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Thermodynamics of aqueous aluminum: Standard partial molar heat capacities of Al3+ from 10 to 55°C
Thermodynamicsof aqueous aluminum:Standard partial molar heat capacities of A13’from 10 to 55°C JAMEYK. HOVEY Oil SandsResearch Department, AIberta Research Council, and Department of Chemistry, University of Alberta, Edmonton, Alberta, T6G 2G2, Canada
PETERR. TREMAINE Oil SandsResearch Department, Alberta Research Council, P.0, Rex 8330,
Station F, Fdmonton, Alberta, T6H 5X2, Canada (ReceivedSeptember 20, 1985;accepted in revisedfom December 17, 1985) Abstract-Apparent molar heat capacities and volumes of Al(NO& and AK& have been measumd at 25°C in dilute aqueous acid solutions to suppress hydrolysis. Heat capacity results for AK& span the range lO-
WC. The measurements yield standard partial molar heat capacities, ep, and volumes, p, for the Alf+(aq) ion: mAi*, aq) = -45.3 cm’ mol-I, &@I*, aq) = 566.2 - 1.452T- 27338&T- 190),where T is the a&oh& temper&z (K). Our muIt for % is consistent with pu&hed scmi+mphical correlations. The result for clopzp) is more negativethan #at predicted from the entropy correspondence principle by 135 J K-i mot-’ and casts doubt upon the correspondence method as a predictive tool. The heat capacities approach Born behaviour at tievated temperatures and appear to be consistent with the He&son-RirkhamFlowers modal (MESON efa& (198 1) Amer./. Sci. 281, 124P- 1516) for extrapolations to higher tem-
peratures. JNTRODUCTION THE THERMODYNAMlC
properties of aqueous ahsmi-
num species are+required over wide ranges of temper-
ature in order to model mineral dissohnion and tram+ port in steam injection and combustion pmcesses for the in situ recovery of bitumen. The same data are needed to model aqueous solutions associated with the formation of hydrothermal ore deposits, geothermal power generation, the marine chemistry of deep hydrothermal vents, hy~rn~l~, and the corrosion behaviour of ~umi~urn alloys. Equilibrium constants for the hydrolysis of AI’+ and some solubihty data have been obtained up to 300°C (MACDONALD et al., 1973; MESMERand BAES, 1971;COUTURIER et al., 1984; KWUNKO etal., 1983; hhRTYNOVA et al., 1962). No other accurate data for aqueous aluminum species at elevated temperatures have been reported to date. The Gibbs energy of formation of the aluminum ion, Al%q), is reasonably well established at 2S°C (HEMINGWAY and ROBIE,1977). Values for the standard partial molar entropy and volume of A13+(aq) from different studies are much less consistent (HEMINGWAY and ROBIE, 1977; MILLJZRO,1972) and there is oniy one study of apparent molar heat capacities, at 25°C (B~AK~OV and LANSHEVA,1974). Entropy, heat capacity and volume data arc important in comprehensive equations of state which describe the standard state and excess properties of aqua-ions over wide mngesof tempemture and pressure (PITTERef al., 1984, HEUZaON et a/., 1981; HoLMEsand MI%%&%, 1983; TREMAINEet al., 1986). The purpose of the present investigation has been to obtain the standard pattial 453
molar heat capacity of A13+(aq)up to 55’C by mcasuring the apparent molar heat capacity of aqueous solutions of the chloride and nitrate salts. Apparent molar volumes at 25”C, which are re@red to interpret the heat capacity measurements, were also measured and are tabulated here. EXPERIMENTAL Water used in all of the experiments was distilled once and pas& through a Mii-Q reagent grade mixed bed ion exchange and activated carbon system (final ~ndu~~ty of I $3 ~m-‘~orlets). FishercertifiedACS Al(NO>),.PH20 was
mxysUzA twice hum 0.02 m HNfS hy cooling the solution slowly from 50°C to room temperature then to 0°C. AQ - 6H2G from ALEd(Puratonic, “certified PP.999 percent”) was used without further purification. To suppmss hydrolysis, the aluminum stock solutions were pmpamd by dissolving the nitrate and chloride salts in standard sohttions of dilute HNOs and HCI, respectively. The nitrate stock sohrtion contained a ~~~~nt ~n~bution from the residuaI acid on the crystah. The total nitric acid mohdity wasthere6ore determined from careful pH measumments using a calibrated glass electrode. The molahty of hydrochloric acid in the chloride stock solution was determined by calculation and confirmed by pH measurem ents. The stock solutions were standard&d gravimetrically by homogenous precipitation of aluminum with 8_hydroxyquinoline, as described by VWEL (1978). Their composition am listed in Table 1. More dilute sohrtions were prepamd by weight fmm the stock sohnions using sta&&& 10-s m HNQ or HCI as a dituent. The heat capacities and densities of ah sdutions were measured relative to water with a Sodev CP-C flow microcaiorimeter @lCKRR efd. 1971) and 03D densimeter (&XER et ul., 1974). Waterand a s&lard solution of 1.0 & NaCl were used to calibrate the densimeter. Temperatures from 10 to 55’C were maintained to ?O.OO1‘C in the calorimeter by a Sodev CT-L temperatum. bath, calibrated with an HP 280449 quartz themtometer traceable to NRS standards.
454
J. K. Hovey and P. R. Tremaine During these runs, the densimeter and calorimeter delay line were thermostated to 25.000 + O.OOS”Cusing a second !Sodevbath. In this configuration, the calorimeter yields a heat capacitydensity ratio of the form [c#&&) - I]. Here, c, and c,,.,are the specific heats of the solution and pure water at the temperature of the calorimeter, and dM and aLm are the corresponding densities at the temperature of the delay line, 25.OOO”C. The need for (less accurate) high temperature densities is therebyeliminated (SMITH-MAG~WANand WOOD, 198 1; TREMAINE et al., 1986). Densities and specific heat capacities for water wenz taken loom KELL’S compilations ( 1967, 1972): &2n = 0.997047 g cm-‘, and c,,., = 4. I9 19, 4.1793, 4.1783 and 4.1821 J K-l g-’ at 10,25,40 and WC, respectively. The experimental values of [c&&c+&& - 1] were corrected for a small heat leak The correction factor was obtained daily at 25°C by calibration with a standard solution of 1 m NaCl (DESNOYERSetal., 1976; WHITEand WOOD,1982) and was assumed to be independent of temperamre. The value fluctuated between 1.002 and 1.007.
RJZSULTS Apparent molar properties Aqueous A13+can form mononuclear and polynuclear hydrolysis products, according to the reactions (E&TERO et al., 1980; BAES and MESMER, 1976) Al’*(aq) + OH-(aq)
* AlOH*+
2A13+(aq) + ZOH-(aq) F? Alz(OH):‘(aq).
(1) (2)
based on critically evaluated hydrolysis constant data (BAES and MESMER, 1976) indicate that the relative concentration of each should be much less than I percent in the solutions studied here. The following analysis is based on the premise that the solutions contain two stoichiometric solutes, HX and Al& (X = Cl- or NO;) of known molality, m, and that no significant hydrolysis takes place. The experimental apparent molar heat capacity, +CTp, or volume, *Vexp, is defined by the expression Calculations
asp
= Y (solution) - 55.509y0, mAUi + mm
(3)
where Y”,is the molar heat capacity or volume of pure water. Values of *Crp and l Fp are listed in Table 1, along with the experimentai data. The contribution of each salt in the mixture can be described by Young’s rule (YOUNG and SMITH, 1954; REILLY and WOOD, 1969).
+
mu,
mw *Y(HX aq) + 6 + mm
(4)
Here, ‘Y(ALY3, aq) and *Y&IX, aq) are the values for the hypothetical solution of the pure components with speciation and ionic strength identical to the mixture; d is an excess mixing term. To the accuracy required here, d may be ignored in calculating the prop erties of the major components, so that
455
Aqueous Althe~~yn~i~
iV = ‘V@+ u4y(3/2)(l/A
- u/3}Z’” + B,rZ+ CVZ’~ (7)
- mHx *Y(HX, aq). m.uxj
(5)
For our calculations, we used parameters for * F(HC1, aq) at 25°C and for *C&HCl, aq) from 10 to 55°C reported by TREMAINEet al. (1986) for molahties up to 1 m. Parameters forCV(HN03, aq) and *C,(HNO,, aq) were taken from measurements by ENEA et at. (1977) up to 0.2 m. The acid cont~bution calculated from these sources will be in error at higher ionic strengths. The effect on +Y(AL& , aq) is small, and must decrease to zero in extrapolations to infmite dilution. The values of *C, and ‘k’ for AQ(aq) and Al(NO&uf) from Eqn. (5) are also tabulated in Tables 1 and 2.
Data representation Severalextended Debye-Hiickel equations have been developed in recent years to describe the molality dependence of apparent molar properties over a wide range oftem~~tu~ (PrrzER et al., 1984; HELGEsoN et al., 198 1; HOLMES and ~&SMER, 1983; MILLERO, 1979). The data in Table 1 is well represented by the expressions (MILLERO,1979; LIWIS and RANDALL, 1961). ‘C, = ‘C$ + oA,(3/2)(l/A
- u/3)Z’n + Z3,Z+ C,Z3/2 (6)
A, and AV are the Debye-Hiickel limiting slopes for apparent molar properties, and were taken from BRADLEY and PITZER'S equation ( 1979) as reported by ANANTHASWAMY and ATKINSON(1984)Theionic strength, Z, and other terms in Eqns. 6 and 7 are defined as follows. For a solution: Z=
wm = BmiZfj2
A = 1 + Zln
(9)
u = 3(A - I/A - 2 In A)/Z3j2.
mbtci
molkg-'
molkp
%JLZW
0.4667 0.4667 0.3179 0.1762 0.1389 0.1076 0.07874
0.0167 0.0167 0.0117 0.00701
- 0.05698
B, = al + alT
(11)
C, = a3 + a,T + a,T2
(12)
Values for all the parameters obtained from this fitting procedure are tabulated in Tables 3 and 4. The fitted and experimental data for W, are plotted in Fig. 1.
Jk'moV
J K-j mol-1
J K-l mol-1
10.OO*c
0.4667 0.3179 0.1762 0.1389 0.1076 0.07674 0.05083 0.03261
X:iiEi 0.00366
0.0167 0.0117 0.00701 0.00668 8:Z 0.00272 0.06210
- 0.05703 -0.03869 -0.02331 -0.01864 -0.01460 -0.01065
- 0.04366
-0.63063 -0.01760
-0.01364 -0.01101 -0.asf17 -0.005413 -0.063626
-421.6 -422.0 -443.4 -463.9 -479.0 -485.8 -464.9
-300.7 -3iJ.f -334.3 -337.8 -346.7 -361.4 -368.6 -382.3
-3.8 -3.8 -4.3 -5.0
-432.9
- 5.4 -5.8
-493.3 -501.0 -501.1
-6.3
-433.3 -455.4 -477.1
-3.8
-350.5
-3.8
-326.3
-4.1 -4.3 -4.8 -5.0
-3461 -350.1 -360.1
-5.8 -7.1
-365.6 -383.3 -402.8
66.00% 0.4667 0.3179 0.1762 0.136s 0.1076 0.07674 0.05083 0.03261
0.0117 0.60701
-0.04041 -0.02901 - 0.01667
8:iEi 0.00366 0.00272 0.60210
-0.01311 -0.01036 -0.007635 -0.004636 -0.003237
0.0167
(10)
Equations 6 and 7 were fitted to all the data for AIXJ , (aq) in Table 1, by the method of least squares. Values below 0.07 m were regarded as suspect and, in the least squares 6% were assigned a statistical weighting of 10% relative to data obtained at higher molalities. Further, the data for *C,(AlC13, aq) could be represented, with an increase in the overall variance of about 3 percent, by using the following expressions to describe the temperature dependence of B, and C, on the absolute temperature, T(K).
Table 2. Experimental apparent molar hoat capacitimsd AtCls(aq)at 10.40 and 55oC
mAiClt
(8)
-274.9 -297.8 -318.0 -315.7 -325.4 -340.0 -332.4 -336.3
-3.4 -3.6 -3.9 -4.1 -4.4 -4.8 -5.5 -6.8
-281.4 -305.2 -324.5 -324.5 -335.2 -351.0 -344.6 -353.3
J. K. Hovey and P. R. Tremaine
456
Tabte 3. Standard partial molar voknnes. heat capacities and ionic strength parameters
m 0
86
I
-
-
@VO
SV
Cv
4:
cm3 mot’
cm* molt kg
cm’ mol” kg=
AttNO&
25.00
43.1
0.1392
0
Al&
25.00
9.0
0.5995
0
t
solute
i
1.0
I
I
heat capacitms solute
-
t
oc AttNQr AICI,”
SJ
cJ
J K-’ mo13kg
J K-l mol-= kg”
- QCPO J K-’ mol.’
25.00
-335.3
- 16.37
14.27
10.00 25.00 40.00 55.00
- 583.3 -499.3 -456.9 -443.2
- 7.867 - 24.34 -40.82 - 57.29
9.023 13.15 19.51 26.89
’ Av
-
1.0743 cm3 kglR molJRat 25.OO*C
A~
I
28.446,32.783,37.446 and 42.699 J K-’ kgrR molJR at lO.W.25.W. 40.00 and 55.W°C
-
303.131 - 1.09835T
“S
J
cJ - 246.073 - 1.90473 T + 0.00376989 Tz where T 18the absolute temperature
Because the ionic strengths are larger than the molalities by the factor o = 6, these measurements only extend to moderately low ionic strengths. Furthermore, the Debye-Htickel limiting slopes @A,, are rather steep relative to those for 1: 1 electrolytes. As a result, the values of ‘c and lV” obtained by extrapolation to zero ionic strength are sensitive to the exact values chosen for AJ and Av , and to the form of the extended Debye-Htickel equation that is used. The standard de viation from the fits in which the B and C terms are unconstrained is less than 0.8 cm3 mol-’ for V’, 2 J K-’ mol-’ for *c”, at 25, 40 and 55”C, and 8 J K-t mol-’ for *c”, at IO’C. The sensitivity of both prop et-ties to values of Av and AJ from different compilations, and to different fitting equations, leads us to assign overall uncertainty limits of f 1 cm3 mol-’ and -+10 J K mol-‘, respectively, to the values for *V’ and *q in Table 3. The temperature dependent values of l ($AlCls, aq) can be represented to within 0.4 J K-’ mol-‘, by an equation of the form used to represent data for HCl(aq) (TREMAINEet al., 1986) and the alkali halides (HOLMES and MESMER, 1983):
‘CO,(AlCls , as) = 2312.8 -X8533-
115406/(T-
190).
Tabk 4. Standard state properties of aquo-ions at 25% iOIl
F
/cm2
mol.’
H+
(aq)
0
cl-
(as)
10.1
NO;
(aq)
Al”’
(aq)
29.5 -45.3
cpO I J K-’ mar’ 0 - 126.6 -72.1 - 119.3
(13)
I
I
I
I
2
3
I/mol-kg-’ FE I. The apparent molar heat capacities of Al(NO&aq) and AlCl&q), plotted as a function of ionic strengthafter subtractingthe Debye-Htickel limiting law (DHLL) slope according to Eqn. 6. The least squares fits are shown as solid curves.
Theterm(T190) describes the steep rise in l c”, from very negative values near 0°C and was chosen to be identical to that used for aqueous HCl (TREMAINE et al., 1986) for convenience in later calculations. DSCUSSION Standard state properties The values for ‘Co, and lV’ presented above are, by definition, identical to the standard partial molar heat capacity, p,, and volume P. Al+3(aq) is known to be so strongly hydrated that it does not form ion pairs with the chloride ion (FlL4-rtELLo et al., 1968) or oxyanions such as S@-(ao) (Axcn-r and FARNSWORTH, 1985; Lo ef al., 1982) and NO;(aq) (FRATIELLOet al., 1968; ROLand WELZW, 1977) at ionic strengths below about 2 m. We therefore assume that the values for eAAIXS, aq) and p(Al&, aq) obtained here correspond to standard state solutions containing only Al+‘(aq) and Cl-(act) or NO&q). Conventional standard state properties for Cl-(aq) and NO&q) are listed in Table 4. Combining these with the values for lV” from Table 3 yields the values p(A13+, aq) = -45.3 cm3 mol-’ and -45.4 cm3 mol-‘, respectively. The values for l c”, both give pp(A13+, aq) = - I 19 J K-’
457
Aqueous Al thermodynamics mol-‘. The excellent agreement between results from both salts strongly supports the assumption that ion pairing has no significant effect. Averaged ‘best” values are listed in Table 4. The temperature dependence of (?@Y, aq) is identical to that for q(HCl, aq) on the conventional ionic scale. From TREMAINEer al. (1986), c(HCl,
aq) = 582.2 - 1.467T - 29356/(T - 190)
(14)
where T is the absolute temperature (K). Combining Eqns. (13) and (14) yields the following expression which is vahd from IO to 55°C: Cz(Al’*, aq) - 566.2 - 1.4523 - 27338/(T - 190).
q(Mr+,
aq) = 174.05 - 0.523(s” - 20.92) - Z(l17.2)
(16)
The value p(Al”, aq) = -308 + 15 J K-r mol-* from HEMINGWAYand RO~IE ( 1977) yields the CrissCobble prediction pP(A13+, aq) = 16 J K-’ mol-‘, in rather poor agreement with our value of - 119 J K-l mol-‘. MORSS and MCCUE (1976) reported much better agreement with the Criss-Cobble equation for Ci(Th*+, aq). The failure of the correspondence principle for Al)+&) suggests that its success with the more highly charged Th”(aq) ion may welI be fortuitous.
Extrapolations to elevated temperatures (15)
There are few other studies to compare with these results. COUTUREand LAIDLER( 1956) obtained the values *lPfAlC&, aq) = 12.9 cm3 mol-’ and, *p(Al(N03)3, aq) = 43.0 cm3 mol -I, while FAJANS and JOHNSON (1942) cited *V@(Alc13, aq) = 11.1 cm3 mol-‘. The nitrate result is in excellent agreement with our values. Both measurements on the chloride are too positive by about 2 cm3 mol-’ for consistency with our result for A13’+(aq).AKITT and FARNSWORTH(1985) have reported data for A12(S0,)3(aq) which leads to the value P(A13+, aq) = -39 cm3 mol-‘. This result has a significant uncertainty due to the rather steep DebyeHiickel slope (W = 15) and to ion-pairing effects at ionic strengths above about 2 m. BABAKUUWand LATYS~VA (1974) have measured *C,,(Al(C104)3, aq) at 25°C from 0.1 to 3 m (I = 0.6 to 18 m). A least squares fit of Eqn. (6) to their data (I zz 9 m) yields *f$((Al(C104)3, aq) = -2 14 f 8 J K-’ mol-‘. From *C$IIO;, aq) = -25 J K-’ mol-’ (Roux et at, 1978), we obtain @A13+, aq) = -133 J K-r mol-‘, in fair agreement with our value of - 119 J K-r mol-’ from Table 4. Because our measurements extended to lower molalities and yielded identical values for pP from two salts, we believe them to be the more accurate. Correlations at 25°C Because of its high charge, A13’(aq) provides a severe test for correlations that attempt to predict standard partial molar properties. SWADDLEand MAK (1983) have reported an equation which relates p(Mz+, aq) to ionic radius, charge and hydration number. The value calculated from the SwaddlaMak equation, p(Al’+, aq) = -42.1 cm3 mol-‘, is in reasonable agreement with our experimental value, -45.3 cm3 moi-‘. The most widely used heat capacity correlation has been the entropy correspondence principle (CIUSSand COBBLE, 1964a,b). For cations, pdMZ+, aq) is calculated from the entropy at 25”C, according to the equation.
HELGESONet al. (198 1) have developed comptehensive equations to describe the dependence of c and P on widely varying temperatures and pressures. This treatment is based on the assumption that, at high temperature, both properties can be described by the simple Born equation for a charged sphere in a dielectric continuum. For heat capacities at constant pressure: q
= cl + qT/(T - 0) + wTX.
(17)
Here, the terms cI , cz and B are adjustable constants which describe the steep rise in pP just above 0°C. The term oTX is from the Born model for f$“,, where X = [(a’ In #T2X, - (a In &3G]jr
(18)
o = 6.9466 X 10’ Z2/r J mol-‘.
(19)
Here, e is the static dielectric constant of water as tabulated by HELGESONand KIRKHAM (1974), and r is an effective electrostatic radius of the ion (HE~ESON et al., 1981) which yields the value o = 30.29 J mol-’ for AiCi&nB. The premise behind Eqn. (17) is that even approximate model.5 for the high temperature behavior of pP yield accurate extrapolations of Gibbs energies if the low temperature heat capacity function is accurately known. Recent data for aqueous HCl (TREMAINEd al., 1986) seem to support this approach. The model fits the results for ($&AICl,, aq) in Table 3 with a m~mum deviation of less than 2 J K-r mol-*, using the value B = 246 which was obtained from our earlier study on HCl(aq). The fit yields the expression: ‘5’64lGI3,
=I)
= I13.2 - E
+ 30.29 X 10-5TX.
(20)
+ 6.093 x 10-5TX.
(21)
From reference 12. p&HCl, aq) = 14.2 - E
458
J. K. Hovey and P. R. Tremaine Sands TechnololIy and Research Authority-Alberta Research Council Joint Gil Sands Program, ARC contribution no. 1368. Editorial handling:L. N. Plummer
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‘i 0
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a-
E
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-I
192. w7X. The broken curve is the extrapolatedheat capacity firnctionaccordingto the Helgeson-Kid&am-Flowers model, BOTTEROJ. Y., CASESJ. M., FLESS~NGERF. and POIRER J. E. ( 1980) Studies of hydrolyzed aluminum chloride e Rqn. 20.
so that c(Al”+, aq) = 70.6 - $$$
f 12.01 x IO-~TX.
(22)
Equation 20 is plotted in Fig. 2, along with the experimental data and the Born Function, oTX. The data approach Rorn behaviour at eievated temperatures and are consistent with the HELGESON et al. model, except for small differences in the Debye-Htickel limiting slopes. We suggest that Eqns. 20 and 22 be used as provisional heat capacity functions for high temperature calculations until direct measurements become available. In principle, a similar approach can be used to correlate excess or “relative” heat capacities in order to extrapolate activity and osmotic coefficients to elevated temperatures. As a 1:3 electrolyte, AK_&poses certain compIe~ti~ in such treatments (PDZER and MAYORGA, 1974; PITZER, 1975). Some of these have been addressed elsewhere (BARTAand HEPLER, 1986). Acknowledgements-We are gratefulto Professor Loren Hepier, Professor Tom Swaddle and Dr. Ian Tasker for extensive discussions at the time this project was initiated and for their help and encouragement as it pmceeded. During this period, Ms. Leslie Barta began the more detailed volumetric measurements and ion-interaction model calculations cited in BARTAand HEPLER, in press.Her detailed and constructive comments on this work are much appreciated. This study forms part of J. K. Hovey’s thesis work at the University of Alberta. The projectwas carriedout as part of the Alberta Oil
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3711. HELG~N H. C. and KIRKHAM D. H. (1974) Theoretical prediction of the ~e~~ynamic behaviour of aqueous
ekctroQtes at high presuns and temperatums: I. Summary of the thetmodynamic/electrosUc properties of the @vent. Amer. J. Sci. 274, 1089-l 198. HELG~N H. C., KIRKHAMD. H. and FL.OWERSG.C. (1981) Theomtical prediction of the thermodynamic behaviour of aqueous electrolytes at high pressures and temperatures: IV. Calculation of activity coefficient osmotic coefficients and apparent molal and standatxI and relative partial molal properties to 600°C and 5 kb. Amer. J. Sci. 281, 12491516. HEMINGWAYB. S. and ROBIER. A. (1977) The entropy and Gibbs free energy of formation of the aluminum ion. Gecchim. Cosmochim. AC~Q 41, 1402-1404. HOLMESH. F. and MESMERR. E. (1983) The~~y~ic properties of aqueous solutions of the alkali metal chknides to 250°C. J. Phys. Chem. 87, 1242-1255. ICELLG. S. (1967) Pmcise representation of volume properties of water at one atmosphere. J. Chem. Eng. Data 12, 66-
69. KJZLLG. S. (1972) Thermodynamic
and transport properties of fluid water. In Wafer-A Comprehensive Treattse. (ed. F. FRANKS),Vol. I, pp. 363-412. Plenum. KUYUNKON. S., MALININ S. D. and KHODAKOVSKE I. L. (1983) An experimental study of aluminum ion hydrolysis at 150,200, and 250°C. Geachim. Int. 20(2), 76-86. LEWISG. N. and RANDALLM. (1961) Thermodynamics (2nd ed. revised by K. S. PiTzER and L. BREWER).Appendix 4. McGraw-Hill. Lo C-C., MEITES L. and MATl.JEVtCE. (1982) A microcalorimetric invention of the ~e~~yn~i~ of formation of the HSO; , AlSO:, and Al(SO& ions in aqueous solutions at temperatures between 25 and 70°C. Anafyt.
Chim. Acta 139, 197-205. MACDONALD D. D.. BUTLERP. and OWEN D. (1973) Hy-
drothermal hydrolysis of A13+ and the precipitation of Boehmite from aqueous solution. J. Phys. Chem. 77,24742479. MARTYNOVA 0. I., REZNIKOV M. I. and VOL~SNIKOVA
A. I. (1962) Solubility of aluminium hydroxide in water up to 360’. Izv. Vyxshikh Vchebn. Zavedenii Energ. 5, 8591. ME%ER R. E. and BAES,JR. C. F, (197 1) Acidity measurements at elevated temperatures. V. ~uminium ion hydrolysis. Inorg. Chem. 10,2290-22%. MILLEROF. J. (1972) Partial molal volumes of electrolytes in aqueous solutions. In Structure and Transport Process in Water and Aqueous Solutions (ed. R. A. HORNE),Chap. 13, pp. 5 19-564, Wiley. MILLEROF. J. (1979) Effects of pressure. and temperature on activity coefficients. In Activity Co@cients in Electrolyte
Solutions (ed. M. PYICOWKZ),Vol. II, Chap. 2, pp. 63151.CRCRess. Mo~ss L. R. and MCCUE M. C. (1976) Partial molal entropy and heat capacity of the aqueous thorium (IV) ion. Thermochemistry of thorium nitrate pentahydrate. J. Chem.
Eng. Data 21, 337-341. PKKER P., LEDUCP. A., PHIUP P. R. and DE~NOYERS J. E.
( 1971) Heat capacity of solutions by Ilow microcalorimetry. J. Chem. Thermodynamics 3,631-642. PICKERP., TREMBLAYE. and JOLIC~EURC. (1974) A high-
precision digital readout flow densimeter for liquids. J. So-
lution Chem. 3,377-384. PilZER K. S. (1975) ~~~~~ of electroiytes V. Effects of higher order electrostatic terms. J. Solution Chem. 4, 249-265. F?TZERK. S. and MAYORGA G. (1974) Thermodynamics of eiectrolytes III. Activity and osmotic coefficients for 2-2 electrolytes. J. Solution Chem. 3, 539-546. PITZERK. S., PEIPERJ. C. and BUSEY R. H. (1984) Thermodynamic propertiesof aqueous sodium chloride solutions. J. Phys. Chem. Ref: Data 13. REILLY P. J. and WOOD R. H. (1969) The prediction of the properties of mixed electrolytes from measurements on common ion mixtures. J. Phys. Chem. 73,4292-4297. Roux A., MUSBALLYG. M., P&ON G., DE~NOYERSJ. E., SINGHP. P.. W~~LLEY E. M. and HEPLER L. G. (1978) Apparent m&al heat capacities and volumes of a&& electrolytes at 25°C NaClOs, NaClO,, NaNOr, NaBrOs, NaIOs, KClOs, KBrO3, KIOs, N&NO,, NH&l and NHLCIOL. Con. J. Chem. 56.24-28. SMIT~&IA&WAN D. and W&D R. H. ( 198 1) Heat capacity of aqueous sodium chloride from 320 to 600 K measured with a new flow calorimeter. J. Chem. Thermodynamics
13, 1047-1073. SWADDLET. W. and MAK M. K. S. (1983) The partial molar volumes of aqueous metal cations: their prediction and relation to volumes of activation for water exchange. Can. J.
Chem. 61,413-480. TREMAINEP. R., SWAYK. and BARBEROJ. A. (1986) The
apparent molar heat capacity of aqueous hydrochloric acid from 10 to 140°C. J. Solution Chem. (in press). VOGELA. ( 1978)Textbook o~~~it~~ve I~OQ@CAnalysis (4th ed. revised by J. BASSET, R. C. DENNEY,G. H. JEFP~BY and J. MENDS). Longman. WHrTE D. E. and WOOD R. H. (1982) Absolute calibration of Sow calorimeters used for measuring differences in heat capacities. A chemical standard for temperatures between 325 and 600 K. J. Solution Chem. If, 223-236. YOUNGT. F. and SMITHM. B. (i954) Thermodynamic prop erties of mixtures of electrolytes in aqueous solutions. J. Phys. Chem. 58,716-724.
PETERR. TREMAINE Oil SandsResearch Department, Alberta Research Council, P.0, Rex 8330,
Station F, Fdmonton, Alberta, T6H 5X2, Canada (ReceivedSeptember 20, 1985;accepted in revisedfom December 17, 1985) Abstract-Apparent molar heat capacities and volumes of Al(NO& and AK& have been measumd at 25°C in dilute aqueous acid solutions to suppress hydrolysis. Heat capacity results for AK& span the range lO-
WC. The measurements yield standard partial molar heat capacities, ep, and volumes, p, for the Alf+(aq) ion: mAi*, aq) = -45.3 cm’ mol-I, &@I*, aq) = 566.2 - 1.452T- 27338&T- 190),where T is the a&oh& temper&z (K). Our muIt for % is consistent with pu&hed scmi+mphical correlations. The result for clopzp) is more negativethan #at predicted from the entropy correspondence principle by 135 J K-i mot-’ and casts doubt upon the correspondence method as a predictive tool. The heat capacities approach Born behaviour at tievated temperatures and appear to be consistent with the He&son-RirkhamFlowers modal (MESON efa& (198 1) Amer./. Sci. 281, 124P- 1516) for extrapolations to higher tem-
peratures. JNTRODUCTION THE THERMODYNAMlC
properties of aqueous ahsmi-
num species are+required over wide ranges of temper-
ature in order to model mineral dissohnion and tram+ port in steam injection and combustion pmcesses for the in situ recovery of bitumen. The same data are needed to model aqueous solutions associated with the formation of hydrothermal ore deposits, geothermal power generation, the marine chemistry of deep hydrothermal vents, hy~rn~l~, and the corrosion behaviour of ~umi~urn alloys. Equilibrium constants for the hydrolysis of AI’+ and some solubihty data have been obtained up to 300°C (MACDONALD et al., 1973; MESMERand BAES, 1971;COUTURIER et al., 1984; KWUNKO etal., 1983; hhRTYNOVA et al., 1962). No other accurate data for aqueous aluminum species at elevated temperatures have been reported to date. The Gibbs energy of formation of the aluminum ion, Al%q), is reasonably well established at 2S°C (HEMINGWAY and ROBIE,1977). Values for the standard partial molar entropy and volume of A13+(aq) from different studies are much less consistent (HEMINGWAY and ROBIE, 1977; MILLJZRO,1972) and there is oniy one study of apparent molar heat capacities, at 25°C (B~AK~OV and LANSHEVA,1974). Entropy, heat capacity and volume data arc important in comprehensive equations of state which describe the standard state and excess properties of aqua-ions over wide mngesof tempemture and pressure (PITTERef al., 1984, HEUZaON et a/., 1981; HoLMEsand MI%%&%, 1983; TREMAINEet al., 1986). The purpose of the present investigation has been to obtain the standard pattial 453
molar heat capacity of A13+(aq)up to 55’C by mcasuring the apparent molar heat capacity of aqueous solutions of the chloride and nitrate salts. Apparent molar volumes at 25”C, which are re@red to interpret the heat capacity measurements, were also measured and are tabulated here. EXPERIMENTAL Water used in all of the experiments was distilled once and pas& through a Mii-Q reagent grade mixed bed ion exchange and activated carbon system (final ~ndu~~ty of I $3 ~m-‘~orlets). FishercertifiedACS Al(NO>),.PH20 was
mxysUzA twice hum 0.02 m HNfS hy cooling the solution slowly from 50°C to room temperature then to 0°C. AQ - 6H2G from ALEd(Puratonic, “certified PP.999 percent”) was used without further purification. To suppmss hydrolysis, the aluminum stock solutions were pmpamd by dissolving the nitrate and chloride salts in standard sohttions of dilute HNOs and HCI, respectively. The nitrate stock sohrtion contained a ~~~~nt ~n~bution from the residuaI acid on the crystah. The total nitric acid mohdity wasthere6ore determined from careful pH measumments using a calibrated glass electrode. The molahty of hydrochloric acid in the chloride stock solution was determined by calculation and confirmed by pH measurem ents. The stock solutions were standard&d gravimetrically by homogenous precipitation of aluminum with 8_hydroxyquinoline, as described by VWEL (1978). Their composition am listed in Table 1. More dilute sohrtions were prepamd by weight fmm the stock sohnions using sta&&& 10-s m HNQ or HCI as a dituent. The heat capacities and densities of ah sdutions were measured relative to water with a Sodev CP-C flow microcaiorimeter @lCKRR efd. 1971) and 03D densimeter (&XER et ul., 1974). Waterand a s&lard solution of 1.0 & NaCl were used to calibrate the densimeter. Temperatures from 10 to 55’C were maintained to ?O.OO1‘C in the calorimeter by a Sodev CT-L temperatum. bath, calibrated with an HP 280449 quartz themtometer traceable to NRS standards.
454
J. K. Hovey and P. R. Tremaine During these runs, the densimeter and calorimeter delay line were thermostated to 25.000 + O.OOS”Cusing a second !Sodevbath. In this configuration, the calorimeter yields a heat capacitydensity ratio of the form [c#&&) - I]. Here, c, and c,,.,are the specific heats of the solution and pure water at the temperature of the calorimeter, and dM and aLm are the corresponding densities at the temperature of the delay line, 25.OOO”C. The need for (less accurate) high temperature densities is therebyeliminated (SMITH-MAG~WANand WOOD, 198 1; TREMAINE et al., 1986). Densities and specific heat capacities for water wenz taken loom KELL’S compilations ( 1967, 1972): &2n = 0.997047 g cm-‘, and c,,., = 4. I9 19, 4.1793, 4.1783 and 4.1821 J K-l g-’ at 10,25,40 and WC, respectively. The experimental values of [c&&c+&& - 1] were corrected for a small heat leak The correction factor was obtained daily at 25°C by calibration with a standard solution of 1 m NaCl (DESNOYERSetal., 1976; WHITEand WOOD,1982) and was assumed to be independent of temperamre. The value fluctuated between 1.002 and 1.007.
RJZSULTS Apparent molar properties Aqueous A13+can form mononuclear and polynuclear hydrolysis products, according to the reactions (E&TERO et al., 1980; BAES and MESMER, 1976) Al’*(aq) + OH-(aq)
* AlOH*+
2A13+(aq) + ZOH-(aq) F? Alz(OH):‘(aq).
(1) (2)
based on critically evaluated hydrolysis constant data (BAES and MESMER, 1976) indicate that the relative concentration of each should be much less than I percent in the solutions studied here. The following analysis is based on the premise that the solutions contain two stoichiometric solutes, HX and Al& (X = Cl- or NO;) of known molality, m, and that no significant hydrolysis takes place. The experimental apparent molar heat capacity, +CTp, or volume, *Vexp, is defined by the expression Calculations
asp
= Y (solution) - 55.509y0, mAUi + mm
(3)
where Y”,is the molar heat capacity or volume of pure water. Values of *Crp and l Fp are listed in Table 1, along with the experimentai data. The contribution of each salt in the mixture can be described by Young’s rule (YOUNG and SMITH, 1954; REILLY and WOOD, 1969).
+
mu,
mw *Y(HX aq) + 6 + mm
(4)
Here, ‘Y(ALY3, aq) and *Y&IX, aq) are the values for the hypothetical solution of the pure components with speciation and ionic strength identical to the mixture; d is an excess mixing term. To the accuracy required here, d may be ignored in calculating the prop erties of the major components, so that
455
Aqueous Althe~~yn~i~
iV = ‘V@+ u4y(3/2)(l/A
- u/3}Z’” + B,rZ+ CVZ’~ (7)
- mHx *Y(HX, aq). m.uxj
(5)
For our calculations, we used parameters for * F(HC1, aq) at 25°C and for *C&HCl, aq) from 10 to 55°C reported by TREMAINEet al. (1986) for molahties up to 1 m. Parameters forCV(HN03, aq) and *C,(HNO,, aq) were taken from measurements by ENEA et at. (1977) up to 0.2 m. The acid cont~bution calculated from these sources will be in error at higher ionic strengths. The effect on +Y(AL& , aq) is small, and must decrease to zero in extrapolations to infmite dilution. The values of *C, and ‘k’ for AQ(aq) and Al(NO&uf) from Eqn. (5) are also tabulated in Tables 1 and 2.
Data representation Severalextended Debye-Hiickel equations have been developed in recent years to describe the molality dependence of apparent molar properties over a wide range oftem~~tu~ (PrrzER et al., 1984; HELGEsoN et al., 198 1; HOLMES and ~&SMER, 1983; MILLERO, 1979). The data in Table 1 is well represented by the expressions (MILLERO,1979; LIWIS and RANDALL, 1961). ‘C, = ‘C$ + oA,(3/2)(l/A
- u/3)Z’n + Z3,Z+ C,Z3/2 (6)
A, and AV are the Debye-Hiickel limiting slopes for apparent molar properties, and were taken from BRADLEY and PITZER'S equation ( 1979) as reported by ANANTHASWAMY and ATKINSON(1984)Theionic strength, Z, and other terms in Eqns. 6 and 7 are defined as follows. For a solution: Z=
wm = BmiZfj2
A = 1 + Zln
(9)
u = 3(A - I/A - 2 In A)/Z3j2.
mbtci
molkg-'
molkp
%JLZW
0.4667 0.4667 0.3179 0.1762 0.1389 0.1076 0.07874
0.0167 0.0167 0.0117 0.00701
- 0.05698
B, = al + alT
(11)
C, = a3 + a,T + a,T2
(12)
Values for all the parameters obtained from this fitting procedure are tabulated in Tables 3 and 4. The fitted and experimental data for W, are plotted in Fig. 1.
Jk'moV
J K-j mol-1
J K-l mol-1
10.OO*c
0.4667 0.3179 0.1762 0.1389 0.1076 0.07674 0.05083 0.03261
X:iiEi 0.00366
0.0167 0.0117 0.00701 0.00668 8:Z 0.00272 0.06210
- 0.05703 -0.03869 -0.02331 -0.01864 -0.01460 -0.01065
- 0.04366
-0.63063 -0.01760
-0.01364 -0.01101 -0.asf17 -0.005413 -0.063626
-421.6 -422.0 -443.4 -463.9 -479.0 -485.8 -464.9
-300.7 -3iJ.f -334.3 -337.8 -346.7 -361.4 -368.6 -382.3
-3.8 -3.8 -4.3 -5.0
-432.9
- 5.4 -5.8
-493.3 -501.0 -501.1
-6.3
-433.3 -455.4 -477.1
-3.8
-350.5
-3.8
-326.3
-4.1 -4.3 -4.8 -5.0
-3461 -350.1 -360.1
-5.8 -7.1
-365.6 -383.3 -402.8
66.00% 0.4667 0.3179 0.1762 0.136s 0.1076 0.07674 0.05083 0.03261
0.0117 0.60701
-0.04041 -0.02901 - 0.01667
8:iEi 0.00366 0.00272 0.60210
-0.01311 -0.01036 -0.007635 -0.004636 -0.003237
0.0167
(10)
Equations 6 and 7 were fitted to all the data for AIXJ , (aq) in Table 1, by the method of least squares. Values below 0.07 m were regarded as suspect and, in the least squares 6% were assigned a statistical weighting of 10% relative to data obtained at higher molalities. Further, the data for *C,(AlC13, aq) could be represented, with an increase in the overall variance of about 3 percent, by using the following expressions to describe the temperature dependence of B, and C, on the absolute temperature, T(K).
Table 2. Experimental apparent molar hoat capacitimsd AtCls(aq)at 10.40 and 55oC
mAiClt
(8)
-274.9 -297.8 -318.0 -315.7 -325.4 -340.0 -332.4 -336.3
-3.4 -3.6 -3.9 -4.1 -4.4 -4.8 -5.5 -6.8
-281.4 -305.2 -324.5 -324.5 -335.2 -351.0 -344.6 -353.3
J. K. Hovey and P. R. Tremaine
456
Tabte 3. Standard partial molar voknnes. heat capacities and ionic strength parameters
m 0
86
I
-
-
@VO
SV
Cv
4:
cm3 mot’
cm* molt kg
cm’ mol” kg=
AttNO&
25.00
43.1
0.1392
0
Al&
25.00
9.0
0.5995
0
t
solute
i
1.0
I
I
heat capacitms solute
-
t
oc AttNQr AICI,”
SJ
cJ
J K-’ mo13kg
J K-l mol-= kg”
- QCPO J K-’ mol.’
25.00
-335.3
- 16.37
14.27
10.00 25.00 40.00 55.00
- 583.3 -499.3 -456.9 -443.2
- 7.867 - 24.34 -40.82 - 57.29
9.023 13.15 19.51 26.89
’ Av
-
1.0743 cm3 kglR molJRat 25.OO*C
A~
I
28.446,32.783,37.446 and 42.699 J K-’ kgrR molJR at lO.W.25.W. 40.00 and 55.W°C
-
303.131 - 1.09835T
“S
J
cJ - 246.073 - 1.90473 T + 0.00376989 Tz where T 18the absolute temperature
Because the ionic strengths are larger than the molalities by the factor o = 6, these measurements only extend to moderately low ionic strengths. Furthermore, the Debye-Htickel limiting slopes @A,, are rather steep relative to those for 1: 1 electrolytes. As a result, the values of ‘c and lV” obtained by extrapolation to zero ionic strength are sensitive to the exact values chosen for AJ and Av , and to the form of the extended Debye-Htickel equation that is used. The standard de viation from the fits in which the B and C terms are unconstrained is less than 0.8 cm3 mol-’ for V’, 2 J K-’ mol-’ for *c”, at 25, 40 and 55”C, and 8 J K-t mol-’ for *c”, at IO’C. The sensitivity of both prop et-ties to values of Av and AJ from different compilations, and to different fitting equations, leads us to assign overall uncertainty limits of f 1 cm3 mol-’ and -+10 J K mol-‘, respectively, to the values for *V’ and *q in Table 3. The temperature dependent values of l ($AlCls, aq) can be represented to within 0.4 J K-’ mol-‘, by an equation of the form used to represent data for HCl(aq) (TREMAINEet al., 1986) and the alkali halides (HOLMES and MESMER, 1983):
‘CO,(AlCls , as) = 2312.8 -X8533-
115406/(T-
190).
Tabk 4. Standard state properties of aquo-ions at 25% iOIl
F
/cm2
mol.’
H+
(aq)
0
cl-
(as)
10.1
NO;
(aq)
Al”’
(aq)
29.5 -45.3
cpO I J K-’ mar’ 0 - 126.6 -72.1 - 119.3
(13)
I
I
I
I
2
3
I/mol-kg-’ FE I. The apparent molar heat capacities of Al(NO&aq) and AlCl&q), plotted as a function of ionic strengthafter subtractingthe Debye-Htickel limiting law (DHLL) slope according to Eqn. 6. The least squares fits are shown as solid curves.
Theterm(T190) describes the steep rise in l c”, from very negative values near 0°C and was chosen to be identical to that used for aqueous HCl (TREMAINE et al., 1986) for convenience in later calculations. DSCUSSION Standard state properties The values for ‘Co, and lV’ presented above are, by definition, identical to the standard partial molar heat capacity, p,, and volume P. Al+3(aq) is known to be so strongly hydrated that it does not form ion pairs with the chloride ion (FlL4-rtELLo et al., 1968) or oxyanions such as S@-(ao) (Axcn-r and FARNSWORTH, 1985; Lo ef al., 1982) and NO;(aq) (FRATIELLOet al., 1968; ROLand WELZW, 1977) at ionic strengths below about 2 m. We therefore assume that the values for eAAIXS, aq) and p(Al&, aq) obtained here correspond to standard state solutions containing only Al+‘(aq) and Cl-(act) or NO&q). Conventional standard state properties for Cl-(aq) and NO&q) are listed in Table 4. Combining these with the values for lV” from Table 3 yields the values p(A13+, aq) = -45.3 cm3 mol-’ and -45.4 cm3 mol-‘, respectively. The values for l c”, both give pp(A13+, aq) = - I 19 J K-’
457
Aqueous Al thermodynamics mol-‘. The excellent agreement between results from both salts strongly supports the assumption that ion pairing has no significant effect. Averaged ‘best” values are listed in Table 4. The temperature dependence of (?@Y, aq) is identical to that for q(HCl, aq) on the conventional ionic scale. From TREMAINEer al. (1986), c(HCl,
aq) = 582.2 - 1.467T - 29356/(T - 190)
(14)
where T is the absolute temperature (K). Combining Eqns. (13) and (14) yields the following expression which is vahd from IO to 55°C: Cz(Al’*, aq) - 566.2 - 1.4523 - 27338/(T - 190).
q(Mr+,
aq) = 174.05 - 0.523(s” - 20.92) - Z(l17.2)
(16)
The value p(Al”, aq) = -308 + 15 J K-r mol-* from HEMINGWAYand RO~IE ( 1977) yields the CrissCobble prediction pP(A13+, aq) = 16 J K-’ mol-‘, in rather poor agreement with our value of - 119 J K-l mol-‘. MORSS and MCCUE (1976) reported much better agreement with the Criss-Cobble equation for Ci(Th*+, aq). The failure of the correspondence principle for Al)+&) suggests that its success with the more highly charged Th”(aq) ion may welI be fortuitous.
Extrapolations to elevated temperatures (15)
There are few other studies to compare with these results. COUTUREand LAIDLER( 1956) obtained the values *lPfAlC&, aq) = 12.9 cm3 mol-’ and, *p(Al(N03)3, aq) = 43.0 cm3 mol -I, while FAJANS and JOHNSON (1942) cited *V@(Alc13, aq) = 11.1 cm3 mol-‘. The nitrate result is in excellent agreement with our values. Both measurements on the chloride are too positive by about 2 cm3 mol-’ for consistency with our result for A13’+(aq).AKITT and FARNSWORTH(1985) have reported data for A12(S0,)3(aq) which leads to the value P(A13+, aq) = -39 cm3 mol-‘. This result has a significant uncertainty due to the rather steep DebyeHiickel slope (W = 15) and to ion-pairing effects at ionic strengths above about 2 m. BABAKUUWand LATYS~VA (1974) have measured *C,,(Al(C104)3, aq) at 25°C from 0.1 to 3 m (I = 0.6 to 18 m). A least squares fit of Eqn. (6) to their data (I zz 9 m) yields *f$((Al(C104)3, aq) = -2 14 f 8 J K-’ mol-‘. From *C$IIO;, aq) = -25 J K-’ mol-’ (Roux et at, 1978), we obtain @A13+, aq) = -133 J K-r mol-‘, in fair agreement with our value of - 119 J K-r mol-’ from Table 4. Because our measurements extended to lower molalities and yielded identical values for pP from two salts, we believe them to be the more accurate. Correlations at 25°C Because of its high charge, A13’(aq) provides a severe test for correlations that attempt to predict standard partial molar properties. SWADDLEand MAK (1983) have reported an equation which relates p(Mz+, aq) to ionic radius, charge and hydration number. The value calculated from the SwaddlaMak equation, p(Al’+, aq) = -42.1 cm3 mol-‘, is in reasonable agreement with our experimental value, -45.3 cm3 moi-‘. The most widely used heat capacity correlation has been the entropy correspondence principle (CIUSSand COBBLE, 1964a,b). For cations, pdMZ+, aq) is calculated from the entropy at 25”C, according to the equation.
HELGESONet al. (198 1) have developed comptehensive equations to describe the dependence of c and P on widely varying temperatures and pressures. This treatment is based on the assumption that, at high temperature, both properties can be described by the simple Born equation for a charged sphere in a dielectric continuum. For heat capacities at constant pressure: q
= cl + qT/(T - 0) + wTX.
(17)
Here, the terms cI , cz and B are adjustable constants which describe the steep rise in pP just above 0°C. The term oTX is from the Born model for f$“,, where X = [(a’ In #T2X, - (a In &3G]jr
(18)
o = 6.9466 X 10’ Z2/r J mol-‘.
(19)
Here, e is the static dielectric constant of water as tabulated by HELGESONand KIRKHAM (1974), and r is an effective electrostatic radius of the ion (HE~ESON et al., 1981) which yields the value o = 30.29 J mol-’ for AiCi&nB. The premise behind Eqn. (17) is that even approximate model.5 for the high temperature behavior of pP yield accurate extrapolations of Gibbs energies if the low temperature heat capacity function is accurately known. Recent data for aqueous HCl (TREMAINEd al., 1986) seem to support this approach. The model fits the results for ($&AICl,, aq) in Table 3 with a m~mum deviation of less than 2 J K-r mol-*, using the value B = 246 which was obtained from our earlier study on HCl(aq). The fit yields the expression: ‘5’64lGI3,
=I)
= I13.2 - E
+ 30.29 X 10-5TX.
(20)
+ 6.093 x 10-5TX.
(21)
From reference 12. p&HCl, aq) = 14.2 - E
458
J. K. Hovey and P. R. Tremaine Sands TechnololIy and Research Authority-Alberta Research Council Joint Gil Sands Program, ARC contribution no. 1368. Editorial handling:L. N. Plummer
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a-
E
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-I
192. w7X. The broken curve is the extrapolatedheat capacity firnctionaccordingto the Helgeson-Kid&am-Flowers model, BOTTEROJ. Y., CASESJ. M., FLESS~NGERF. and POIRER J. E. ( 1980) Studies of hydrolyzed aluminum chloride e Rqn. 20.
so that c(Al”+, aq) = 70.6 - $$$
f 12.01 x IO-~TX.
(22)
Equation 20 is plotted in Fig. 2, along with the experimental data and the Born Function, oTX. The data approach Rorn behaviour at eievated temperatures and are consistent with the HELGESON et al. model, except for small differences in the Debye-Htickel limiting slopes. We suggest that Eqns. 20 and 22 be used as provisional heat capacity functions for high temperature calculations until direct measurements become available. In principle, a similar approach can be used to correlate excess or “relative” heat capacities in order to extrapolate activity and osmotic coefficients to elevated temperatures. As a 1:3 electrolyte, AK_&poses certain compIe~ti~ in such treatments (PDZER and MAYORGA, 1974; PITZER, 1975). Some of these have been addressed elsewhere (BARTAand HEPLER, 1986). Acknowledgements-We are gratefulto Professor Loren Hepier, Professor Tom Swaddle and Dr. Ian Tasker for extensive discussions at the time this project was initiated and for their help and encouragement as it pmceeded. During this period, Ms. Leslie Barta began the more detailed volumetric measurements and ion-interaction model calculations cited in BARTAand HEPLER, in press.Her detailed and constructive comments on this work are much appreciated. This study forms part of J. K. Hovey’s thesis work at the University of Alberta. The projectwas carriedout as part of the Alberta Oil
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