J. Phys. Chem. 1985,89, 5541-5549 TABLE I: Ratio of the Mass-Transfer Coefficients to a Thin Ring Electrode Calculated by Using the Models of Nonuniform and Uniform Accessibility as a Function of r'/Ar r'/Ar
ratio of mass-transfer coeff
10 20 26 27
1.159 1.034 1.004 0.999
r'/Ar
ratio of mass-transfer coeff
100 200 1000
0.831 0.763 0.644
Table I compares the ratio of the mass-transfer coefficients derived from the two assumptions as a function of r ' / A r . Measurements will normally be carried out using thin fiber cores (0.5 pm < r' < 5 wm say) so as to minimize the characteristic time for the approach to the steady state, eq 24, and using thin coatings to form the rings (0.005< Ar < 0.05 pm say) so as to maximize the mass-transfer coefficient, eq 27. These structures are readily prepared by metal film evaporation onto quartz or glass fibers, and subsequent mounting in capillary or tubes for ease in handling. The polishing of the end of the assembly exposes the ring electrode. Alternately, metal printing inks can be painted onto fibers and thermally reduced to adhering thin films.I8 For the likely range of r'/Ar, 10 < r'/Ar < 100 the ratio of the mass-transfer coefficients calculated by using the two assumptions do not differ markedly from unity, Table I. For the determination of the complete voltammetric curves, it would be best to choose electrodes having r'/Ar in the range 26-27. For such electrodes k, will show minimal changes with increase of overpotential as the surface reaction moves from kinetic to mass-transfer control. It should be noted, however, that the changes indicated in Table I are upper limits as edge effects will be reduced by the throwing power of the electrode reaction (see above).
Acknowledgment. The support of the United States Office of Naval Research is gratefully acknowledged. Glossary Ci
ciC? COOD
concentration of species i, mol cm+ bulk concentration of species i, mol cm-3 surface concentration of species i, mol cm-3 bulk concentration of species 0, mol cm-3
5541
surface concentration of species 0, mol cm-3 bulk concentration of species R, mol cm-3 surface concentration of species R, mol cm-3 dimensionless concentration parameter dimensionless concentration parameter in the steady state diffusion coefficient of species i, cm2 s-l diffusion coefficient of species 0, cm2 s - ~ diffusion coefficient of species R, cm2 s-I the Faraday, C mol-' current, A a limiting current, A modified Bessel Function of order zero mass-transfer coefficient of species i, cm s-I rate of an electrode reaction, mol cm-2 s-l standard rate constant of an electrode reaction, cm s-' an integer an integer continuous line source, mol cm-' s-I continuous source, mol s-I instantaneous point source, mol instantaneous line source, mol cm-l radial position, cm radius of a ring electrode, cm radius of a micro spherical electrode, cm radius of a microdisc electrode, cm half-thickness of a ring electrode, cm the gas constant, s mol-' continuous surface source, mol cm-2 SKI the time, s a time, auxilary variable, s a time, s temperature, K a variable ( p / 4 D i ( t - t ' ) ) a variable ( r R / 2 D i ( r- t')) a variable (rr'/2Di(t - r')) axial distance from the surface, cm transfer coefficient the gamma function overpotential, V angular position, rad angular position, auxillary variable, rad a time, s Registry No. Fe(CN)63-,13408-62-3;Fe(CN)6e, 13408-63-4;gold, 7440-57-5.
Thermodynamics of the Complexes of Aqueous Iron( I 1I ) , Aluminum, and Several Divalent Cations with EDTA: Heat Capacities, Volumes, and Variations in Stability wlth Temperature Jamey K. Hovey* and Peter R. Tremaine* Alberta Research Council, Oil Sands Research Department, P. 0. Box 8330, Station F, Edmonton, Alberta, T6H 5x2,Canada (Received: April 17, 1985; In Final Form: July 26, 1985) Apparent molar heat capacities and volumes at 25 OC have been determined for aqueous H2EDTA2-and for the complexes of aqueous EDTA4- with Ca2+,MgZ+,A13+,Fe3+,Mn2+,Co2+,Ni2+,Cu2+,and Zn2+,all as the sodium salts. The standard-state partial molar heat capacities, and volumes, V",derived from these measurements were treated by using the simple Born model to calculate the Coulombic effects on the surrounding water. The non-Coulombic contributions to and t" are very similar for all the complexes, and small systematic variations are consistent with known structures of the aqueous complexes. Values for the partial molar properties and 7 were combined with critically evaluated literature data to calculate the temperature dependence of the stability constants at 0.1 m ionic strength. The relative stability of the complex ions MgEDTA2-(aqj, FeEDTA-(aq), and AIEDTA-(aq) increase sharply relative to CaEDTA2-(aq) and the complexes with other Mz+ ions.
cpo,
cpo
cp
Introduction
Aqueous solutions of ethylenediaminetetraaceticacid (EDTA) salts are used as sequestering agents in a number of industrial applications. These include cleaning conventional boilers, decontaminating nuclear reactor systems, and treating conventional
and heavy oil wells to remove scale and certain clay minerals. Many of these applications involve temperatures in the range 40 to 150 O C . The complexation equilibria of EDTA have been studied thoroughly near 25 "c, and, in most cases, stability constants and enthalpies of reaction are However, no
0022-3654/85/2089-5541$0lSO/O 0 1985 American Chemical Society
5542
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
measurements above 50 "C have been reported. The standardstate heat capacities and volumes of formation have also received little attention. Heat capacities and volumes define the temperature and pressure dependence of the stability constants, respectively, and values measured at 25 "C can be used with accurate enthalpy data to calculate stability constants under a wide enough range of temperature to include most industrial conditions. They are also of considerable theoretical interest because both are sensitive to the state of hydration of the aquo complex. In this study, we report apparent molar heat capacities and volumes at 25 OC for aqueous H2EDTAZ-and for the complexes of EDTA with Ca2+,Mg2+,AI3+, Fe3+, and a series of first-row transition-metal ions (Mn2+,Co2+,Ni2+,Cuz+, and ZnZ+),all as the sodium salts. The partial molar heat capacities and volumes derived from these measurements are combined with literature data to calculate the changes in heat capacity and volume of the complexation reactions and, hence, the temperature dependence of stability. Systematic variations in the partial molar properties of this series of EDTA complexes are also examined. Experimental Section
Water used to prepare all solutions was distilled once, then passed through a Milli-Q reagent grade mixed-bed ion-exchange and activated carbon system (final conductivity 1 WScm-' or less). Fisher Certified NaC1, used to prepare standard solutions, was dried at 110 "C and used without further purification. Solutions of the sodium salts of H2EDTA2-and the EDTA complexes were prepared by weight from the dried salts. The number of waters of hydration, and hence the molecular weight, of each salt was calculated from the weight loss recorded after dehydrating a small sample of the purified product under vacuum, at progressively higher temperatures until the samples reached constant weight. All the salts studied here were observed to dehydrate at temperatures below 150 "C. Some discolored above 170 "C, indicating that vacuum drying at higher temperatures may cause decomposition. The details of preparing each sample are given below. Fisher Certified Na2H2EDTA.2H20,dried at 80 "C before use," yielded the final product Na2H2EDTA.1.77H20which was used without purification. The pH of a 0.027 m solution was 4.6, in close agreement with the expected value of 4.5 for the pure salt, as calculated later in this paper. Hydrated Na2CaEDTA from Alfa was dried at 80 "C for 5 days to yield a partially dehydrated product, Na,CaEDTA.l .58H20, which was also used without purification. The other EDTA salts were obtained from Fisher (magnesium), Alfa (copper, ferric), and ICN Pharmaceuticals (manganese, cobalt, nickel, and zinc). They were recrystallized by a method derived from VogeL4 Ethanol (95%) was slowly added to the saturated solution of each complex until the first permanent precipitate appeared. After filtering off the precipitate, an equal volume of ethanol was added dropwise to the filtrate over a period of up to about 4 h with vigorous stirring. Even very slow additions did not prevent the solutions of nickel, cobalt, and copper from separating into a light ethanol-rich phase and a heavier water-rich phase. The final homogeneous or two-phase mixtures typically contained a 4:1 ethanol-water ratio and were stirred continuously until crystallization was complete, at which point only one liquid phase remained. This typically required 12-48 h. The resulting, well-defined, crystalline products were washed with ethanol and then recrystallized again by using the identical procedure. The Na2MgEDTA was recrystallized three times to completely remove a faint green coloration and a slight smell of acetate. The ( I ) Anderegg, G., Ed. 'Critical Survey of Stability Constants of EDTA Complexes"; Pergamon Press: Oxford, 1977; IUPAC Chemical Data Series No. 14. (2) Martell, A. E.; Smith, R. M . "Critical Stability Constants"; Plenum: New York. 1974. Vol. I. (3) Christensen, J. J.; Eatough, D. J.; Izatt, R. M. "Handbook of Metal Ligand Heats"; Marcel Dekker: New York, 1975; 2nd ed. (4) (a) Vogel, A. "Textbook of Quantitative Inorganic Analysis"; Longman: New York, 1978; 4th ed.,Chapter 10, p 317. See also (b) Blaedel, W. J.; Knight, H. T. Anal. Chem. 1954, 26, 741-746.
Hovey and Tremaine Na2NiEDTA mixture required 72 h to nucleate crystals and so the second recrystallization was not attempted, for fear that the salt would not have been recovered. Drying at 80 OC for 5 days yielded the following stoichiometries: N a 2 M g E D T A . 2 . 0 0 H 2 0 , Na2CoEDTA.1 . 5 5 H 2 0 , and Na2NiEDTA.0.83H20, Drying at 60 "C for 5 days yielded the following stoichiometries: Na2ZnEDTA.2.88H20 and Na2MnEDTA.4.00H20. The copper salt was dehydrated in bulk in the vacuum oven ( 5 days at 110 "C) and was used in the anhydrous form. The ferric salt, NaFeEDTA.1 .00H20, was prepared by drying the recrystallized product at 110 "C for 5 days. Finally, the aluminum complex was prepared by reacting a slightly acidic, aqueous solution of Fisher certified A1C1,.6H20 in 0.001 m HC1, with an aqueous solution of Na,HEDTA obtained from Alfa ("99+% purity"), at 80 "C. The mixture was reduced in volume and treated with ethanol to precipitate a hydrate of NaAlEDTA. The crystals, obtained in 70% yield, were recrystallized twice from ethanol/water, as described above, and dried at 80 "C for 5 days. Elemental analysis yielded the following results (in percent), with the values calculated for the monohydrate NaAlEDTA.H20 in parentheses: C, 33.38 (33.72); H, 4.20 (3.96); and N, 7.75 (7.86). Weight loss after vacuum dehydration at 150 "C confirmed the hydration number to be 1.00 H 2 0 . The densities of all solutions were measured relative to water with a SODEV-03D vibrating tube densimeters with platinum cells. This cell material was found to have a slightly nonlinear response which introduced an error of about 1 cm3 mol-' below 0.1 m when the cells were calibrated with water and nitrogen gas, as is usually the case. Calibration with water and a 1.O m standard solution of aqueous NaCl reduced the effects of this nonlinearity to less than 0.02 cm3 mol-'. The heat capacities were measured relative to water with a Picker flow microcalorimeter,6 SODEV Model CP-C, also equipped with platinum cells. Temperature was controlled to 25 f 0.01 OC (constant to rtO.001 "C) with the SODEV Model CT-L bath and measured with a thermistor set in a well deep in the coolant circuit. These were calibrated against a Hewlett Packard Model 2804A quartz thermometer traceable to NBS standards. The density and specific heat capacity of water at 25 OC were taken to be d o , = 0.997047 g cm-3 and cP," = 4.1793 J K-' g-I, respe~tively.',~The density increments for the standard NaCl solutions were taken from Picker et al.,5 [ d - d,"] = 3.8015 X lo-, g cm113at 0.9690 mol kg-I. All heat capacities obtained from the flow microcalorimeter were corrected for a very slight heat loss by the method described by Desnoyers et aL9 The heat loss factor f = 1.005 f 0.002 was obtained daily by measurement of the heat capacity of a standard NaCl solution. Results
Apparent Molar Properties. The apparent molar properties of a solute are defined by the equation
where Y is the extensive property of the solution (volume or heat capacity). Y," is the property for 1 mol of water, n, is the number of moles of water, and n the number of moles of solute so that, if n, = 55.509, n is equal to the molality, m. The vibrating tube densimeter and Picker calorimeter yield the experimental parameters, [ d - d,"] and [cpd/cPwod,"- l], from which @Vand @Cpcan easily be c a l c ~ l a t e d .Here ~ ~ ~ d, cp, dw0,and cp," are the density and specific heat capacity of the aqueous solutions and water, respectively. The experimental parameters and the cor( 5 ) Picker, P.; Tremblay, E.; Jolicoeur, C. J . Solution Chem. 1974, 3, 377-384. (6) Picker, P.; Leduc, P. A,; Philip, P. R.; Desnoyers, J. E. J . Chem. Thermodyn. 1971, 3, 631-642. (7) Kell, G . S.J . Chem. Eng. Data 1967, 12, 66-69. (8) Kell, G. S.In "Water-A Comprehensive Treatise", Franks, F., Ed.; Plenum Press: New York, 1972; Vol. 1. (9) Desnoyers,J. E.; de Visser, C.; Perron, G.; Picker, P. J . Solution Chem. 1976, 5, 605-6 16.
Heat Capacities and Volumes of EDTA Complexes
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5543
TABLE I: Apparent Molar Properties for Stoichiometric Aqueous Solutions of EDTA Complexes
( d - do,)/ g cm-3
W/cm3 mol-l
0.267 50 0.21 1 86 0.16385 0.1 11 16 0.08006 0.053 78
0.045 387 0.036 382 0.028428 0.019493 0.014 149 0.009590
Na2H2EDTA 159.28 158.67 158.17 157.73 157.18 156.32
0.41278 0.41278 0.311 40 0.21268 0.145 24 0.10920 0.058 13 0.033 02
0.081 476
mlmol kg-'
(c,d/
cpo,do,) - 1
%,/J
K-l
mol-'
mlmol kg-'
(d - do,)/ g
W/cm3 mol-l
cpowdow) -1
mol-'
-0.025 20 -0.020 17 -0.017 21 -0.013 05 -0.007 916 -0.005449
273.77 256.75 246.67 233.01 213.42 203.23
(cpd/
$Cp/J K-'
-0.02293 -0.018 90 -0.01522 -0.01078 -0.007977 -0.005512
289.16 274.68 259.76 243.80 232.03 218.11
0.267 37 0.205 37 0.170 78 0.125 39 0.072 77 0.049 02
0.057 369 0.044694 0.037428 0.027754 0.016305 0.011 047
Na2MnEDTA 164.95 164.01 163.69 163.09 162.25 161.80
0.062 886 0.043758 0.030349 0.023045 0.012382 0.007 118
NazCaEDTA 163.47 -0.031 46 -0.031 39 162.02 -0.025 54 161.34 -0.01878 160.30 -0.013 70 159.41 -0.01059 159.14 -0.005986 157.42 -0.003481
340.70 341.45 314.53 289.97 263.82 25 1.20 228.08 212.37
0.21034 0.163 30 0.13329 0.10902 0.08 1 39 0.054 45
0.045 266 0.035 492 0.029 194 0.024002 0.018 041 0.012 141
NazCoEDTA 170.09 169.63 169.02 168.75 168.26 167.97
-0.021 84 -0.017 58 -0.01457 -0.012 15 -0.009 237 -0.006316
257.21 242.43 235.09 226.75 218.17 208.53
0.035 563 0.030018 0.024 285 0.018 753 0.015404 0.010385
Na2MgEDTA 164.97 164.61 164.03 163.70 163.24 162.91
-0.01747 -0.01499 -0.012 32 -0.009680 -0.008074 -0.005515
287.75 278.82 268.68 259.27 249.86 242.02
0.193 18 0.16055 0.120 36 0.096 24 0.077 36 0.054 17
0.042 108 0.035272 0.026688 0.021 468 0.017 341 0.012217
NazNiEDTA 167.71 167.15 166.56 166.12 165.70 165.19
-0.02061 -0.01750 -0.013 48 -0.01097 -0.008 937 -0.006358
236.51 226.73 214.37 206.16 199.25 191.18
0.12963 0.10989 0.10665 0.090 55 0.067 29 0.047 04 0.047 04
0.021 652 0.018452 0.017924 0.015 274 0.011 430 0.008 051
Na AlEDTA 167.53 167.18 167.13 166.94 166.41 165.68
-0.011 56 -0.009925 -0.009686 -0.008 324 -0.006301 -0.004495 -0.004 469
314.66 309.70 307.57 303.06 295.06 285.23 287.56
0.21676 0.15840 0.11481 0.083 38 0.061 96
0.047980 0.035 517 0.025 999 0.019038 0.014213
NazCuEDTA 168.16 167.40 166.77 166.06 165.80
-0.02261 -0.017 22 -0.012 84 -0.009 524 -0.007206
245.51 227.53 214.83 204.26 196.02
0.186 44 0.14323 0.11914 0.09065 0.073 02 0.055 01 0.044 48
0.035 484 0.027 490 0.022 965 0.017568 0.014 197 0.010727 0.008 683
NaFeEDTA 170.62 170.37 170.32 170.18 170.12 170.15 170.29
-0.018 50 -0.01451 -0.012 20 -0.009435 -0.007647 -0.005 825 -0.004 776
266.59 261.56 259.22 255.08 254.42 252.17 248.01
0.186 92 0.151 63 0.12255 0.087 79 0.067 90 0.047 15
0.041 453 0.033 885 0.027 568 0.019 928 0.015493 0.010812
Na2ZnEDTA 170.57 170.17 169.76 169.02 168.60 168.25
-0.01979 -0.01643 -0.013 54 -0.009 91 1 -0.007 792 -0.005 524
25 1.47 241.85 233.44 222.69 214.66 204.72
0.18958 0.15893 0.12754 0.097 85 0.079 96 0.053 58
responding values of @Vand W,, for the aqueous EDTA salts are tabulated in Table I. The values in Table I refer to the stoichiometric solutes, that is to the dissolved sodium salts of the complexes, without distinguishing whether significant equilibrium amounts of the free metal ion or hydrolyzed EDTA complex are present in equilibrium. The pH of all the solutions of the EDTA complexes with divalent ions lay in the range pH 6 to 7, except for magnesium and cobalt which ranged from 8.0 to 8.5. The solutions containing iron and aluminum were at pH 4.5 to 5.0. From tabulated stability constants,1*2 we calculate that less than 0.1% of the EDTA complex anions in these solutions has dissociated to form the free EDTA anions. Ionization reactions involving H+ are also negligible. The apparent molar properties for stoichiometric solutions of the EDTA complexes with M2+and M3+ions in Table I are therefore identical with those for the species 2Na+(aq) + MEDTA2-(aq) and Na+(aq) MEDTA-(aq), respectively. Partial Dissociation of Na2H2EDTA(aq). The interpretation of the apparent molar properties of Na2H2EDTA(aq)is somewhat more complicated. Stoichiometric solutions contain small concentrations of the ions HEDTA3-(aq) and H,EDTA-(aq), which form according to the equilibria
temperature increment in the heat capacity measurement, the so-called chemical relaxation effect.10-12 The expression is
+
= (1 - a - P)Wp(H2EDTA2-,aq) @C,e"Pt1(Na2H2EDTA,aq) a@Cp(HEDTA3-,aq)+ P@CP(H3EDTA-,aq) ( a /3)@Cp(H+,aq) 2@Cp(Na+,aq) @Cpfll+ @Cparel (3)
+
+
+
Here, a and p are the degree of dissociation to form HEDTA3-(aq) and H3EDTA-(aq), respectively. The chemical relaxation contributions are given byl0-l2
@Cparel = AH(eq 2 a ) ( a a / a ~ ) ,
(4a)
@ c p= ~ m I( e q 2 b ) ( a p / a ~ ) , Further, in dilute solutions that are only slightly dissociated1°
+
H2EDTA2-(aq) e HEDTA3-(aq)
+ H+(aq)
H2EDTA2-(aq) + H+(aq) e H,EDTA-(aq)
(2a)
(ap/aT),
=
P - AHo(eq 2b) RT2
Anderegg' lists critically compiled values of log K = -6.18 and 2.78 for reactions 2a and 2b at 0.1 m ionic strength, from which we calculated the values for a and /3 listed in Table 11. The
(2b)
The experimental apparent molar heat capacities, @CFptl(Na2H2EDTA,aq),are considered to result from the sum of the contribution of each species in solution, plus an additional term to correct for the shift in the degree of dissociation caused by the
(10) Woolley, E. M.; Hepler, L. G. Cun. J . Chem. 1977, 55, 158-163. (1 1) Barbero, J. A.; Hepler, L. G.; McCurdy, K. G.; Tremaine, P. R. Can. J . Chem. 1983.61, 2509-2519. (12) Mains, G. J.; Larson, J. W.; Hepler, L. G. J . Phys. Chem. 1984, 88,
1257-1261.
5544 The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
Hovey and Tremaine
TABLE II: Contributions of Speciation and Relaxation to the Apparent Molar Heat Capacities of Na,H,EDTA(ag) exptl results speciation and relaxation contribution values" m/mol $C CXPtI/ CpaY OCp='/ $Cf(2Na++H2EDTA2-,aq)b/ kg-' J ~3 mol-' ff J K-I mol-' P J K- mol-' J K-I mol-' 289.2 0.01925 4.94 0.019 13 0.76 282.8 0.267 50 274.7 0.019 27 4.94 0.019 11 0.21 1 86 0.76 268.3 259.8 0.01929 4.95 0.019 09 0.76 253.4 0.16385 243.8 0.01934 0.111 16 4.96 0.019 04 0.76 237.5 232.0 0.019 39 4.97 0.018 98 0.080 06 0.75 225.7 218.1 0.019 49 5.00 0.01 8 89 0.75 211.8 0.053 78
+
'Here, a and 0 refer to the degree of dissociation according to the reactions H2EDTA2-(aq) e H+(aq) + HEDTA3-(aq) and H2EDTA2-(aq) H+(aq) s H,EDTA-(aq), respectively. The relaxation contributions were calculated from eq 4 and 5 by using enthalpy and heat capacity data from V a ~ i l e v , ' ~listed . ' ~ in Table V, and assuming A H = AHo = AR(O.1 m). *Values for aqueous species.
TABLE III: Partial Molar Heat Capacities and Volumes at Infinite Dilution and at Z = 0.1 OP heat capacity at 25 OC Cfo/J K-' B,w/J K-l Cp(I = 0.1 m)/ solute mol-' mol-2 kg J K-I molv1 P/cm3 moP Na,H,EDTA 168.8 f 1.0 101.5 f 6.3 221.8 f 1.5 154.31 f 0.08 125.4 f 1.9 235.6 i 0.6 156.09 i 0.26 NaiCaEDTA 181.0 i 0.5 249.2 f 2.4 160.51 f 0.10 196.9 f 1.4 90.98 f 10.9 Na2MgEDTA 339.8 f 4.1 164.99 i 0.12 290.9 f 12.4 266.2 f 1.3 NaAlEDTA 109.8 f 4.6 283.4 f 1.6 169.47 f 0.05 NaFeEDTA 246.0 f 0.6 213.6 f 0.3 93.76 f 1.4 159.55 f 0.09 Na2MnEDTA 161.1 f 0.2 214.5 f 2.3 74.53 f 9.8 165.38 f 0.11 Na2CoEDTA 163.3 i 1.4 85.69 f 2.0 197.5 f 0.5 162.74 f 0.03 145.5 f 0.3 Na2NiEDTA 200.2 f 1.4 163.20 i 0.09 148.5 f 0.9 81.19 f 6.6 Na2CuEDTA 216.5 f 1.2 165.99 f 0.08 69.91 f 5.5 Na2ZnEDTA 165.6 f 0.7
volume at 25 OC BVw/cm3 mol-2 kg -0.159 f 1.0 2.61 i 1.2 1.15 i 0.80 14.5 f 1.2 1.66 f 0.38 0.996 f 0.56 1.40 i 0.78 3.58 f 0.27 2.09 f 0.62 2.36 f 0.65
P(I = 0.1 m)/ cm3 mol-' 156.95 f 0.20 158.92 f 0.34 163.24 f 0.18 168.77 i 0.40 170.69 f 0.13 162.27 f 0.14 168.13 f 0.18 165.63 f 0.06 165.99 f 0.14 168.80 f 0.14
Error limits are the standard deviations from the least-squares fit.
equilibrium pH at m = 0.267 was measured, as a check, and agreed exactly with the calculation, p H = -log [(a- P)m] = 4.5. These values for a and @ were used with enthalpy and heat capacity data for reactions 2a and 2b from V a ~ i l e v ' ~to* 'calculate ~ +Cpand +Cc,. These are also summarized in Table 11, along with the final values for the species +Cp(2Na++H2EDTA2-,aq). The relaxation contributions are all of the order of 5 J K-' mol-'. The effect of partial dissociation on +Vis much less pronounced, in part because there is no contribution from chemical relaxation. Our analysis indicates that the correction would be insignificant, less than 0.1 cm3 mol-I. The effect of sodium complexation with H2EDTA2- is also negligible at these Partial Molar Properties. The dependence of +Cpand +Von molality was obtained from a least-squares fit of a simple Debye-Huckel equation 4Y =
P + A y ~ 3 / 2 m 1+/ Bywm 2
320
I
l
l
I
1
!
!
I
1
240-
(6)
which was fitted to the heat capacity and volume data in Tables I and 11. AY is the Debye-Huckel limiting slope on the molal scale at 25 O C , as calculated by Bradley and Pitzer;I5 A, = 32.51 J K-I mol-3/2 kg112and A , = 1.865 cm3 kg112. BY is an adjustable parameter and w, the "valence factor", is defined by
m
m
The experimental data and fitted curves are plotted in Figures 1-3. Values for the standard state properties, P",and the slopes, Byw, obtained from the fit are tabulated in Table 111. Partial molar properties at the standard ionic strength of 0.1 M are useful in relating heat capacities and volumes to other thermodynamic constants. These were obtained from the fitted parameters using the relationship
P = +Y + m(8*Y/dm)p,T
(8)
(13) Vasilev, V. P.; Kochergina, L. A.; Orlova, T. D. Zh. Obshch. Khim. 1976,46, 2192-2195. J . Gen. Chem. USSR 1976,46, 2109-2112 (English translation). (14) Vasilev, V. P.; Kochergina, L. A.; Orlova, T . D. Zh. Obshch. Khim. 1978,48,2770-2776. J . Gen. Chem. USSR 1978.48, 2511-2515 (English translation). (15) Bradley, D. J.; Pitzer, K. S. J. Phys. Chem. 1979, 83, 1599-1603.
1601
1 0.30 0 0
0
0.10
0.20
0.40
Molality
Figure 1. Experimental values of @Cp minus the Debye-Huckel limiting slope, plotted as a function of molality for H2EDTA2-(aq) and several EDTA complexes. Lines are least-squares fits of eq 6.
at m = O . l / w , and are also tabulated in Table 111. It is convenient to tabulate the partial molar heat 5apacities and volumes of individual ions on the conventional scale, C,(H+,aq) = 0, V(H+,aq) 0. Accurate apparent molar properties for
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5545
Heat Capacities and Volumes of EDTA Complexes I
I
1
1
1
1
1
1
170
1
I
I
I
NaFeEDTA
t
185
1
Na AIEDTA
3 J
N%ZnEDTA 166
Na2CoEDTA
+
N a2CuE DT A Na2NiEDTA
Na2ZnE DT A
. .
//
N
