,E to be studied. It appears that the temperature dependence of the excess thermodynamic functions for molten salt mixtures has never been analysed due to a lack of sufficiently precise experimental data. The main aim of the present research was to provide sufficient results on a series of related mixed cation + common anion molten salt mixtures to enable such an analysis to be carried out and to analyse the results in terms of existing theories of molten salt solutions. Shortly after this researchon NaF -t LiF, NaF + KF, NaF c RbF, and NaF + CsF was initiated, Holm and Kleppa”’ published values of HF for LiF -t NaF, LiF + KF, LiF + RbF, NaF + KF, NaF + RbF, and KF + RbF obtained from a new hightemperature calorimeter operating at temperatures up to 1300 K. At such high temperatures there are severeexperimental difficulties associatedwith direct reaction calorimetry, not least being the problems arising out of calibration, evaporation errors, and chemical incompatibility of the molten salts with the calorimeter parts. In view of this, and the errors involved in determining H," by drop calorimetry, it would not be surprising to find a lack of agreement between the values obtained by the two methods. 2. Experimental MATERIALS

In the present investigation, where two large enthalpy values are subtracted to obtain the required result, the level of impurity that can be tolerated in the samples must be quite small. Accordingly, the materials selected for investigation were, wherever possible, vacuum-grown samples of optical clarity. Single crystals of NaF and LiF were obtained from Gulton Industries Ltd. while single crystals of KF and CsF were prepared in the laboratory by a simple vacuum-melting and zone-refining technique. The potassium fluoride was produced by reacting excess of AristaR HF with AnalaR K,CO, in a platinum dish. This produces acid fluorides in addition to the neutral fluoride so that the resulting sample had to be rendered neutral by slow heating in a stream of dry H2 at 820 K (about 50 K above the decomposition temperature of KF-HF). The powdered KF was then placed in a stainless-steel tube with nimonic end-plugs and melted several times in an electron beam furnace at a pressure of 3 x IO-’ Torr.7 The end-plug was then welded to the walls by use of the electron beam so that the pressure inside the tube was 10m5Torr. On removal from the furnace the tube was subjected to a zone-refining sequenceas previously described by Weaver et al. (5) for the production of optical quality LiF. After completion of the sequence,which lasted about 90 h, the tube was transferred to a dry-box for opening and removal of the boule of optically clear material. The top third of the boule, to which most of the impurities had migrated, was discarded and the bottom two-thirds was transferred to a vacuum desiccator and stored until required. The starting material for the production of single crystal CsF was B.D.H. laboratory grade CsF of not lessthan 98 moles per cent purity. This material was subjectedto t Throughout this paper calth = 4.184 J ; Torr = (101.325/760) kPa.

MOLTEN

FLUORIDE

105

MIXTURES

the samevacuum-melting and zone-refining sequencesas describedfor KF except that the temperatures involved were not so high and the total sequencetook about 60 h. A boule of CsF was finally obtained and the bottom two-thirds stored as before. The RbF sample was reagent grade material which was not subjected to the elaborate purification processesdescribed above. It was simply vacuum-melted a few times in a conventional furnace and, after slow cooling, the pieces with the best appearance were picked out and stored in a vacuum desiccator. The molten fluorides possesssignificant vapour pressuresand are highly corrosive. In order to carry out the enthalpy determinations in the drop calorimeter it was therefore necessary to contain the fluoride samples in a vacuum-tight capsule made of some material with which they are chemically compatible at temperatures as high as 1400 K. For this purpose capsulesof dimensions 35 mm by 13.5 mm were specially manufactured from a (platinum + 10 mass per cent of rhodium) alloy by Johnson Matthey Ltd. The wall thickness was 0.5 mm but a base 2 mm thick was required to withstand the mechanical shock of hitting the copper-block calorimeter after a fall of 1 m. ‘The welded lid of the capsule had a ring for attaching a suspension wire and a tube 3 mm by 15 mm for filling and evacuating. After heating the capsule at 1700K to constant massit was carefully filled with about 10g of sample and evacuated to a pressure of IO-’ Torr in an electron-beam furnace. The tube was then sealed off by electron-beam welding and tested for leakage by heating to 1700 K followed by weighing DROP

CALORIMETRY

Enthalpy measurements were made using an adiabatic drop calorimeter operating at a pressure of 1O-5 Torr. This calorimeter, together with its associated precision potentiometric equipment and adiabatic control system, has previously(6) been fully described. The capsule, containing either a pure salt or a mixture of pure salts, was suspended from the dropping mechanism and held in the temperature-controlled zone of the furnace at some temperature Tfor a least 3 h. By de-energizing an electromagnet in the dropping mechanism the capsule + specimen was then made to fall rapidly into the copper-block calorimeter causing its temperature to rise from 298.15 K to T’. The function {H”(T)-H”(298.15 K)} for the capsule + specimen was then calculated from the fundamental equation : (N”(T)-H”(298.15

K)}capsu,e+specimen = ((T’e298.15 K)‘+c”+qI+ +C;(T’-298.15

K)= (x+q),

where k is the calibration constant of the calorimeter, c’ is the correction for the heat lost by the calorimeter to its surroundings, q is the heat lost by the capsule + specimen during transit, and CL is the heat capacity of the capsule + specimen at T’; the last term is a small correction arising from the fact that the final calorimeter temperature was always slightly above the reference temperature of 298.15 K. The constant k, essentially the heat capacity of the calorimeter, was obtained as previously describedc7’and the quantity c’, which never exceeded0.5 per cent of the total temperature rise, was evaluated by a method suggested by West.@)Repetition of this procedure for the empty capsule under exactly the sameconditions as before resulted

106

A. C‘. iMACLEOD

AND

J. CLELANI)

m a temperature rise of the calorimeter from 298.I5 K to T”, yielding the relation : (H”( 7’) - H”(298.15 K))capru,e= ((T”-298.15 K)k+c”k+qj+C;(T’‘-298.15 K) = (y+q). The value of {H:(T)- Hi(298.15 K)) for the specimen at the temperature T was then found from H~(T)-H~(298.15K)={(x+q)

- (y+q))/(n,+n,),

where (n, +n,) is the amount of substance. It is emphasized that the quantity q is never evaluated but cancels out on the assumption that the heat lost in transit by the capsule is the same whether it is empty or full. In order to obtain H,” for the mixing of salts 1 and 2 at some temperature T it was necessary to proceed as described above and determine the function (Hi(T) -Hg(298.15 K)} for pure salt 1, pure salt 2, a mixture of pure salt 1 + pure salt 2, and the empty capsule. As an example of such a determination we consider the mixing of NaF and LiF according to the reaction: xNaF(l, T) + ( I- s)LiF(l, 7’) = (xNaF + ( I - x)LiF)(l, T),

(1) for which AH, = HF. The enthalpy changes involved in the process are given by the following scheme: NaF(1, T) = NaF(s, 298.15 K), LiF(1, T) = LiF(s, 298.15 K), {xNaF+(l-x)LiF)(l, T) = {xNaF+(l --x)LiF}(s, 298.15 K), xNaF(s, 298.15 K)+(l-x)LiF(s, 298.15 K) = (xNaF+(l-x)LiF}(s, 298.15 K),

(2)

(3) (4) (5)

from which we obtain H; = xAH,+(l

-x)AH,+AH,-AH,.

(6)

In the determination of AH,, AH,, and AH, some of the liquid sample will have vaporized at the temperature T and a quantity of heat Q will be evolved on cooling the sealed capsule containing the liquid in equilibrium with its vapour from T to 298.15 K. It is necessaryto determine a rough value of Q and it is a simple matter to show”’ that this quantity is given approximately by the relation: Q = { T(V - mv)dp/dT - pV ),-(T(~-~~u)dpldT-p~),,,.,,., where m is the mass of sample, v is the specific volume of liquid, p is the vapour pressure, and V is defined as V = mxv'+m(l-x)o, where a’ is the specific volume of the saturated vapour. Q was evaluated using the vapour pressures of Ruff et aZ.(l’) and specific volumes derived from the densities tabulated by Janz.(ii) The results are given in table 1 and it evident that the correction is negligible for all the salts except CsF but even in this case it amounts to only 0.1 per cent of the molar enthalpy at a given temperature. The only unknown in equation (1) is the term AH5 which represents the enthalpy of formation of the solid mixture at 298.15K. Although the mixtures chosenfor study,

MOLTEN

FLUORIDE

107

MIXTURES

for the effect of vaporizationof the liquid samples(G&, = 4.184 J)

TABLE 1. Correction term

Salt LiF NaF KF CsF

Q/calth mol - 1 1273 K

1323 K

1373 K

0.019 0.022

0.02 0.04 0.32

0.02 0.07 0.79 16

0.11 6.1

11

apart from NaF + KF, were expected to have AH5 = 0 (and this is usually evident from the drop calorimetric results) it is neverthelessessential to determine the value of AH, for each mixture. SOLUTION

CALORIMETRY

The value of AH, was found by solution calorimetry as the difference between the molar enthalpy of solution of a mechanical mixture of the pure salts and the molar enthaIpy of solution of mixed crystal of the pure salts at 298.15 K.

FIGURE 1. Solution calorimeter. A, copper cylinder with calibration heater and thermistor bridge; B, glass ampoule containing sample; C, brass plunger; D, electric motor; E, flexible coupling; F, PTFE flange; G, water level.

The calorimeter assembly (shown in figure 1) consisted essentially of a copper cylinder with a heater and thermistor bridge immersed in 600 cm3 of pure distilled water contained in a Dewar vessel. The whole assembly was placed in the thermostatted bath of the drop calorimeter which was controlled at (298.15f0.001) K as previously described.(W The thermistor bridge consisted of two arms of 0.15 mm

108

A. C’. iblhCi.tOi~

AND

J. (‘I 1’1 ANi)

diameter manganin wire UT resistance 235.6 R at 298.i5 K and two arms made up of two matched pairs of STC/M52 thermistors connected in parallel, of resistance 234.3 Q at 298.15 K. The calibration heater, of 0.15 mm diameter diamel-coated Minalpha wire, was wound non-inductively on a recess in the copper cylinder and had a total resistance of 168.7 Q. The fact that this was exactly the resistance of the corresponding heater in the drop calorimeter meant that the calibration system previously described(“) for that apparatus could be used in this case without any modification. Three coats of Megasil varnish, baked at 400 K between each coat, were applied to the calorimeter wiring, thermistors, and copper parts. All precision electrical measurements were made on a Tinsley high-precision potentiometer type 5205A-Auto reading in steps of 0.1 ktV. The potentiometer current was held constant to a few parts in IO6 by means of a Tinsley automatic controller and a double standard cell maintained at (298.15-tO.01) K in an oil bath. A Tinsley galvanometer photocell amplifier type 5214, used in conjunction with a thermal compensator type 5214A and a Tinsley galvanometer type 4500A operating on a 2 m optical system, was used for null detection. All switches in precision circuits were of the Leeds and No;thrup copper -+ beryllium knife pattern, the electrical leads were of shielded cable, and the soldered joints were made with thermal-free solder. Current to the thermistor bridge was supplied from a 4 V accumulator and adjusted by means of a Tinsley minimus resistance which could be varied in steps of 0.001 ,Q. The heat capacity of the calorimeter was determined by supplying it with a known quantity of electrical energy from the calibration heater and observing the change in the potential output of the thermistor bridge. A series of 10 determinations under isoperibol conditions gave the result tlyat 1 PV & 0.1416 Cal,, with a mean deviation of 0.05 per cent. Thus the thermistor bridge was about six times more sensitive than the Maier bridge wound on the drop calorimeter. The samples (about 0.1 g) were contained in specially designed glass ampoules which were evacuated to a pressure of less than lo--’ Torr, sealed off, and annealed at 500 K. Eight ampoules were loaded into the sample holder, situated above the stirrer, and a numbering arrangement permitted the positioning of any ampoule below the brass plunger. The ampoule end was broken by striking the plunger and the resulting implosion of water ensured that the sample was quickly and efficiently dissolved. Dummy runs on sealed and empty ampoules indicated that the energy of breaking was negligible. Thermistor bridge readings were taken at 10 min intervals in the fore-period and after-period and the corrected temperature rise of the calorimeter was obtained as described by Gunn. (“) A calibration experiment then gave the heat capacity of the calorimeter which, when multiplied by the corrected temperature rise, gave the enthalpy of solution for the contents of a particular ampoule. On completion of one experiment the dilute solution was sucked out of the calorimeter by means of a specially designed vacuum system. The calorimeter was then flushed out three times with a volume of distilled water and finally filled with 600 cm3 of distilled water at 298.15 K in preparation for another experiment. It was estimated, from the reproducibility of the values for x(KF) = 0.41, that the accuracy of the calculated enthalpies of formation is about +4 Cal,, mol-‘. The results are shown in table 2.

MOLTEN TABLE

x

2.

FLUORIDE

109

MIXTURES

Enthalpy of formation at 298.15K of the solid mixture jxNaF + (1 - x)MF) (M = K, Li, and Cs) (calth = 4.184J)

AHsodcalth md- 1 AH 5 Mechanical Fused mixtllre C& mol-’ mixture

.Y

AH,,,&&, mol - 1 Mechanical Fused Elmixture mixture th

xNaF i- (I - s)KF 0.058 0.142 0.200 0.505

5.520 5080 4740 3040

4800 4518 4320 2820

120 562 420 220

0.590 0.693 0.785 0.890

2560 2010 1460 880

2180 1430 702 -so

380 580 758 960

sNaF + (1 - x)LiF IAH,! did no! exceed14 Cal,, mol-’ in the range0.15 < x i: 0.80. xNaF + (1 - s)CsF jAH,l did not exceed9 calth mol-l in the range0.1 < x < 0.85.

3. Results The reliability of the enthalpies determined in the drop calorimeter was established before and after the series of determinations on the molten salts by measuring the enthalpy of the Calorimetry Conference sample of a-alumina over the temperature range 500 to 1300 K. Good agreement was found with the values computed from the NBS “corrected” equation (13) for the enthalpy of a-alumina, the mean deviation being kO.2 per cent. The results obtained for the excess enthalpies of the chosen molten salt mixtures are listed in order of study in tables 3 to 6 and shown graphically in figures 2 to 6. NaF+ LiF The ratio of interionic distances (14) is 1. 16 which is very close to the limiting value of about 1.15 below which solid solubility is usually found. However, a more sensitive criterion for the appearance of solid solubility seems to be the polarization coefficient (M) test of Plyuschsheva and Samuseva (15) which indicates that solid solutions are formed for a,/clz < 5. For NaF+LiF this ratio has the value 6.5 which points to the absence of solid solutions. This conclusion is supported by the phase diagrams of Bergman and Dergunov(“’ and of Aukrust et aZ.‘17) which indicate a eutectic at 923 K and x(NaF) = 0.61, and by the results in table 2 which show that AH4 N” 0 in the composition range 0.15 < x(NaF) < 0.80. The excess enthalpies, shown in table 3 and figure 2, are strongly temperature dependent varying from - 860 Cal,, mol- ’ at 1185 K to -1620 Cal,, mol-’ at 1370 K for x = 0.5. This variation for the six selected compositions is shown in figure 3 and it is evident that dHF/dT = -4 Cal,, K-’ mol-’ is a constant across the whole composition range.

110

A. C. MACLEOD

AND

J. CLELAND

TABLE 3. Enthalpy changes for sodium fluoride + lithium fluoride 25.937 g mol-1) (Cal,, = 4.184 J; M(NaF) : 41.987 g mol-I; M(LiF)

T K --..

n(NaF) mol

n(LiF)

1370.4 1332.6 1286.2 1184.7

0.0396 0.0396 0.0396 0.0463

0.0098 0.0098 0.0098 0.0115

0.801 0.801 0.801 0.801

21954 21502 20884 19606

23049 22405 21624 19954

-1095 -903 -740 -~ 348

1331.4 1283.7 1233.1 1182.4

0.0396 0.0396 0.0396 0.0396

0.0241 0.0241 0.0241 0.0241

0.621 0.621 0.621 0.621

20531 19935 19279 18677

21879 21081 20249 19428

1348 -~-1146 ---970 --- 75 1

1371.2 1331.1 1267.2 1232.6

0.0463 0.0589 0.0589 0.0463

0.0369 0.0465 0.0465 0.0369

0.556 0.558 0.558 0.556

20773 20242 19410 19024

22369 21691 20628 20062

-1596 -1449 -1218 -1038

1369.7 1328.5 1287.5 1230.8 1184.5

0.0463 0.0396 0.0396 0.0396 0.0396

0.1381 0.1190 0.1190 0.1190 0.1190

0.251 0.249 0.249 0.249 0.249

19979 19432 18939 18225 17686

21481 20786 20107 19189 18541

-1502 -~ 1354 -1169 -964 -765

1372.2 1328.7 1282.8 1229.2 1185.7

0.0463 0.0396 0.0396 0.0396 0.0396

0.2167 0.1900 0.1900 0.1900 0.1900

0.176 0.175 0.175 0.175 0.175

20000 19453 18850 18204 17692

21311 20584 19828 18962 18272

-1311 -1131 -978 ---758 -. 580

1370.8 1332.7 1285.3 1231.3 1186.0

0.0463 0.0463 0.0463 0.0463 0.0463

0.0680 0.0680 0.0680 0.0680 0.0680

0.405 0.405 0.405 0.405 0.405

20313 19812 19205 18543 18023

21936 21294 20507 19626 18899

-1623 -- 1482 -- 1302 -~ 1082 -876

Ill01

:xAHzf(l -~x)AH, ~-__ calth mol- l

x(NaF)

i

H,” calth molkl

NaF+CsF

For this mixture the ratio of interionic distances is 1.29 and al/clz = 13.7 so that a eutectic of pure solids is predicted. This is confirmed by the phase diagram of Deadmore and Mach&‘*) which indicates a eutectic temperature of (883+ 5) K at x(NaF) = 0.234 and the fact that AH4 w 0 in the range 0.10 < x(NaF) < 0.85 as shown in table 2. The excessenthalpies, listed in table 4 and plotted in figure 4, exhibit a similar temperature dependence to that found for NaF+LiF. In this case the values range from - 1220Cal,, mol-’ at 1095 K to - 1640 Cal,, mol-’ at 1375 K for x = 0.5 and dHF/dT = - 1.5 Cal,, K-i mole1 is once again a constant for all the compositions at which enthalpies were determined (figure 5).

MOLTEN FLUORIDE MIXTURES TABLE4. Enthalpy (Cal,, = 4.184 J; M(NaF) T i

--n(NaF) mol

n(CsF)

changes for sodium fluoride

+ caesium fluoride

= 41.987 g molP1; M(CsF) x(NaF)

-AH4 ___.calth mol- 1

mol

111

= 151.903 g mol-‘)

{xAH, +(l -x)AHa -- -__~___c& mol-l

}

If, calth mol-l

1374.6 1337.8 1273.6 1188.2 1094.8

0.0113 0.0089 0.0089 0.0089 0.0089

0.0159 0.0124 0.0124 0.0124 0.0126

0.415 0.418 0.418 0.418 0.414

21287 20734 19782 18502 18086

22931 22327 21271 19857 18297

-1644 -1593 -1489 -1355 -1211

1374.8 1338.7 1273.8 1188.6 1094.8

0.0061 0.0113 0.0061 0.0061 0.0061

0.0134 0.0254 0.0134 0.0134 0.0134

0.312 0.308 0.312 0.312 0.312

21259 2073 1 19766 18480 17043

22790 22204 21142 19732 18156

-1531 -- 1473 -1376 -1252 -1113

1372.6 1337.9 1273.9 1188.5 1095.2

0.0113 0.0113 0.0089 0.0127 0.0121

0.0123 0.0123 0.0086 0.0138 0.0138

0.479 0.479 0.508 0.479 0.479

21337 20815 19861 18570 17162

22975 22404 21347 19933 18381

-1638 -1589 -- 1486 -1363 -1219

1374.8 1338.2 1274.4

0.0395 0.0423 0.0423

0.0126 0.0134 0.0134

0.758 0.759 0.759

22223 21698 20732

23376 22759 21692

-1153 -1061 -960

1375.1 1338.7 1273.8

0.0113 0.0113 0.0113

0.0453 0.0453 0.0453

0.199 0.199 0.199

21405 20903 19957

22653 22066 21010

- 1248 -1163 -1054

1375.0 1338.3 1274.1

0.0113 0.0113 0.0113

0.0068 0.0068 0.0068

0.624 0.624 0.624

2177’ 21169 20197

23204 22592 21525

--- 1482 - 1423 -1328

1274.7

0.0026

0.0155

0.144

20145

20953

-808

NaF+KF The phase diagrams quoted for this mixture are discordant. Kurnakov and Zemezuzny” 9, and Dombrowskaja and KolshowaIzO’ reported considerable solid solubility of NaF in KF but Bergman and Dergunov (16) found no solid solubility and a eutectic of pure solids at x(NaF) = 0.4 and 983 K. This latter conclusion is the accepted one in phase diagram compilations. (‘l) However, the ratio of interionic distances of 1.13 and the polarization coefficient ratio of 4.7 strongly suggeststhat solid solutions must be formed. This is confirmed by the results of the solutioncalorimetry experiments shown in table 2 from which it is evident that there is considerable solid solubility at the limiting compositions and restricted solid solubility in the composition range 0.2 < x(NaF) < 0.45. The behaviour of the mixture is unusual in the sense that a plot of AH5 against x(NaF) is concave downwards rather than concave upwards and further study, especially in the limiting composition regions, is clearly desirable, However, since statistical-mechanical theories of molten

II:!

A. C. MACLEOD TABLE

5. Enthalpy

AND

J. CLELAND

changes for sodium

(Cal,,, = 4.184 J; M(NaF)

fluoride

! potassium fluoride

: 41.987 g mol- 1; M(KF)

T K

n(NaF) mol

n(KF) .mol

x(NaF)

1374.8 1338.2 1274.9

0.1291 0.1291 0.1291

0.0143 0.0143 0.0143

0.900 0.900 0.900

22279 21773 20797

1374.4 1338.2 1274.6

0.0550 0.0550 0.0550

0.0143 0.0143 0.0143

0.794 0.794 0.794

3175.9 1338.3 1274.5

0.0344 0.0344 0.0344

0.0143 0.0143 0.0143

1374.2 1338.5 1278.3

0.0204 0.0204 0.0204

1375.3 1338.2 1274.3

=- 58.100 g mol

AH5 Cal‘,, molt i

H,” calu, mot- L

23524 22902 21839

970 970 970

-275 ~-159 72

22153 21659 20740

23343 22734 21677

760 760 760

-430 ---315 --177

0.706 0.706 0.706

22109 21607 20715

23223 22596 21544

600 600 600

p-514 -389 -229

0.0143 0.0143 0.0143

0.588 0.588 0.588

22027 21579 20763

23001 22412 21431

380 380 380

--594 -453 m-288

0.0139 0.0139 0.0139

0.0138 0.0138 0.0138

0.502 0.502 0.502

22097 21596 20729

22878 22271 21238

200 200 200

-581 --475 -309

1375.0 1338.2 1274.4

0.0101 0.0101 0.0101

0.0138 0.0138 0.0138

0.423 0.423 0.423

22201 21684 20800

22742 22145 21122

0 0 0

-541 -461 -322

1375.3 1339.0 1274.5

0.0069 0.0069 0.0069

0.0138 0.0138 0.0138

0.333 0.333 0.333

22024 21543 20658

22600 22017 20991

40 40 40

1374.7 1337.8 1274.1

0.0047 0.0047 0.0047

0.0165 0.0165 0.0165

0.2216 0.2216 0.2216

22047 21071 19145

22407 21821 20818

390 390 390

1374.8 1338.1 1274.4

0.0024 0.0024 0.0024

0.0138 0.0138 0.0138

0.148 0.148 0.148

21368 21649 20326

22288 21709 20714

540 540 540

-380 -t 480 i152

1368.0 1331.0 1274.4

0.0011 0.0011 0.0011

0.0165 0.0165 0.0165

0.063 0.063 0.063

21917 20999 19511

22042 21463 20474

730 730 730

i 605 -1-266 233

TABLE

6. Enthalpy

(catch = 4.184 J: M(NaF) T ti -__-.1375.2 1338.3 1274.7

n(NaF) mol __ 0.0132 0.0132 0.0132

n(RbF) mol

-~____ 0.0143 0.0143 0.0143

-AH, --- {xAH&(l x)Alfa i ~~~~ caith mol- 1 calch mol. 1

I)

changes for sodium fluoride = 41.987 g mol.I; x(NaF) 0.48 0.48 0.48

+ rubidium

M(RbF)

-AH, __-.~ cab mol-’ 23083 22474 23445

-536 ~--434 ~- 293 +30 -360 -1283

fluoride

= 104.468 g mol.‘)

- (xAHz+(l -.x)AHz) C& mol - 1 23012 22370 21280

H,” calth mol-r +71 t104 +142

MOLTEN

FLUORlDE

MIXTURES

113

FIGURE 2. Excess enthalpies for sodium fluoride + lithium fluoride: 13, 1370 K; v, 1333 K; n, 1286 K; 0, 1233 K; V, 1185 K.

FIGURE 3. Variation of excess enthalpy with temperature for sodium fluoride + lithium fluoride: x, x(NaF) = 0.41; a, x(NaF) = 0.56; V, x(NaF) = 0.25; 0, x(NaF) = 0.62; 0, x(NaF) = 0.18; m, x(NaF) = 0.80.

114

A. C. MACLEOD

AND J. CLELAND

1200 3

;

960

2 $a

720

:: 480 240 0

0

0.2

0.6 0.4 s(NaF)

0.8

1

FIGURE 4. Excess enthalpies for sodium fluoride f caesium fluoride: 0, 1375 K; ‘1. 1338 K: 0, 1273 K; .,1185 K; v, 1095 K.

FIGURE 5. Variation of excessenthalpy with temperature for sodium fluoride -t- caesium fluoride: CJ,x(NaF) = 0.42 and x(NaF) = 0.48; x, x(NaF) = 0.31; 0, x(NaF) = 0.76; V, x(NaF) = 0.20; 0, x(NaF) y 0.62.

salt mixtures are always tested at x = 0.5 we are here primarily interested in obtaining values of H,” at this composition for a series of related mixed cation + common anion molten salt mixtures. Thus, although it is apparent from table 5 that excess enthalpies for x(NaF) < 0.2 are quite erratic, there is no reason to suppose that values around x = 0.5 are not sufficiently reliable for use in testing theories. The variation of H,” with temperature at the different compositions is not linear except at x(NaF) = 0.50 and x(NaF) = 0.423, near the eutectic composition, where dHz/dT = -2.75 Cal,, K-’ mol- r. Since this is the region of negligible solid solubility it is reasonable to supposethat the non-linear variation of H," with temperature is connected with the appearance of solid solubility.

MOLTEN

“0

FLUORIDE

0.2

115

MIXTURES

0.4

0.6

0.8

1

s(NaF) enthalpies for sodium fluoride

FIGURE 6. 0, 1275 K.

+ potassium fluoride:

0, 1375 K; V, 1338 K;

NaFfRbF The phase diagram for this mixture, quoted by Thorna,@*) shows a eutectic of pure solids at 950 K and x(NaF) = 0.27. The absence of solid solubility is predicted by a ratio of interionic distances of 1.19 and a polarization coefficient ratio of 8.0. In contrast to the other systems studied the excessenthalpies listed in table 6 are positive with dHF/dT = -0.7 Cal,, K- ’ mol -I. Time did not permit further measurements of II,” as a function of composition or the determination of AH, by solution calorimetry. The three results obtained may be less reliable than the corresponding results for the other systems studied because of the relatively impure nature of the RbF sample. The experimental results for the three pairs of salts investigated as a function of composition can be represented by an analytical expression of the type: H,Elcal,, mol - 1 = --Xl x*(u + bx, + cx1 x2). (7) Values of a, b, and c were deduced by a least-squares method and are listed in table 7. TABLE

7. Representation

a

b

1374 1330 1286

9421 6342 4978

2841 3158 3180

1314 1330 1270

8344 7692 7115

-2879 -2570 -2383

1374 1338

2492 1859

797 55

of excess enthalpies for binary liquid alkali fluoride mixtures by equation (7)

c

a

b

+ xlLiF 1230 1185

3017 2431

2719 2043

-

+ (1 - x,)CsF 1188 1094

6221 5827

-1492 -1951

-

+ (1 - xl)KF 1274

1795

TIK

(1 - xl)NaF - 18348 -8941 -5877 xlNaF -767

C

xlNaF -2481 -

-1022

-

I I6

A. C‘. MACI.EOD

AND J. ~‘I~l‘LANl~

The present results are compared in table 8 with those obtained by HoIm and KleppaC4’ by direct reaction calorimetry; it is clear that a large discrepancy exists between the two sets. However, when we compare in table 9 Kleppa and co-workers’ results for other mixtures with those obtained by workers who used either a similar TABLE 8. Comparison between Holm and Kleppa’s excess enthalpies at .Y and those of the present work (cal,,, ~~4.184 J) HF(.u = 0.5)/cal,h mol-’

NaF $ LiF NaF i- RbF

Helm and Kleppa’4’ --500 23 “A r> ]

0.5

11OOAj”

This work -1280 4 142

(iHE(CO1. ?)I )/:~H’:(col.

61 84 3)i I.

TABLE 9. Comparison between Kleppa and co-workers’ excess enthalpies at x = 0.5 and those of other workers (Cal,, : 4.184 J) H,“(x =-=0.5)/cal,, mol- 1

NaCl -t- NaBr KC1 $- KBr RbCl + RbBr

NaCl + PbCI, KC1 + PbCI,

11OOA/

Hersh and Kleppa(z’ -+25

Murgulescu and Marchidan’23’ i-50

50

-1 15 -i 12

+55 1- 63

73 80

McCarty and Kleppatz5) --100

Bloom and Tricklebank’z4’

- 1300

-603 -712

83 86

direct-calorimetric technique, e.g. Murgulescu and Marchidan,‘23’ or a dropcalorimetric technique, e.g. Bloom and Tricklebank, (24)a discrepancy almost exactly the same as shown in table 8 is found. Despite the magnitude of the discrepancy Bloom and Tricklebank claim that it is just within the combined experimental error and regard it as satisfactory in view of the errors likely to be associatedwith the use of an unsealed calorimetric system by Kleppa and co-workers. Nevertheless, the fact remains that Holm and Kleppa’s excessenthalpies were directly measured whereas those obtained from drop-calorimetry were derived as a small difference between large quantities. Fortunately, in the present case it is possible to judge the reliability of these quantities by reference to the results obtainedW) for the high-temperature thermodynamic properties of the pure alkali-metal fluorides which were measured in the range 500 to 1600 K as part of the same research programme.

MOLTEN

FLUORIDE

MIXTURES

117

A surprising feature of all the excessenthalpies obtained by Kleppa and co-workers by direct-reaction calorimetry is that no variation of HF with temperature has been reported. The strong dependenceof H,” on temperature is, of course, a well-established fact both for ionic and non-ionic liquid mixtures. For example, it has been found(27’ by direct reaction calorimetry that AgCl + KCI, which was studied by Kleppa and Hersh 12fshows a variation in H,” with temperature of - 1.0 Cal,, K-’ mol-‘. Also, it can’be deduced from the e.m.f. measurementsof Panish et a1.“*’ on AgCl +LiCl and on AgCl f NaCl that dHF/dT is - 1.0 and - 1.85 Cal,, K-’ mol-’ respectively. These variations in HF with temperature are very similar to those found for the four mixtures studied here. Holm and Kleppac4’ analysed their results for the series of mixtures LiF+NaF, LiF+KF, LiF+RbF, and LiFtCsF by plotting the quantity [{HF/x(l -x)) - U,“] at x = 0.5 against the size parameter S:, = ((d, -d2)/(d,d2}2; Vi+ represents the

FIGURE 7. Plot of “corrected” enthalpy interaction parameter ({H,E/x(l - x.)) - Ug +) for x = 0.5 against the parameter ST, (from reference 4). X, ( 1024r,/cm3)1/2+ 4.974.

contribution to the enthalpy of mixing from the London dispersion interaction between next-nearest neighbout cations and d is the anion-to-cation hard-core separation, The plot obtained is shown in figure 7; it is evident that the value of H,” reported here for LiF + NaF fits on a straight line with the other results whereas Holm and Kleppa’s value does not. The form of the plot then suggests that an interaction, probably a polarization contribution, has been neglected in the analysis. In fact Lumsden(29) has claimed that such a contribution to H," should be greater in magnitude than the coulombic contribution and should be roughly proportional where CL,is the Gaussian polarizabi1ity.t It may be significant that the to Q3:2, dimensionless quantity - ((1024a,/cm3)“2 +4.974}, calculated from Pauling’s’30’ values of c(, for the cations Na+, Kf, Rb+, and Cs+, can be fitted exactly on the straight line in figure 7 as shown by the points marked with a cross. Another remarkable correlation is obtained by use of the enthalpies of formation’3” at 298.15 K t a, = a,/lrxs, where Q, is the permittivity of a vacuum,

A. C. MACLEOD

118

AND J. CLELAND

of the monatomic gases of NaF (-69.2 kcal,,, mol-‘), KF (-77.2 kcal,, mol- ‘), RbF (- 77.7 kcal,, mol- ‘), and CsF (- 82 kcal,, mol- ‘); these values can be plotted in figure 7 so that they fall exactly on the points for (4HE-- U,+‘). REFERENCES 1. Kleppa, 0. J.; Hersh, L. S. J. Chern. P/IJK 1961, 34, 351. 2. Hersh, L. S.; Kleppa, 0. J. J. C’hem.Phys. 1965, 42, 1309. 3. Gilbert, R. A. J. Phys. Chem. 1963, 67, 1143. 4. Holm, J. L.; Kleppa, 0. J. J. Chem. Phys. 1968, 49, 2425. 5. Weaver, C. F.; Ross, R. G.; Sturm, B. J.; Eorgan, J. E.; Thoma, R. E. U.S. Atomic Energy Comm. ORNL-3341, 1964. 6. Macleod, A. C. Trans. Faraday Sot. 1967, 63, 300. 7. Macleod, A. C. Trans. Faraday Sot. 1967, 63, 289. 8. West, E. D. J. Appl. Phys. 1968, 39, 4206. 9. Osborne, N. S. J. Res. Nat. Bur. Stand. 1930, 4(A), 609. 10. Ruff, 0.; Schmidt, G.; Mugdan, S. Z. Anorg. Allg. Chem. 1922, 123, 86. 11. Jam, G. J. Molten Salts Handbook. Academic Press Inc., New York, 1967. 12. Gunn, S. R. J. Chem. Thermo&namics 1971, 3, 19. 13. Ginnings, D. C. J. Phys. Chem. 1963, 67, 1917. 14. Gourary, B. S.; Adrian, F. J. Solid State Phys. 1960, 10, 128. 15. Plyuschsheva, V. E.; Samuseva, R. G. Russ. J. Znorg. Chem. 1966, 11, 636. 16. Bergman, A. G.; Dergunov, E. P. C. R. Acad. Sci. U.R.S.S. 1941, 31, 753. 17. Aukrust, E.; Bjorge, B.; Flood, H.; Forland, T. Ann. N. Y. Acad. Sci. 1960, 79, 830. 18. Deadmore, D. L.; Machin, J. S. J. Phys. Chem. 1960, 64, 824. 19. Kurnakov, N. S. ; Zemezuzny, S. F. Z. Anorg. Alfg. C’hem. 1907, 52, 186. 20. Dombrowskaja, N. S.; Koloshowa, Z. A. Zzv. Sekt. Fiz. Kim Anulitza 1938, 10, 211. 21. Phase Diagrams for Ceramists (1969 Supplement). Reser, M. K.; editor. The American Ceramic Society, 1969. 22. Thoma, R. E. Declassified Rep. U.S. Atomic Energy Comm. ORNL-2548, 1959. 23. Murgulescu, I. G.; Marchidan, D. I. Rev. Roumaine Chim. 1964, 9, 793. 24. Bloom, H.; Tricklebank, S. B. Aust. J. Chem. 1966, 19, 187. 25. McCarty, F. G.; Kleppa, 0. J. J. Phys. C’hem. 1964, 68, 3846. 26. Macleod, A. C. J. Chem. Sac. Far. Trans. I. 1973, 69, 2026. 27. Baboian, R.; Flengas, S. N. Can. J. Chem. 1967, 45, 813. 28. Panish, M. B.; Blankenship, F. F. ; Grimes, W. R.; Newton, R. F. J. Phys. Chem. 1958, 62, 1325; 1959, 63, 668.

29. Lumsden, J. Disc. Far. Sot. 1961, 32, 138. 30. Pauling, L. Proc. Roy. Sot. 1927, A114, 193; J. Amer. Chem. Sot. 1927,49, 765. 31. Brewer, L. Report distributed by the Lawrence Radiation Lab., University of California, UCRL9952, UC-4 Chemistry; TID-4500, Nov. 1961.