Thermodynamics of aqueous zinc: Standard partial molar heat capacities and volumes of Zn2+(aq) from 10 to 55°C

Geochimica et Cosmochimica Acta,Vol. 58, No. 22, pp. 4867-4874, 1994 Copyright 0 1994 Elsevier Science Ltd Printedin theUSA. All rightsreserved

Pergamon

0016-7037/94 $6.00+ .OO

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Thermodynamics of aqueous zinc: Standard partial molar heat capacities and volumes of Zn”+(aq) from 10 to 55°C PUJING PAN* and PETER R. TREMAINE Department of Chemistry, Memorial University of Newfoundland, St. John’s, Nfld, Canada, AlB 3X7

(Received November 20, 1993; accepted in revisedform June 11, 1994)

Abstract-The apparent molar heat capacities and volumes of aqueous Zn( CIO,), have been measured from lo-55°C in a Picker flow microcalorimeter and vibrating tube densimeter. The Guggenheim form of the extended Debye-Hiickel equation was fitted to the experimental data, to obtain the following expressions for the standard-state properties from IO-55°C: C;(Zn(C104)2,

aq)/JK-’

- 8.4956T

mol-’ = 3850.8 -E

(1)

and V”(Zn(C104)2,

aq)/cm3 mol-’ = 116.65 - -

4073 - 0.050374T. 190

T-

(2)

The standard partial molar heat capacities and volumes for Zn*+ (aq) were extrapolated to higher temperatures by employing the He&son-K&ham-Flowers (HKF) equations, amended to include a standardstate correction term. Gibbs energies calculated from the extrapolated heat capacity and volume functions are consistent with limited experimental data for the solubility of ZnO in acidic to near-neutral aqueous solutions at 200-300°C ( B~URCIER and BARNES, 1987). INTRODUffION

temperatures and pressures from tabulated low temperature Gibbs energies and enthapies of formation (See, for example, HELGESON et al., 198 1 and TREMAINE et al., 1986). The apparent molar heat capacity of aqueous Zn2+ has been reported only at 25°C (SPITZER et al., 1978, 1979). Although the apparent molar volumes of aqueous Zn2+ have been measured over a range of temperatures ( SPITZERet al., 1978, 1979; SURDOand MILLERO,1980; HERRINGTONet al., 1986; POGUE and ATKINSON, 1988a, 1989), there are some discrepancies between the results from different laboratories. A number of workers ( TREMAINEand GOLDMAN, 1978; HELGESON et al., 1981; TANGER and HELGESON, 1988; SHOCK and HELGESON, 1988; TANGER and PITZER, 1989; ANDERSON et al., 1991) have developed semiempirical equations of state to describe the temperature and pressure dependence of various thermodynamic properties. The equations developed by Helgeson and his coworkers are based on the premise that, at high temperatures, the standard partial molar heat capacities and volumes are dominated by longrange solvent polarization, which can be adequately modelled by the Born equation. It has been demonstrated that the extrapolations based on the HKF model (HELGESON et al., 198 1; SHOCK et al., 1992) for standard partial molar heat capacities and volumes agree well with experimental results for some systems at higher temperatures (See, for example, TREMAINEet al., 1986; CONTI et al., 1992). The objective of the present study was to determine the standard partial molar volumes and heat capacities of aqueous Zn*+ from IO-55’C by measuring the apparent molar properties of the non-complexing aqueous perchlorate salts, and to compare Gibbs energy extrapolations from the new and older versions of the HKF equation with those reported from solubility studies.

THERMODYNAMIC DATA FOR aqueous zinc species are required over a wide range of temperature and pressure to understand and model mass-transport and speciation in a number of industrial and natural systems. Zinc is often a significant constituent of hydrothermal/geothermal fluids, and thermodynamic data for Zn 2+(aq) and its complexes are important in understanding the formation of zinc-bearing sulfide ore deposits. Many modem thermal power stations employ phosphate to buffer the boiler-water pH, and localized hideout of Fe and Zn phosphates is often a problem. 65Zn has also been responsible for high radiation fields in some nuclear reactors through activated-corrosion-product transport. Solubility data for zinc oxide and zinc hydroxide at or near room temperature have been reviewed by DIRKSE ( 1984). There are considerable discrepancies in the values reported by different laboratories, presumably because of different methods of preparation and uncertainties in the nature of the saturating phase. Solubility studies at high temperatures include work by KHODAKOVSKIYand YELKIN (1975), RUAYA and SEWARD( 1986), BOURCIERand BARNES ( 1987), PLYASUNOV et al. ( 1988), and ZIEMNIAK et al. ( 1990). The majority of these solubility studies were aimed at deriving stability constants for various Zn complexes and yield little information about the stability of Zn’+(aq) at elevated temperatures. Standard partial molar heat capacities and volumes of aqueous ions are of interest in this context, because they provide a means of calculating equilibrium constants at elevated

* Presentaddress: Research Chemistry Branch, Atomic Energy of Canada Limited, AECL Research, Whiteshell Laboratories, Pinawa, Manitoba, ROE 1LO,Canada. 4867

4868

P. Pan and P. R. Tremaine EXPERIMENTAL

Solution Preparation Zinc perchlorate was synthesized by neutralizing 5 mol kg-’ solutions of the metal carbonate to pH 5 with 60% perchloric acid, then recrystallized at least twice from dilute aqueous perchloric acid (pH 3-5 ). The concentration of the stock solution prepared from recrystallized Zn( C104)2was determined to be 0.8369 * 0.000 I moi kg-’ by titration with standardized EDTA solution using xylenol orange as an indicator (VOGEL,1989). Nanopure water (resistivity z I8 MQ cm) was used to dilute the stock solution by mass to prepare lower concentrations. The pH of the prepared solutions was between 4.0-5.5. No precipitation of hydroxide was observed. BDH-certified KS grade NaCl was dried at 110°C overnight before using. Solutions of ANALAR Na2H2EDTA were standardized by titration against Aldrich ZnC& (“99.999%“). dried at 160°C before use. Instrumentation

sented by the three parameter equations used in previous studies ( HOVEY et al., 1989). Fitted values for the adjustable constants were determined by a nonlinear least squares analysis of the data in Table 1, with both temperature and molality as the independent variables. Because the experimental uncertainties in *l/and @C,are larger at lower moralities, a relative statistical weight of 10% was assigned to the data below 0.03 mol kg-‘. The fitted functions for “C, and “c’ together with the experimental data, are plotted in Figs. 1 and 2, rcspectively. The data of SPITZER et al. ( 1978) at 25°C were also included in the least squares analysis with arbitrary statistical weights of 50% for “C,, and IO%for +V. The final fitted expressions and the standard deviation ofeach parameter are listed below: 4vo

A Sodev CP-C flow microcalorimeter (PICKERet al., 197 I ) and a Sodev 03D vibrating flow densimeter ( PICKERet al., 1974) equipped with Pt cells were employed in this work. Procedures are described elsewhere( HOVEYet al., 1989; HOVEYand TREMAINE,1986 ). The temperatures of Ihe calorimeter and densimeter were independently controlled by two Sodev CT-L circulating baths to +O.OOl“C. The thermistors (Omega, 44107) used to measure the temperatures of the calorimeter and densimeter were calibrated periodically to 20.01 “C with an HP2804A quartz thermometer traceable to NBS standards. The densimeter was calibrated daily with pure water and a standard I m NaCl solution. The experimental values of (c,d/c,“d”) for the standard NaCl solution were compared with literature values (ARCHER, 1992) to correct for a small heat leak effect ( DESNOYERS et al., 1976). The heat-leak factor,f, at each temperature is given by the usual expression for the chemical calibration method, (3) where @C,*and *C, are the literature and experimental values for the apparent molar heat capacity of the standard solution ‘V is the apparent molar volume of the standard solution, and o0is the volumetric heat capacity of pure water (c,” do ). The calibration yielded fvalues of 1.027, 1.004, l.OOl,and 1.009 at 10,25,40, and 55”C, respectively.

=

116.65 -t- 21.1 1 - 4073.2 f 638.0 7‘-

190

- (0.050374 + O.O5074)T,

(7)

BI, = -144.22 -+ 117.20 + (1.0177 ? 0.7703)7 - (1.8009 & 1.2630) x 10-3T2,

(8)

Cv = 102.04 -t- 67.16 - (0.69186 + 0.4416O)T + (1.1815 + 0.7239) X 10-37-2, Q-,0

=

3850.8 + 285.0 -

(9)

150,720 t- 8610 T190 - (8.4956 -t 0.6870)T,

(10)

Bcb = 5371.0 + 1677.0 - (33.648 & 11.02O)T

+ (5.2475 rt 1.8080) X lo-‘T2,

(1 t)

C,, = -1785.3 + 971.7 + (11.284 +- 6.388)T - (1.7687 + 1.0480) X 10~‘T2.

(12)

The values of mY“, By, and Cy from Eqns. 7- 12 at our experimental temperatures are tabulated in Table 2.

RESULTS Data Treatment

Standard Partial Molar Properties

The experimental values for the apparent molar heat capacities and volumes of aqueous Zn( Clod)2 from lo-55°C

are tabulated iri Table 1. Expressions for the standard partial molar properties were obtained by fitting the Guggenheim form of the extended Debye-Hiickel equation (MILLERO, 1979; HOVEY et al., 1989) to the experimental data:

By definition, ionic standard partial molar properties for Zn2+( aq) can be calculated according to the additivity principle, +Y”(Zn’+aq)

= “Y”(Zn(C10p)2,

aq)

- 2tiYo(C104, “Y = “Y” + 3 wAr[l - 21’/2 + 2 In (1 + l”‘)]/I -t Byl + Cyz3’*.

(4)

Here, Y stands for C, or V, AY is the Debye-Htickel limiting law slope as defined by BRADLEY and PITZER ( 1979), By and Cr are empirical parameters, and I is the ionic strength, I=wm,

(5)

(6) Values for AY were taken from ARCHER and WANG ( 1990). The temperature dependence of “Y O,By, and Cy was repre-

aq).

(13)

While several determinations of +C’; and +V” for aqueous perchlorate have been reported over the temperature range of interest, fairly large discrepancies exist in the literature. For example, POCXJEand ATKINSON ( 1988a) reported -22.5 J K-’ mol-’ for mC,“(CIO;, aq) at 25°C while SINGH et al. ( 1977) reported -27.1 J K-’ mol-’ , and HOVEYand HEPLER ( 1989) reported -25.0 J K-’ mol-’ . In this study, the values of “C,O and +V o for ClO;( aq) at all temperatures were taken from HOVEY and HELPER ( 1989). The calculated values for “C,“(Zn’+, aq) and +‘V”(Zn*+, aq) are listed in Table 3. The standard state properties for Zn2+ (aq) in Table 3 can be compared with the values reported by others using different salts. SPITZER et al. ( 1979) reported +C,O and @V’O for

4869

Thermodynamic properties of Zn*+(aq) Table 1. Experimental apparent molar volumes 0 and beat capacities CCJ of aqueoa Zn(ClO&, at different concentrations and 10 to WC

m

(mol kg“)

10 (d-d”)

‘V

(g cm.‘)

(cm’ mol”)

lO?c#c;d=l)

‘CP (J K’

mol-‘)

lO.O”C 0.8369 0.8369 0.8369 0.6463 0.5209 0.2795 0.2795 0.2795 0.1315 0.1315 0.09167 0.09167 0.02920 0.02385 0.02135

15.8484 15.8644 15.8391 12.4777 10.1559 5.5569 5.5754 5.5639 2.6552 2.6556 1.a509 1.8559 0.59564 0.48783 0.43579

64.639 64.464 64.740 63.291 62.895 61.989 61.349 61.748 60.722 60.689 60.346 60.671 59.904 59.415 59.872

-5.3597 -5.2515 -5.5123 -4.5521 -3.8440 -2.2196 -2.2828 -2.1842 -1.1261 -1.1337 -0.80715 -0.82246 -0.27547 -0.21647 -0.20052

-19.56 -22.09 -28.50 -51.34 -65.52 -87.84 -101.65 -92.54 -127.00 -119.61 -138.39 -133.96 -155.63 -142.11 -153.76

-4.8833 -4.8427 -3.9468 -2.9126 -1.9209 -0.95699 -0.67830 -0.22453 -0.18527 -0.16399

28.12 30.24 15.22 -0.95 -14.43 -32.23 -37.57 -51.82 -52.36 -52.46

-4.6358 -4.6274 -4.6074 -3.0884 -1.8713 -1.7849 -1.7282 -0.88432 -0.62339 -0.20719 -0.17298 -0.10736

54.09 54.32 54.50 37.75 21.93 21.14 18.15 6.74 3.88 -10.65 -16.96 -12.10

-4.5217 -4.5018 -3.0073 -1.8155 -1.7180 -1.6694 -0.86019 -0.85229 -0.60009 -0.60175 -0.19785 -0.14750 -0.10682

65.79 64.36 48.50 33.91 35.35 32.37 22.06 21.39 19.21 20.97 9.18 5.46 -8.61

25.O”C 0.8369 0.8369 0.6463 0.4486 0.2795 0.1315 0.09167 0.02920 0.02395 0.02135

15.4351 15.4242 12.1325 a.5643 5.4015 2.5775 1.a037 0.57925 0.47452 0.42433

68.883 69.002 67.966 67.25 1 67.037 66.187 65.947 65.145 65.457 64.865 4o.O’C

0.8369 0.8369 0.8369 0.5209 0.2956 0.2795 0.2697 0.1315 0.09167 0.02920 0.02395 0.01495

15.0800 15.0850 15.1051 9.6546 5.5836 5.2762 5.1098 2.5171 1.7606 0.56559 0.46469 0.28920

72.340 72.285 72.061 71.172 70.529 70.847 70.296 70.150 70.038 69.220 68.957 69.664 55.O”C

0.8369 0.8369 0.5209 0.2956 0.2795 0.2697 0.1315 0.1315 0.09167 0.09167 0.02920 0.02135 0.01495

14.8202 14.8424 9.4950 5.4934 5.1907 5.0208 2.4709 2.4756 1.7311 1.7294 0.55492 0.40598 0.28591

74.641 74.389 73.441 72.794 73.129 72.809 72.905 72.538 72.493 72.684 72.122 72.111 71.082

d, density of solution; d”, density of pure water; cP. specific heat capacityof solution; I$, specific heat capacityof pure water.

P. Pan and P. R. Tremaine

4870

,

68

Thiswork,10 _40°C Thiswork,55’C Spitz%et ab, 1978,25Yz

0 This work, 10 - 4O’C 0 Thiswork, 55’C

0.0

0.2

0.4

0.6

0.8

1.0

FIG. I. Apparent molar volumes (cm3 mol-‘) of aqueous Zn( CIO,), minus the Debye-Hiickel limiting law term (DHLL, Eqn. 2) vs. molarity (m). The solid lines are the non-linear least squares fits (Eqns. 7-9).

Standard partial molar volumes, heat capacities W”,

ionic strength parameters for aqueous Zn(ClOJ,

t

‘V’

(“C)

cm3 mol“

A” cm’ Lg’Rmol””

from

B” cm’kg

mot’

‘C,“),

and

10” to 55°C C” cm’k~nmol-‘”

d” g cm.’

10

58.66iO.11

1.6006

-0.4337io.349

0.8621 fO.1589

0.999705

25

63.97iO.08

1.8272

-0.8704*0.1925

0.7860&0.1531

0.997041

40

67.8OiO.04

2.1248

-2.1174*0.1660

1.241610.1393

0.992206

55

70.6410.16

2.4915

-4.1749*0.4290

2.2289*0.2003

0.989686

t

‘C,O

PC)

J K’mol”

10

-172.19il.96

AC J

K”kgl”mol.‘”

0.6

0.8

J 1.0

ZnC12, somewhat larger than our value of -24.1 I cm3 mol-’ . HERRINGTONet al. ( 1986 ) reported 9V ’ for ZnC12( aq ) from 25-75”C, and POGUE and ATKINSON(1988a) reported @V” for ZnC&(aq) and Zn(C104)2(aq) from 15-55°C. To compare our results with those reported by HERRINGTONet al. ( 1986) and POGUE and ATKINSON ( 1988a), we have calculated * V ’ ( Zn 2+, aq ) at each temperature of interest using Eqn. 7 for “V( Zn( C10.,)2, aq), the equation of HOVEYand HEPLER (1989) for “V”(HC104, aq), and the equation of POGUE and ATKINSON(1988b) for “V’(HCl, as). The calculated results are tabulated in Table 4. Our values lie within

Zn(NOB)z(aq) at 25°C as -165.3 J K-’ mol-’ and 33.6 cm3 = -69.0 J K-’ mol-’ mol-‘, respectively. Taking%;(NO;) and eV” (NO;) = 29.4 cm3 mol-’ ( HOVEY and HEPLER, 1989), yields 4CpO(Zn2+, aq) = -27.3 J K-’ mol-’ and +V(Zn’+, aq) = -25.2 cm3 mol-‘, in reasonable agreement with our values of -25.8 J K-’ mol-‘, and -24.11 cm3 mol-‘. SURDO and MILLERO (1980) reported -26.6 cm3 mol-’ at 25°C for “V(Zn’+, aq) from measurements on

2.

0.4

FIG. 2. Apparent molar heat capacities (J K-’ mol-‘) of aqueous Zn( ClO& minus the Debye-Hiickel limiting law term (DHLL, Eqn. 2) vs. molality (m). The solid lines are the nonlinear kast squares fits (Eqns. 10-12).

Molality

Table

0.2

0.0

v Spitteret al., 1!378,2S”C

B, J kg K-‘mol.’

cc J kg,EK”mo15”

0 CP J g”

24.256

50.617k6.232

-8.339i3.160

4.1940 4.1800

25

-75.8OiO.55

32.058

3.448+1.420

6.696kl.279

40

-33.49*0.05

37.099

-20.107*0.935

13.771*1.003

4.1773

5s

-28.04k2.16

41.752

-20.048k7.685

12.886~3.990

4.1809

4871

Thermodynamic properties of Zn”(aq) Table 3. Conventional ionic partial mohu volumes and heat cnpacitig for WY&q) and Zd+(nq) from 10 lo WC and based on V’(H+,aq) - 0.

Zn’+(aq)

Clo, 6-l) *v” (cm’ mot’)

‘@, (J K‘l mol-‘)

41.63 44.04 46.24

-62.2 -25.0 -9.0

10 25

47.31

‘v” (cm) mot’)

-5.2

‘@, (J K’ mol”)

-24.60&0.1 I -24.11 f0.08 -24.68iO.04

-48.4?~2.0 -25.8ztO.6 -15.5iO.l

-23.98k0.16

-17.6k2.8

The conventional ionic partial molar volumes and heat capacities for the perchlorate ion are from and Hepler (1989). Errors are statistical uncertainties only.

1.5 cm3 mol-’ of values calculated from the POGUE and AT(1988b) measurements on ZnClO,(aq) and ZnC12( aq). The values derived from measurements on ZnC12( aq) by HERRINGTON et al. (1986) differ from ours by up to 2.8 cm3 mol-’ .

c2T

Extrapolation to Elevated Temperatures

Helgeson and coworkers ( HELGESONand KIRKHAM, 1974; HELGESONet al., 1981) have developed a semi-empirical equation of state to describe the standard partial molar properties of aqueous electrolytes. The HKF equation of state has been used with some success to extrapolate the standard partial molar properties of aqueous electrolytes to temperatures as high as 300°C (TREMAINEet al., 1986; CONTI et al., 1992). When pressure effects are ignored, the original HKF equations ( HELCESONet al., 198 1) for standard partial molar heat capacity and volume can be written as

c; = c, + p+wTX

(14)

P’=o+&-,a,

(15)

T-O

KINSON

DI!XU!SSION

Hovey

*

where, c, , c2and (r, E are parameters to be determined from experimental data; w is the Born coefficient (note the unit conversion for Eqn. 15, w/cm3 bar-’ = 10 w/J mol-‘); and 19is a structural temperature which is solute dependent. X and Q are defined as:

X=$[[-$],-:[$]I] and

(17)

where c is the static dielectric constant of the solvent. By definition 7” = @Y”.

Table 4. Comparison of Partial Apparent Molar Volumes of aqueow ZIP

VC)

Hovey & Helper ‘VO(C1OJ

Pogue and Atkinson ‘V”(zn(ClO~J

*vO(zn*+)

This work *vO(zn(aoJ~

‘V”(zn”)

15

42.506

59.31

-25.70

60.63

-24.38

25

44.084

63.14

-25.03

63.97

-24.20

35

45.417

65.66

-25.17

66.65

-24.18

45

46.507

69.20

-23.81

68.84

-24.17

55

47.352

70.71

-23.99

70.64

-24.07

Pogue & Atkinson(1988b, 1989)

T-C)

(16)

Herrington et al. (1986)

‘VO(CI-)

‘VYZnCI,)

‘V’(Zll2+)

‘V’(ZnC1~

‘W((zn”‘)

15

17.11

9.27

-24.97

25

17.75

9.96

-25.64

9.252

-26.35

35

17.98

10.86

-25.14

10.838

-25.16

45

17.90

10.30

-25.68

12.674

-23.31

55

17.65

10.66

-24.82

14.263

-21.22

4872

P. Pan and P. R Tremaine

The Born coefficient, w, for an electrolyte k can be calcuiated according to wk

=

c

iQ$jt

(181

where Pj,kis the stoichiometric coefficient of the jth ion, Z, is its charge, and the Born coefficient is 6J, = OTbs-

(19)

ZjW”,“:,

webs = 6.94657 x 10’ z:, J

where r, is the effective radius of the ion; Iv is Avogadro’s number; X F is the isothermal compressibility of pure water, &’ is the isobaric thermal expansion coefiicient of pure water; and R is the ideal gas constant. The first terms in Eqns. 24 and 2.5 represent the electrostatic contribution, and the last term of Eqn. 24 and the last three terms of Eqn. 25 are the standard state correction terms. Adding these terms to the original HKF equations ( 14 and 15) yields the expressions

(20)

(26)

%j

and wgHb: = 2.2539 X 10’

(J mol-‘1.

(21)

Here rcejis the effective radius of the jth aqueous ion, which is equal to the crystallographic radius for anions, and to the crystallographic radius plus 0.94Zj A for cations ( HELGES~N et al., 1981). Data for the Born coefficient, X, and Q were taken from SHOCKand HELGESON( 1988) and TANGERand HELGE~ON( 1988). Recently, the HKF ~ua~ons were revised by TANGER and HELGESON ( 1988). Ignoring the pressure dependent terms, the revised HKF equations for the standard partial molar heat capacity and volume for an aqueous ion or electrolyte can be written as -0 c, =cI(T~o)2+wTx

and

and /O__+.

G

67

-

wQ + ~[RTK,D].

(27)

Our values of “C,O and mV’ for aqueous Zn( ClO,), at lo-55’C were extrapolated up to 300°C by fitting the parameters in each of the three types of HKF equations: the original, Eqns. 19 and 20; the revised Eqns. 21 and 22, and the revised equations with the standard state correction term, Eqns. 26 and 27. Data for CY”,(&P/aT),, and x r”were taken from HELCESONand KIRKHAM( 1974). The results are plotted in Fig. 3. Inclusion of the standard-state term improves the standard deviation of V” from 0.46-0.36 cm3 mol-’ for I

p~=o+--.-- F T-O

wQ

in the revised model the effective radius of an aqueous ion is no longer considered as a constant, but a function of both temperature and pressure at temperatures above 175’C. The structural temperature, 0, has been fixed to 228 K in the revised model. SHOCK et al. ( 1992) have reported correlations for estimating the coefficients in Eqns. 22 and 23. Their estimated values for C,O( Zn *+) , based on the values of SPITZER et al. ( 1978,1979) at 25°C are in remarkably good agreement with the experimental values in Table 3 (-49.4, -25.9, - 16.7, and -14.6 J K-’ mol-’ at 10, 25, 40, and 55°C). Both the original and revised HKF equations of state have omitted a standard state correction term from the Bjom equation without explanation. This term (TREMAINE and GOLDMAN, 1977; WOOD et al., 1990 ) arises because the different standard states are used for the gas and liquid phases. Below, we assess the magnitude of this standard state term and compare the heat capacity and volume function extrapolations from the original and revised HKF models. According to WOOR et al. ( 1990), the partial molar volume and heat capacity of an ion in solution can be represented as: 7

= AVet + i *riN + RTK;!

and C”P = Ac;l+2R&” P

+ RT2

(251

FIG. 3. Extrapolations of the standard partial molar volumes and heat capacities for aqueous Zn(ClO,& using the HI@ model. Dotted lines are the results of the original HKF equations (Eqns. 14 and 15); dashed lines are for the revised HKF equations (22 and 23); and the solid lines are for the or&&al HKF equations with the s@ndard state correction terms ( 26 and 27).

4873

Thermodynamic properties of Zn2’(aq) Eqn. 15 and 0.68-0.60 cm3 mol-’ for Eqn. 23. The standard deviation of the heat capacity expression, Eqns. 14 and 22, increases from 5.3 to approximately 5.6 J K-’ mol-‘. It is apparent that, while the standard state corrections become large at temperatures above 2OO’C they are much smaller than the Born terms which assume very large negative values as the critical temperature is approached. The difference between the original and the revised HKF models is most pronounced between 100 and 25O’C. In this range, it appears that the addition of the standard-state term to the original HKF model would account for some of the discrepancies with experimental data that led to the development of the revised model.

x

F - 8 6

High temperature solubility data for zincite provide a means of testing the success of the extrapolation procedures outlined above. Complexation with OH-(aq), Cl”‘(aq), and other anions is enhanced at elevated temperatures and, although several solubility studies have been reported, only BOURCIERand BARNES( 1987) have reported solubility constants for the equilibrium involving Zn*+(aq): ZnO(S) + 2H+(aqf = Zn2’(aq)

+ H,O(l)

(28)

and =

4Znzt)a(HD)

I

(29)

a(H+)*

AC& and AS& for Eqn. 28 are known ( ROBIEet al., 1978), so that KI can be calculated according to Eqns. 30 and 3 1: AG;,p = AC&,

-T

s= 298

- A&,,,(

AC; -y-dT+

T - 298.15) T

s 298

P

AC; dT +

i

4

Solubility of ZnO in Acidic Solutions

K

10

sI

AVPdP

(30)

50

0

1 200

Temperature

250

340

(“C)

FIG. 4. The solubility product of zincite (ZnO), based on extrapolated values of the partial molar heai capacity of Zn*+(aq) determined in this work. Solid symbols are experimental results with ZnO as the solid phase. Open symbols are experimental volubilityproducts

for Zn(OH)2. in Eqn. 30 were taken from data compiled by ROBIE et a$ (1978). Data for H20(l) were taken from ARCHER(1992). The calculated values of log K for reaction (28) at steam saturation pressure are shown in Fig. 4, together with some experimental results. For completeness, we have also included the experimental results reported by REICHLEet al. (1975) for the solubility of +Zn f OH)z as the solid phase. These correspond to the reaction Zn(OH)z(s)

+ 2H*(aq)

K

where AC; and Av” are, respectively, the standard molar heat capacity change and volume change for reaction 28. Values for log K have been calculated as a function of temperature from Eqns. 30 and 3 1, using Eqns. 26 and 27 for the heat capacity and volume functions of Zn’+( aq). Values for the other properties of Znzf( aq) and ZnOf s) required Table 5. “Equation of State” Parametem for Zn(ClO,),(q) HeatCbacity

c,

150

= Zn*+(aq) f 2Hz0(l)

(32)

and (31)

=I

100

8

eqn 14

246.53

-24.836

259

eqn22 eqn26

207.29

-7.60x lb

228

199.19

-7.63 x 10’

228

=

2

~fZn2%N%Of2 a(H+)’

*

(33)

Zn*+(aq) is a minor contributor to the solubility model reported by BOURCIERand BARNES( 1987). In view of the large (unreported) uncertainties in their values for log K,, the agreement between the calculated and experimental values in Fig. 4 is quite satisfactory. Because the experimental problems in resolving the contribution of the unbomplexed ions from solubility measurements are severe, we suggest that Gibbs energies for Zn”(aq) calculated from the constants listed for Eqns. 22 and 23 should be used as provisional values until reliable direct measurements are available. ~cknowie~g~e~ts-This work was jointed supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Memorial University of Newfoundland. The stock solution of Zn( C10.,)2was prepared by Dr. Robert Haines and Mr. Murray Park to whom we express our gratitude. Editorial handling: D. Wesolowski

eqn 15 eqn 23 e&p 27

175.5 98.15 100.5

-51.343

150

-1768

228

-1786

228

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P. Pan and P. R. Tremaine

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