Thermodynamic Properties of Solid Systems AgCl + NaCl and AgBr + NaBr from Miscibility Gap Measurements

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1 Thermdynamic Prperties f Slid Systems AgCl + NaCl and + frm Miscibility Gap Measurements CESARE SINISTRI, R I C C A R D O R I C C A R D I, C H I A R A MARGHERITIS, a n d P A O L O TITTARELLI Centr di studi per la termdinamica ed elettrchimica dei sistemi salini fusi e slidi del C.N.R.-Institute f Physical Chemistry, University f Pavia (Italy) ( Z. Naturfrsch. 27 a, [1972] ; received 20 July 1971) Miscibility gaps fr the slid systems AgCl + NaCl and A g B r + N a B r have been measured by a high temperature X-ray technique. Fr the tw studied systems the slubility curves are very nearly symmetrical in respect t the cmpsitins znacl = -513 and N a B r = -506, while the upper critical temperature are 198 C fr AgCl + NaCl and 285 C fr A g B r + N a B r. The thermdynamic prperties f the tw slid systems have been calculated using nly experimental slubility data. Values f activity and f enthalpy f mixing were estimated and cmpared with thse reprted in literature. In KLEPPA and MESCHEL 1 measured the heats f frmatin f slid slutins in the systems AgCl + NaCl and +. On the basis f a previus wrk 2 reprting fr AgCl + NaCl a miscibility gap (MG) with a critical temperature near 175 C, the authrs 1 stated: "since the psitive enthalpies f frmatin f the brmide slutins are abut 20% smaller than thse fr the crrespnding chlrides" fr the system + "a critical temperature smewhat belw 175 C is predicted". Mre recently fr the slid system +, Japanese authrs 3 fund, by study f galvanic cells, a MG cnfirmed by X-ray diffractin measurements. Accrding t these authrs the critical temperature fr an equimlar mixture is between 300 C and C. Owing t latter findings that cntrast with Kleppa and Meschel's predictin we decided t experimentally reexamine the extensin f the MG in the slid phase fr bth systems AgCl + NaCl and +. In rder t describe as accurately as pssible the limits f the MG, high temperature X-ray diffractin measurements were carried ut giving particular care t the sample preparatin. Thrugh these data, we attempted a descriptin f the general thermdynamic prperties f these systems. The results were cmpared, when pssible, with thse reprted in literature. Finally, fr a cmplete descriptin f the phase diagrams f the tw systems, slid-liquid (SL) curves were determined by DTA measurements. Reprint requests t Prf. CESARE SINISTRI, Istitut di Chimica Fisica, Universitä di Pavia, 1-27 PAVIA. Experimental a) Apparatus and Materials The apparatus fr DTA measurements has already been described4. Fr X-ray measurements a Philips apparatus, emplying Ni-filtered CuKa radiatin fitted with a high temperature camera (MRC md. X-86 N-II), was prperly mdified 5 t imprve temperature hmgeneity and cntrl. Thus it was pssible t reach temperatures up t 600 C, cntrlled within + 1 C. NaCl and were C. E r b a RP; AgCl and were btained by precipitatin frm AgN0 3 (C. E r b a RP). All salts were dried fllwing the usual literature methds. b) Prcedures The mixtures t be analyzed by X-ray diffractin were prepared by melting the cmpnents in a quartz tube and quenching the melt in liquid xygen in rder t btain a unifrm mixture. The finely pwdered mixture transferred n the sample hlder f the camera was held at 350 C under N2 fr abut 6 hurs. After the existence f a slid slutin was cnfirmed, the sample was slwly cled t the desired temperature and there held fr a lng time until the equilibrium between the tw new slid phases was reached. It is wrth t underline that, while the mixtures + reached equilibrium in a relative shrt time (15 20 hurs), the mixtures AgCl + NaCl required a much lnger time (10 20 days) thus shwing a large demixing hysteresis. In every case the equilibrium was shwn by the cnstancy f the diffractin patterns taken at different times. The annealing f the samples was carried ut in a separate thermstat thrugh perids as lng as suggested by preliminary tests. Results Figure 1 reprts ur results fr the SL curves in cmparisn with ZEMCZUZNY'S data 6 : fr the Dwnlad Date 3/14/18 3:41 AM

2 T C Zemczuzny this wrk a[a) -800 AgCl " T "C T*C a(a) T C Fig. 1. SL curves fr AgCl + NaCl and -f systems. + system the tw sets f data agree fairly well, whilst fr the AgCl + NaCl system there are sme discrepancies that fr ^NaCi >0.5 can reach even C in the equilibrium temperature f the slid curve. Figure 2 shws the lattice cnstants vs. temperature fr the pure salts: as it is well knwn, all these salts crystallize in the same spatial grup f the cubic system (FM3M). It is interesting t bserve that up t 370 C sdium halides shw linear expansin whilst silver halides d nt. The anmalus increase in the expansin f AgCl and was interpreted n the basis f the vlume requirements f Frenkel defects with mixed Frenkel-Schttky disrder 7. Befre studying the slid phase, the validity f Vegard's law was prved. This law states that the lattice cnstant a f a substitutinal slid slutin f substances with the same crvstal structure is given by a + x{a2 ax) (T = cnst) (1) T*C Fig. 2. Values f the lattice cnstants vs. temperature fr AgCl, NaCl, and pure salts. where and a2 are the lattice cnstants f the pure cmpnents 1 and 2 and x is the mlar fractin f cmpnent 2. Figure 3 shws the values f the lattice cnstants fr the slid slutins at tw different temperatures (365 and 248 C fr the system AgCl + NaCl; 351 and 291 C fr the system + ). Fr temperatures belw 198 C fr the system AgCl + NaCl and 285 C fr the system +, the diffractgrams n equimlar mixtures indicate tw slid phases in equilibrium. The cmpsitins f the tw phases can be deduced frm the values f the tw lattice cnstants by Eq. (1). Table 1 reprts the cmpsitins f the tw phases alng with their "pint f symmetry" (PS) at the different temperatures. Dwnlad Date 3/14/18 3:41 AM

3 Table 1. Slubility limits f the tw slid systems AgCl + NaCl and +. System AgCl (1 -X) + NaCl (X) T K The MG extends PS frm t X = X = X = UCP is at 198 C (471.2 K) and X = mean value X = = ± System (1 - X) + (x) R K The MG extends PS frm t Fig. 3. Test f additivity f lattice cnstants (Vegard's law) fr the slid slutins AgCl+NaCl and +. Figure 4 shws the slid-slid equilibrium curves (SS) btained frm Table 1. These curves are very nearly symmetrical in respect t the cmpsitins ^XaCi = and xxabr = Fr the tw studied systems the fllwing values f the upper critical pint (UCP) were thus deduced: AgCl + NaCl: *c = 198 C, *NaCi, c = 0.513, fc = 285 C, 2 ^ ^ = Thermdynamics fr the Binary System C^A + C2A a) General Principles Let us cnsider the cmmn anin binary system C1 A + C2 A, where x is the mlar fractin f cmpnent 2 (C A) and 1 a; is that f cmpnent 1 (CtA). The activities f the tw cmpnents are 8 : ai = fi( 1 ~ x ); a2 = f2x. (2) X = X X -= UCP is at 285 C (558.2 K) and X = mean value X = = ± The excess ptentials f cmpnents 1 and 2 may be written as: juf =RT\nf1 = Ax 2 + Br i +..., (3) jug = RT\nf2=(A + B +...)(l-x) 2 -B(l-x) (4) The dependence n temperature f the parameters A, B,... in Eqs. (3), (4) can be assumed, as a first but sufficient apprximatin, as: A = A0 + A'T; B = B0 + B'T. (5) The excess mlar Gibbs free energy f mixing can be easily calculated frm Eqs. (3) and (4) : G* = x(l-x)(a+hb+ lbx +...). (6) The excess entrpies can be calculated frm Eqs. (3), (4), (6) witheq. (5). Dwnlad Date 3/14/18 3:41 AM

4 b) Evaluatin f A and B frm Miscibility Gap Data When the binary system C1A+C2A can be fully described by the tw parameters A and B f Eqs. (3), (4) ("tw parameters system"), it is pssible, using MG data, t evaluate these parameters by ne f the fllwing methds. The first ne, already reprted 9, emplyes the UCP f the MG. At the critical pint, bth the secnd and the third derivative f the Gibbs free energy f the mixture G must be null, that is: AgCl NaCl (d 2 G/dx 2 )Tt p = 0; (d 3 G/dx 3 )TfP = 0. (8) Using Eqs. (3), (4), (6) with Eq. (8), the fllwing values f A and B are btained: Fig. 4 a. Slid-slid equilibrium curve btained fr AgCl + NaCl system frm X-ray measurements (circles). The black dts are the pint f symmetry between the tw crrespnding circles Fig. 4 b. Slid-slid equilibrium curve btained fr -{- system frm X-ray measurements (circles). The black dts are the pint f symmetry between the tw crrespnding circles. Finally the enthalpy f mixing is given by: AHm = 7/ E = z(1 a:) [(A-A'T) + \ (B-B'T) + i (B-B'T) x+...] (7) = x(l-x) [(A0 + i50) + ib0x +...]. A = B = R T C 2(1-Zc) 2 *c R T C 3(1-XC) 2 *C 2 (2 3 xc); (2 xc 1) (9) Avhere xc and Tc are the experimental values f the cmpsitin and temperature at the critical pint. In this way, values f A and B at the critical temperature nly are btained, besides, the precisin f the tw parameters is strngly dependent n the precisin with which the critical values are measured. The general cnditins f equilibrium between different phases allws ne t calculate values f A and B thrugh a secnd, mre cmplete, prcedure. If the tw slid phases in equilibrium are indicated with "'" and """ at each temperature must be (x">x') : ju' = l-i^.' % (10 a, b) Frm Eq. (10 a) with Eqs. (2), (3) and using the abbreviatin Ax n = (x") n - {x') n it fllws: RT\n[(l-x')/(l-x")] =AAx 2 + BAi? (11) while frm Eq. (10 b) with Eqs. (2), (4) it fllws: RT\nx"/x = -AA(l-x) 2 (12) + Z? [Zl (1 a;) 3 f Zl (1 a;) 2 ]. Equatins (11) and (12), at the same temperature, allws ne t estimate A and B. If this prcedure is applied t all the experimental pints f SS equilibrium (r t as many interplated pints as desired), explicit values f A and B vs. T can be btained. By Eqs. (2) (7) the thermdynamic prperties f the system can thus be described. Dwnlad Date 3/14/18 3:41 AM

5 Discussin If the tw studied systems can be treated as "tw parameters systems" [see f. e. Kleppa's experimental results 1 expressed by a type (7) relatin], then it is pssible t use the data f Table 1 in cnnectin with Eqs. (2) - (12). The experimental values f the UCP's applied t Eq. (9) give the fllwing data at the Tc f the tw systems (198 and 285 C respectively) AgCl + NaCl: ^ = 1.77; B = 0.13 kcal/mle..4 = 2.17; B = 0.07 kcal/mle. The values f A and B btained, as functins f temperature, by Eqs. (11), (12) are reprted in Fig. 5. It can be bserved that in bth systems B is independent f temperature, while A shws a small dependence. In the investigated temperature range, the values f A fr the + system are always larger than thse fr AgCl + NaCl, while the B values are always rather small. These findings are cnsistent with the shape f the slubility curves (see Fig. 4 ). Assuming each pint has the same weight, interplatin f the data thrugh the least square methd gives: AgCl + NaCl : A = (2.5 ± 0.5) + (0.002 ± 0.001) T kcal/mle, B = 0.2 ± 0.2 kcal/mle, Kcal/mle A= T t C 150 T Fig. 5 a. Values f A and B vs. temperature f r A g C l + NaCl. T h e starred pints have been btained f r m U C P data. Kcal/mle A= T O -d* % B= O.I t C F i g. 5 b. Values f A and B vs. temperature f r A g B r + N a B r. T h e starred pints have b e e n btained f r m U C P data. (13) A = (1.8 ± 0.3) - (0.001 ± 0.001) T kcal/mle, B= kcal/mle. small psitive excess entrpies" which amunt t abut 0.2 e. u. fr equimlar mixtures. On the ther hand, Tsuji et al. 3, frm emf measurements, cncluded that fr the slid system + "the partial mlar entrpy is the same as it wuld be in the ideal slutin". Our findings are cnsistent with these statements. Figure 5 reprts (starred pints) the values f A and B at Tc as calculated by means f Eq. (9) using the UCP values. As can be bserved, these values are in gd agreement with thse btained frm Eqs. (11) and (12). (14) All stated errrs are standard deviatins 10. As can be nted, the temperature cefficients f A (directly cnnected t the excess entrpy terms) have ppsite signs in the tw systems. In particular, fr an equimlar mixture, the cefficients A' f Eqs. (13), (14) give an excess entrpy f 0.5 ± 0.25 e. u. fr AgCl + NaCl and ± 0.25 e. u. fr +. These values indicate that in the first case the excess entrpy is psitive, whilst in the secnd ne the excess entrpy is either zer r slightly negative. K L E P P A 1 cmpared the values f the enthalpy f mixing with thse f the excess free energy btained by P A N I S H et al. 11 frm emf measurements. He fund that "slid slutins (AgCl + NaCl) have Nw, using the explicit values f A and B given by Eqs. (13), (14), it is pssible t describe the thermdynamic prperties f the tw studied systems thrugh Eqs. (2) ( 7 ). Fr bth systems, activity measurements btained by galvanic cells 3 ' 1 1 have been reprted. P A N I S H ' S data 11 fr slid AgCl + NaCl are very scattered and must be cnsidered merely as indicative. In fact, accrding t this authr, "the upper critical slutin temperature fr the slid system (AgCl + NaCl) is between 400 and 500 C ". Figure 6 shws Panish's data with their deviatins at 300 C in cmparisn with the activities f AgCl as calculated n the basis f Eqs. ( 2 ), ( 3 ), (13). Fr the slid system +, the same figure reprts Tsuji's data at 400 C in cmparisn with thse btained thrugh Eqs. ( 2 ), ( 3 ), (14). The agreement in this case is fairly gd. A further cmparisn can be made referring t the enthalpies f mixing measured by K L E P P A 1. Dwnlad Date 3/14/18 3:41 AM

6 Kleppa's data can be represented by the fllwing equatins valid at 350 C: Fig. 6. Cmparisn between the activity data calculated frm ur A and B values (cntinuus line) and the experimental values reprted in literature u ' 13 (circles). Dashed lines represent the limits given by the standard deviatins f the temperature cefficients in Eqs. (13) and (14). AgCl + NaCl : AHm = x{1 - x) ( x) kcal/mle, AHm=x( \ x) ( z) kcal/mle. The data derived frm Eqs. (7), (13), (14) are: AgCl + NaCl : AHm=x(l-x) [(2.6±0.6) + (0.1 ± 0.1) x] kcal/mle, (15) AHm = x(l-x) [(1.85±0.4) + (0.05±0.1) x] kcal/mle. (16) Figure 7 cmpares Kleppa's data (circles with standard deviatins) with urs btained by Eqs. (15), (16). The dtted lines represent the limits prvided Fig. 7. Cmparisn between the enthalpy f mixing calculated frm ur A and B values (cntinuus line) and KLEPPA'S 1 experimental values (circles). Dashed lines represent the limits given by the standard deviatins. by the standard deviatins f the A0 and B0 parameters. It can be nted that in this case the agreement is highly satisfactry. Abut Kleppa's predictin that the upper critical temperature shuld be lwer in the + than in the AgCl + NaCl system a further cmment can nw be made. This previsin des nt take int accunt the excess entrpy terms, which instead, as it was already pinted ut, are psitive fr AgCl + NaCl system, whilst they are zer r slightly negative fr +. Thus, even thugh the enthalpy f mixing is larger in the AgCl + NaCl than in the + system, the crrespndent upper critical temperatures, related t the free energy values, fllw an inverse rder. 1 O. J. KLEPPA and S. V. MESCHEL, J. Phys. Chem. 69, 3531 [1965]. 2 R. J. STOKES and C. H. Li, Acta Met. 10, 535 [1962]. 3 T. Tsuji, K. FUEKI, and T. MUKAIBO, Bull. Chem. Sc. Japan 42, 2193 [1969]. 4 R. RICCARDI and C. SINISTRI, Ric. Sei. 35(II-A) [1965]. 5 M. COLA. Y. MASSAROTTI, R. RICCARDI, and C. SINISTRI, Z. Naturfrsch. 26 a [1971]. 6 S. F. ZEMCZUZNY, Z. Anrg. Allg. Chem. 153, 47 [ B. R. LAWN, Acta Cryst. 16, 1163 [1963]. 8 C. SINISTRI. J. Chem. Educ. 48, 753 [1971]. 9 C. SINISTRI, Quad. Ric. Sei. 35,15 [1965]. 10 Y. BEERS, Thery f Errr, Addisn Wesley Pub. C., Reading, Mass. 1958, p. 37 and fllwing. 11 M. B. PANISH. F. F. BLANKENSHIP, W. R. GRIMES, and R. F. NEWTON, J. Phys. Chem. 62,1325 [1958]. Dwnlad Date 3/14/18 3:41 AM

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