Thermodynamic investigations of aqueous solutions of aluminium chloride

J. Chem. Thermodynamics 2000, 32, 145–154 doi: 10.1006/jcht.1999.0557 Available online at http://www.idealibrary.com on

Thermodynamic investigations of aqueous solutions of aluminium chloride Uwe Richter, Paul Brand, Klaus Bohmhammel, Technische Universit¨at Bergakademie Freiberg, Fakult¨at f¨ur Chemie und Physik, Institut f¨ur Physikalische Chemie, D-09596 Freiberg, Germany

and Thomas K¨onnecke Forschungsinstitut Karlsruhe GmbH, Institut f¨ur nukleare Entsorgungstechnik, Germany The activity of water in {x1 AlCl3 + (1 − x1 )H2 O} has been determined by measurement of vapour pressures in the temperature range (300 to 342) K, and the molality range (0.421 to 3.033) mol · kg−1 . The behaviour of the solution is described by the Pitzer model. The [Al(OH)(H2 O)5 ]2+ in the system is calculated by considering the first hydrolysis step in c 2000 Academic Press the aluminium chloride solutions. KEYWORDS: vapour pressure; water activity; aluminium chloride; aqueous solutions; Pitzer model

1. Introduction The present state of knowledge of the thermodynamic properties of {x1 AlCl3 + (1− x1 )H2 O} is unsatisfactory. Data on the activities, and osmotic coefficients(1–4) are only available for molalities up to 1.8 mol/kg and for T = 298.15. These data were derived from vapour pressure measurements, or obtained by e.m.f. or isopiestic methods. The difficulty is caused by an increase in the formation of hydrolysis products with rising temperature, mainly through reaction (1): [Al(H2 O)6 ]3+ + H2 O = [Al(OH)(H2 O)5 ]2+ + H3 O+ .

(1)

Data on this first hydrolysis product were reported by Bohmhammel(5) who investigated the equilibrium among different species in dilute solutions at T = (298 and 373) K. In the present work the activities of water in concentrated solutions of AlCl3 were determined from vapour pressure measurements in a static apparatus. 0021–9614/00/020145 + 10 $35.00/0

c 2000 Academic Press

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W+P

P

TH

K

PP

P

F

F

F

F

SM

SM

SM

SM

FIGURE 1. Schematic diagram of the vapour pressure apparatus: W+P, Wheatston bridge and printer; TH, thermistor; P, pump; K, cold trap; PP, Penning/Pirani gauge; p, pressure sensor; F, flask; SM, stirring motor.

2. Experimental For the preparation of AlCl3 solutions, AlCl3 · 6H2 O (supra pur, Merck, Germany) was dissolved in double-distilled water. Their molalities were determined by complexometric titration using EDTA (back titration with 0.1 m solution of ZnSO4 ), with a relative standard deviation of 0.35 per cent. The vapour pressure apparatus used is shown in figure 1. It is a glass instrument which consists of four flasks, a pressure sensor, and a thermostat. The pressure sensor (PDCR 911 Druck Meßtechnik GmbH Bad Nauheim, Germany) is of the strain gauge type, and can operate up to 35 kPa with an absolute uncertainty of ±0.06 per cent in the measured pressure. The flasks and the sensor were housed in a thermostat whose temperature was controlled within ±0.05 K. A thermistor was used to measure the temperature; its calibration was carried out by comparison with a Pt resistance thermometer (Pt 10) certified by the Office of Weights and

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TABLE 1. Experimental water vapour pressures pexpt and corresponding values from the Saul and Wagner(6) equation T /K

pcalc /kPa

pexpt /kPa

(Saul and Wagner) 303.5

4.221

310.35

6.348

4.20

322.75

12.102

12.36

337.78

24.614

24.43

346.76

36.377

36.13

6.313

Measures. The working temperature range of the thermistor was (300 to 350) K, and its uncertainty was < ±0.06 K. After equilibrium was attained the measurements were delayed for 2 more hours. The operation of the vapour pressure apparatus was successfully tested by measuring the vapour pressure of water. The measured vapour pressure data were compared with pressures calculated by using the equation of Saul and Wagner,(6) and were also used for the computation of the water activities aw . The Saul and Wagner equation represents ( p/ pcrit ) as a polynomal function of (1 − T /Tcrit ) from the triple point to the critical point of water. At the final pressure of 35 kPa, the estimated uncertainty of the measured pressure was ±0.06 per cent. Table 1 compares the experimental pressure data with corresponding values calculated by using the Saul and Wagner equation.

3. Results and discussion According to equation (1) hydronium ions are generated and HCl gas is formed. Because HCl has a great affinity for water a noticeable partial pressure of HCl would exist only if the concentration of the hydronium ions was very high. Gokcen(9) calculated the partial pressures of HCl and water in {x1 AlCl3 + x2 HCl + (1 − x1 − x2 )H2 O} on the basis of activity data from the literature. He assumed, however, that the HCl partial pressure above a pure solution of AlCl3 was zero. M¨unkner(8) disputed this assumption. She found that the HCl partial pressure increased only above T = 343.15 K. At this temperature she found pHCl = 0.184 kPa. The solutions studied in this work had lower HCl concentrations and were investigated up to a temperature of 343 K. The HCl partial pressure was therefore not taken into account. The activity of water is the ratio of the fugacity of water in the solution to that of pure water under the same conditions of temperature. The water activities were calculated from water pressure data through the relation: Z pw Z pw,s 1 pw 1 g g,2 + (Vw − Vw )d p + Vwl d p, (2) ln aw = ln ps RT pw,s RT ps

148

U. Richter et al. m m0 = 0.421 m m0 = 1.071

–0.4

m m0 = 1.765

ln aw

–0.2

–0.6 m m0 = 2.566

–0.8 m m0 = 3.033

–1 2.9

3

3.1

3.2

3.3

3.4

103·(T/K)–1 FIGURE 2. Logarithm of the activity aw for different molalities m as a function of the inverse of temperature T where m 0 = 1.0 mol · kg−1 .

where l and g designate a liquid and a gaseous phase, respectively, Vw is the molar volume g g,2 of water (Vw refers to the real state and Vw refers to the ideal gas standard state), pw is the vapour pressure above the solution, and ps is the vapour pressure of pure water. The first term in equation (2) results from Raoult’s law, and the second is needed to correct for real gas behaviour. The molar volume was calculated from the equation of state of Saul and Wagner.(6) The third term describes the dependence of the liquid water activity on pressure; its value is within the measurement error and may therefore be neglected. The relative uncertainty of water activities is estimated to be ±0.9 per cent. The water activity data were represented by the following relation: ln aw = a + b/(T /K).

(3)

Figure 2 shows plots of AlCl3 solutions at different molalities which are well represented by equation (3). The osmotic coefficients φ were calculated by equation (4): φ=−

1000 · ln aw , ν · m · MH2 O

(4)

where m is the molality of AlCl3 , ν is the number of ions per molecule, and MH2 O is the molar mass of water. Table 2 contains the osmotic coefficients φ calculated from the experimental vapour pressures of {x1 AlCl3 + (1 − x1 )H2 O}. Because of lack of data a direct comparison of

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149

TABLE 2. Molality m of AlCl3 {x1 AlCl3 + (1 − x1 )H2 O} at temperature and pressure p m/mol · kg−1

T /K

p/kPa

aw

φ

0.421

302.55

3.985

0.972

0.95

0.421

317.25

8.922

0.972

0.95

0.421

327.76

15.150

0.972

0.95

0.421

343.58

30.822

0.972

0.95

1.071

302.55

3.695

0.896

1.42

1.071

317.30

8.244

0.898

1.40

1.071

327.81

14.022

0.899

1.38

1.071

343.49

28.510

0.902

1.34

1.765

302.55

3.115

0.760

2.16

1.765

317.32

7.060

0.769

2.07

1.765

327.84

11.981

0.773

2.03

1.765

343.53

24.713

0.781

1.94

2.566

302.55

2.274

0.555

3.18

2.566

317.30

5.209

0.568

3.06

2.566

327.81

8.952

0.579

2.96

2.566

343.49

18.740

0.594

2.82

3.033

303.15

1.750

0.412

3.49

3.033

317.30

3.940

0.429

3.34

3.033

327.81

6.798

0.440

3.23

3.033

343.58

14.437

0.457

3.09

in T

water activities and osmotic coefficients of the present measurements with literature values is not possible. Only extrapolated values of the present data can be compared with literature values. For this purpose, water activities, fugacities, and osmotic coefficients have been calculated at T = 298.15 K by means of equation (3). To this end, the present pressure data have been extrapolated to lower temperatures by (4 to 5) K. Osmotic and activity coefficients in the molality range up to 1.8 mol · kg−1 at T = 298.15 K are available in the literature. It was therefore possible to compare the osmotic coefficients directly. Using the activity coefficients of the literature, the osmotic coefficients were calculated by equation (5): Z 1 m φ =1+ md ln γ± (m), (5) m 0 where γ± is the mean activity coefficient of AlCl3 in the solution. The Debye–H¨uckel region dominates the integration region. Therefore, this region must be well covered by experimental data. Because of lack of values the integration of

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3.5 3

φ

2.5 2 1.5 1 0.5

0

0.5

1

1.5

2

2.5

3

m / mol·kg–1 FIGURE 3. Osmotic coefficients φ as a function of molality m at T = 298.15 K: ×, Robinson and Stokes;(2) ◦, Mason;(3, 4) , this work.

equation (5) is not possible. To perform the integration despite a lack of data the osmotic coefficient at m = 0.1 mol · kg−1 (reported by Mason(4) ) was used. The deviations of the resulting values from the literature ones are less than 1.5 per cent. Figure 3 shows the values determined in this work and the osmotic coefficients calculated from activity coefficients.

4. Modelling of water activities The modelling of {x1 AlCl3 + (1 − x1 )H2 O} is based on the ionic interaction model of Pitzer. In this model, besides coulombic interactions, specific ionic interactions are considered in equation (6):     2 · v+ · v− 2 · (v+ · v− )3/2 φ − 1 = |z + · z − | · f φ + m · Bφ + m2 · · C φ , (6) v v with, B φ = β 0 + β 1 exp(−x), f φ = −Aφ · {I 1/2 /(1 + b · I 1/2 )},    2 3/2 1 2π · N · ρw 1/2 e Aφ = · · , 3 1000 DkT x = α · I 3/2 ,

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151

and b = 1.2,

α = 2,

v− = 3,

v+ = 1,

z − = −1,

z + = +3,

where D is the absolute dielectric constant, k is the Boltzmann constant, N is the Avogadro number, ρw is the density of water, I is the ionic strength, and β 1 , β 2 , and C φ are the parameters of the Pitzer equation. TABLE 3. Values of the temperature-dependent coefficient Aφ as a function of temperature T T /K

Aφ

298.15

0.391439

308.15

0.398485

318.15

0.406188

328.15

0.414549

338.15

0.423573

343.15

0.431276

The Pitzer equation consists of a virial expansion of the excess Gibbs energy in terms of molalities of dissolved species. The osmotic coefficient in equation (6) is derived from the partial derivative of the excess Gibbs energy. For the calculation of the temperaturedependent coefficient Aφ the equation of state of Saul and Wagner(6) and the equation of Bradley and Pitzer(7) were used for computing the dielectric constant. Table 3 shows some Aφ values as a function of temperature. The interpolation was performed according to Pitzer using the available literature data (T = 298 K and up to m = 1.8 mol · kg−1 ) by means of an iteration procedure. The experimental data were found to differ from the calculated values by up to ±12 per cent. Only pure dissociation of AlCl3 into Cl− and [Al(H2 O)6 ]3+ ions is considered in the Pitzer model. In AlCl3 solutions, however, some hydrolysis of the six-fold coordinated Al ion according to reaction (1) must be taken into account besides dissociation. Therefore, it is reasonable to include this chemical equilibrium into the interpolation using the equilibrium data of Bohmhammel.(5) The activities of water, calculated in this manner, were found to differ from the experimental results by less than ±2 per cent. The Pitzer parameters in the molality range (0.05 to 3.033) mol · kg−1 , and temperatures (298.15 to 343.58) K are: β 0 = 0.61241 + 0.000682134 · {(T /K) − 298.15} − 4.7535 · 10−6 · {(T /K)2 − 298.152 } β 1 = 1.64267 + 0.0269706 · {(T /K) − 298.15} − 1.24372 · 10−4 · {(T /K)2 − 298.152 } C φ = 0.0469624 + 0.000189762 · {(T /K) − 298.15} − 3.92423 · 10−8 · {(T /K)2 − 298.152 }. (7)

152

U. Richter et al. TABLE 4. Comparison of the Pitzer coefficients β 0 , β 1 , and C φ determined in this work with literature values Cφ

Substance

β0

β1

AlCl3

0.61241

1.64267

AlCl3

0.68627

6.0203

LaCl3

0.59602

YCl3

0.62570

CeCl3

m max

Reference

0.0469624

3.033

This work

0.00810

1.800

2

5.6000

−0.02464

3.800

10

5.6000

−0.01571

3.800

10

0.63509

7.4991

−0.03001

2.000

10

ScCl3

0.72087

6.5317

0.03367

1.800

10

FeCl3

0.23617

−5.3975

−0.00796

10.000

10

CrCl3

0.69081

2.7849

−0.04390

1.200

10

T = 343. 15 K

5

102·mAl2+

4 T = 323. 15 K

3 2

T = 303. 15 K

1

0 0

1

2 m / (mol·kg–1)

3

4

FIGURE 4. Molality per cent of [Al(OH)(H2 O)5 ]2+ represented as 102 mAl2+ of AlCl3 as a function of the total molality m of aluminium chloride.

Table 4 compares the calculated Pitzer coefficients at T = 298.15 K with literature data for other 3–1 electrolytes (Kim and Frederick(10) ). The second data set with coefficients derived from activities of {x1 AlCl3 + (1 − x1 )H2 O} is by Stokes and Robinson. By comparison with the Pitzer coefficients for other chlorides the value of β 0 for AlCl3 falls in the range (0.59602 to 0.72087) with the exception of FeCl3 . However for the values of β 1 and C φ the picture is not clear. Again, the values for AlCl3 lie within the

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153

TABLE 5. Distribution of mAl2+ at different temperatures T , where m is the total molality of aluminium chloride m Al2+ /mol · kg−1

m Al2+ /mol · kg−1

m Al2+ /mol · kg−1

T = 302.15 K

T = 323.15 K

T = 343.15 K

0.400

0.0015

0.0024

0.0043

0.500

0.0018

0.0029

0.0050

0.700

0.0025

0.004

0.0068

0.900

0.0035

0.0055

0.0092

1.100

0.0049

0.0075

0.0123

1.300

0.0068

0.0103

0.0165

1.500

0.0095

0.0142

0.0223

1.700

0.0134

0.0196

0.0304

1.901

0.0377

0.0273

0.0415

2.102

0.0396

0.0380

0.0570

2.302

0.0415

0.0795

0.0788

2.502

0.0432

0.0792

0.1093

2.702

0.0450

0.0824

0.1435

2.902

0.0466

0.0854

0.1489

3.009

0.0474

0.0869

0.1515

m/mol · kg−1

range of other substances, but here the differences are much larger, with the coefficients even changing signs. In this case, the strongly differing molality ranges have to be taken into consideration. That they strongly affect the values of β 1 and C φ can be deduced by comparing the values of this work with the compilation of Kim and Frederick.(10) By including equilibrium (1) the computation of [Al(OH)(H2 O)5 ]2+ molalities as a function of the total molality of aluminium m becomes possible. Using the expression for the equilibrium constant: a 2+ · aH+ m 2+ · γ± · m H+ · γ± K = Al = Al aAl3+ · aH2 O m Al3+ · γ± · aH2 O with m Al2+ =m H+ , and m = m Al3+ +m Al2+ , [Al(H2 O)6 ]3+ =Al3+ , and [Al(H2 O)5 OH]2+ = Al2+ , the equilibrium condition becomes: K =

m 2Al2+ (m − m Al2+ )aH2 O

· γ± .

The functions m Al2+ = f (T ) and γ± = f (T ) can be finally calculated. The distribution of the hydrolysis product Al2+ thus obtained is presented in table 5, and shown in figure 4. The molality mAl2+ resulting from hydrolysis is small (<5 per cent) and it rises with increasing temperature. When the total molality of aluminium m increases the percentage of mAl2+ decreases at the beginning, and reaches a flat minimum with no visible

154

U. Richter et al.

dependence on m. A steep increase then follows until a maximum discontinuity is reached beyond which the value starts to decrease again. This behaviour is difficult to interpret. From equation (1) an increase in mAl2+ causes a decrease in pH. This would counteract further hydrolysis. This is the case up to the minimum only. Obviously, the model is not adequate for concentrated solutions since additional hydrolysis and condensation must be considered. With an increase in pH the Al3+ ion forms multinuclear aluminum hydroxo-complexes because of its small radius and its high charge. Their formation is often a slow process, and partially unstable complexes are produced, which can only be proved definitely in some cases (Fitzgerald(11) ). The present work has shown that, despite shortcomings of the model used, electrolytes which undergo a proton transfer reaction can be described by combining interaction with chemical equilibrium. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Robinson, R. A.; Harned, H. S. Chem. Rev. 1941, 28, 419–476. Robinson, R. A.; Stokes, R. H. Trans. Faraday Soc. 1949, 45, 612–639. Mason, C. M. J. Amer. Chem. Soc. 1938, 60, 1638–1647. Mason, C. M. J. Amer. Chem. Soc. 1940, 63, 220–223. Bohmhammel, K. Freiberger Forschungshefte 1993, A832, 49–59. Saul, A.; Wagner, W. J. Phys. Chem. Ref. Data. 1987, 16, 893–901. Bradley, D. J.; Pitzer, K. S. J. Phys. Chem. 1979, 83, 1599–1603. M¨unkner, S. Diplomarbeit Bergakademie Freiberg. Personal communication. 1988. Gokcen, N. A. Partial Pressures of Gaseous HCl and H2 O Over Aqueous Solutions of HCl, AlCl3 and FeCl3 . Bureau of Mines Report of Investigations, 1980. 10. Kim, H.-T.; Frederick Jr., W. J. J. Chem. Eng. Data 1988, 33, 177–184. 11. Fitzgerald, J. J. Antiperspirants and Deodorants, Cosmetic Sci. and Techn. Ser. 7. Laden, K.; Felger, C. B.: editors. Marcel Dekker Inc.: New York and Basel. 1988. (Received 5 January 1998; accepted in revised form 10 June 1999)

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