Julkaisu 112. Freezing Point Depressions of Dilute Solutions of Alkali Metal Chlorides and Bromides. Jaakko I. Partanen [ ] γ ) ln( m d(ln ± I = ±)

Transcription

1 Julkaisu 112 Freezing Point Depressions o Dilute Solutions o Alkali Metal Chlorides and Bromides Jaakko I. Partanen = = ) / ( ) ( 2 ) ( 2 us 1 1 H I m RM I m M R [ ] ) / ( ) ( 2 / ) ) ln ( ( us 1 * p p H I m RM C C I = ±) ln( γ m d(ln ± γ )

2 2 Lappeenrannan teknillinen yliopisto UDK Kemiantekniikan osasto Freezing Point Depressions o Dilute Solutions o Alkali Metal Chlorides and Bromides Jaakko I. Partanen Lappeenranta 1999 ISBN (Paperback) ISBN (PDF) ISSN

3 3 able o Contents ABSRAC 4 INRODUCION 4 RESULS 5 DISCUSSION 1 ACKNOWLEDGEMENS 15 REFERENCES 15

4 4 Freezing Point Depressions o Dilute Solutions o Alkali Metal Chlorides and Bromides Jaakko I. Partanen Department o Chemical echnology, Lappeenranta University o echnology, P.O. Box 2, FIN Lappeenranta Finland ABSRAC Freezing point depressions ( ) o dilute solutions o several alkali metal chlorides and bromides were calculated by means o the best activity coeicient equations. In the calculations, Hückel, Hamer and Pitzer equations were used or activity coeicients. he experimental values available in the literature or dilute LiCl, NaCl and KBr solutions can be predicted within experimental error by the Hückel equations used. he experimental values or dilute LiCl and KBr solutions can also be accurately calculated by corresponding Pitzer equations and those or dilute NaCl solutions by the Hamer equation or this salt. Neither Hamer nor Pitzer equations predict accurately the reezing points reported in the literature or LiBr and NaBr solutions. he values available or dilute solutions o RbCl, CsCl or CsBr are not known at the moment accurately because the existing data or these solutions are not precise. he reezing point depressions are tabulated in the present study or LiCl, NaCl and KBr solutions at several rounded molalities. he values in this table can be highly recommended. he activity coeicient equations used in the calculation o these values have been tested with almost all high-precision electrochemical data measured at K. INRODUCION In a previous paper [1], it has been shown that the reezing points o dilute KCl solutions can be predicted within an experimental error by using in the calculation the best activity coeicient equations available in the literature. he most accurate equations or activity coeicients have been determined rom experimental data measured at a temperature o K. Nevertheless, they predict almost all experimental reezing points or KCl solutions up to a molality o.1 mol kg -1 within.5 K. In this study, the cryoscopy o dilute solutions o the other alkali metal chlorides and bromides was studied by using the best activity coeicient equations or these electrolytes. As in the previous study [1], Hückel, Hamer and Pitzel equations were here used or activity coeicients. he experimental data used in this study were taken rom the literature. Freezing point depressions ( ) in dilute NaCl solutions were measured by Hausrath [2], Osaka [3], Jahn [4, 5], Flügel [6], Rivett [7], Harkins and Roberts [8], Scatchard and Prentiss [9], Momicchioli et al. [1], and Gibbard and Gossmann [11]. Jahn [4, 5], Scathard and Prentiss [9] and Momicchioli et al. [1] investigated cryoscopically dilute LiCl solutions. Freezing point depressions o RbCl and CsCl solutions were studied by Momicchioli et al. [1] and Karagunis et

5 5 al. [12], and o CsCl solutions additionally by Jahn [4]. Scathard and Prentiss [9] and Damköhler and Weinzierl [13] measured in this way values or LiBr, NaBr and KBr solutions. Finally, Jahn [4] studied LiBr and NaBr solutions and Damköhler and Weinzier[13] CsBr solutions. It is shown here that the experimental values or LiCl, NaCl and KBr solutions can be accurately predicted by means o the activity coeicient equations used in calculations. In the best cases, these values can be predicted within experimental error. As or KCl solutions, thereore, it is probable that the most reliable reezing point depression at any dilute solution o these electrolytes can be obtained by the means o the best activity coeicient equations at K. At several rounded up molalities, the recommended values are tabulated below or the solutions o LiCl, NaCl and KBr. RESULS he ollowing equation can be derived between the reezing point depression ( ) and the molality (m) or a pure solution o uni-univalent electrolyte: = C p - = + C 2RM p 1 ( 2R M1( m + I) 2RM ( m + I) + ( H ( m + I) + ( H 1 )ln ( us / * [ ) / ] us / ) ) + (1) where I = ln( γ ±) m d(ln γ ± ) (2) In eqn. (1), is the reezing point o pure water (= K) and that o the solution, H us is the molar enthalpy o usion o water at (= 68 J mol -1 ), C p is the dierence between the molar heat capacities o water as liquid and as solid at a pressure o 11.3 kpa (this dierence is 38.7 J K -1 mol -1 and it is assumed to be independent o the temperature), M 1 is the molar mass o water (=.1815 kg mol -1 ), and R is the gas constant (= J K -1 mol -1 ). In eqn. (2), γ ± is the mean activity coeicient o the electrolyte on the molality scale, and it can be calculated rom the molality by any o the activity coeicient equations considered in this study. he use o eqn. (1) or requires iterative calculations because the second term on the right-hand side contains quantity. In the present study, the experimental values or all these chlorides and bromides were irst compared to the predictions obtained by the activity coeicient equations used. he ollowing equations were used: ln γ ± = -α m 1/2 / (1 + βa * m 1/2 ) ln(1 +2M 1 m) + b 1 (m/ m ) (3)

6 6 lg γ ± = - A m 1/2 /(1+B m 1/2 ) + C 1 (m/m o ) + C 2 (m/m o ) 2 C 3 (m/m o ) 3 + C 4 (m/m o ) 4 + C 5 (m/m o ) 5 + C 6 (m/m o ) 6 (4) ln γ ± = γ + B γ (m/m o ) + C γ ( m/m o ) 2 (5) where γ = -A ϕ {m 1/2 [ (m/m o ) 1/2 ] + [2(m o ) 1/2 /1.2] ln[ (m/m ) 1/2 } (6) B γ = 2β + [β 1 /2(m/m o )]{1 - exp[-2(m/m o ) 1/2 ][1+2(m/m o ) 1/2 2(m/m o )]} (7) C γ = 3C φ /2 (8) he equations are given or a uni-univalent electrolyte, and eqn. (3) is the Hückel equation (see Re. 14), eqn. (4) is the Hamer equation [15] and eqn. (5) is the Pitzer equation [16]. he general parameters have in those the ollowing values: α= (mol kg -1 ) -1/2, β = nm -1 (mol kg -1 ) -1/2, A = α/ln(1), and A φ = α/3. he parameters depending on the electrolyte are shown in ables 1 and 2 or the electrolytes considered here. he parameters a the Hückel equation have been determined by the author [14] and those o the Pitzer equation by Pitzer and Mayorga [17]. he results o the comparison between theoretical and experimental values or NaCl solutions are shown in Figs.1 and 2. In both igures, the dierence ε( ) = (observed) - (predicted) (9) is presented as unction o the molality. he results or the dilute NaCl solutions are shown in Fig. 1 and those or the stronger solutions in Fig. 2. he Hückelequation results were omitted rom Fig. 2 because this equation is usually not valid at molalities larger than.1 mol kg -1 (see Re. 14). he results obtained rom LiCl solutions are illustrated in the same way in two graphs o Fig. 4. he results o the other alkali metal bromides are reported in three graphs o Fig. 5. Only the errors or the Hamer and Pitzer equations are presented in these graphs because no reliable Hückel equations are available or these bromides. he results or RbCl and CsCl are shown in Fig. 6, and these igures show also errors obtained by using the Hückel equation determined or KCl (see able 1). his model was included in this igure because RbCl and CsCl in dilute aqueous solutions resemble thermodynamically KCl (no reliable Hückel equation is available in the literature or RbCl or CsCl).

7 7 able 1. Parameters or the Hückel equation [eqn. (3)] and the Pitzer equation [eqn (5)] o the electrolytes considered in this study. Electrolyte a * / nm b 1 β β 1 C φ LiCl NaCl RbCl.37 a.97 a CsCl.37 a.97 a LiBr NaBr KBr CsBr a ) Determined in Re. 14 or KCl. able 2. Parameters or the Hamer equation [eqn. (4)] o the electrolytes considered in this study. Electrolyte B a 1 3 C C C C C C 6 LiCl NaCl RbCl CsCl LiBr NaBr KBr CsBr a ) Expressed in a unit o nm -1 (mol kg -1 ) -1/2

8 A(NaCl) 1 5 e( ) / K m / mol kg -1 Osaka (Hl) 3 Osaka (Hr) 3 Osaka (Pr) 3 Harkins (Hl) 8 Harkins (Hr) 8 Harkins (Pr) B(NaCl) 1 5 e( ) / K m / mol kg -1 Hausrath (Hl) 2 Hausrath (Hr) 2 Hausrath (Pr) 2 Jahn (Hl) 4 Jahn (Hr) 4 Jahn (Pr) 4 Figure 1. Dierence between the measured and predicted reezing point depression e( ) deined by eqn. (9), as a unction o the molality or dilute NaCl solutions. he data sets and activity coeicient equations (Hl = Hückel equation, Hr = Hamer equation and Pr = Pitzer equation) are shown in the legends o graphs. Graphs C and D are shown on the next page.

9 9 Figure 1 continues 1 5 e( ) / K C(NaCl) m / mol kg -1 Scathard (Hl) 9 Scathard (Hr) 9 Scathard (Pr) 9 Momicchioli (Hl) 1 Momicchioli (Hr) 1 Momicchioli (Pr) D(NaCl) 1 5 e( ) / K m / mol kg -1 Jahn (Hl) 5 Jahn (Hr) 5 Jahn (Pr) 5 Fluegel (Hl) 6 Fluegel (Hr) 6 Fluegel (Pr) 6

10 1 DISCUSSION According to Fig. 1, the experimental reezing points o dilute NaCl solutions can be excellently predicted by means o the activity coeicient equations used in this study. Most o those can be predicted within.5 K. Only the ollowing points in the more precise data sets are exceptions: one point in the set o Harkins and Roberts [8] (in that point m =.836 mol kg -1 and / m = K kg mol -1 and that point is not shown in graph A o Fig. 1; also Guggenheim [18] emphasized that this is probably an erroneous point) and three points in Jahn s more precise set [5] [this set is probably not reliable within its precision in the same way as the corresponding KCl set (see Re. 1)]. In Jahn s older set [4] and in the set o Momicchioli et al. [1], several errors are larger than.5 K but in both sets the pattern ormed by the errors (see graphs B and C) seems to be random. hereore the reezing points in these sets can also be predicted in dilute solutions within the precision o measurements. here is no dierence between eqns. (3), (4) and (5) in the ability to predict the experimental data at molalities less than.5 mol kg -1. Above this molality, the Pitzer equation predicts smaller values or than the other two equations. According to Fig.1, the experimental data can be slightly better predicted by the Hückel and Hamer equations than by the Pitzer equation, but the dierences are probably not signiicant he results o less dilute NaCl solutions are presented in Fig. 2. Because the Pizer and Hamer equations predict too high values or the reezing points in this igure, these equations do not apply to the accurate calculation o the reezing point depressions o NaCl solutions above.1 mol kg -1. According to Fig. 3, the experimental reezing points o dilute LiCl solutions can be predicted accurately up to molality o.6 mol kg -1 by means o the activity coeicient equations used. All three equations predict almost the same values or up to a molality o.5 mol kg -1. Above this limit, the Pitzer equation applies better to the experimental data than the other two equations. O the three data sets available in the literature or KBr solutions, only the set o the Scatchard and Prentiss [9] is, according to Fig. 4, very precise and reliable. he reezing points in this set can be predicted very accurately up to a molality o.16 mol kg -1 by means o the Hückel equation or KBr. In this case, unexpectedly, the applicability o this equation extends ar beyond its normal limit (i.e., ar beyond.1 mol kg -1, see Re. 14). According to graphs A and B o Fig. 5, neither Hamer nor Pitzer equation could predict within experimental error the reezing point depressions measured in dilute solutions o LiBr or NaBr. Because the experimental reezing points o Scatchard and Prentiss [9] seems to be entirely reliable and very precise also in these cases, it is possible that the activity coeicients predicted by the Hamer and Pitzer equations are somewhat erroneous or dilute solutions o these electrolytes. Activity coeicients in dilute LiBr and NaBr solutions at K are not known very accurately because no one (as ar as the author knows) has made precise electrochemical measurements on concentration cells with transerence in these solutions.

11 11 5 A(NaCl) 1 5 e( ) / K m / mol kg -1 Scathard (Hr) 9 Scathard (Pr) 9 Momicchioli (Hr) 1 Momicchioli (Pr) 1 Harkins (Hr) 8 Harkins (Pr) 8 5 B(NaCl) 1 5 e( ) / K m / mol kg -1 Jahn (Hr) 4 Jahn (Pr) 4 Rivett (Hr) 7 Rivett (Pr) 7 Gibbard (Hr) 11 Gibbard (Pr) 11 Figure 2. Dierence between the measured and predicted reezing point depression, e( ) deined by eqn. (9), as a unction o the molality or less dilute NaCl solutions. he data sets and activity coeicient equations (Hl = Hückel equation, Hr = Hamer equation and Pr = Pitzer equation) are shown in the legends o graphs.

12 e( ) / K A(LiCl) m / mol kg -1 Jahn (Hl) 5 Jahn (Hr) 5 Jahn (Pr) 5 Momicchioli (Hl) 1 Momicchioli (Hr) 1 Momicchioli (Pr) 1 Scathard (Hl) 9 Scathard (Hr) 9 Scathard (Pr) 9 1 B(LiCl) 1 5 e( ) / K m / mol kg -1 Jahn (Hr) 4 Jahn (Pr) 4 Momicchioli (Hr) 1 Momicchioli (Pr) 1 Scathard (Hr) 9 Scathard (Pr) 9 Figure 3. Dierence between the measured and predicted reezing point depression e( ) deined by eqn. (9), as a unction o the molality or LiCl solutions. he data sets and activity coeicient equations (Hl = Hückel equation, Hr = Hamer equation and Pr = Pitzer equation) are shown in the legends o graphs.

13 e( ) / K A(KBr) m / mol kg -1 Jahn (Hl) 4 Jahn (Hr) 4 Jahn (Pr) 4 Damkoehler (Hl) 13 Damkoehler (Hr) 13 Damkoehler (Pr) 13 Scathard (Hl) 9 Scathard (Hr) 9 Scathard (Pr) 9 5 B(KBr) 1 5 e( ) / K m / mol kg -1 Jahn (Hr) 4 Jahn (Pr) 4 Damkoehler (Hr) 13 Damkoehler (Pr) 13 Scathard (Hr) 9 Scathard (Pr) 9 Figure 4. Dierence between the measured and predicted reezing point depression e( ) deined by eqn. (9), as a unction o the molality or LiCl solutions. he data sets and activity coeicient equations (Hl = Hückel equation, Hr = Hamer equation and Pr = Pitzer equation) are shown in the legends o graphs.

14 A(LiBr) 1 5 e( ) / K m / mol kg -1 Scatchard (Hr) 9 Scatchard (Pr) 9 Damkoehler (Hr) 13 Damkoehler (Pr) B(NaBr) 1 5 e( ) / K m / mol kg -1 Jahn (Hr) 4 Jahn (Pr) 4 Damkoehler (Hr) 13 Damkoehler (Pr) 13 Scatchard (Hr) 9 Scatchard (Pr) 9 Figure 5. Dierence between the measured and predicted reezing point depression e( ) deined by eqn. (9), as a unction o the molality or LiCl solutions. he data sets and activity coeicient equations (Hl = Hückel equation, Hr = Hamer equation and Pr = Pitzer equation) are shown in the legends o graphs. Graph C is shown on the next page.

15 15 6 C(CsBr) 1 5 e( ) / K m / mol kg -1 Damkoehler (Hr) 13 Damkoehler (Pr) 13 his technique is the most reliable method to study thermodynamically dilute electrolyte solutions (see Re. 14). In the case o CsBr solutions (graph C), the set o Damköhler and Weinzierl [13] is not suiciently precise or a critical consideration. In addition, the Hamer and Pietzer equations or this electrolyte predict completely dierent values or reezing point depressions. he results o Fig. 6 show that the reezing points o RbCl solutions are not known so precisely that the existing data can be used in very critical tests o dierent activity coeicient equations. he reezing points calculated by means o the Hückel equation or KCl (see able 1) are considerably dierent rom those obtained by either he Hamer or Pitzer equation near to the molality o.1 mol kg -1 or both electrolytes. On the other hand, the latter equations give almost same values, and apply also slightly better to the data. According to all conclusions presented above, the reezing points o dilute LiCl, NaCl and KBr solutions can be predicted almost within experimental error by means o eqns. (3), (4) and (5). Owing to the great amount o experimental evidence presented in Figs. 1-4, it seems probable that accurate estimates or the correct reezing-point depressions o LiCl, NaCl and KBr solutions at any dilute molality can be calculated rom these activity coeicient equations. he estimates obtained in this way at several rounded molalities are shown in the able 3. Primarily the values in this table have been computed by using the Hückel equation [eqn. (3)] or the activity coeicients. For LiCl solutions, however, the values o the two strongest solutions shown in the table were calculated by using the Pitzer equation [eqn. (5)]. he values obtained rom the Hückel equation or these two solutions dier rom those in the table by only two or three units in the last digit.

16 A(RbCl) 1 5 e( ) / K m / mol kg -1 Momicchioli (Hl) 1 Momicchioli (Hr) 1 Momicchioli (Pr) 1 Karagunis (Hl) 12 Karagunis (Hr) 12 Karagunis (Pr) B(CsCl) 1 5 e( ) / K m / mol kg -1 Momicchioli (Hl) 1 Momicchioli (Hr) 1 Momicchioli (Pr) 1 Karagunis (Hl) 12 Karagunis (Hr) 12 Karagunis (Pr) 12 Jahn (Hl) 4 Jahn (Hr) 4 Jahn (Pr) 4 Figure 6. Dierence between the measured and predicted reezing point depression e( ) deined by eqn. (9), as a unction o the molality or LiCl solutions. he data sets and activity coeicient equations (Hl = Hückel equation, Hr = Hamer equation and Pr = Pitzer equation) are shown in the legends o graphs.

17 17 able 3. Recommended reezing point depressions o LiCl, NaCl and KBr solutions at rounded molalities. m / mol kg -1 (LiCl) / K (NaCl) / K (KBr) / K , he reezing point depressions in able 3 can be highly recommended. hey have been based on the activity coeicient equations that reproduce accurately, in addition to the experimental values, almost all high-precision thermodynamic data measured at K by dierent electrochemical techniques (see Re. 14).

18 18 ACKNOWLEDGEMENS he author is indebted to the Research Foundation o Lappeenranta University o echnology (he Lahja and Lauri Hotinen s Fund) or inancial support. REFERENCES 1. Partanen, J. I. Acta Chem. Scand. 44 (199) Hausrath, H. Ann. Physik. [4] 9 (192) Osaka, Y. Z. Phys. Chem 41 (192) Jahn, H. Z. Phys Chem. 5 (194) Jahn, H. Z. Phys Chem. 59 (197) Flügel, F. Z. Phys. Chem. 79 (1912) Rivett, A.C.R.Z. Phys. Chem. 8 (1912) Harkins, W.D. and Roberts, W. A. J. Am. Chem. Soc. 38 (1916) Scatchard, G. and Prentiss, S. S. J. Am. Chem. Soc. 55 (1933) Momicchioli, F.; Devoto, O.; Grandi, G., and Cocco, G. Ber. Bunsenges. Phys. Chem. 74 (197) Gibbard, H. F., Jr. and Gossmann, A. F. J. Solution Chem. 3 (1974) Karagunis, G.; Hawkinson, A., and Damköhler, G. Z. Phys. Chem. [A] 151 (193) Damköhler, G. and Weinzierl, J. Z. Phys. Chem. 167 (1934) Partanen, J. I. Acta Polytech. Scand., Chem. echnol. Metall. Ser. 188 (1989) Hamer, W. J. and Wu, Y. J. Phys. Chem. Re. Data 1 (1972) Pitzer K. S. J. Phys. Chem. 77 (1973) Pitzer K. S. and Mayorga, G. J. Phys Chem. 77 (1973) Guggenheim E. A. Phil. Mag. [7] 19 (1935) 588.