6242
J . Phys. Chem. 1986, 90, 6242-6247
iii. A virtually reduced form, resulting from a strong twoelectron charge transfer from water to the copper porphyrazine, which is seen in LB films built on pure water and in solutions containing other reducing agents. Each of these species exhibits its own characteristic spectral features. This explains the large difference between spectra of LB films made in various conditions. Molecular interactions modify only slightly these spectra by broadening and slightly shifting the absorption electronic bands. Because of its lesser net charge, the reduced species exhibits a higher tendency to interact with its neighbors. Clearly, the very easy donating complexation of this porphyrazine macrocycle arises from the substitution of the pyridinium rings for the benzo rings of the phthalocyanine. A similar effect was observed by Louati et ai. with cyano substituents.’ The accepting complexation with Lewis acids undergoes a weaker charge transfer, since the spectral features and the ESR data remain similar to those of the parent tetrapyridinoporphyrazine. This macrocycle can therefore be considered as an amphoteric Lewis species. Besides these chemical properties, ESR measurements show that LB films of this copper porphyrazine are well ordered, with the macrocycle lying flat on the substrate. The combination of these two properties is a particuiarly powerful tool to study electron transfer between a donor and an acceptor in a controlled geometry. Since amphiphilic phthalocyanines are (i) particularly easy to handle by the LB method and (ii) particularly versatile from their two degrees of freedom in their donor-acceptor properties (peripheral substitution and choice of central ion), they exhibit the right characteristics to be used as an adjustable material for basic studies on molecular electronics.
Experimental Section Syntheses. Copper tetrap”idin0[3,4-b:3’4’-g:3’’,4”-1:3’~’,4~~’qlporphyrazine (CuTPyPz) was prepared as described by Iwashuma3’ and purified by repeated recrystallizations from (37) Iwashuma, S.;Sawada, T. Res. Bull. Meisei Uniu., Phys. Sei. Eng. 1983, 19, 43.
concentrated sulfuric acid. It was characterized by infrared and UV-visible spectroscopy. I R (KBr): 1608 cm-I; 15 10, 1405 cm-’(vc-c); 1108 cm-’@CH); 750 cm-’(yCH). UV (HSO,): 705 nm (log t = 4.9); 680 nm (4.78); 375 nm (4.36). CuTPyPz was quaternized by refluxing in dimethylformamide for 7 h in the presence of a 20-fold excess of octadecyl bromide. The crude copper tetraoctadecyltetrapyridino[3,4-b:3’,4‘-g:”,4”-f:3‘‘f,4“’qlporphyrazinium bromide (CuSls) [Figure 11 was purified by repeated Soxhlet extractions with diethyl ether, in order to remove the excess of the long-chain reagent, and a final recrystallization from a chloroform-diethyl ether solution. A gel filtration chromatography on Sephadex LH20 was performed, in order to separate CuSls from the less quaternized macrocycles, but this purification remained unsatisfactory. Anal. Calcd for ClooH160N12CuBr3(OH)(H20)(NH3): C, 63.7; H, 8.8; N, 9.6; Cu, 3.4; Br, 17.7. Found: C, 63.8; H, 8.6; N, 9.5; Cu, 3.5; Br, 12.7. IR (KBr) 2926-2854 cm-’(yCH2), 1640 cm-’(C=N+ ).38 Mono- and Multilayer Experiments. Homolayers were built on a trough patented by B a r r a ~ d .The ~ ~ trough used in the present work for alternate layers was recently described by Barraud et a1.40 The subphase was Millipore Q-grade water, unless notice, and all experiments were conducted at 20.22 OC in a nitrogen atmosphere. The solid substrates, which were cleaned by the usual rigorous procedure, were either quartz (for ESR measurements) or calcium fluoride. Transfer speed generally ranged between 0,5 c m - m i d (especially for the first layers) and 2 cmmin-I; the coated substrates were dried between each dip under an additional dry nitrogen jet. Spectroscopic Study. Infrared spectra were carried out on a Perkin Elmer 180 under nitrogen atmosphere. A Cary 2390 was used for UV-visible absorption spectroscopy. ESR measurements were performed on a ER 200 D Bruker apparatus, in the X band. (38) Bellamy, L. J. The Infrared Spectra of Complex Molecules; Chapman-Hall: London, 1975; Vol. I. (39) Barraud, A.;Leloup, J. French Patent No. 83 19770. (40)Barraud, A.;Leloup, J.; Gouzerh, A.;Palacin, S. Thin Solid Films 1985, 132-134.
Thermodynamics of the Unsymmetrical Mixed Electrolyte HCI-SrCi,. Pltzer’s Equations
Applications of
Rabindra N. Roy,* James J. Gibbons,+ Lakshmi N. Roy, and Michael A. Greene Department of Chemistry, Drury College, Springfield, Missouri 65802 (Received: February 18, 1986; In Final Form: July 1 1 , 1986)
Emf measurements were carried out on solutions at temperatures from 278.15 to 318.15 K, for ten values of the constant ionic strength between 0.1 and 5.0 mol kg-I, using a cell without liquid junction of the type Pt;H,(g, 1 atm)lHCl(ml), SrCl2(m,)1AgCl,Ag(A). The results are interpreted in terms of ionic interactions specific to the mixtures by use of Pitzer’s formalism of mixed electrolyte solutions. The estimates of Pitzer mixing parameters S6H,Srand $H,Sr,CI, as well as linear representations of temperature-invariant estimates of 6SOH,s,/6Tand 6$Hsr,cJ6T, have been made. A brief table of the activity coefficients is also given.
Introduction In earlier studies,’-” we have investigated ion-ion interactions in mixtures of hydrochloric acid with bivalent (and trivalent) chloride salts by emf measurements, which are particularly useful for examining the thermodynamic properties of mixed-electrolyte solutions, since they directly yield the activity coefficients of the solute in which the electrodes are reversible. These systems of the type HCI + MClz + H 2 0have been successfully treated by ‘Present address: Analytical Services, D A Y C O Technical Center, P.O. Box 3258, Springfield, MO 65808.
0022-3654/86/2090-6242$01.50/0
the equations of PitzerS for cases in which ion association is negligible and the effects of higher-ordbr electrostatic terms6 on (1) Roy, R. N.;Gibbons, J. J.; Peiper, J. C.;Pitzer, K.S.J . Phys. Chem. 1983, 87, 2365. (2) Roy, R. N.;Gibbons, J. J.; Ovens, L. K.;Bliss, G. A.;Hartley, J. J.
*
Chem. sot.* Faraday Trans. 1405. (3) Roy, R. N.; Gibbons, J. J.; Trower, J. K.; Lee, G. A.J . Solution Chem. 1980, 9, 535, (4) Roy, R. N.;Gibbons, J. J.; Bliss, D. P.; Baker, B.; Casebolt, R. G. J . Solution Chem. 1980, 9, 12. ( 5 ) Pitzer, K . S.J . Phys. Chem. 1973, 77, 268. J.
19813
783
0 1986 American Chemical Society
Thermodynamics of HC1-SrClz Electrolyte
The Journal of Physical Chemistry, Vol. 90, No. 23, 1986 6243
the binary interactions H+-M2+ in the mixtures3v4were taken into account. The theory of Debye-Hfickel is based on the assumption that long-range (electrostatic) attractions and repulsions between ions at finite concentrations of an electrolyte are operative. Recently Friedman' and Pitzer6 developed theories for unsymmetrical mixing of ions of the same sign and concluded that, in addition to long-range forces, the properties of an electrolyte solution at finite concentration are complex functions of shortrange interionic attractions. There are many common-ion mixtures of practical interest for which reliable emf data as a function of ionic strength and temperature are not available in the literature. Thus the present investigation extends our understanding of unsymmetrical mixing effects by very precise emf measurements over a range of temperature and ionic strength on the system HCl-SrCl,. Thermodynamic quantities for aqueous solutions of HCl SrClz are rare at temperatures below and above 298.15 K and in the ionic strength range of 0.1 to 5.0 mol kg-'. Harned and Gary* studied the activity coefficients of HCl for the system HCl SrClz H 2 0a t 298.15 K at total ionic strengths of 1.0, 3.0, and 5.0 mol kg-I from emf measurements using hydrogen and silver-silver chloride cells. Mussini and his co-workersg have investigated the activity coefficients of SrC12 in the temperature range 283.15 to 343.15 K at molalities up to 0.3 mol kg-I with the use of amalgam cells. The results of activity coefficients and Harned interaction coefficients for HCl-SrClz-H2O for 298.15 K at concentrations of 0.03 mol kg-I have been reported by Downes'O from electrochemical cell measurements. Very recently, Holmes and Mesmer" have made isopiestic measurements on SrClZover the temperature range 382.96 to 473.61 K and the molality range of 0.5 to 3.75 mol kg-'.
+
+
+
of cell A with HCl solutions of molality 0.01 mol kg-' and molality of SrClz = 0 mol kg-l.lS The standard potentials thus obtained were in excellent agreement with our previous r e s ~ l t s . ~
Theory and Equations Table I lists the experimental results for the emf of cell A at the experimental barometric pressures given by the Nernst equation
where EoAg,A8C1 is the standard potential for the silver-silver chloride electrode, R and T have their usual physical significances, and F is the Faraday constant. Ionic activities are given by the product q y i in which m is the molality with the dimension of mol kg-I and y is the ionic activity coefficient. The iterative computer calculation is used for the required correction to constant hydrogen fugacity, since the vapor pressure of water contributes to the total pressure over the experimental cell solutions. These are accomplished by calculating the activity of water for each solution, and consequently hydrogen fugacity corrections are made based on these calculated water activities and experimental barometric pressures. The values (Table I) of the quantities mo and Poare 1.0 mol kg-I and 1 atm (or 101.325 kPa), respectively. The physical constants were obtained from Cohen and TaylorI6 and the values of EoAe-kclwere taken from ref 4 after considering the results of Bates et al.Is (based on the behavior of silversilver chloride electrodes). The ionic strength fraction y2 of SrClZis given by YZ
=
(2)
Experimental Section Hydrochloric acid (azeotropic mixture), twice distilled, was diluted to form stock solutions of 0.3 mol kg-', which were standardized by gravimetric analysis as silver chloride. Strontium chloride (ACS certified reagent grade) was recrystallized once. The concentration of this stock solution was determined, in triplicate, by weighing the chloride as silver chloride. The molalities of HCl and SrClz were known to within fO.O1 and f0.02%, respectively. Solutions for all the runs were made by direct weighing of the appropriate stock solutions. Buoyancy corrections were applied to all weighings. All emf readings were made with a cell of the type
In (YHCI) = p + (mH + mCl)(BH,Cl + mCICH,CI) + msr(Bsr,ci + mciCsr,~i+ ~H,sJ + ~ H ~ C I ( B ' H+, CCH,CI) I + mSrmCI(Bkr,CI + CSr,CI + 1/Z$H,Sr,CI) + mHmSr(e'H,Sr + 1/2+H,Sr,CI) (3)
using a digital voltmeter (Keithley Model 191) and were precise to within fO.05 mV from I = 0.1 to 2.0 mol kg-I and to within 0.2 mV from I = 2.5 to 5.0 mol kg-I a t 278.15, 288.15, 308.15, and 318.15 K. The emf value was recorded every 5 min until equilibrium was reached (i.e., agreement well within 0.2 mV for 30 min a t ionic strengths below 1.0 mol kg-I, and about 20 min above 1.O mol kg-I). All the data reported in Table I appear to represent stable and reversible cells. Electrode preparations (thermal electrolytic type),lZJ3temperature fluctuations (f0.02 K), purification of the hydrogen gas, cell design, preparation of cell solutions, and other experimental details have been described p r e v i o ~ s l y . ~The . ~ ~detailed explanations as to how the poisoning effect (or irreversible behavior) of the hydrogen electrode at high ionic strength was avoided have been given e1~ewhere.l~The standard emf of the cell was derived from measurements of emf
cij = q / ( 2 ~ z i z j ~ l ~ ~ ) (34 and the effects associated with the mixing of ions of the same sign are largely incorporated into the mixing parameter OH,Sr. These effects arise from differences in short-range interactions between H+ and Sr2+from the appropriate mean of like pairs of the same sign, that is, H+-H+ and Sr2+-Sr2+. The term OH,& can be represented as
(6) Pitzer, K . S . J. Solution Chem. 1975, 4, 249. (7) Friedman, H. L. In Ionic Solution Theory; Interscience: New York, 1962. (8) Harned, H. S.;Gary, R. J. Am. Chem. SOC.1955, 77, 1994. (9) Longhi, P.; Mussini, T.; Vaghi, E. J. Chem. Thermodyn. 1975, 7, 767. (10) Downes, C. J. J . Phys. Chem. 1970, 74, 2153. (1 1) Holmes, H. F.; Meamer, R. E. J. Chem. Thermodyn. 1981,18, 1025. (12) Bates, R. G. In Determination of p H , 2nd ed; Wiley: New York, 1973; p 331. (13) Robinson, R. A.; Roy, R. N.; Bates, R. G. J . Solution Chem. 1974, 3, 837. (14) Bates, R. G. NBS Tech. Note (US.) 1965, No. 271, 28.
where I = ml
+ 3mz.
Pitzer's Equations The activity coefficient of HCl appearing in eq 1 in mixtures containing the salt, SrClZ,is given by Pitzer and Kim" and by Pitzer6
eH.Sr = EeH,Sr + SeH,Sr; e'H,Sr = Ee'H,Sr + se'H,Sr (3e) is the Debye-Hiickel function for the activity In eq 3-3e, coefficient with parameter A,, which has the valuei8 of 0.3921 1 kg1l2 for water at 298.15, and b = 1.2 kg1/2 The
(15) Bates, R. G.; Guggenheim, E. A.; Hamed, H. S.; Ives, D. J. G.; Janz, G. J.; Monk, C. B.; Prue, J. E.; Robinson, R. A.; Stokes, R. H.; Wynne-Jones, W. F. K. J. Chem. Phys. 1956, 25, 361. 1957, 26, 222. (16) Cohen, E. R.; Taylor, B. N. J. Phys. Chem. ReJ Data 1973,2,663. (17) Pitzer, K. S.; Kim, J. J. J. Am. Chem. SOC.1974, 96, 5701. (18) Bradley, D.J.; Pitzer, K. S. J. Phys. Chem. 1979, 83, 1599.
6244
The Journal of Physical Chemistry, Vol. 90, No. 23, 1986
Roy et al.
TABLE I: Experimental Potentials for the Cell Pt,HzIHCl(m1),SrC12(mz)IAgC1,A& I = 0.10 mol kg-l 85.520 69.380 103ml/(mol kg-I) 100.00 103m2/(mol kg-l) E(278 K, 96.75 kPa)/mV E(288 K, 96.86 kPa)/mV E(298 K, 96.93 kPa)/mV E(308 K, 96.70 kPa)/mV E(318 K, 96.73 kPa)/mV
0 354.57 353.37 351.64 349.15 345.93
103ml/(mol kg-') 1O3m2/(mol k g ' ) E(278 K, 96.70 kPa)/mV E(288 K, 96.82 kPa)/mV E(298 K, 96.91 kPa)/mV E(308 K, 96.70 kPa)/mV E(318 K, 96.73 kPa)/mV
250.00 0
103ml/(mol kg-') 103m,/(mol kg-') E(278 K, 97.46 kPa)/mV E(288 K, 97.46 kPa)/mV E(298 K, 97.73 kPa)/mV E(308 K, 97.33 kPa)/mV E(318 K, 97.31 kPa)/mV
500.00 0 279.23 275.72 27 1.66 266.64 261.29
103ml/(mol kg-l ) 103m2/(mol kg-I) E(278 K, 96.45 kPa)/mV E(288 K, 96.51 kPa)/mV E(298 K, 96.62 kPa)/mV E(308 K, 96.43 kPa)/mV E(3 18 K, 96.42 kPa)/mV
1500.00 0 217.40 212.24 206.45 200.10 192.76
103ml/ (mol kg-')
2000.00 0 197.49 192.00 185.67 179.10
103m2/(molkg-') 1 (278 K, 97.19 kPa)/mV (288 K, 97.18 kPa)/mV E(298 K, 97.25 kPa)/mV E(308 K, 97.19 kPa)/mV E(318 K, 97.19 kPa)/mV
310.59 307.27
103ml/(mol kg-I) 103m2/(mol kg-') E(278 K, 98.02 kPa)/mV E(288 K, 97.95 kPa)/mV E(298 K, 97.95 kPa)/mV E(308 K, 98.07 kPa)/mV E(318 K, 98.11 kPa)/mV
2500.03 0 180.33 174.43 167.74
103ml/(mol kg-I) 103mz/(mol kg-') E(278 K, 96.33 kPa)/mV E(288 K, 96.34 kPa)/mV E(298 K, 96.38 kPa)/mV E(308 K, 96.33 kPa)/mV E(318 K, 96.33 kPa)/mV
3000.00 0 165.42 158.81 150.97
103ml/(mol kg-I) 103m2/(molkg-I) E(278 K, 96.82 kPa)/mV E(288 K, 96.81 kPa)/mV E(298 K, 96.87 kPa)/mV E(308 K, 96.8 1 kPa)/mV E(3 18 K, 96.83 kPa)/mV
3500.07
103mI / (mol kg-I) 103m2/(mol kg-l) E(278 K, 96.37 kPa)/mV E(288 K, 96.35 kPa)/mV E(298 K, 96.38 kPa)/mV E(308 K, 96.38 kPa)/mV E(318 K, 96.35 kPa)/mV
4000.22 0
4.830 359.54 358.59 354.74 351.73
10.210 365.34 363.81 361.97 358.69
I = 0.25 mol kg-l 171.71 127.02 26.100 40.990 324.93 333.98 322.98 332.36 320.14 329.82 3 16.63 326.66 3 12.44 322.75 I = 0.50 mol kg-I 464.36 358.22 11.880 47.260 28 1.88 290.53 278.39 287.35 274.41 283.74 269.51 279.15 264.12 274.18
28.760 23.750 391.89 391.60 391.17 389.98 387.64
73.720 58.760
26.430 74.520
346.27 343.73
239.35 86.880 303.30 300.53 297.09 293.10
376.13 375.28 373.48
119.85 126.7 1
46.810 151.06
321.12 318.30 314.93
346.72 269.51
I = 1.5 mol kg-I 1311.20 1027.50 62.920 157.52 222.78 232.21 217.74 227.40 212.10 222.02 205.85 215.99 199.04 209.34
787.44 237.52 241.70 237.16 232.13 226.34 219.65
435.37 354.88 260.86 256.88 252.56 247.15
168.57 443.82
I = 2.0 mol kg-l 1778.67 1413.85 73.780 195.39 202.78 212.25 197.31 207.04 190.97 201.12 184.66 194.76 177.55 187.74
978.89 340.76 226.25 221.32 215.80 209.91 203.09
648.84 450.39 240.01 235.42 230.25 224.74 218.34
235.01 588.34 269.66 265.98 261.73 257.06 25 1.47
I = 2.5 mol kg-' 2152.34 1703.45 1 15.90 265.53 187.29 197.48 181.59 191.93 175.07 185.73 168.48 179.34 172.12
1201.68 432.78 21 1.44 206.07 200.26 193.86 187.09
699.64 600.12 230.83
180.66 773.12 268.59 264.86 260.69 256.01 250.76
899.40 700.20
277.22 907.59 249.15 245.05 240.29 234.78
I = 3.0 mol kg-I 2750.82 2059.33 83.060 313.55 183.56 177.12 155.54 170.41 234.78 155.66
0
3118.08 127.32
2419.30 360.23
135.55 128.05
141.68 134.40
154.55
121.42
5 1.420 16.190 375.10 374.59 373.63 371.87
I = 4.0 mol kg-l 3540.79 2841.59 153.52 387.15 154.36 148.00 128.60 141.08
209.66 203.47 197.38 190.53
214.49 207.85
1737.68 587.40 182.46 176.54 170.25 163.38 155.96
1186.26 771.19 197.06 191.41 185.40 178.84 171.74
2162.60 614.03 167.40 161.08 154.39
1254.58 917.46 188.14 182.32 176.17 169.06
284.30 280.64 276.31
625.46 1127.66 21 1.58 206.32 200.76 194.74 188.05
The Journal of Physical Chemistry, Vof. 90, No. 23, 1986 6245
Thermodynamics of HC1-SrCl2 Electrolyte TABLE I (continued)
I = 4.5 mol kg-' 103ml/(mol kg-I)
4499.91
103m2/(molkg-I) E(278 K, 96.50 kPa)/mV E(288 K, 96.57 kPa)/mV E(298 K, 96.57 kPa)/mV E(308 K, 96.46 kPa)/mV E(318 K, 96.45 kPa)/mV 103rnl/(mol kg-I) lo3m2/(mol kg-I) E(278 K, 96.22 kPa)/mV E(288 K, 96.23 kPa)/mV E(298 K, 96.25 kPa)/mV E(308 K, 96.19 kPa)/mV E(318 K, 96.17 kPa)/mV
0
4033.63 155.44
3208.10 430.63
107.49
114.41
134.61 127.70
4999.77 0 94.17
I = 5.0 mol kg-' 4444.30 3457.92 185.65 116.10 102.04
116.10
2176.11 774.66 159.95 153.64 146.79 139.79 132.19
1463.03 1012.36 176.45 170.45 163.85 156.85
593.78 1302.14 204.90 200.36 195.23 189.69
2557.88 816.11 146.20 139.72 132.72 125.27 116.77
1629.65 1126.34 165.60 159.46 152.77 146.24
610.70 1466.89 193.19 187.36 180.85
" I is the ionic strength.
molality of ion i is given by mi and the ionic strength Z both having are contributions dimensions mol kg-'. The terms and E@'Hsr from higher order electrostatic effects of unsymmetrical mixing with the omission of short-range forces, and %H,Sr and %'H,Sr account primarily for the effects of short-range forces, as well as the effects due to the use of molarities instead of molalities in the Debye-Hiickel term. The quantity S@'H,Sr arises due to the variation of '0H,S, with I and was set equal to zero according to the suggestions of Pitzer and Kim.17 The second and third virial coefficients for a pure electrolyte ij (with i and j being charges of the ions, where i = H+ and j = Sr2+in the present case) are Bij and Cijand have dimensions of kg mol-r and kg2 mol-2, respectively. The second virial coefficient is dependent on ionic strength with two adjustable parameters, and Pi), which have for 1:l the units of kg mol-l; a is assumed to be 2.0 kg1l2 or 2:1 electrolytes.6 The term + H ~ r , is ~ Ieq 3 in the parameter representing the effect of short-range forces between these three ions in a mixed electrolyte. s@'Hsr, also shown is eq 3, indicates a possible ionic strength dependence of %H,S, and is usually neglected since it is expected to be very small. Once again, it is emphasized that the quantities 8,B', and are properties characteristic of the mixture, while B, B', and 0 are properties of single electrolyte solutions.
of)
+
Higher Order Electrostatic Effects The most important features of the two electrostatic terms E6Hsr and E6'H,Sr from eq 3e are that they do not constitute additional parameterization and they are dependent on (i) ionic strength, (ii) temperature, and (iii) charges of the ions i and j. Recently, it has been shown that these special terms are important for 1:2 mixtures24,19-22 and 1:3 mixtures1p6even though they are zero when ions i and j are of the same charge. The electrostatic effects of, unsymmetrical mixing were noted by Friedman7 and the equations for calculating these terms were derived by Pitzer6 based on cluster-integral theory.23 The relevant equations for calculating these parameters are EeH,Sr EO'H,Sr
=
(ZSrZH/4q[[J(XH.Sr)
-
1/ZJ(XH,H)
= -[EeH,Sr/q + 812) [XH,SJ'(XSr,Sr) - 1/2xH.HJ'(XH,H)
(ZSrZH/
- j/2J(XH,Sr)l
(4)
- 1/2xSr,SJ'(XSr.Sr)l (5)
The variable xij (
x ~ in , ~the ~
TABLE II: Ion Interaction Parameters at 298.15 K
HCI 0.1775' 0.2945" 0.00080" -3.081' 1.419' 0.6213'
$0)
p(1)
C# 104(i@(o)/ar) 104(a,w/ar) 104(acm/ar)
SrCI2 0.2858' 1.6673' -0.00130" -3.073' (7.125)' 122.379b (28.425)' -6.688' (0.0)'
'
" From ref 25. From this work. From ref 30. Temperature coefficient for SrCI2in ref 30 is valid up to rn = 0.1 mol kg-' whereas those in the present study are valid up to m = 1.5 mol kg-'. rivative J'are given by Pitzer.1,6*23,24After the subscripts on x are dropped, the equations are reproduced for ease of reference: (7) 1 J'(x) = 4
+
1
1
0
(t/q2)[1 - (1 - q)eq] dt
with q = xt/ln t
(9) Pitzer6 has given approximate forms for evaluating J and J'. However, we have chosen to compute these integrals using a 200-point Gauss-Legendre numerical integration methods1 It is important to note that for x > 0.10, the numerical methods are most precise, whereas, for x I0.10, the numerical integration is difficult. In this region, the functions J and J'can be evaluated in series form which has been used recently for HCl + L a c & + H 2 0 system.' and EO'H,Sr is determined The temperature dependence of by that of A,, as shown before in eq 6 . This information as well as the precise emf measurements explained and interpreted by employing both eq 2 and 3 permit the computations of '0H,Sr and +H,Sr,CI as functions of temperature. All the values of the virial coefficients (except the unknown mixing parameters and +H,Sr,CI) appearing in eq 3 must be determined over the entire temperature range of interest for the type of Pitzer treatment used here. The parameters for the single electrolyte are assumed to have the representations, e.g.
present case) is defined by
X H , S ~= 6 Z ~ Z , , . 4 1 ~ / *
(6)
where zH and zSrare the valencies of the ions of the same sign, H and Sr, respectively. The univariant functions J and its de-
and similarly for the remaining pure-electrolyte parameters. The values for all HCl and SrClz parameters at 298.15 K and their temperature derivatives are summarized in Table 11.
(19) Khm, K.H.; Lim, T. K.; Chan, C. Y . J. Solution Chem. 1978,7,291. (20) Khm, K.H.; Lim, T. K.; Chan, C. Y . J. Solution Chem. 1979,8,277. (21) Khm, K. H.; Lim, T. K.; Chan, C . Y . J. Chem. Soc., Faraday Trans. 1 1978, 74, 2037. (22) Harvie, C . E.; Weare, J. H. Geochim. Cosmochim., Acfa 1980, 44, 981. (23) Peiper, J. C.; Pitzer, K. S. J . Chem. Thermodyn. 1982, 14, 613.
Results and Discussion Linear least-squares isothermal fittings were made by using eq 1 and 3 with the experimental emf data given in Table I. All (24) Pitzer, K. S.;Kim, J. J. J . Am. Chem. SOC.1974, 96, 5701.
6246 The Journal of Physical Chemistry, Vol. 90, No. 23, 1986
TABLE III:
Mixing Parameters from Isothermal Fits to Data of Table I
5 "C
15 O C
With JeH,Sr/(kg
$Hsr,ct/(kg2mol-*) ufi,/mv
*
0.0486 f 0.0068 0.0099 f 0.0031 0.35
0.0528 0.0052 0.0081 i 0.0024 0.31
-0.0499 f 0.0075 0.0268 f 0.0034 0.39
-0.0500 f 0.0060 0.0267 f 0.0028 0.36
$H,sr,Ct/(kgZ mol-*) uIi,/mv
-
I
0.1 6
-0
.
a
v)
0
00
-
e
0
I
0.
0
?* a
-
-@-e
O .
OC
0.0648 f 0.0062 0.0042 f 0.0030 0.40
0.0653 f 0.0092 0.0012 f 0.0045 0.46
-0.0425 f 0.0085 0.0240 f 0.0041 0.56
-0.0403 f 0.01 11 0.0189 & 0.0054 0.55
Included -0.0378 f 0.0054 0.0208 f 0.0024 0.38
m
-
a
0 0 . 0
0
a - 0 F
0 .
0.
,o,o 0 0
0 0
,o
0 0
n
-
0
n
0
a
- '
u
-
00
HCI-SrC12
0.80
>
-
E
Without
0)
L
Ee, Ee/ 0
0 a
a 0
0
0 0
-
-
a)
-
\
25%
e! With Ee,~e/
-8 L
@ O
0
0
V
IP
3
and
45
0
-0.16
W
0.0642 f 0.0047 0.0033 f 0.0021 0.34
Do-
0
W I
-
35 "C
25 OC Included
and
Without eH,Sr/(kg
'E- 0 .
Roy et al.
0
.oo
0
@a
Y
a
Qo
-
a
m
Q
n g ~ a a -" a 0
a*"
- _.
i8
0 "
@ O
8
a
0 0
n
a
a
a
0 .
O
a 0 -0.80
-
E@
0
a
0
-
'0
-
00
r
0
I
1
1
2
1
I
1
3
4
EB'H.Sr are included.
data points were weighted equally as measurements of E . The single electrolyte parameters were taken from ref 25 and have been entered in Table 11. The unknown parameters eH,Sr and #H,sr,cI(without the inclusion of and E O ' ~ , ~ r )and the corresponding terms and +H,Sr,CI (with EeH,Sr and Ee'H,Sr) were obtained from two separate isothermal fits. All these values of the mixing parameters along with the standard deviation of the fit determined at each temperature via the least-squares procedures are given in Table 111. Another common approach to estimate these mixing parameters is by a graphical procedure by using the relation6 (A In
YHCI)/mSr
= SeH.Sr -k
YdmH
+ "&'H,Sr.CI
(11)
where the quantity A In yHClis the difference between In Y ~ C I (experimental values from eq 1) and that calculated by eq 3 with the inclusion of all pure-electrolyte terms and assuming %H,Sr and ( 2 5 ) Pitzer, K. S.;Mayorga, G . J . Phys. G e m . 1973, 77, 2300
fiHSrC1are equal to zero, and, alternatively, with or without EOH,Sr and %H,Sr. At 298.1 5 K, a plot shown in Figure 1 of the quantity (A In Y H c I ) / m s r vs. l / 2 ( m H + ma) from eq 11 gives a straight line with the intercept SOH,Sr and slope fiH,sr,cl. It is worth mentioning the difficulties in such a procedure (or plot) since the uncertainty in (A In -yHcl)/msrcan be greatly enhanced at lower molalities of Sr2+which, in turn, reflect a constant uncertainty in the experimental emf values. The lower part of the Figure 1 shows the quality of the measurements by plotting the residuals, that is, the deviation from the measured and the calculated values of E . The solid circles represent the inclusion of EO and and the deviations are random (both positive and negative) not exceeding 0.6 mV in most cases. The empty circles indicate the results when higher order electrostatic terms are omitted. As expected, departures are somewhat larger for dilute solutions. Figure 2 indicates the graphical representation of the results of the temperature dependence of %HSr and fiH,sr,cI with the error bars corresponding to the standard deviations of the parameters
The Journal of Physical Chemistry, Vol. 90, No. 23, I986 6247
Thermodynamics of HCl-SrC1, Electrolyte
TABLE IV: Activity Coefficients for the System H+-S$+-CI--H20 at Ionic Strength Fraction y of SrQ' at 25 OC Based on Electrostatic Treatment
5r
0.0 4 L
O'O'
0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
4
A
1
S r, C I
T
0.765 0.820 0.895 1.011 1.150 1.318 1.520 1.761 2.048 2.390
0.781 0.752 0.802 0.866 0.946 1.042 1.152 1.285 1.432 1.561
0.548 0.562 0.625 0.716 0.827 0.968 1.145 1.365 1.638 1.987
0.702 0.707 0.713 0.741 0.776 0.816 0.854 0.924 0.980 1.104
0.515 0.506 0.528 0.563 0.614 0.675 0.754 0.847 0.960 1.088
0.482 0.443 0.431 0.433 0.448 0.474 0.495 0.522 0.548 0.576
'The trace activity coefficients of HCI and SrCI2 are given in columns 4 and 5, respectively.
-0.00 5 1
'
5
1
I
15
25
35
45
t/*C
Figure 2. Temperature dependence of the mixing coefficients SOH3r and The fitted lines are given by eq 12 and 13.
+H,Sr,CI.
as evaluated by the least-squares treatment. The mixing coefficients can be conveniently represented by the equations:
'0H,Sr = 0.0591 +H,Sr,Ci
+ 0.00045(T-
298.15)
(12)
= 0.0054 - 0.00021 ( T - 298.15)
(13)
whereas the temperature coefficients of these parameters are
a
-(sOH,sr) = 0.00045 f 0.00012 aT
a aT(+H,Sr,Ci) = -0.00021
f 0.00004
(14) (15)
It is h o w n from eq 1 and 3 that the emf of cell A is a function of Om rather than 6. Thus, 0 varies with I. But, it has been shown by Khoo and his associates26 that, by assuming 0' = 0, the Pitzer treatment did not alter the results significantly. Hence, it is a common p r a c t i ~ e ~to~ .evaluate ~' 0 and at each I by setting 0' to be zero, then weighting the values of the mixing parameters according to the molalities. This gives a single value of 0 and within the range of ionic strength studied but was not the procedure followed in this work. All of the earlier emf measurementss+l0for this system were limited to 298.15 K. The values of 'OH,srand + H , s ~ at 298.15 K
+
+
(26)Khoo, K.H.; Lim, T. K.; Chan, C . Y . J. Solution Chem. 1977,7,855. (27)Roy, R. N.;Swenson, E. E. J . Solution Chem. 1975,4, 431.
based on previous studies6q8J0are 0.065 and 0.003, respectively, which can be satisfactorily compared with our results of 0.0642 and 0.0033 (Table 111). Thus, Pitzer's treatment for HC1 + alkaline-earth metal chlorides yields values of and which fall in the narrow range2 of (0.06 to 0.09) and (-0.0014 to 0.004). For most practical purposes, reliable estimates of activity coefficients for asymmetrical mixtures can be made based on the average value of and by assuming = 0, if very precise values of activity coefficients are not required. However, the value of the activity coefficients of HC1 and SrC12 reported in Table IV have been calculated based on the precise mixing coefficients based on electrostatic effects, shown in Table 111. Bates and his co-workers28have compared their results derived from the osmotic coefficient data for similar systems such as NaCl SrC12 H 2 0at 298.15 K based on ion-component treatment of S c a t ~ h a r dand ~ ~ion-interaction treatment of Pitzeres They have demonstrated the suitability of the Pitzer treatment. For this reason, Pitzer's equations have been applied in the present study. A forthcoming paper3' in this series deals with the system HBr CaBrz H 2 0 in the temperature range 278.15 to 318.15 K and the molality range of 0.01 to 5.0 mol kg-I.
+
+
+
+
+
+
+
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work, and to the National Science Foundation through Grant No. CH-8543947. Registry No. HC1, 7647-01-0; SrC12, 10476-85-4. (28)Macaskill, J. B.;White, D., R., Jr.; Robinson, R. A.; Bates, R. G. J . Solution Chem. 1978,7, 339. (29)Scatchard, G.;Rush, R. M.; Johnson, J. S. J . Phys. Chem. 1970,74, 3786.
(30)Silvester, L. F.;Pitzer, K. S. J . Solution Chem. 1978,7, 327. (31) Roy, R. N.;Wood, M. D.; Johnson, D.; Roy, L.N. J . Chem. Thermodyn., in press.
