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Apparent molar heat capacity of aqueous hydrolyzed and non-hydrolyzed AlCl3 between 50 and 150°C
0016-7037/92/$5.00 + .JO
Geochimica et Cosmochrmica ACM Vol. 56, pp. 4125-4133 Copyright 0 1992 Pergamon Press Ltd. Printed in U.S.A.
Apparent molar heat capacity of aqueous hydrolyzed and non-hydrolyzed AlQ between 50 and 150°C GIOVANNICON-H,‘.* PAOLOGIANNI,’ and ENRICOMATTEOLI’ ‘Dipartimento di Chimica e Chimica Industriale, Via Risorgimento, 35, 56 100 Piss, Italy ‘Istituto di Chimica Quantistica ed Energetica Molecolare,CNR, Via Risorgimento, 35, 56100, Pisa, Italy (Received September
18, 1990; accepted in revised,form May I, 1992 )
Abstract-By means of a flow calorimeter, the specific heats of aqueous solutions containing AlC13 with and without added HCI have been measured at 50, 100, and 150°C. The apparent molar heat capacity C,,$ of the HCI-containing solutions have allowed the calculation of the standard molar heat capacity of AlCl3, c;,A,C,, . These data satisfactorily link together with those of Hovey and Tremaine in the range lo-55°C ( HOVEYand TREMAINE,1986), afterwards reassessed by BARTAand HEPLER, 1986. The treatment of the C,,# data with the ionic interactions model of Pitzer has provided the values of pco)J and pc’)J for the calculation of C’;,$ 3 in the concentration range 0.03-0.75 mol kg-’ at the temperatures studied. Experimental values of the apparent molar heat capacities obtained for hydrolyzed solutions have been compared with the analogous quantities calculated accounting for the CD,@,, of all species present at equilibrium, as well as for the chemical relaxation term, C’EL, which is due to the energy absorbed by the hydrolysis shift induced by the heating inherent in the specific heat measurement. The calculation has been carried out on the basis of some hydrolytic schemes proposed in the literature and has provided useful insights on the hydrolysis reaction at temperatures where the extent of reaction is quite marked. INTRODUCIION MUCH ATTENTIONHAS BEENdevoted to the thermodynamic characterization of aqueous acidic systems containing Al 3t ion and its hydrolysis products for its impact in applicative, environmental, as well as scientific areas. A review can be found in a comprehensive treatise edited by SPOSITO( 1989). On the contrary, the quantity of data regarding the thermodynamic properties of aqueous Al( H20):+ and relevant complex hydrolytic species at high temperature is still rather limited. Some data of stability constants of hydroxo-complex species exist above room temperature ( MESMER and BAES, 1971; MCDONALD et al., 1973; COUTURIERet al., 1984; KuYUNKO et
al., 1983; MICHARD, 1983; REED and SPYCHER, 1984), and more recent studies provide accurate values of partial molar volumes and heat capacities of limiting species such as A13+ up to 55°C (HOVEY and TREMAINE, 1986; BAR~A and HEPLER, 1986) and Al(OH); up to 250°C (HOVEY et al., 1988; CAIANI et al., 1989). The above properties play a fundamental role in the thermodynamic treatment of natural aqueous systems which extend over wide ranges of temperature and pressure. Every study aimed at the increase of the knowledge in this field is therefore welcome. The purpose of this work has been the extension of the heat capacity data of aqueous non-hydrolyzed solutions of Al 3+to the temperature range 50- 15O”C, as well as to measure the same property for solutions of A13+ ion in conditions such as to undergo hydrolysis. In this way, it has been possible to make comparisons between the apparent molar heat capacities, Ct., , of the hydrolyzed AlC13obtained from the experimental specific heats and the corresponding
* Author to whom correspondence
should be addressed. 4125
values calculated using apparent molar heat capacities of all species predicted at equilibrium by some different schemes proposed in literature. The calculation has been performed by taking into account the chemical relaxation contribution, Czl, a property to deal with whenever specific heat measurements on systems of equilibrated reacting species are carried out. The procedure followed here is the same as that introduced by previous authors ( MCCOLLUM, 1927; EIGEN and DE MAYER, 1963; WOOLLEYand HEPLER, 1977; JOLICOEUR et al., 1979; PEIPER and PITZER, 1982; BARBEROet al., 1983; MAINS et al., 1984; HOVEY and HEPLER, 1990); here it is applied to parallel chemical reactions. This quantity is determined by the stoichiometry, the equilibrium constants, and the enthalpies of the reactions taking place and therefore contains important information relevant to the process itself.
EXPERIMENTAL Apparatus Specific heat measurements were carried out by means of a differential flow calorimeter previously described ( CONTI et al., 1988) and recently modified and improved ( CONTIet al., 1991).The constant pressure specific heats, c,,, were calculated through Eqn. ( I ), as follows: c,,
=-.
c,-d, d,
AT, (AT,
+ 0) ’
(1)
where c, is the specific heat of water at the temperature of the experiment; d, and d, are the densities of water and solution at 298. I5 K. respectively; and AT, and (AT,, + 0) are the temperature increments observed on water and on sample solution, respectively, which circulate in the calorimeter at the same flow value (p = 0.025 cm3 s-l) and are heated with the same power P (usually P - 0.5 W). The 6 value is the immediate result of the calorimetric measurement on the sample solution. The AT, quantity is a constant for constant values of the flow, of the heating power, and of temperature, variables
G. Conti, P. Gianni, and E. Matteoli
4126
which characterize a set of measurements. AT, was accurately determined by means of physical calibration experiments carried out with water using the following equation: AT = 0 ((p - ‘,) W LL,’
Table 1. Experimental specific heats, cp,, and apparentmolarheat capacities, CD*, of aqueous AlCls or AlCJa + HCI mixtures at various compositionsand
where L, represents a known small leak (maximum 2% of flow) applied to the solvent flow, cp,in the measuring cell; this leak brings about a temperature increase tTL,which simulates a small specific heat decrease. Solution densities were measured at 25’C by means of an Anton Paar model DMA 60 densimeter with measuring cell model DMA 602. Measurements have been carried out at room pressure, and the variation of the density with pressure was neglected, in consideration of the fact that the pressure in the calorimetric experiments was never over I.0 MPa.
50
100
Solutions
All solutions were prepared in mass. Stock solutions of aluminum chloride were prepared using AlC13*6H20 from Merck, whose purity, controlled periodically as Al203 by calcination in a platinum crucible, resulted in about 99.9%. The water used was deionized and deaerated. HCI solutions were prepared according to standard procedures. Sample solutions were prepared by diluting amounts of stock solution either with water or with the HCI solution. The quantities of HCI to be added were calculated taking the equilibrium constants from hydrolytic model II described and used later (see Results and Discussionsection). At 50 and lOO”C,the residual hydrolysis resulted, in any case, less than 0.5%; whereas at lSO”C, it was comprised between I and 2% for the most diluted solution. Larger HCI/AI ratios were not considered in order to avoid acidic chemical attack to the calorimetric cell and also to allow that the specific heat effect measured was due mostly to the aluminum species. At 15O”C, therefore, the heat capacities were corrected for the residual hydrolysis with a procedure described later. The samples without HCI addition were used some days after preparation. RESULTS
Specific heats of all solutions examined, and the corresponding values of the apparent molar heat capacities, are reported in Table I for the three following temperatures considered: 50, 100, and 150°C. In the same table, the composition of the solutions, as well as other details about the experimental method followed for specific heat measurement, are also collected. At 15O”C, C,,4 data have been obtained only for low concentrations because, due to the large quantity of HCl necessary for repressing hydrolysis at rn > 0.1, the material constituting the cell tubing, Inconel600, underwent acid attack. In fact, at this temperature, in spite of the added HCl, the maximum hydrolysis extent was about 2%. Non-hydrolized
Solutions
The C,,+ data of solutions containing AK& + HCI have been obtained through the following general equation for mixture of electrolytes: (1000 + C CP.9
mjh4i)Cp.s
I
=
C llli 1
K
CPLC Jg-‘K-’
d, cP,+ Jml -‘K-I
1.01 1.03 1.61 1.65 2.43 2.50 3.16 9.10 14.67 21.42
4.1533 4.1532 4.1368 4.1362 4.1146 4.1142 4.0942 3.9373 3.7980 3.6343
-3lWO -359t20 -316i15 -34of15 -3wilO -34DflO -299ilO -272s -254s -230-z
1.00163 1.00067 1.0@404 1.00301 1.00390 l.OC672 lm592 1.00949 1.00883 1.03227 1.03146 1.05432 1.05331 1.08042
1.53 0.65 1.99 1.12 1.94 2.61 1.66 303 2.22 7.62 6.50 11.46
-203f20 -251f20 -232i15 -261i20 -22&15 -261ilO -252ilO -259ilO -251flO -237s -227i5
10.34 15.99
4.1752 4.1915 4.1588 4.1751 4.16&l 4.1391 4.1556 4.1220 4.1358 3.9705 3.9863 3.8392 3.8569 3.6924
-275(e) -146f20
@lOZb’
(2)
-
100OC~ (3)
In this equation, c,, and c, are the specific heat of the solution and of water, respectively, at the same temperature and pressure; mi and Mi are the molality and the molecular weight of the ith electrolyte, respectively. At 15O”C, the small con-
150
3.013 3.013 4.910 4.591 7.4% 7.484 10.00 29.94 49.41 75.15
0.242
3.026 3.012 5.149 4.991 5.032 7.511 7.484 9.998 9.987 29.% 30.00 49.99 50.02 74.78
4.996
2.974 3.coo
4.958
1.00156 1.0&X5
1.85 0.41
4.2636 4.2882
0.276 0.373 0.432 1.120 1.752 2.462
4.336 4.342 3.814 3.165 4.053 5.041 5.235
l.OCW-2 1.00x7 1.00297 1.00301 1.00602 1.00592 1.00892 1.03164 1.05302 1.08028
-206s -203s -185i2
5.030
6.049
1.Ou421
2.93
4.2369
-320(e)
4.983 4.960
5.963
1.00414
2.97 0.74
4.2367 4.2735
7.432 7.521
7.963
1.00737 l.OW7
3.60 1.32
4.2142 4.2525
-329(e) -159i15 -273(e)
10.03 9.9%
6.011
l.Olca l.CQW
3.53 1.42
4.2039 4.2390
1.00296
-193ztlO .255(c) -143ilO
Densities at 25Dc. b) Calorimetric response. c) Calculated by eq.(l). Reported data are mean values obtained in at least three separate experiments. Observed deviations are quoted in the cp,, column. The values 3.471, 2.980 and 2.955 K determined by physical calibration experiments at 50, 100 and 150°C respectively, were used for the difference AT,,. kq.1). Used values of specific heat for pure water c, at the same temperatures were 4.1807,4.2159 and 4.3097 J g-l K-’ (Conti et al, 1988). The value 0.997048 g anJ was taken for the density of pure water at 25OC. d) Calculated by eq. (3) for mixties containing AK& + HCI and by eq. (12) for solutions containing only (hydrolyzed) AM& e) These values were calculated accoundng for hydrolysis according to a procedure described in the Lext (Results section). Corresponding values calculated from eq. (3) using direct stoichiometric quantities of AM& and HCl, are: -269k16, -316k9, -325i5, -271s and -251flO J mol-’ K-l, respectively. a)
centrations of the hydrolytic species, calculated according to scheme II (described later), have been considered. The C,,* data have then been corrected and referred to a hypothetical solution containing only AK&( 1) and HCI( 2) through the following relationship: C,,$ (corr.) =
Cp-9 - 2 N,C,,., - CF: I N,+N, ’
(4)
where N, and N2 are the mole fractions of components I and 2, respectively; and the terms N,, C,,@,,, and C’,?: will be defined in the Hydrolyzed Solutions section (Eqns. I5 and 16). The corrections were, in any case, smaller than 10 J mol-’ K-‘. The C,,+ values of the solutions containing A1C13+ HCl have been treated following the procedure proposed by FSIPER
4127
Molar heat capacity of AlCIr and PITZER ( 1982) and adopted afterwards by BARTA and HEPLER (1986) for solutions of mixed electrolytes. This method allows representation of the apparent molar heat capacity of a mixture as a function of the parameters of each electrolyte as a single component. For a mixture containing AQ and HCl only, the corresponding equation is as follows: Cp,+ = C;,m,x + ‘$
In ( 1 + bZ”*)
-R~~(3m,~m*)[2(m,Bi+m*B:) +(3m,+m2)
)I, (5)
(
zCj+m2Ci
and m,, m2, N,, N2, where CE,Eix = NICE*, f N2&; r?z,, , and Cz,* are the molalities, the internal mole fractions, and the standard apparent molar heat capacities of the two solutes, respectively. The parameters B: and C: (k = 1, 2) are defined by the following: B’k = PIP” + 8:1”(2/X*)[l x=(rZ’/*
with
- (1 + x)e_“];
(u=2
(6)
CL= (s)p,m +y$)p,m,
(7)
AJ being the limiting slope for the heat capacity, whose value was taken according to BRADLEYand PITZER ( 1979), and b = 1.2. The experimental C’,,$ data have been fitted to Eqn. (5) by means of a standard least-squares method. By using the values of TREMAINEet al. ( 1986) for HCl, the @,O,’and B (I,’ values for AlC& have been obtained. The C’ value for AlC& could not be determined. The standard heat capacity of AlC13, t?E,Alcl,,was obtained by extrapolating Eqn. (8) to m = 0, as follows: CP4
-
Nd$!:
NAICI,
~AJ - 7 In (1 + bZ’/*) =
c;,A,C,,
+-f(m).
(8)
CF$, was calculated from data reported by TREMAINEet al. ( 1986) for the same ionic strengths of C,,4. In Fig. 1, Eqn. (8) is plotted at T = 50 and 100°C. At 15O”C, due to the small concentration range explored and the low molar fraction of AK& in the mixture, a correct extrapolation procedure was not possible; nevertheless, an estimated value of C-0P.A,Ch = -720 J mol-’ K-’ was obtained using the available data. In Table 2, the values of the quantities c:, /3(O)‘, B(‘,‘, necessary for calculating with Eqns. (5)-( 6), the apparent molar heat capacity, Cp,*, of AlC& and HCl in aqueous solution either as single salts or in mixtures, are reported at the three temperatures examined. It is to be pointed out that in our calculation procedure the Pitzer mixed terms have been neglected, and a simplified equation without additional terms linked to the dependence of ions with Z > 3 on ionic strength has been used; for this reason, the Pitzer parameters for AlCl, are to be considered as simple fitting parameters, only able to reproduce, at best, the HCl + AlC& mixture.
.l
.3
.S
.7
.9
m; / mol kg-’ FIG. 1. Plots, at different temperatures, of the quantity Y = (C,,+ - DHLL (see Eqn. 8) vs. total molality M for solutions containing AIClr + HCI mixtures. - NmC~~‘V&,~
We believe, however, that these are able to describe mixtures in which A1C19is mixed with other salts in a fairly accurate way, as long as these bear a small charge and solutions have concentration and ionic strength values not larger than those of the mixtures here considered. For the same reasons, TREMAINEet al. ( 1986) provide, for HCl, parameter /3(O)’only, which we have used and reported together with cj values in Table 2. In Fig. 2, for the three temperatures considered, the CD,+ trends obtained by applying Eqn. (5) to mixtures containing A1C19+ HCl are compared with experiments. The comparison is satisfactory, with due cautions for 150°C because of the reasons already discussed. In Fig. 3, the standard heat capacity values, cE,A,C,,, obtained in this work are plotted vs. temperature together with the data of HOVEY and TREMAINE(1986) and those recalculated by BARTA and HEPLER ( 1986) from the above authors’ experiments. Also, the figure shows the curve obtained by treating the whole set of data with the equation of HELGESON et al. ( 198 1) in the version revised and extended by TANGER and HELGESON(1988), which in our conditions assumes the following simplified form: 2 +
oTX,
where c, and c2 are adjustable parameters characteristic of a single aqueous ion (or of an electrolyte), and 6 is a parameter which equals 228 K for water. The oTX term originates from the Born hydration model and can be calculated for ion j by means of the following relationships defined by HELGESON and KIRKHAM (1976): wj = 6.9466.10’
z: - 2.2539.lO*Z, ‘r,J
X = [(a* In c/aT*),
- (d In t/dT)i]/t,
(10)
where Zj, r,j, and t are the charge, the effective electrostatic ionic radius, and the water dielectric constant, respectively. For the System A13+ + 3Cl- (WA,,-,)= wA,+ 3wc,), by using
G. Conti. P. Gianni, and E. Matteoli
4128
Table 2. Parameters for calculationof Cp,+/J mol-’ K” by Pitzer method, for AlCI) + HCI mixtures at various temperatures.
50
2.0071
0.57433
1.8249
-112.3
-410
100
-7.2203
0.52378
1.4651
-125.5
-490
150
-19.627
-70.07
17.64
-164.4
-720
a) Tremaine b) This
et al. (1986).
work.
the rc,,, values reported by SHOCK and HELGESON ( 1988 ), the value o = 30.29 - lo5 J mol-’ is calculated. The following values c, = -2.5077 J mall’ K-’ and c2 = -9.8556.10’ J K mol _’ have been obtained using the X function of the data compiled by TANGER and HELGESON ( 1988). The curve fairly represents the entire set of experimental data with a standard deviation amounting to & 15 J mol-’ K-‘. Hydrolyzed Solutions The apparent molar heat capacity, CD,,, of the solute mixture constituted by the aqueous species produced in the hydrolysis of the Al (H,O)i+ cation according to the scheme, x,A13+ + y,H20
= Al,( OH)lj+-jj’+
+ y,H+,
( 11)
where j = 1, 2, . , n (n being the number of the complex species formed) can be expressed through Eqn. (3), accounting for all species in the terms 1 mi and 1 m,M,. The cal-
0 T /
FIG. 3. Standard partial molar heat capacities, cz, of aqueous AICY&: n, this work; 0, HOVEY and TREMAINE, (1986); 0, BARTA and HEPLER, ( 1986). The curve was calculated according to the revised model of HELGESON et al. (1981 ); see Eqn. (9).
culation of C,, through Eqn. ( 3 ), beside the determination of experimental quantities, also requires the knowledge of the stoichiometry of the reaction ( 1 I ) and of the stability constants of the complexes formed. A purely empirical quantity, C;,,, which can be determined by the only knowledge of the experimental c,,~ data and the analytical molality of the Al salt, rn”,‘, can, however, be defined similarly to Eqn. (3) through the following equation:
I
I
CL = -200 I& 7 ;j
“C
G6 and CL
(1000 + milMAI)~p,s - IOOOc, (12)
&
are related to each other by the following re-
lationship: -260 I
-
E
?
CL
-320 2 w -150
C m, =LC m%
C m,M P.@-
(
L
&
-
MAI
cp.3.
(13)
1
If in an aqueous solution of an Al salt, AM,, the hydrolytic process did not take place, the C,*,+ value would be equal to the apparent molar heat capacity, C’i.7, of the non-hydrolyzed salt. When the hydrolysis is in effect, the difference %d >where
-210
-270 -200
(14)
-260
-32C I.5
.9
1.3
1.7
2.1
I
2.5
di
FIG. 2. Plots of C,, vs. fi for AICI, + HCI aqueous mixtures. Comparison between experimental (symbols) and calculated values (curves) using Eqn. (5).
is a sort of a thermodynamic excess quantity which can be calculated from experimental data and is particularly useful to provide information on the hydrolytic process ofthe metal cation. In fact, SC,,+ lends itself to a comparison with an analogous quantity which can be obtained by calculation according to the following procedure. For a solute undergoing a process described by Eqn. ( 1 I ), the apparent molar heat capacity, C,,, can be expressed as the sum of two contributions:
Molar heat capacity of Al&
4129
previous choice of the proper chemical model able to describe the hydrolytic process of the A13+ion. _________________-___ As far as this latter problem is concerned, we deemed the 15Ooc following schemes as those tests suited particularly for our II m I experimental data.
Table 3. Values of equilibrium constants (- log & and - log Qr,r) at various temperatures for the species considered by hydrolytic schemes I, II andIIIa).
Species I (x,y)
5ooc II
m
1oOaC ll
I
m
1) Scheme I considers four monome~c species only, namely, 4.33 f4.87J
4.34 (4.88)
3.31 (3.92)
3.32 2.60 (3.93) (3.301
2.61 (3.31)
I,2
9.22 (10.02)
7.47 03.27)
7.32 (8.22)
5.57 5.95 (6.47) (6.98)
4.20 (5.23)
I,3
14.58 (15.37)
14.58 11.27 (15.37) (12.16)
11.27 8.74 (12.16) (9.76)
8.74 (9.76)
1,4
19.85 (20.41)
16.34 (16.%1
13.92 fl4.63f
I,1
22 3,4
6.40 5.22 (5.91) (6.86) 11.45 (10.69)
1336 14,34
4.81 (4.24)
3.49 (5.32)
8.20 (7.30) 86.08 (96.78)
93.50 (91.02)
3.40 w2)
2.26 (4.35)
5.95 (4.87) 55.03 (67.04)
67.89 (64.78)
32.75 (46.52) 46.50 142.56)
a) Equilibrium constants refer to reaction (11). Values reported are those originally given by the respective authors. They refer to I=0 (&,r) for schemes I and ill, and to I=1 (QX,r)for schemeII. Values in parentheses are log Qx,Ycalculated at I = 0.18, corresponding to the most diluted solutions examined.
where C;:+ represents the contribution of all species present at equilib~um, and CEk is the chemical relaxation term brought about by the equilib~um shift induced by the temperature increment inherent to the procedure for the specific heat measurement. The Cii$ term can be easily expressed, to a good approximation, as a function of the equilibrium composition of the system and of the apparent molar heat capacity of each single species, as follows:
AI(OH
Al(OH):,
species, Al*(OH):+ and A13(0H)p, and a polymeric one, Al14(OH);4+, are considered. 3) Scheme III is a scheme proposed by BOTTERO et al. (1980); five species are dealt with: three monomeric, AI(OH Al(OH):, and AI(O one polynuclear, A&(OH)j+; and one polymeric, Al,,04( OH):: (for convenience, it is also written as AIIr(OH):i). Scheme I, which involves mononuclear species only, although improbable in our experimental conditions, was considered as a limiting reference model. Scheme II is particularly suited because, to our knowledge, it is the sole model applied so far to experimental data collected up to 150%. Scheme III was considered because it allows identification of the combined effect of the different complex species f mono- and polynuclear, and polymeric) formed in the Al( H20)? hydrolysis and is supported by measurements of free acidity and by 27Al NMR experiments. Values of the relevant stability constants are summarized in Table 3. The corresponding enthalpy and heat capacity changes am collected in Table 4. Details concerning the calculation of the actual equilib~um quotients & in our Table 4. Standard enthalpies (kJ mol-*) and heat capacities 0 mol-1 K-1) for the formation of hydroxo-complexes of AIs+, Al,(OH)Y@X-Y)+.
A&,,Yt” I,1
T mi +S(C,?i
-C,),
with
S=T;
mAi
Use of Eqn. ( 17) requires the knowledge of speciation, of the apparent molar heat capacities Cp,+,j of the complexes, and of the relaxational heat capacity; all these quantities need the
and Al(OH);.
BAES (1971); two polynuclear
T/T
In Eqn. ( i6), obtained by applying the Young rule (YOUNG and SMITH, 1954), NAIX,, NUX, N,, C,“l,“‘, CEf, and C,,6s, are the internal mole fractions (NAIX3+ NHX + 2 Nj = 1) and the apparent molar heat capacities of the salt, of the acid, and of the complexes, respectively. By introducing the expression for CP,*, as given by Eqn. ( 15 ) into Eqn. ( 13) and expressing C;:+ as in Eqn. ( 16), the following relationship is obtained for bCP,4:
Al(OH)!,
2) Scheme II is the scheme (II) proposed by MESMERand
1.2
I,3
wx
@) A&(c) AC;o”(d) AC;o,*)
IA
50
49.18 89.73
130
169.62
-11.7
-9.6
192
115
100
44.87 84.91
122
153.72
-3.80
-0.085
165
116
150
40.48 80.10
114
137.82
-0.10
6.53
140
149
AgX.+values, reported for different couples x,y, refer to reaction (11) and are taken from Michard (1963). Values for the neutral species AI(OHg were interpolated at y = 3 on the AH& sequence 1‘1 to 1,4. Values of AH” I,y for potynudear
species were calculated through eq. (A4) using
A!& values of column 7 and the following values of N (kJ mol-1): 50918,42010 and 32109 at 50, 100 and 150’ C, respectively (Olofsson and Olofsson, 1981). Experimental AHoHvalues of reaction (A3) at ionic strength I = 0.2 (Conti et al., 1991). Values of AH& calculated at I = 0 by the following relation: For $ values oi AlCls and co&plexes &&script c) see Appendix. $aa and L+,N,c, are taken from Conti et aL(I98Ef and Silvester and Pitzer (1977), respectively. From temperature dependence of AH& values of column 7. Calculated as averaged value for monomeric complexes using eq. (A4) as described in the appendix.
G. Conti. P. Gianni, and E. Matteoli
4130
Table 5. Comparison between experimental and calculated SC,, values for aqueous hydrolyzed AlCl$‘).
0.03 -19 0.05 -12 0.075 -22 loo 0.03 130 0.05 100 0.075 91 n 0.1 38 0.3 0.5 26 150 0.03 455 0.05 392 0.075 27-7 238 0.1
50
7 5
-7 -5
29 21
2.9
15
4 23 16 12 9 4 3
-4 -24 -17 -12 -10 -5 -4
16 53 38 29 24 14 12
21 16 52 37 29 23 13 11
72
-67
R
77
48 31 21
46 -33 -27
50 36 30
52 34 24
11 8 61 43 31 25 14 13 240 173 118 82
-11 -8 -6 -54 -38
543 43 33 155 117 92
62 46 35 162 122 95
1; -12 -11 -22lX25 -169i18 -126i14 -102Ztll
78 54 59
so 56
2w1 144f20 113i16 9Bf13
&t56 148ti8 IO%30 78iz24
9 7 5 32 21 15 12
-7 -5 -4 -25 -16 -12
73 51 39 302 220 158
-10
6 5
-5 -4
132 85 54 36
-125i26 -f33*19 -59+14
130 77 74 421i44
#ill
299t32 222X24 183i18
75 53 40 3ce 223 161 132 78 7.5 428i70 301m 217i38 173zt29
a) All heat capacity data are in J moi-’ K-‘. b) Average experimental values obtained from eq. (141 among those corresponding to the different ionic strengths predicted by the schemes. Deviations from the mean are always much lower than experimental uncertainty. c) Calculated values: SC,, = A + B + C where the terms A, B and C are the Ist, 2nd, and 3rd term of the right hand side of “I. (17). req?ctively. d) Listed uncertainties represent the effect of an arbitwy change off 50.~~J mol-1RI on C,,,,
e) Listed uncertainties represent the effect of an arbitrary change of ti.O.y, kJ mob’ on AHt,Y. 0 Listed uncertainties represent the maximum deviation due to the combined uncertainties of points d) and e)
expe~mentai conditions, of the Cp,+,j values of the various complexes, and of the relaxation term C$ are described in the Appendix. Experimental values of 6C,,,, together with the corresponding calculated ones for each scheme considered, are listed in Table 5. The separate contributions (A, B, C) to the calculated &I,,* values made up by the three terms which appear in the right-hand side of Eqn, ( 17) are also specified in Table 5. Values of SC,,, vs. rn!, are also plotted in Fig. 4 at the three temperatures examined. In addition, at 5O”C, the experimental data obtained using the C’$‘) values of BARTA and HEPLER (1986) are represented; the observed slightly higher values are due mainly, to the difference by -25 J mol-’ K-’ between our cop,AIcI,value and that reported by the above authors.
would result in a smaller contribution to the relaxation heat capacity. The experimental SC,,,+values reported by us would be underestimated in such a hypothesis, the larger true values being observable in conditions of fast occurring reactions. For the sake of clarity, in Table 5, the calculated SC,,$ values have been subdivided into the three contributions A, B, C, corresponding to three terms in the right-hand side of Eqn. ( 17), respectively. Some useful observations emerge from Table 5. The heat capacity increase due to A13+ disappearing (A) is always almost fully compensated for by the formation of the hydrolysis products ( B), This suggests that the sum of the three terms, A + B + C, is, in most cases, not very different from C and therefore that the extent of the calculated excess quantity is determined mostly by the
DISCUSSION The analysis proposed here, even if it cannot constitute a method for exactly identifying the hydrolytic species of Al”+, can nevertheless provide useful information on the hydrolysis reaction
of this ion. It requires one to select some hydrolytic
schemes among those available in the literature, then to calculate SC,,+ and test how this quantity is related to the thermodynamic properties of the occurring reactions. As a matter of fact, significant nonzero values of SC,,+ are brought about by a change in heat capacity of the solute species and/or by the relaxational heat capacity of the reacting system, thus being indicative of the nature of the hydrolytic process. Unfortunately, in the calculation of SC,,,4, many thermodynamic quantities are involved; two of them, the apparent molar heat capacities of the complex species, iZ&+ and the reaction enthalpies, AH,,,, need to be estimated. This reduces the validity of this procedure to some extent, but we shall later point out that this estimation is quite less a dramatic drawback than one might think. Also, we would like to emphasize that the possible presence of slow chemical reactions unable to closely follow the temperature change associated to the heat capacity determination
FIG. 4. Comparison between experimental and calculated (Eqn. 17) values of the difference SC,,+ vs. total molality at various temperatures: 0, this work; n, obtained using data of BARTA and HEPLER ( 1986) for iI’,,+of AK&. Curves were calculated following the three hydrolytic schemes: I, (p); II, (- - - -); III, (----).
4131
Molar heat capacity of AlCll
value (C practically equals C$, owing to compensating G,‘m effects of C, and S). Uncertainties deriving from the estiquantities appearing mation procedure ofthe C,,3, and L?lcHX,Y in B and C, respectively, do not substantially modify this assertion. At 15O”C, where hydrolysis is more marked, the changes in B and C and on the overall quantity SC,,@,brought about by uncertainties as large as +50. y, J mol-’ K-’ for CD,@,, and f2 - y, kJ mol-’ for AH,,, , are generally less than 20%. It is evident from Fig. 4, where these uncertainties are reported, that the calculated curves still preserve their identity with respect to the relevant hydrolytic scheme. In Table 6, for the smallest aluminum concentration where the hydrolysis extent is largest, the values of aC,,+, of the hydrolysis degree, Xhydr= C xjm,/mil, ofthe average number I of OH groups bound per Al atom, 5, and of the quantity noH = ii/X,,,,,, which represents the average number of OH groups bound per metal ion involved in complex species, are reported. It shows that at each temperature as the calculated SC,,+ values are larger so the rioH is larger. This correlation also holds at the other concentrations. No correlation is found instead, either with respect to 5 or to Xhydr. It is also to be noticed that the largest ZoH and I~C,,~values are obtained for cases in which high percentages of hydrolyzed Al are engaged in polymeric species. For example, the couples of values rioH = 1.93 and SC,,+ = 309 J mol-’ K-’ at lOO”C, and coOH = 2.48 and SC,,* = 428 J mol-’ K-’ at 15O”C, correspond to fractions of the overall A13+ ion hydrolyzed which is engaged in the species Al,, by 42% and 79%, respectively. Figure 4 shows that at 5O”C, the experimental SC,,@values are close to zero, according to the very low hydrolysis degree calculated at this temperature. At these hydrolysis levels, the only species AlOH 2+is able to justify the experimental results. At lOO”C, the fi values calculated for the three schemes at the concentration rnt, = 0.03 mol kg-’ are still low and, anyway, less than 0.2. This value was considered by MESMER and BAES ( 197 1) as a limit beneath which the presence of slowly forming, large-size complex species cannot be justified because, as they observed, short times are employed by the solutions to reach equilibrium. As a matter of fact, at lOO”C, the experimental aC,,+ values closely approach (see Fig. 4) those calculated by scheme II, which, at this temperature,
Table 6. Correlation between &C,, and various hydrolysis
parameters for
predicts only very scanty quantities of the AlI4 species in the concentration range here studied. The values calculated by scheme III, which predicts fairly large quantities of AlI3 species, are quite high, about twice as high as the experimental ones. Our data seem to indicate, therefore, that up to lOO’C, and for n < 0.2, large-size complexes are not present, as MCDONALD et al. (1973) and BERTSCH( 1987) also found. In contrast, at 15O”C, the high experimental SC,,+ values can be justified only by a large rioH value and therefore by the presence of a large polymeric species as the predominant one. MESMER and BAES ( 197 1) had already observed that the steep increase of the n curves vs. pH at about fi = 0.4 was to be ascribed to the formation of a large-size polymeric complex with high stability. Applying scheme II to our solutions at 15O”C, in spite of the high hydrolysis extent (Xhydr z 0.4), the polymeric species is always found present in small quantity, and no agreement (see Fig. 4) is found with the large experimental 6C,,d values. At this temperature, scheme III calculates a lesser hydrolysis degree (Xhydr= 0.2) but also a quite large fraction of AlI3 species, which brings about large calculated values of SC,,@,the nearest to the experimental ones. By simulating changes that are not too dramatic of the hydrolysis extent and of the species distribution without altering the H+ concentration from a value consistent with experimental e.m.f. measurements ( MESMER and BAES, 197 1)) it is possible, at 150°C by using Scheme III, and only by means of it, to obtain still larger calculated SCP,4values which agree with the experimental behaviour. On the other hand, we are confident that no kinetic effect should skew our experimental results at 150°C since, at this temperature, the formation of polymeric species should also be a sufficiently fast process. But even if this were not fully true, the actual SC,,+ values would be larger than those here obtained, as previously mentioned. In conclusion, we can only confirm the large presence of polymeric species in our conditions of high hydrolysis extent ( 150°C). Unfortunately, the complexity of the system studied, which is not yet fully characterized both in its thermodynamic and kinetic aspects, does not allow us to draw any more definite conclusion on the basis of the unique property studied. We believe, however, that the observed phenomenology may be helpful in the further development of this subject.
different hydrolytic schemes?
Acknowledgments-We
are grateful to Mr. A. Giannotti for his valuable skill in the maintenance of the heat capacity calorimeter and to Ms. M. R. Carosi for her patience in typing the manuscript.
--------__........._.........i~----.--------------------i~_~..... 5ooc I SC,, ”
29
&I,.& (=’ 2.1 -Cd, ” 0.021 w
II
III
I
II 162
m
II
62
75
52
4.4
2.7
6.1
16
0.048
0.032
0.063
0.166
0.162
1.09
1.19
1.03
1.16
1.93
1.08
1.21
1.01
309
I
a.4
III
77
234
426
12
40
22
0.130
0.483 0.545
Editorial handling: F. J.
Miller0 REFERENCES
2.46
BARBERO J. A., HEPLER L. G., MCCURDY K. G., and TREMAINE P. R. ( 1983) Thermodynamics of aqueous carbon dioxide and
(a) All numbers refer to the lowest lluminum concentration (mk = 0.03 mol kg-l) where maximum extent of hydrolysis is observed. (b) J mol-‘K-‘. Calculated by eq. (17). (c) Percent of hydrolyzed AIs+ ion.
sulphur dioxide: Heat capacities, volumes, and the temperature dependence of ionization. Canadian J. Chem. 61, 2509-25 19. BARTA L. and HEPLER L. G. ( 1986) Densities and apparent molar volumes of aqueous aluminum chloride. Analysisof apparent molar volumes and heat capacities of aqueous aluminum salts in terms of the Pitzer and Helgeson theoretical models. Canadian J. Gem.
%”
(d) n = m&t&. (e) i&=ii//Xhydr.
64.353-359.
4132
G. Conti, P. Gianni. and E. Matteoli
P. M. ( 1987) Conditions for Aill polymer formation in partially neutralized aluminum solutions. Soil Sci. Amer. J. 51, 825-828. BOTTEROJ. Y., CASES J. M., FLESSINCERF., and POIRIERJ. E. ( 1980) Studies of hydrolyzed aluminum chloride solutions. I. Nature of aluminum species and composition of aqueous solutions. J. Phys. Chem. 84, 2933-2939. BRADLEYD. J. and PITZERK. S. ( 1979) Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye-Hiickel parameters to 350°C and I kbar. J. Phys. Chem. 83, 1599-1603. CAIANI P., CONTIG., GIANNIP., and MA~EOLI E. ( 1989) Apparent molar heat capacity and relative enthalpy of aqueous sodium hydroxoaluminate between 323 and 523 K. J. Sol. Chem. 18, 447461. CONTI G., GIANNI P.. PAPINIA., and MATTEOLI E. ( 1988) Apparent molar heat capacity and relative enthalpy of aqueous NaOH between 323 and 523 K. J. Sol. Chrm. 17.481-496. CONTI G., GIANNI P., GIANNARELLI S., and MATTEOLIE. ( 1992) Enthalpies of the hydrolysis reaction of A13+ion between 25°C and 150°C. Thermochim. Acta (in press). CO~JTURIERY.. MICHARDG., and SARAZING. ( 1984) Constantes de formation des complexes hydroxidCs de l’aluminium en solution aqueuse de 20 a 70°C. Gcochim. Cosmochim. Acta 48,649-659. EIGEN M. and DE MAYERL. ( 1963) Relaxation methods. In Technique qforganic Chemistry. Investigation ofRates and Mechanisms ofReactions (ed. A. WEISSBERCER), Vol. VIII, Part II, Chap. XVIII, pp. 895-1054. Interscience. HELGESONH. C. and KIRKHAMD. H. ( 1976) Theoretical prediction of the thermodynamic properties of aqueous electrolytes at high pressures and temperatures: III. Equation of state for aqueous species at infinite dilution. Amer. J. Sci. 276, 97-240. HELGESONH. C.. KIRKHAM D. H., and FLOWERSG. C. ( 1981) Theoretical prediction of the thermodynamic behaviour of aqueous electrolytes at high pressures and temperatures. IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600°C and 5 kb. Amer. J. Sci. 281, 1249-15 16. HOVEY J. K. and TREMAINEP. R. (1986) Thermodynamics of aqueous aluminum: Standard partial molar heat capacities ofA13’ from 10 to 55°C. Geochim. Cosmochim. Acta SO, 453-459. HOVEYJ. K. and HEPLERL. G. ( 1990) Thermodynamics of sulphuric acid: Apparent and partial molar heat capacities and volumes of aqueous HSO; from IO-55°C and calculation of the second dissociation constant to 350°C. J. Chem. Sot. Faradav Trans. 86. 283 l-2839. HOVEYJ. K., HEPLERL. G., and TREMAINEP. R. (1988) Thermodynamics of aqueous aluminate ion: Standard partial molar heat capacities and volumes of AI( (aq) from 10 to 55°C. J. Phys. Chem. 92, 1323-1332. J~LICOEURC., LEMELINL., and LAPALMER. ( 1979) Heat capacity of potassium-crown ether complexes in aqueous solution. Manifestations and quantitative treatment of important relaxational heat capacity effects. J. Phys. Chem. 83, 2806-2808. KUYUNKON. S., MALININS. D., and KHODAKOVSKIY I. L. (1983) An experimental study of aluminum ion hydrolysis at 150, 200, and 250°C. Geochim. Intl. 20, 76-86. MAINS G. J.. LARSONJ. W., and HEPLER L. G. (1984) General thermodynamic analysis of the contributions of temperature dependent chemical equilibria to heat capacities of ideal gases and ideal associated solutions. J. Phys. Chem. 88, 1257- 126 I. MCCOLLUME. D. ( 1927) The specific heat of gaseous nitrogen tetroxide. J. Amer. Chem. Sot. 49, 28-38. MCDONALDD. D., BUTLERP., and OWEND. ( 1973) Hydrothermal hydrolysis of Al ‘+ and the precipitation of boehmiie f&m aqueous solution. J. Phvs. Chem. 77. 2474-2479. MESMERR. E. and BAESC. F., JR. ( I97 1) Acidity measurements at elevated temperatures. V. Aluminum ion hydrolysis. Inorg. Chem. 10,2290-2296. MICHARDG. ( 1983) RecueiI des donnees thermodynamiques concernant les equilibres eaux-mineraux dans Ies reservoirs hydrothermaux. Rapport EUR 8590 FR. Pub. Commis. Commun. Europ., Bruxelles. BERIXH
OLOF~SONG. and OLOFSSONI. ( I98 I ) Empirical equations for some thermodynamic quantities for the ionization of water as a function of temperature. J. Chem. Therm. 13,437-440. PARKERV. B. ( 1965) Thermal properties of aqueous uni-univalent electrolytes. NSRDS-NBS. US Govt. Printing Office. PEIPERJ. C. and PITZERK. S. ( 1982) Thermodynamics of aqueous carbonate solutions including mixtures of sodium carbonate, bicarbonate, and chloride. J. Chem. Therm. 14, 6 13-638. REED M. and SPYCHERN. (1984) Calculation of pH and mineral equilibria in hydrothermal waters with application to geothermometry and studies of boiling and dilution. Geochim. Cosmochim. Acta 48, 1479- 1492. SHOCKE. L. and HELGESONH. C. ( 1988) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Correlation algorithms for ionic species and equation of state predictions to 5 kb and 1000°C. Geochim. Cosmochim. Acta 52,2009-2036. SILVESTERL. F. and PITZERK. S. ( 1977) Thermodynamics of electrolytes. 8. High-temperature properties, including enthalpy and heat capacity, with application to sodium chloride. J. Phys. Chem. 81, 1822-1828. SPOSITOG. (ed.) ( 1989) The Environmental Chemistry ofAluminum. CRC Press. TANGERJ. C., IV, and HELGESONH. C. ( 1988) Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Revised equations of state for the standard partial molal properties of ions and electrolytes. Amer. J. Sci. 288, 19-98. TREMAINEP. R., SWAYK., and BARBEROJ. A. ( 1986) The apparent molar heat capacity ofaqueous hydrochloric acid from IO to 140°C. J. So/n. Chem. 15, I-22. WOOLLEYE. M. and HEPLERL. G. ( 1977) Heat capacities of weak electrolytes and ion association reactions: Method and application to aqueous MgSO, and HI03 at 298 K. Canadian J. Chem. 55, 158-163.
YOUNGT. F. and SMITHM. B. (1954) Thermodynamic properties of mixtures of electrolytes in aqueous solutions. J. Phys. Chem. 58,7 16-724.
APPENDIX Speciation
The equilibrium quotients Qx!,. necessary for calculating the species distribution in the actual condltlons of our experiments, have been obtained using activity coefficients evaluated according to the procedure proposed by HELGESONet al., I98 I, and already followed previously (CONTI et al., 1991). In this procedure, the hydrolyzed complex cations have been attributed an electric charge equal to the average charge per aluminum atom. As an example, values of the quotients Qx,y are reported in Table 3 for the smallest AICI, concentration considered in our experiments. Apparent Molar Heat Capacities of Complex Species
Values
of
C,,,,
of
the
complexes
of general
formula
Al,( OH ),jCl, 3x,-,j~were estimated through the following approximated equations:
cp,m,,=cz,,+(4x,-y,)
+1.21”*)
(Al)
co =$;,A,c,, + Y,(~;,,oH - ~;,a,,+ K;,oH)-
(AI)
Bd
$In(I
Eqn. (A 1) was devised by us to describe a hypothetical situ&on in which the complex cation is dissociated to give .,, ions with charge (3 - y,/x,). We believe that this situation is nearer to reality than considering these complexes to behave like highly charged monoatomic ions, so that Eqn. (A I ) estimates, at best, the C,,. , quantities without diminishing the validity of the conclusions re&&. In Eqn. (A2), the criterion of the additivity of the standard thermodvnamic properties of ions is assumed. The-data of &,,c, and c&,,, were taken from SILVESTERand PITZER ( 1977) and from CONTI et al.
Molar heat capacity of AIC& ( 1988), respectively. The quantity AC~.on refers to the following reaction: .K,/‘Y,AI~++ OH- = 1/yjAi~j(OH)~~~-~“,
t.43)
whose standard thermodynamic functions can be expressed (CONTI et al., 1991) by the equation AX& = AX;,,.,‘y - AX”,,
(A4)
where AX!,, refers to reaction ( 1t ), and Afi refers to the ionization of water. ACj,o, values for mononuclear complexes were obtained from Eqn. (A4) (X = C,) using AC:,,, values given by MICHARD ( 1983 ) and AC:,, values given by OLOF~SONand OLOPSSON( 1981). AC;,OHvalues for polynuclear forms were obtained instead by differentiating, with respect to temperature, the function AH”,, =f( T) determined by CONTIet al. ( 199 1) in the temperature range 25150°C. The AC’&,, and AH& values can be found in Table 4. Relaxations1 Contribution to Heat Capacity For a solution in which n parallel reactions having mutual reagents are in effect. Cg+ can be expressed as follows:
where m is the total molality, and ( AHHx,y),(abbreviated as AH%,, throughout this paper) and 4, are the enthalpy and the extent of the jth reaction (Eqn. L1). respectively, the latter expressed as moles of complex formed per kg of pure solvent. The n derivatives in Eqn. (A5), due to the presence of common reagents, depend each on the thermodynamic parameters of the others and constitute the n unknowns of the following n-equation system: C Aj.k*L)k= H,,
k-1
j=
1,2 * ++ R.
tAbI
4133
A,,k, Dk and H, are so defined:
Ajk=z+!?$ A+
A,,
=
(j#k)
(A7)
+
I + A._ +A_ ml
m4+
(A81
m+
(A9) where mArI+,mH+, and m, are the equilibrium molality of the free A13+,of the acid, and of the jth complex, respectively. Values of the enthalpies of reaction ( I I ) for the various hydrolytic species, AHH,,,, were calculated as follows. Standard enthalpies of reaction from A13’ and water, AH:., , were taken from literature for monomeric species ( MICHARD, 1983); while for polynuclear and polymeric species, they were calculated by solving Eqn. (A4) (X = H) for AH’&,, using AH& values from Table 4. In regard to the validity of this method for calculating AHx,? of polymeric and polynuclear species, it is worth mentioning that the values calculated by us for A&(OH):+, A13(OH)F, and Alder compare well with those obtained by applying the van? Hoff method to the experimental log Qx,, data of MESMERand BAES,( 197 1) in the temperature range 2%125°C. The AH,,, values at the ionic strengths, I, of our experimental conditions were calculated using Eqn. (AIO), as follows: AH,,,, = AH:,, + Y*&,Hc@) + Al,,
- &AIC&),
(AlO)
where the apparent relative enthalpies, L,, ofA1C.I~and ofcomplexes (subscript j) were estimated using the equation of HELGESONet al., I98 1;those for HCI were taken at 25°C from PARKER( 1965) and, at higher temperatures, calculated from heat capacity values reported by TREMA~NEet al. ( 1986).
Geochimica et Cosmochrmica ACM Vol. 56, pp. 4125-4133 Copyright 0 1992 Pergamon Press Ltd. Printed in U.S.A.
Apparent molar heat capacity of aqueous hydrolyzed and non-hydrolyzed AlQ between 50 and 150°C GIOVANNICON-H,‘.* PAOLOGIANNI,’ and ENRICOMATTEOLI’ ‘Dipartimento di Chimica e Chimica Industriale, Via Risorgimento, 35, 56 100 Piss, Italy ‘Istituto di Chimica Quantistica ed Energetica Molecolare,CNR, Via Risorgimento, 35, 56100, Pisa, Italy (Received September
18, 1990; accepted in revised,form May I, 1992 )
Abstract-By means of a flow calorimeter, the specific heats of aqueous solutions containing AlC13 with and without added HCI have been measured at 50, 100, and 150°C. The apparent molar heat capacity C,,$ of the HCI-containing solutions have allowed the calculation of the standard molar heat capacity of AlCl3, c;,A,C,, . These data satisfactorily link together with those of Hovey and Tremaine in the range lo-55°C ( HOVEYand TREMAINE,1986), afterwards reassessed by BARTAand HEPLER, 1986. The treatment of the C,,# data with the ionic interactions model of Pitzer has provided the values of pco)J and pc’)J for the calculation of C’;,$ 3 in the concentration range 0.03-0.75 mol kg-’ at the temperatures studied. Experimental values of the apparent molar heat capacities obtained for hydrolyzed solutions have been compared with the analogous quantities calculated accounting for the CD,@,, of all species present at equilibrium, as well as for the chemical relaxation term, C’EL, which is due to the energy absorbed by the hydrolysis shift induced by the heating inherent in the specific heat measurement. The calculation has been carried out on the basis of some hydrolytic schemes proposed in the literature and has provided useful insights on the hydrolysis reaction at temperatures where the extent of reaction is quite marked. INTRODUCIION MUCH ATTENTIONHAS BEENdevoted to the thermodynamic characterization of aqueous acidic systems containing Al 3t ion and its hydrolysis products for its impact in applicative, environmental, as well as scientific areas. A review can be found in a comprehensive treatise edited by SPOSITO( 1989). On the contrary, the quantity of data regarding the thermodynamic properties of aqueous Al( H20):+ and relevant complex hydrolytic species at high temperature is still rather limited. Some data of stability constants of hydroxo-complex species exist above room temperature ( MESMER and BAES, 1971; MCDONALD et al., 1973; COUTURIERet al., 1984; KuYUNKO et
al., 1983; MICHARD, 1983; REED and SPYCHER, 1984), and more recent studies provide accurate values of partial molar volumes and heat capacities of limiting species such as A13+ up to 55°C (HOVEY and TREMAINE, 1986; BAR~A and HEPLER, 1986) and Al(OH); up to 250°C (HOVEY et al., 1988; CAIANI et al., 1989). The above properties play a fundamental role in the thermodynamic treatment of natural aqueous systems which extend over wide ranges of temperature and pressure. Every study aimed at the increase of the knowledge in this field is therefore welcome. The purpose of this work has been the extension of the heat capacity data of aqueous non-hydrolyzed solutions of Al 3+to the temperature range 50- 15O”C, as well as to measure the same property for solutions of A13+ ion in conditions such as to undergo hydrolysis. In this way, it has been possible to make comparisons between the apparent molar heat capacities, Ct., , of the hydrolyzed AlC13obtained from the experimental specific heats and the corresponding
* Author to whom correspondence
should be addressed. 4125
values calculated using apparent molar heat capacities of all species predicted at equilibrium by some different schemes proposed in literature. The calculation has been performed by taking into account the chemical relaxation contribution, Czl, a property to deal with whenever specific heat measurements on systems of equilibrated reacting species are carried out. The procedure followed here is the same as that introduced by previous authors ( MCCOLLUM, 1927; EIGEN and DE MAYER, 1963; WOOLLEYand HEPLER, 1977; JOLICOEUR et al., 1979; PEIPER and PITZER, 1982; BARBEROet al., 1983; MAINS et al., 1984; HOVEY and HEPLER, 1990); here it is applied to parallel chemical reactions. This quantity is determined by the stoichiometry, the equilibrium constants, and the enthalpies of the reactions taking place and therefore contains important information relevant to the process itself.
EXPERIMENTAL Apparatus Specific heat measurements were carried out by means of a differential flow calorimeter previously described ( CONTI et al., 1988) and recently modified and improved ( CONTIet al., 1991).The constant pressure specific heats, c,,, were calculated through Eqn. ( I ), as follows: c,,
=-.
c,-d, d,
AT, (AT,
+ 0) ’
(1)
where c, is the specific heat of water at the temperature of the experiment; d, and d, are the densities of water and solution at 298. I5 K. respectively; and AT, and (AT,, + 0) are the temperature increments observed on water and on sample solution, respectively, which circulate in the calorimeter at the same flow value (p = 0.025 cm3 s-l) and are heated with the same power P (usually P - 0.5 W). The 6 value is the immediate result of the calorimetric measurement on the sample solution. The AT, quantity is a constant for constant values of the flow, of the heating power, and of temperature, variables
G. Conti, P. Gianni, and E. Matteoli
4126
which characterize a set of measurements. AT, was accurately determined by means of physical calibration experiments carried out with water using the following equation: AT = 0 ((p - ‘,) W LL,’
Table 1. Experimental specific heats, cp,, and apparentmolarheat capacities, CD*, of aqueous AlCls or AlCJa + HCI mixtures at various compositionsand
where L, represents a known small leak (maximum 2% of flow) applied to the solvent flow, cp,in the measuring cell; this leak brings about a temperature increase tTL,which simulates a small specific heat decrease. Solution densities were measured at 25’C by means of an Anton Paar model DMA 60 densimeter with measuring cell model DMA 602. Measurements have been carried out at room pressure, and the variation of the density with pressure was neglected, in consideration of the fact that the pressure in the calorimetric experiments was never over I.0 MPa.
50
100
Solutions
All solutions were prepared in mass. Stock solutions of aluminum chloride were prepared using AlC13*6H20 from Merck, whose purity, controlled periodically as Al203 by calcination in a platinum crucible, resulted in about 99.9%. The water used was deionized and deaerated. HCI solutions were prepared according to standard procedures. Sample solutions were prepared by diluting amounts of stock solution either with water or with the HCI solution. The quantities of HCI to be added were calculated taking the equilibrium constants from hydrolytic model II described and used later (see Results and Discussionsection). At 50 and lOO”C,the residual hydrolysis resulted, in any case, less than 0.5%; whereas at lSO”C, it was comprised between I and 2% for the most diluted solution. Larger HCI/AI ratios were not considered in order to avoid acidic chemical attack to the calorimetric cell and also to allow that the specific heat effect measured was due mostly to the aluminum species. At 15O”C, therefore, the heat capacities were corrected for the residual hydrolysis with a procedure described later. The samples without HCI addition were used some days after preparation. RESULTS
Specific heats of all solutions examined, and the corresponding values of the apparent molar heat capacities, are reported in Table I for the three following temperatures considered: 50, 100, and 150°C. In the same table, the composition of the solutions, as well as other details about the experimental method followed for specific heat measurement, are also collected. At 15O”C, C,,4 data have been obtained only for low concentrations because, due to the large quantity of HCl necessary for repressing hydrolysis at rn > 0.1, the material constituting the cell tubing, Inconel600, underwent acid attack. In fact, at this temperature, in spite of the added HCl, the maximum hydrolysis extent was about 2%. Non-hydrolized
Solutions
The C,,+ data of solutions containing AK& + HCI have been obtained through the following general equation for mixture of electrolytes: (1000 + C CP.9
mjh4i)Cp.s
I
=
C llli 1
K
CPLC Jg-‘K-’
d, cP,+ Jml -‘K-I
1.01 1.03 1.61 1.65 2.43 2.50 3.16 9.10 14.67 21.42
4.1533 4.1532 4.1368 4.1362 4.1146 4.1142 4.0942 3.9373 3.7980 3.6343
-3lWO -359t20 -316i15 -34of15 -3wilO -34DflO -299ilO -272s -254s -230-z
1.00163 1.00067 1.0@404 1.00301 1.00390 l.OC672 lm592 1.00949 1.00883 1.03227 1.03146 1.05432 1.05331 1.08042
1.53 0.65 1.99 1.12 1.94 2.61 1.66 303 2.22 7.62 6.50 11.46
-203f20 -251f20 -232i15 -261i20 -22&15 -261ilO -252ilO -259ilO -251flO -237s -227i5
10.34 15.99
4.1752 4.1915 4.1588 4.1751 4.16&l 4.1391 4.1556 4.1220 4.1358 3.9705 3.9863 3.8392 3.8569 3.6924
-275(e) -146f20
@lOZb’
(2)
-
100OC~ (3)
In this equation, c,, and c, are the specific heat of the solution and of water, respectively, at the same temperature and pressure; mi and Mi are the molality and the molecular weight of the ith electrolyte, respectively. At 15O”C, the small con-
150
3.013 3.013 4.910 4.591 7.4% 7.484 10.00 29.94 49.41 75.15
0.242
3.026 3.012 5.149 4.991 5.032 7.511 7.484 9.998 9.987 29.% 30.00 49.99 50.02 74.78
4.996
2.974 3.coo
4.958
1.00156 1.0&X5
1.85 0.41
4.2636 4.2882
0.276 0.373 0.432 1.120 1.752 2.462
4.336 4.342 3.814 3.165 4.053 5.041 5.235
l.OCW-2 1.00x7 1.00297 1.00301 1.00602 1.00592 1.00892 1.03164 1.05302 1.08028
-206s -203s -185i2
5.030
6.049
1.Ou421
2.93
4.2369
-320(e)
4.983 4.960
5.963
1.00414
2.97 0.74
4.2367 4.2735
7.432 7.521
7.963
1.00737 l.OW7
3.60 1.32
4.2142 4.2525
-329(e) -159i15 -273(e)
10.03 9.9%
6.011
l.Olca l.CQW
3.53 1.42
4.2039 4.2390
1.00296
-193ztlO .255(c) -143ilO
Densities at 25Dc. b) Calorimetric response. c) Calculated by eq.(l). Reported data are mean values obtained in at least three separate experiments. Observed deviations are quoted in the cp,, column. The values 3.471, 2.980 and 2.955 K determined by physical calibration experiments at 50, 100 and 150°C respectively, were used for the difference AT,,. kq.1). Used values of specific heat for pure water c, at the same temperatures were 4.1807,4.2159 and 4.3097 J g-l K-’ (Conti et al, 1988). The value 0.997048 g anJ was taken for the density of pure water at 25OC. d) Calculated by eq. (3) for mixties containing AK& + HCI and by eq. (12) for solutions containing only (hydrolyzed) AM& e) These values were calculated accoundng for hydrolysis according to a procedure described in the Lext (Results section). Corresponding values calculated from eq. (3) using direct stoichiometric quantities of AM& and HCl, are: -269k16, -316k9, -325i5, -271s and -251flO J mol-’ K-l, respectively. a)
centrations of the hydrolytic species, calculated according to scheme II (described later), have been considered. The C,,* data have then been corrected and referred to a hypothetical solution containing only AK&( 1) and HCI( 2) through the following relationship: C,,$ (corr.) =
Cp-9 - 2 N,C,,., - CF: I N,+N, ’
(4)
where N, and N2 are the mole fractions of components I and 2, respectively; and the terms N,, C,,@,,, and C’,?: will be defined in the Hydrolyzed Solutions section (Eqns. I5 and 16). The corrections were, in any case, smaller than 10 J mol-’ K-‘. The C,,+ values of the solutions containing A1C13+ HCl have been treated following the procedure proposed by FSIPER
4127
Molar heat capacity of AlCIr and PITZER ( 1982) and adopted afterwards by BARTA and HEPLER (1986) for solutions of mixed electrolytes. This method allows representation of the apparent molar heat capacity of a mixture as a function of the parameters of each electrolyte as a single component. For a mixture containing AQ and HCl only, the corresponding equation is as follows: Cp,+ = C;,m,x + ‘$
In ( 1 + bZ”*)
-R~~(3m,~m*)[2(m,Bi+m*B:) +(3m,+m2)
)I, (5)
(
zCj+m2Ci
and m,, m2, N,, N2, where CE,Eix = NICE*, f N2&; r?z,, , and Cz,* are the molalities, the internal mole fractions, and the standard apparent molar heat capacities of the two solutes, respectively. The parameters B: and C: (k = 1, 2) are defined by the following: B’k = PIP” + 8:1”(2/X*)[l x=(rZ’/*
with
- (1 + x)e_“];
(u=2
(6)
CL= (s)p,m +y$)p,m,
(7)
AJ being the limiting slope for the heat capacity, whose value was taken according to BRADLEYand PITZER ( 1979), and b = 1.2. The experimental C’,,$ data have been fitted to Eqn. (5) by means of a standard least-squares method. By using the values of TREMAINEet al. ( 1986) for HCl, the @,O,’and B (I,’ values for AlC& have been obtained. The C’ value for AlC& could not be determined. The standard heat capacity of AlC13, t?E,Alcl,,was obtained by extrapolating Eqn. (8) to m = 0, as follows: CP4
-
Nd$!:
NAICI,
~AJ - 7 In (1 + bZ’/*) =
c;,A,C,,
+-f(m).
(8)
CF$, was calculated from data reported by TREMAINEet al. ( 1986) for the same ionic strengths of C,,4. In Fig. 1, Eqn. (8) is plotted at T = 50 and 100°C. At 15O”C, due to the small concentration range explored and the low molar fraction of AK& in the mixture, a correct extrapolation procedure was not possible; nevertheless, an estimated value of C-0P.A,Ch = -720 J mol-’ K-’ was obtained using the available data. In Table 2, the values of the quantities c:, /3(O)‘, B(‘,‘, necessary for calculating with Eqns. (5)-( 6), the apparent molar heat capacity, Cp,*, of AlC& and HCl in aqueous solution either as single salts or in mixtures, are reported at the three temperatures examined. It is to be pointed out that in our calculation procedure the Pitzer mixed terms have been neglected, and a simplified equation without additional terms linked to the dependence of ions with Z > 3 on ionic strength has been used; for this reason, the Pitzer parameters for AlCl, are to be considered as simple fitting parameters, only able to reproduce, at best, the HCl + AlC& mixture.
.l
.3
.S
.7
.9
m; / mol kg-’ FIG. 1. Plots, at different temperatures, of the quantity Y = (C,,+ - DHLL (see Eqn. 8) vs. total molality M for solutions containing AIClr + HCI mixtures. - NmC~~‘V&,~
We believe, however, that these are able to describe mixtures in which A1C19is mixed with other salts in a fairly accurate way, as long as these bear a small charge and solutions have concentration and ionic strength values not larger than those of the mixtures here considered. For the same reasons, TREMAINEet al. ( 1986) provide, for HCl, parameter /3(O)’only, which we have used and reported together with cj values in Table 2. In Fig. 2, for the three temperatures considered, the CD,+ trends obtained by applying Eqn. (5) to mixtures containing A1C19+ HCl are compared with experiments. The comparison is satisfactory, with due cautions for 150°C because of the reasons already discussed. In Fig. 3, the standard heat capacity values, cE,A,C,,, obtained in this work are plotted vs. temperature together with the data of HOVEY and TREMAINE(1986) and those recalculated by BARTA and HEPLER ( 1986) from the above authors’ experiments. Also, the figure shows the curve obtained by treating the whole set of data with the equation of HELGESON et al. ( 198 1) in the version revised and extended by TANGER and HELGESON(1988), which in our conditions assumes the following simplified form: 2 +
oTX,
where c, and c2 are adjustable parameters characteristic of a single aqueous ion (or of an electrolyte), and 6 is a parameter which equals 228 K for water. The oTX term originates from the Born hydration model and can be calculated for ion j by means of the following relationships defined by HELGESON and KIRKHAM (1976): wj = 6.9466.10’
z: - 2.2539.lO*Z, ‘r,J
X = [(a* In c/aT*),
- (d In t/dT)i]/t,
(10)
where Zj, r,j, and t are the charge, the effective electrostatic ionic radius, and the water dielectric constant, respectively. For the System A13+ + 3Cl- (WA,,-,)= wA,+ 3wc,), by using
G. Conti. P. Gianni, and E. Matteoli
4128
Table 2. Parameters for calculationof Cp,+/J mol-’ K” by Pitzer method, for AlCI) + HCI mixtures at various temperatures.
50
2.0071
0.57433
1.8249
-112.3
-410
100
-7.2203
0.52378
1.4651
-125.5
-490
150
-19.627
-70.07
17.64
-164.4
-720
a) Tremaine b) This
et al. (1986).
work.
the rc,,, values reported by SHOCK and HELGESON ( 1988 ), the value o = 30.29 - lo5 J mol-’ is calculated. The following values c, = -2.5077 J mall’ K-’ and c2 = -9.8556.10’ J K mol _’ have been obtained using the X function of the data compiled by TANGER and HELGESON ( 1988). The curve fairly represents the entire set of experimental data with a standard deviation amounting to & 15 J mol-’ K-‘. Hydrolyzed Solutions The apparent molar heat capacity, CD,,, of the solute mixture constituted by the aqueous species produced in the hydrolysis of the Al (H,O)i+ cation according to the scheme, x,A13+ + y,H20
= Al,( OH)lj+-jj’+
+ y,H+,
( 11)
where j = 1, 2, . , n (n being the number of the complex species formed) can be expressed through Eqn. (3), accounting for all species in the terms 1 mi and 1 m,M,. The cal-
0 T /
FIG. 3. Standard partial molar heat capacities, cz, of aqueous AICY&: n, this work; 0, HOVEY and TREMAINE, (1986); 0, BARTA and HEPLER, ( 1986). The curve was calculated according to the revised model of HELGESON et al. (1981 ); see Eqn. (9).
culation of C,, through Eqn. ( 3 ), beside the determination of experimental quantities, also requires the knowledge of the stoichiometry of the reaction ( 1 I ) and of the stability constants of the complexes formed. A purely empirical quantity, C;,,, which can be determined by the only knowledge of the experimental c,,~ data and the analytical molality of the Al salt, rn”,‘, can, however, be defined similarly to Eqn. (3) through the following equation:
I
I
CL = -200 I& 7 ;j
“C
G6 and CL
(1000 + milMAI)~p,s - IOOOc, (12)
&
are related to each other by the following re-
lationship: -260 I
-
E
?
CL
-320 2 w -150
C m, =LC m%
C m,M P.@-
(
L
&
-
MAI
cp.3.
(13)
1
If in an aqueous solution of an Al salt, AM,, the hydrolytic process did not take place, the C,*,+ value would be equal to the apparent molar heat capacity, C’i.7, of the non-hydrolyzed salt. When the hydrolysis is in effect, the difference %d >where
-210
-270 -200
(14)
-260
-32C I.5
.9
1.3
1.7
2.1
I
2.5
di
FIG. 2. Plots of C,, vs. fi for AICI, + HCI aqueous mixtures. Comparison between experimental (symbols) and calculated values (curves) using Eqn. (5).
is a sort of a thermodynamic excess quantity which can be calculated from experimental data and is particularly useful to provide information on the hydrolytic process ofthe metal cation. In fact, SC,,+ lends itself to a comparison with an analogous quantity which can be obtained by calculation according to the following procedure. For a solute undergoing a process described by Eqn. ( 1 I ), the apparent molar heat capacity, C,,, can be expressed as the sum of two contributions:
Molar heat capacity of Al&
4129
previous choice of the proper chemical model able to describe the hydrolytic process of the A13+ion. _________________-___ As far as this latter problem is concerned, we deemed the 15Ooc following schemes as those tests suited particularly for our II m I experimental data.
Table 3. Values of equilibrium constants (- log & and - log Qr,r) at various temperatures for the species considered by hydrolytic schemes I, II andIIIa).
Species I (x,y)
5ooc II
m
1oOaC ll
I
m
1) Scheme I considers four monome~c species only, namely, 4.33 f4.87J
4.34 (4.88)
3.31 (3.92)
3.32 2.60 (3.93) (3.301
2.61 (3.31)
I,2
9.22 (10.02)
7.47 03.27)
7.32 (8.22)
5.57 5.95 (6.47) (6.98)
4.20 (5.23)
I,3
14.58 (15.37)
14.58 11.27 (15.37) (12.16)
11.27 8.74 (12.16) (9.76)
8.74 (9.76)
1,4
19.85 (20.41)
16.34 (16.%1
13.92 fl4.63f
I,1
22 3,4
6.40 5.22 (5.91) (6.86) 11.45 (10.69)
1336 14,34
4.81 (4.24)
3.49 (5.32)
8.20 (7.30) 86.08 (96.78)
93.50 (91.02)
3.40 w2)
2.26 (4.35)
5.95 (4.87) 55.03 (67.04)
67.89 (64.78)
32.75 (46.52) 46.50 142.56)
a) Equilibrium constants refer to reaction (11). Values reported are those originally given by the respective authors. They refer to I=0 (&,r) for schemes I and ill, and to I=1 (QX,r)for schemeII. Values in parentheses are log Qx,Ycalculated at I = 0.18, corresponding to the most diluted solutions examined.
where C;:+ represents the contribution of all species present at equilib~um, and CEk is the chemical relaxation term brought about by the equilib~um shift induced by the temperature increment inherent to the procedure for the specific heat measurement. The Cii$ term can be easily expressed, to a good approximation, as a function of the equilibrium composition of the system and of the apparent molar heat capacity of each single species, as follows:
AI(OH
Al(OH):,
species, Al*(OH):+ and A13(0H)p, and a polymeric one, Al14(OH);4+, are considered. 3) Scheme III is a scheme proposed by BOTTERO et al. (1980); five species are dealt with: three monomeric, AI(OH Al(OH):, and AI(O one polynuclear, A&(OH)j+; and one polymeric, Al,,04( OH):: (for convenience, it is also written as AIIr(OH):i). Scheme I, which involves mononuclear species only, although improbable in our experimental conditions, was considered as a limiting reference model. Scheme II is particularly suited because, to our knowledge, it is the sole model applied so far to experimental data collected up to 150%. Scheme III was considered because it allows identification of the combined effect of the different complex species f mono- and polynuclear, and polymeric) formed in the Al( H20)? hydrolysis and is supported by measurements of free acidity and by 27Al NMR experiments. Values of the relevant stability constants are summarized in Table 3. The corresponding enthalpy and heat capacity changes am collected in Table 4. Details concerning the calculation of the actual equilib~um quotients & in our Table 4. Standard enthalpies (kJ mol-*) and heat capacities 0 mol-1 K-1) for the formation of hydroxo-complexes of AIs+, Al,(OH)Y@X-Y)+.
A&,,Yt” I,1
T mi +S(C,?i
-C,),
with
S=T;
mAi
Use of Eqn. ( 17) requires the knowledge of speciation, of the apparent molar heat capacities Cp,+,j of the complexes, and of the relaxational heat capacity; all these quantities need the
and Al(OH);.
BAES (1971); two polynuclear
T/T
In Eqn. ( i6), obtained by applying the Young rule (YOUNG and SMITH, 1954), NAIX,, NUX, N,, C,“l,“‘, CEf, and C,,6s, are the internal mole fractions (NAIX3+ NHX + 2 Nj = 1) and the apparent molar heat capacities of the salt, of the acid, and of the complexes, respectively. By introducing the expression for CP,*, as given by Eqn. ( 15 ) into Eqn. ( 13) and expressing C;:+ as in Eqn. ( 16), the following relationship is obtained for bCP,4:
Al(OH)!,
2) Scheme II is the scheme (II) proposed by MESMERand
1.2
I,3
wx
@) A&(c) AC;o”(d) AC;o,*)
IA
50
49.18 89.73
130
169.62
-11.7
-9.6
192
115
100
44.87 84.91
122
153.72
-3.80
-0.085
165
116
150
40.48 80.10
114
137.82
-0.10
6.53
140
149
AgX.+values, reported for different couples x,y, refer to reaction (11) and are taken from Michard (1963). Values for the neutral species AI(OHg were interpolated at y = 3 on the AH& sequence 1‘1 to 1,4. Values of AH” I,y for potynudear
species were calculated through eq. (A4) using
A!& values of column 7 and the following values of N (kJ mol-1): 50918,42010 and 32109 at 50, 100 and 150’ C, respectively (Olofsson and Olofsson, 1981). Experimental AHoHvalues of reaction (A3) at ionic strength I = 0.2 (Conti et al., 1991). Values of AH& calculated at I = 0 by the following relation: For $ values oi AlCls and co&plexes &&script c) see Appendix. $aa and L+,N,c, are taken from Conti et aL(I98Ef and Silvester and Pitzer (1977), respectively. From temperature dependence of AH& values of column 7. Calculated as averaged value for monomeric complexes using eq. (A4) as described in the appendix.
G. Conti. P. Gianni, and E. Matteoli
4130
Table 5. Comparison between experimental and calculated SC,, values for aqueous hydrolyzed AlCl$‘).
0.03 -19 0.05 -12 0.075 -22 loo 0.03 130 0.05 100 0.075 91 n 0.1 38 0.3 0.5 26 150 0.03 455 0.05 392 0.075 27-7 238 0.1
50
7 5
-7 -5
29 21
2.9
15
4 23 16 12 9 4 3
-4 -24 -17 -12 -10 -5 -4
16 53 38 29 24 14 12
21 16 52 37 29 23 13 11
72
-67
R
77
48 31 21
46 -33 -27
50 36 30
52 34 24
11 8 61 43 31 25 14 13 240 173 118 82
-11 -8 -6 -54 -38
543 43 33 155 117 92
62 46 35 162 122 95
1; -12 -11 -22lX25 -169i18 -126i14 -102Ztll
78 54 59
so 56
2w1 144f20 113i16 9Bf13
&t56 148ti8 IO%30 78iz24
9 7 5 32 21 15 12
-7 -5 -4 -25 -16 -12
73 51 39 302 220 158
-10
6 5
-5 -4
132 85 54 36
-125i26 -f33*19 -59+14
130 77 74 421i44
#ill
299t32 222X24 183i18
75 53 40 3ce 223 161 132 78 7.5 428i70 301m 217i38 173zt29
a) All heat capacity data are in J moi-’ K-‘. b) Average experimental values obtained from eq. (141 among those corresponding to the different ionic strengths predicted by the schemes. Deviations from the mean are always much lower than experimental uncertainty. c) Calculated values: SC,, = A + B + C where the terms A, B and C are the Ist, 2nd, and 3rd term of the right hand side of “I. (17). req?ctively. d) Listed uncertainties represent the effect of an arbitwy change off 50.~~J mol-1RI on C,,,,
e) Listed uncertainties represent the effect of an arbitrary change of ti.O.y, kJ mob’ on AHt,Y. 0 Listed uncertainties represent the maximum deviation due to the combined uncertainties of points d) and e)
expe~mentai conditions, of the Cp,+,j values of the various complexes, and of the relaxation term C$ are described in the Appendix. Experimental values of 6C,,,, together with the corresponding calculated ones for each scheme considered, are listed in Table 5. The separate contributions (A, B, C) to the calculated &I,,* values made up by the three terms which appear in the right-hand side of Eqn, ( 17) are also specified in Table 5. Values of SC,,, vs. rn!, are also plotted in Fig. 4 at the three temperatures examined. In addition, at 5O”C, the experimental data obtained using the C’$‘) values of BARTA and HEPLER (1986) are represented; the observed slightly higher values are due mainly, to the difference by -25 J mol-’ K-’ between our cop,AIcI,value and that reported by the above authors.
would result in a smaller contribution to the relaxation heat capacity. The experimental SC,,,+values reported by us would be underestimated in such a hypothesis, the larger true values being observable in conditions of fast occurring reactions. For the sake of clarity, in Table 5, the calculated SC,,$ values have been subdivided into the three contributions A, B, C, corresponding to three terms in the right-hand side of Eqn. ( 17), respectively. Some useful observations emerge from Table 5. The heat capacity increase due to A13+ disappearing (A) is always almost fully compensated for by the formation of the hydrolysis products ( B), This suggests that the sum of the three terms, A + B + C, is, in most cases, not very different from C and therefore that the extent of the calculated excess quantity is determined mostly by the
DISCUSSION The analysis proposed here, even if it cannot constitute a method for exactly identifying the hydrolytic species of Al”+, can nevertheless provide useful information on the hydrolysis reaction
of this ion. It requires one to select some hydrolytic
schemes among those available in the literature, then to calculate SC,,+ and test how this quantity is related to the thermodynamic properties of the occurring reactions. As a matter of fact, significant nonzero values of SC,,+ are brought about by a change in heat capacity of the solute species and/or by the relaxational heat capacity of the reacting system, thus being indicative of the nature of the hydrolytic process. Unfortunately, in the calculation of SC,,,4, many thermodynamic quantities are involved; two of them, the apparent molar heat capacities of the complex species, iZ&+ and the reaction enthalpies, AH,,,, need to be estimated. This reduces the validity of this procedure to some extent, but we shall later point out that this estimation is quite less a dramatic drawback than one might think. Also, we would like to emphasize that the possible presence of slow chemical reactions unable to closely follow the temperature change associated to the heat capacity determination
FIG. 4. Comparison between experimental and calculated (Eqn. 17) values of the difference SC,,+ vs. total molality at various temperatures: 0, this work; n, obtained using data of BARTA and HEPLER ( 1986) for iI’,,+of AK&. Curves were calculated following the three hydrolytic schemes: I, (p); II, (- - - -); III, (----).
4131
Molar heat capacity of AlCll
value (C practically equals C$, owing to compensating G,‘m effects of C, and S). Uncertainties deriving from the estiquantities appearing mation procedure ofthe C,,3, and L?lcHX,Y in B and C, respectively, do not substantially modify this assertion. At 15O”C, where hydrolysis is more marked, the changes in B and C and on the overall quantity SC,,@,brought about by uncertainties as large as +50. y, J mol-’ K-’ for CD,@,, and f2 - y, kJ mol-’ for AH,,, , are generally less than 20%. It is evident from Fig. 4, where these uncertainties are reported, that the calculated curves still preserve their identity with respect to the relevant hydrolytic scheme. In Table 6, for the smallest aluminum concentration where the hydrolysis extent is largest, the values of aC,,+, of the hydrolysis degree, Xhydr= C xjm,/mil, ofthe average number I of OH groups bound per Al atom, 5, and of the quantity noH = ii/X,,,,,, which represents the average number of OH groups bound per metal ion involved in complex species, are reported. It shows that at each temperature as the calculated SC,,+ values are larger so the rioH is larger. This correlation also holds at the other concentrations. No correlation is found instead, either with respect to 5 or to Xhydr. It is also to be noticed that the largest ZoH and I~C,,~values are obtained for cases in which high percentages of hydrolyzed Al are engaged in polymeric species. For example, the couples of values rioH = 1.93 and SC,,+ = 309 J mol-’ K-’ at lOO”C, and coOH = 2.48 and SC,,* = 428 J mol-’ K-’ at 15O”C, correspond to fractions of the overall A13+ ion hydrolyzed which is engaged in the species Al,, by 42% and 79%, respectively. Figure 4 shows that at 5O”C, the experimental SC,,@values are close to zero, according to the very low hydrolysis degree calculated at this temperature. At these hydrolysis levels, the only species AlOH 2+is able to justify the experimental results. At lOO”C, the fi values calculated for the three schemes at the concentration rnt, = 0.03 mol kg-’ are still low and, anyway, less than 0.2. This value was considered by MESMER and BAES ( 197 1) as a limit beneath which the presence of slowly forming, large-size complex species cannot be justified because, as they observed, short times are employed by the solutions to reach equilibrium. As a matter of fact, at lOO”C, the experimental aC,,+ values closely approach (see Fig. 4) those calculated by scheme II, which, at this temperature,
Table 6. Correlation between &C,, and various hydrolysis
parameters for
predicts only very scanty quantities of the AlI4 species in the concentration range here studied. The values calculated by scheme III, which predicts fairly large quantities of AlI3 species, are quite high, about twice as high as the experimental ones. Our data seem to indicate, therefore, that up to lOO’C, and for n < 0.2, large-size complexes are not present, as MCDONALD et al. (1973) and BERTSCH( 1987) also found. In contrast, at 15O”C, the high experimental SC,,+ values can be justified only by a large rioH value and therefore by the presence of a large polymeric species as the predominant one. MESMER and BAES ( 197 1) had already observed that the steep increase of the n curves vs. pH at about fi = 0.4 was to be ascribed to the formation of a large-size polymeric complex with high stability. Applying scheme II to our solutions at 15O”C, in spite of the high hydrolysis extent (Xhydr z 0.4), the polymeric species is always found present in small quantity, and no agreement (see Fig. 4) is found with the large experimental 6C,,d values. At this temperature, scheme III calculates a lesser hydrolysis degree (Xhydr= 0.2) but also a quite large fraction of AlI3 species, which brings about large calculated values of SC,,@,the nearest to the experimental ones. By simulating changes that are not too dramatic of the hydrolysis extent and of the species distribution without altering the H+ concentration from a value consistent with experimental e.m.f. measurements ( MESMER and BAES, 197 1)) it is possible, at 150°C by using Scheme III, and only by means of it, to obtain still larger calculated SCP,4values which agree with the experimental behaviour. On the other hand, we are confident that no kinetic effect should skew our experimental results at 150°C since, at this temperature, the formation of polymeric species should also be a sufficiently fast process. But even if this were not fully true, the actual SC,,+ values would be larger than those here obtained, as previously mentioned. In conclusion, we can only confirm the large presence of polymeric species in our conditions of high hydrolysis extent ( 150°C). Unfortunately, the complexity of the system studied, which is not yet fully characterized both in its thermodynamic and kinetic aspects, does not allow us to draw any more definite conclusion on the basis of the unique property studied. We believe, however, that the observed phenomenology may be helpful in the further development of this subject.
different hydrolytic schemes?
Acknowledgments-We
are grateful to Mr. A. Giannotti for his valuable skill in the maintenance of the heat capacity calorimeter and to Ms. M. R. Carosi for her patience in typing the manuscript.
--------__........._.........i~----.--------------------i~_~..... 5ooc I SC,, ”
29
&I,.& (=’ 2.1 -Cd, ” 0.021 w
II
III
I
II 162
m
II
62
75
52
4.4
2.7
6.1
16
0.048
0.032
0.063
0.166
0.162
1.09
1.19
1.03
1.16
1.93
1.08
1.21
1.01
309
I
a.4
III
77
234
426
12
40
22
0.130
0.483 0.545
Editorial handling: F. J.
Miller0 REFERENCES
2.46
BARBERO J. A., HEPLER L. G., MCCURDY K. G., and TREMAINE P. R. ( 1983) Thermodynamics of aqueous carbon dioxide and
(a) All numbers refer to the lowest lluminum concentration (mk = 0.03 mol kg-l) where maximum extent of hydrolysis is observed. (b) J mol-‘K-‘. Calculated by eq. (17). (c) Percent of hydrolyzed AIs+ ion.
sulphur dioxide: Heat capacities, volumes, and the temperature dependence of ionization. Canadian J. Chem. 61, 2509-25 19. BARTA L. and HEPLER L. G. ( 1986) Densities and apparent molar volumes of aqueous aluminum chloride. Analysisof apparent molar volumes and heat capacities of aqueous aluminum salts in terms of the Pitzer and Helgeson theoretical models. Canadian J. Gem.
%”
(d) n = m&t&. (e) i&=ii//Xhydr.
64.353-359.
4132
G. Conti, P. Gianni. and E. Matteoli
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APPENDIX Speciation
The equilibrium quotients Qx!,. necessary for calculating the species distribution in the actual condltlons of our experiments, have been obtained using activity coefficients evaluated according to the procedure proposed by HELGESONet al., I98 I, and already followed previously (CONTI et al., 1991). In this procedure, the hydrolyzed complex cations have been attributed an electric charge equal to the average charge per aluminum atom. As an example, values of the quotients Qx,y are reported in Table 3 for the smallest AICI, concentration considered in our experiments. Apparent Molar Heat Capacities of Complex Species
Values
of
C,,,,
of
the
complexes
of general
formula
Al,( OH ),jCl, 3x,-,j~were estimated through the following approximated equations:
cp,m,,=cz,,+(4x,-y,)
+1.21”*)
(Al)
co =$;,A,c,, + Y,(~;,,oH - ~;,a,,+ K;,oH)-
(AI)
Bd
$In(I
Eqn. (A 1) was devised by us to describe a hypothetical situ&on in which the complex cation is dissociated to give .,, ions with charge (3 - y,/x,). We believe that this situation is nearer to reality than considering these complexes to behave like highly charged monoatomic ions, so that Eqn. (A I ) estimates, at best, the C,,. , quantities without diminishing the validity of the conclusions re&&. In Eqn. (A2), the criterion of the additivity of the standard thermodvnamic properties of ions is assumed. The-data of &,,c, and c&,,, were taken from SILVESTERand PITZER ( 1977) and from CONTI et al.
Molar heat capacity of AIC& ( 1988), respectively. The quantity AC~.on refers to the following reaction: .K,/‘Y,AI~++ OH- = 1/yjAi~j(OH)~~~-~“,
t.43)
whose standard thermodynamic functions can be expressed (CONTI et al., 1991) by the equation AX& = AX;,,.,‘y - AX”,,
(A4)
where AX!,, refers to reaction ( 1t ), and Afi refers to the ionization of water. ACj,o, values for mononuclear complexes were obtained from Eqn. (A4) (X = C,) using AC:,,, values given by MICHARD ( 1983 ) and AC:,, values given by OLOF~SONand OLOPSSON( 1981). AC;,OHvalues for polynuclear forms were obtained instead by differentiating, with respect to temperature, the function AH”,, =f( T) determined by CONTIet al. ( 199 1) in the temperature range 25150°C. The AC’&,, and AH& values can be found in Table 4. Relaxations1 Contribution to Heat Capacity For a solution in which n parallel reactions having mutual reagents are in effect. Cg+ can be expressed as follows:
where m is the total molality, and ( AHHx,y),(abbreviated as AH%,, throughout this paper) and 4, are the enthalpy and the extent of the jth reaction (Eqn. L1). respectively, the latter expressed as moles of complex formed per kg of pure solvent. The n derivatives in Eqn. (A5), due to the presence of common reagents, depend each on the thermodynamic parameters of the others and constitute the n unknowns of the following n-equation system: C Aj.k*L)k= H,,
k-1
j=
1,2 * ++ R.
tAbI
4133
A,,k, Dk and H, are so defined:
Ajk=z+!?$ A+
A,,
=
(j#k)
(A7)
+
I + A._ +A_ ml
m4+
(A81
m+
(A9) where mArI+,mH+, and m, are the equilibrium molality of the free A13+,of the acid, and of the jth complex, respectively. Values of the enthalpies of reaction ( I I ) for the various hydrolytic species, AHH,,,, were calculated as follows. Standard enthalpies of reaction from A13’ and water, AH:., , were taken from literature for monomeric species ( MICHARD, 1983); while for polynuclear and polymeric species, they were calculated by solving Eqn. (A4) (X = H) for AH’&,, using AH& values from Table 4. In regard to the validity of this method for calculating AHx,? of polymeric and polynuclear species, it is worth mentioning that the values calculated by us for A&(OH):+, A13(OH)F, and Alder compare well with those obtained by applying the van? Hoff method to the experimental log Qx,, data of MESMERand BAES,( 197 1) in the temperature range 2%125°C. The AH,,, values at the ionic strengths, I, of our experimental conditions were calculated using Eqn. (AIO), as follows: AH,,,, = AH:,, + Y*&,Hc@) + Al,,
- &AIC&),
(AlO)
where the apparent relative enthalpies, L,, ofA1C.I~and ofcomplexes (subscript j) were estimated using the equation of HELGESONet al., I98 1;those for HCI were taken at 25°C from PARKER( 1965) and, at higher temperatures, calculated from heat capacity values reported by TREMA~NEet al. ( 1986).