3840 S. V. NESCHEL AXD 0. J. KLEPPA

A Thermochemical Study of Some Reciprocal Fused-Salt

Systems Involving the Monovalent Liquid Nitrates

by S. V. Meschel and 0. J. Kleppa

Department o f Chemistry and Institute fo r the Study of MetaZs, The University o.f Chicago, Chicago, Illinois 606S7 (Received Ju ly 17, 1964)

The enthalpies of solution in liquid monovalent nitrates of some solid alkali and alkaline earth chlorides and bromides have been measured. The results have been analyzed as the sum of two binary steps, BX(s) + B?JO3(1) = dilute solution and ANO3(1) + BN03(1) = dilute solution, plus a metathetical step, AX(s) + BxO3(1) = AN03(1) + BX(s). The energy changes obtained for the latter step have been compared with literature data and discussed in terms of a simple ionic model and departures from this model.

Introduction Mixtures of fused salts may be classified into four

basic types according to the following scheme: (I) systems with symmetrical charge structure containing a common ion; this ion may be either (a) the anion, as in (Na-K)N03, or (b) the cation, as in Na(C1-NO3); (11) systenis with asymmetrical charge structure, but containing a coniinon ion; again this ion may be (a) the anion, as in (Ca-Na)N03, or (b) the cation, as in Na(RIo04-N03) ; (111) systems with syinnietrical charge structure, but containing no common ion, for example KC1-n’aN03; (IV) systems which possess neither charge symmetry nor a common ion, such as CaBrz-KaNOa.

This list outlines, in the order of increasing com- plexity, a series of basic problems in the solution chem- istry of fused salts: How do the solution properties of each class of mixed system depend on such parameters as the size, charge, and structure of the participating ions?

Through systematic calorimetric investigations car- ried out in this laboratory during recent years, we have attempted to provide answers to these questions. Thus, Kleppa and Hershl found that all the binary liquid alkali nitrate mixtures (type Ia) have negative enthalpies of mixing, with the magnitude increasing in a regular manner with increasing difference in size be- tween the two participating cations. This has been attributed, in the main, to the reduction in coulombic repulsion between second nearest neighbor cations, as proposed by F@rland.2

The alkali chloride-nitrate and bromide-nitrate sys- tems (I(b)), on the other hand, all show sinall positive enthalpies of n~ix ing .~ We believe that this change in sign may be related to the radius-ratio effect, ie., to the importance of the core repulsion between the large anions.

I n most cases the alkaline earth-alkali nitrate mix- tures (IIa) exhibit negative enthalpies of mixing, which are comparable in magnitude or somewhat larger than those found for the binary alkali nitrate^.^ On the other hand, charge-unsymmetrical anion systems (IIb) appear to be more ~ o m p l e x . ~ So far it has proved difficult to rationalize the solution behavior of such systems in t e r m of the simple physical ideas outlined above.

In the present work, our systematic study of the solu- tion properties of fused-salt mixtures is extended to simple reciprocal mixtures (111 and IV). Presently, we shall restrict our attention to solutions in the liquid monovalent nitrates. We report below the results ob- tained in a Calorimetric investigation of the heats of solution of simple alkali and alkaline earth halides (AX and AX2) in solvents such as n’aN03, KK03, T1N03, and AgN03.

(1) 0. J. Kleppa and L. S. Hersh, J . Chem. Phus., 34, 351 (1961). (2) T. Fedand, “On the Properties of Some Mixtures of Fused Salts,” N. T . H. Trykk, Trondheim, Norway, 1958.

(3) 0. J. Kleppa and S. V. Meschel, J . Phys. Chem., 67, 668 (1963). (4) 0. J. Kleppa, ibid., 66, 1668 (1962). (5) 0. J. Kleppa and S. V. RIeschel, ibid., 67, 2750 (1963).

The Journal of Physical Chemistry

THERMODYNANICS OF RECIPROCAL FUSED-SALT SYSTEMS 3841

In the course of the present study we have deter- mined experimentally the molar changes in enthalpy, AHA, associated with reactions of the type

AX(s) + BNOa(1) =

dilute solution of A + and X- in BKOs (A) If the solution of ,4 + and X- in BY03 is quite dilute,

interaction between A + and X- in the dilute solution may be neglected. Under these conditions process A, through a thermodynamic argument related to that used by Flood, Fgrland, and Grjotheim6J in their theory of simple reciprocal fused-salt mixtures, may be considered to represent the sum of three part processes

AX(s) + BNO,(1) = BX(s) + AR'Oa(1); AHB (B)

BX(s) + BNOa(1) =

dilute solution of X- in BNO,(l); AHc ( C )

AKOa(1) + BT\'Oa(l) =

dilute solution of A + in BN03(1); AHD (D)

Under the stated assumption we have

A H A == AHB + AHc f AHD

The significance of this relation is that it reduces the problem of describing the reciprocal solution process A to the sum of a metathetical or exchange step B, plus two simple binary steps C and D.

The present investigation, which is concerned with dilute solutionfi of AX: in BNO3 only, does not address itself to the more basic question of to what extent a reciprocal fused salt mixture of arbitrary composition also can be described fully in terms of binary steps plus a metathetical step.* We propose to return to this problem in future work.

For the various solutes (AX and AX2) considered in the present work, the quantities AHc and AHD already have been reported in earlier communications from this laboratory. 3-5 In principle, the quantities A H B may be calculated from the standard heats of forma- tion of the four substances involved, suitably corrected for the difference in enthalpy between 25' and our ex- perimental temperature. Thus, one should, a t least in some cases, be able to calculate AHA from already pub- lished information.

In attempting to check this point experiinentaJy we found a number of discrepancies between our own ex- perimental results and the values which we calculated on the basis of literature data. While soine of these discrepancies may be due to our neglect of the inter- action between A + and X-, most of them probably arise from uncertainties in the heat contents. For this reason and also in order to check the internal con-

sistency of own therinochemical data (AHc and AHu), we report in the present work the results of a survey of the heats of solution of various simple haiides in the monovalent nitrates. The results will be discussed in terms of a simple ionic model.

Experimental and (Chemicals

The calorimeter used in the present investigation has been described previously. Most experiments were performed a t 450 + 1'. However, in order to avoid thermal decomposition, all work involving the salts of calcium, thallium, and silver was carried out at 350 f 1'.

Calibrations were generally by the "gold-drop" method, i.e., based on the heat content equation for pure gold as given by Kelley.'" In experiments where silver nitrate was the solvent, we used an electrical calibration method. This was done in order to avoid the small spurious heat effect which results from a slight deposition of silver on the surface of the gold, as notrd by Kleppa, Clarke, and Hersh."

The sodium and potassium halides and nitrates and the alkaline earth halides were Mallinckrodt A.R. grade reagents. The rubidium, cesium, and thalliuiv halides and thallium nitrate were purchased from Millmaster Chemical Corp. as "99.90j, pure., The silver salts were of analytical grade and furnished by Goldsmith Brothers. Thallium nitrate was recrystal- lized twice from distilled water before use. The re- maining salts were used without further purification.

With the exception of lithium chloride and bromide, which were dried by heating under vacuum, the salts were dried as required in the atmosphere. After dry- ing, the lithium salts were tested for alkalinity by dis- solution in distilled water. These solutions were neu- tral with respect to phenolphthalein.

All the experiments carried out in the present study involved the solution of a small amount of a solid salt in a large surplus of solvent. The final concentrations always were below 1 mole % of solute. Thus, the as- sumption discussed in the Introduction, that the inter- action between the two solute ions may be neglected, is a reasonable one.

(6) H. Flood, T. Feirland, and K. Grjotheim, 2 unorg. allgem. Chem , 276, 289 (1954).

(7) IM. Blander and E. B. Luchsinger, J . A m Chem. Soc.. 86 , 31'3 (1964).

(8) M. Blander and S. J . Yosim, J . Chem. Phys. , 39, 2610 (1963). (9) 0. J . Kleppa, J . Phys. Chem., 64, 1937 (1960). (10) K. K. Kelley, U. S. Bureau of Mines Bulletin No. 584, U. S Govt. Printing Office, Wmhington, D. C., 1960.

(11) 0. J. Kleppa, R. B. Clarke, and L. S. Hersh, J . Chem. Phys., 35, 175 (1961).

Volume 68, Number 18 December, 1964

3842 5. V. MESCHEL AND 0, J. RLEPPA

Table I : Summary of Thermocheniical Data (in kcal./mole) for Mono-monovalent Reciprocal Halide-Nitrate Systems. (Unless otherwise stated, experimental uncertainty in AHA is about 10 .03 kcal., the mean deviation of four experiments)

Syatem solute- t , AHA, AHn = A H B (lit.) solvent “C. measured AHoa AHD* AHA - A H c - AHD 81 + 12 = aa 4- 11

LiC1-NaNOa 450 +2.64 6.40 -0.46d -3.30 -2.72 LiBr-NaN03 450 + O . 43c 6.10 -0.46d -5.21 -4.49 LiCl-KN03 450 +1.64 5 .43 -1.76d -2.03 -1.63 LiBr-KXOa 450 -1.85 5 .42 -1.76d -5.51 -5.17 KC1-KaN08 450 +4 .71 6.40 -0.48 -1.21 -1.09 KBr-NaN03 450 f 5 . 9 2 6.10 -0.48 + 0.30 + O . 67 RbC1-NaNOa 450 +3 I53 6 .40 -1.01d -1.86 -2.20 RbBr-NaNOa 450 +5.49 6.10 -1.01d +0.40 +0.12 RbCl-KN03 450 +4.77 5.43 -0.06d -0.60 -1.12 RbBr-KX08 450 +5 ,28 5.42 -0.06d -0.08 -0 .55 CsC1-NaN03 490 +2.93e 6 .40 -1 .48 -1.99 -1.53 CsBr-NaNOX 450 +5.90 6.10 -1.48 +1.28 $1.47 TlC1-NaXOa 350 +9 .12 5.91’ +0.13 +3.08 t 3 . 2 8 NaBr-T1N03 350 -2.67 4.75 f 0 . 3 7 -7.79 -7.69

KBr-TlN03 350 -2.08 4.75 + 0 .43 -7.26 -7.02 RbC1-TlNOs 350 -0 .65 4.22 +0 .23 -5.10 -5.48

NaC1-AgN03 350 -9.72 2.72’ +0.52 -12.96 -13.31 NaBr-AgNOa 350 -16.46 1.46’ +0.52 -18.44 -18.93 KCI-AgNOa 350 -12.01 2.72’ -0.60 -14.13 -14.40 KBr-AgN03 350 -16.88 1.46’ -0.60 -17.74 -18.26

RbBr-AgNOa 350 -17.75 1,46’ -1.28 -17.93 -18.81

KCl-TlKO3 350 + O . 23 4.22 + 0.43 -4.42 -4.37

RbBr-TINOa 350 -2.37 4.75 +0.23 -7.38 -7.57

RbC1-AgNOa 350 -13.55 2,72’ -1.28 -14.99 -15.51

a See ref. 3. b See ref. 1, 11, and 0. J. Kleppa and L. S. Hersh, J. Chem. Phys., 36, 544 (1962). Experimental uncertainty f O . l kcal. d Measured a t 345’. Experimental uncertainty i 0 . 0 6 kcal. ’ Measured in this investigation.

The actually measured heat effects ranged from as little as 0.2 cal. (for KCl in TISOs) to as much as 30 cal. (for alkali bromides and chlorides in AgN03). In the tables below we report only the calculated molar enthal- pies of solution, usually as the average of four separate determinations which agreed to 1% or better. The ac- curacy of the reported data for the enthalpy of ex- change (AHB) is estimated to be of the order of hO.1 kcal. /mole.

Results and Discussion 1. Monovalent Halides in Nitrate ( T y p e I I I ) . The

experimental heats of solution, AHA, obtained in the course of the present study are recorded in Table I. This table also contains data on AHc and A H D , based on recent publications from this laboratory. From these quantities we have calculated the experimental ex- change terms, AHB, which also are given in the table.

These values may be compared with corresponding data calculated from standard heat of formation infor- mation. Since the standard heats of formation all are

temperature of the calorimeter. In general, detailed and reliable heat content data are not available for most of the substances used. However, as shown by Blander and Luchsinger,’ a good approximation to the heat content difference can be made by taking into ac- count only the sum of the heats of transformation and of fusion of the nitrates. Apart from this, the heat content correction appears to be quite small in these charge-symmetrical systems. Using the standard heats of formation12 and in each case what we considered to be the most reliable data in the literature on the heats of fusion and heats of transformation of the nitrates, we calculated the values of A H B (lit,) given in the last column of Table I . While there is no quantitative agreement between our own exchange data and the literature values, the discrepancies, on the whole, fall within the range of h 1 kcal./mole. The major part of these discrepancies undoubtedly must be attributed to the heat content corrections.

We noted, by way of introduction, that in binary

referred to the ‘‘lid state and 2501 these must be ‘Or- (12) National Bureau of Standards Circular 500, U. S. Govt. Print- rected for the heat content of all species a t the working ing Office, Washington, D. c., 1952.

The Journal of Physical Chemistry

THERMODYNAMICS OF RECIPROCAL FUSED-SALT SYSTEMS 3 84 3

+25.0

+20.0

+ I 5.0

b, 0 - E \ +10.0 - 0

2 L 4 .I- 5.0

0

- 5.0

-I 0.0

R9-- OSolvent NaNO, 450' 0 Solvent NaNO, , 350" t3 Solvent KN03 , 450" A Solvent

Solvent TIN03 , 350" AgN03 , 350"

Figure 1. eter ( d l - &)(dl - d d d l + dd/dld*d$dd.

Plot of enthalpies of exchange for monovalent halide-nitrate systems ( AHeiexch = AHB) us. size param-

fused-salt mixtures containing a common ion it is pos- sible to relate the enthalpy of mixing to the changes in second nearest neighbor populations. In general, the enthalpy changes associated with reciprocal systems tend to be considerably larger since here changes occur even in the nearest neighbor ionic populations. The dominant term often will be the enthalpy of exchange,

If all four species in (B) were in the solid state, we should in principlc be able to relate AHB to the "latticte enthalpies" of the participating species as follows : Let H A x be the enthalpy of formation of AX(s) from A+(g) and X-(g). Similarly, let HBNO, be the enthalpy of forination of BN03(s) from B+(g) and NO,-@. For the exchange process, with all species solid, we ac- cordingly have

AHB.

AHB' = H B X W + HANO~W - HAXM - HBNO~M

In the ionic approxima,tion we may set

where dAx is the interionic distance in the compound AX, while the proportionality constant, C, includes the Madelung constant, the correction for repulsion, etc. Similar relationships hold for the other species. To a first approximation, C may be assumed to have the same value for each species. Thus, we obtained

C(dAx - dsx)(dAx - daxo,)(dAx + dsso,)/

dsxdA;vo,dAxdBNo,

The latter expression arises from the additivity of the ionic radii. Also, aince the heats of fusion of AXO3 and BNO, are of comparable magnitude and are very small compared to the lattice enthalpy, we have AHB

AHB'.

Volume 68, Number 12 December, 1964

3844 S. V. MESCHEL AND 0. J, KLEPPA

We have in Fig. 1 plotted our experimentally deter- mined values of ANB 5s. the parameter (dl - da)(dl - dz ) (d l + d4) /d ld2d3d4 where dl = AX, etc. In calculat- ing this parameter we have, as usual, set d = T+ + 7 - ,

where T+ and T- are the ionic radii of cation and anion, respectively. For the alkali metals, thallium, and the chloride and bromide ions we have used the Pauling radii, while for silver me have adopted the value T A ~ + = 0.95 A. This choice was dictated by the fact that the lattice parameters of AgCl and KaC1 are very similar, suggesting that the “ionic” radius of silver must be very nearly the same as that of sodium.

Soniemhat greater uncertainty is associated with the proper choice of an ionic Jadius for the nitrate ion. For this ion Janz13 lists 2.3 A. while Kleppa and Hersh,l on the basis of crystal chemical data, adopted the value 2.19 A. On the other hand, the “thermochemical radius” of Kap~s t insk i i , ’~ which is based on arguments related to those presented previously in the calculation of AHB, is 1.89 8. In the course of the present study we noted that AHB for potassium chloride + sodium nitrate is negative (-1.21 kcal.) while the value for potassium bromide + sodium nitrate is positive (+0.30 kcal.). Since, according to the expression for ANB given previously, the enthalpy of exchange should change sign for rx- = T S O ~ - , these results suggested strongly that the effective radius of the nitrate ion in a fused-nitrate medium should be int2rinediate between that of C1- (1.81 A.) and Br- (1.96 A). Interpolation gave TVO,- = 1.93 A . This value was confirmed by other data on AHB and has been adopted in the present work. As might be expected, this value is, close l o Kapustinslrii’s thermochemical radius of 1.89 -4.

Lct us no\T examine Fig. 1 in soiiiewhat greater de- tail. ;\rote first that most of the values for the alkali chlorides and broiiiides in sodium and potassiuin nitrate fall on a single straight line. The slope of this line is about 400 kcal./&, L e . , of an order of magnitude con- sistent with the lattice enthalpies of simple ionic salts. However, even among the considered alkali halides, there are some that do not fall on this line. hlost im- portant among these are lithium chloride and bromide, which show a negative deviation of about .5 kcal./mole. This exothermic shift may be attributed either to an abnormally low cohesive energy of the solid lithium halides or to an abnormally high cohesive energy of Ziquzd lithium nitrate. Here i t is recalled that lithium chloride and bromide, in spite of an unfavorable radius ratio, both crystallize with the sodium chloride struc- ture. Also, since the lithium ion is very small, it may be able to approach the nonspherical nitrate ion some- what more closely than do the other alkali metal ions. Both of these effects may contribute to the negative

shift. On the other hand, since the shift appears to be the same for bromide and chloride, we consider it prob- able that it is caused by added stability of the liquid lithium nitrate. On this basis, using arguments re- lated to those given above for the radius of the nitrate ion in more typical alkali nitrates, ye estimate an “ef- fective ionic radius” of about 1.85 A. for XOa- in com- bination with the lithium ion.

Among the other alkali halides studied we also find a small positive sbift for cesium bromide. Probably, this is due to the added stability of solid cesium bromide, which exists a t 450” in the cesium chloride modifica- tion. Cesium chloride itself, on the other hand, at t8his teniperature has the sodium chloride structure and shows no anomaly.

The reciprocal mixtures of the typical alkali halides with thallium nitrate again exhibit the same linear dependence of AHE on the size parameter, as do the alkali systems. However, now the line is shifted in the positive direction by about 5 kcal./mole for the chlo- rides and by an additional 2 kcal./mole for the bro- mides. We attribute these shifts to the extra cohesive energy of the thallium salts, compared to the alkali salts of the same interionic separation, which contribu- tions presumably increase in the sequence, nitrate < chloride < bromide. Here it is of intercst to correlate our results with those found in a recent n.m.r. study of solid and liquid thallium salts. This study, by Hafner and Na~h t r i eb , ’~ shows an increasing chemical shift of the thallium resonance, z.e., increasing ‘Lcovalency,” in the riequence, T1;COa < TlCl < TlBr.

Finally, we see from Fig, 1 that the alkali halide- silver nitrate systems also show a linear dependence of the enthalpy of exchange on the size parameter, and again the slope is of the same magnitude as that for the alkali halide-alkali nitrates. However, now the posi- tive shift is quite large, roughly three times as large as for the thallium systems, about + 15 kcal./mole for chloride-nitrate and + 18 kcal./niole for bromide- nitrate. These larger endothermic shifts clearly re- flect the larger nonionic contributions to cohesion in the silver salts. Of particular significance is the very con- siderable difference between silver nitrate, on the one hand, and chloride and bromide, on the other. 9. Alkaline Earth Halides-Sodium NitTate (Type

I V ) . The experimental heats of solution (AHA) are recorded in Table 11. Other columns in this table give AHc, AHD, and the enthalpy of exchange, AHB” =

(13) G. J. Jnnz and D. W. James, Electrochim. Acta, 7, 427 (1962). (14) A. F. Kapustinskii, Quart. Ret. (London), 10, 283 (1956). (15) S. Hafner and N . H. Nachtrieb, J . Chem. Phys. , 40, 2891 (1964).

The Journal o f Physical Chemistry

THERMODYNAMICS OF RECIPROCAL FUSED-SALT SYSTEMS 3845

Table I1 : (Quoted experimental uncertainties are mean deviations of four experiments)

Summary of Thermochemical Data (in kcal. /mole) for Alkaline Earth Halide-Sodium Nitrate Reciprocal Systems.

System AHB” = 4HB” (lit.) solute- 1 , A H A , A H A - SI + 211 = solvent O C . measured AH^^ 4Hob 2 A H c - A H , 2ss + 14

CaCl2-Na1VOs 350 -2.O6ZkO0.15 5 , 9 l C -0 .9 -13.0 -10.50 CaBrz-Na:NOa 350 ( -6 .0 f 0 . 3 ) d 5.54c -0 .9 ( - 16.2) -14.80 SrClz-NaN03 450 +2.28ZkO0.O3 6.40 -- 0.26 -10.27 -6 .80 SrBrp-NaKOs 450 - 1 , 3 1 1 0 . 0 2 6 , l O -0.25 -13.26 -9.30 BaClz-NaNOa 450 f 6 . 1 5 + 0.02 6.40 +0.40 -7 .05 -3 .75 BaBr2-NaNOa 450 +4 .90Zk0.02 6 .10 -1-0.40 -7 .70 -4 .51

a Unless otherwise staled, see ref. 3. * From Kleppa, et al., Discussions Faraday SOC., 32, 99 (1961); see also ref. 4. Measured in this investigation. d .Approximate value only.

AHA - 2AHc - AHD. In this case the exchange process is

CaX,(s) + NaNO,(l) = 2T\’aCl(s) + Ca(NO&(l)

This accounts for the coefficient which is applied to AHc in the calculation of AHB”, Otherwise, the calcu- lation is analogous to the one for the monovalent halides, with the exception that, since the alkaline earth nitrates are solid a t the temlperature of the experiments, the values for AND have been corrected for the heats of fusion of these compound^.^ Note also that in the cal- cium halide-sodium nitrate systems, because of a slight decomposition of the melt, the values for A H A are not as precise as [n most of the other experiments. We estimate the errors to be about k0.15 kcal./mole for calcium chloride in sodium nitrate and *0.3 kcal./mole for calcium bromide.

In the last column of Table I1 we finally give values of AHB” (lit.) Calculated as given previously from litera-

ture data on the enthalpies of forniation, fusion, and transformation. It will be noted that for the alkaline earth-sodium nitrate systems there is a much larger dis- crepancy between our own data and the literature values. In all cases our experiments give significantly more negative values of AHB” than calculated. We attribute this to the unsymmetrical character of tlhe metathetical step, which presumably prevents the extensive cancellation of the heat contents noted for the charge-symnie trical systems. Unfortunately, re- liable heat content data are not available to throw further light on this.

Acknowledgments. This work has been supported by the National Science Foundation (GP-1993) and by the Office of Naval Research (Nonr-2121(11)). Geii- era1 support of the Institute for the Study of Metals by the Advanced Research Projects Agency is also ac- knowledged.

Velum 68, ‘Vumber 12 December, 19G4