metal-organic complexes in geochemical processes: temperature dependence of the standard...

Geochimica er Cosmochimica Ada Vol. 57, pp. 4899-4922 Copyright 0 1993 Pergamon Press Ltd. Printed in U.S.A.

0016-7037/93/$6.00 + .oO

Metal-organic complexes in geochemical processes: Calculation of standard partial molal thermodynamic properties of aqueous acetate complexes at high pressures and temperatures

EVERETT L. SHOCK and CARLA M. KORETSKY

Department of Earth and Planetary Sciences, Washington University, St. Louis, MO 63 130, USA

(Received October 5, 1992; accepted in revisedform June 28, 1993)

Abstract-Estimates of standard partial molal properties at high temperatures and pressures for aqueous acetate complexes of major and trace elements in geologic fluids were made with the aid of experimental data from the literature and correlation algorithms. A system of correlation expressions allows the incorporation of all available experimental data, but also allows estimates in the absence of any measurements. Likely uncertainties for each type of estimate were assessed. Thermodynamic data and equation of state parameters permit calculation of standard partial molaI properties including dissociation constants for 114 acetate complexes. Incorporation of many of these dissociation constants with those for hydroxide, chloride, and sulfate complexes demonstrate that acetate complexes are ineffectual in transporting major rock forming elements or trace metals in sedimentary basin brines. In contrast, these complexes could be considerably more efficient in metal transport in low salinity groundwater solutions with elevated concentrations of organic solutes. Calculations indicate that up to 40% of the acetate may be present as sodium and calcium complexes in basin brines with total salinities around 1 .O molal.

INTRODUCTION

CONSIDERABLE INTEREST in complex formation between metal cations and organic acid ligands in oilfield brines was generated by the attention drawn to the high concentrations of acetate and other carboxylic acid anions found by WILLEY et al. ( 1975) and CAROTHERS and KHARAKA ( 1978). Many investigators have recognized the possible potential which metal-organic complexes could have for enhancing the solubility of silicates in sediments (GRAHAM, 1941; VAN DER MAREL, 1949; KONONOVA et al., 1964; SCHNITZER and HANSEN, 1970; BAKER, 1973; HEALD and LARESE, 1973; PARKER, 1974; SINGER and NAVROT, 1976; MCBRIDE, 1977; SCHMIDT and MCDONALD, 1979a,b; TAN, 1980, 1986; MA- GARA, 198 1; ANTWEILER and DREVER, 1983; SURDAM et al., 1984,1989; BJ~LYKKE, 1984,1988; FRANKS and FORESTER, 1984; SURDAM and CROSSEY, 1985; CROSSEY et al., 1986; MESHRI, 1986; LUNDEGARD and LAND, 1986; GILES and MARSHALL, 1986; GILES, 1987; SURDAM and MACGOWAN, 1987; MACGOWAN and SURDAM, 1987, 1988, 1990a,b, BJ~RLYKKE et al., 1988; MILLIKEN, 1988, 1989; GILES and DE BOER, 1989; LUNDEGARD and KHARAKA, 1990), and transporting trace elements in basinal brines and hydrothermal fluids ( FREISE, 193 1; FETZER, 1934; SHCHERBINA, 1956, 1962; ZUBOVIC et al., 196 1; ONG and SWANSON, 1969; BAKER, 1973; RASHID and LEONARD, 1973; GARDNER, 1974; BARNES, 1979, 1983; GIORDANO and BARNES, 198 1; GIOR-

DANO, 1985, 1990; DRUMMOND~~~ PALMER, 1986; HENNET et al., 1988 ). These potentials are confirmed in experiments which show that metal-organic complexes increase the solubility of minerals in aqueous solutions containing organic acids ( GRUNER, 1922; GRAHAM, 1941; SCHALSCHA et al., 1967; ONG et al., 1970; HUANG and KELLER, 1970, 197 1, 1972a,b,c; HUANG and KIANG, 1972; LIND and HEM, 1975;

SCHNITZER et al., 1976; GRAUSTEIN et al., 1977; SURDAM et

al., 1984; STUMM et al., 1985; MANLEY and EVANS, 1986;

MAST and DREVER, 1987; HEDLUND and OHMAN, 1988; BENNETT et al., 1988; BEVAN and SAVAGE, 1989; STOESSELL and PITTMAN, 1990; HINMAN, 1990; WOGELIUS and WALTHER, 1991; WIELAND and STUMM, 1992). Many of these experiments are conducted at or near room temperature, and quantitative tests of the full impact of metal-organic complexes are limited by the scarcity of pertinent experimental data at the actual temperatures and pressures of geochemical processes.

However, the last few years have seen considerable increases in the variety and extent of higher temperature experimental measurements which yield thermodynamic data for aqueous metal-organic complexes, and many of these investigations have focussed on metal-acetate complexes (HENNET et al., 1988; PALMER and DRUMMOND, 1988; GIORDANO, 1989; FEIN, 199 I; GIORDANO and DRUMMOND, 1991; CASTET et al., 1992; PALMER and BELL, 1993). At the same time, advances in theoretical geochemistry have pro- duced a unified method for regressing experimental data and making highly accurate predictions of standard state thermodynamic data for many types of aqueous solutes which are involved in geochemical processes (SHOCK and HELGE- SON, 1988, 1990; SHOCK et al., 1989, 1992, 1993; SASSANI and SHOCK, 1990, 1992, 1993a,b; HELGESON, 1992; SVER- JENSKY et al., 1992; SHOCK, 1992, 1993a,b,d; SCHULTE and SHOCK, 1993; WILLIS and SHOCK, 1993).

These experimental and theoretical advances provide the framework for the research described in the present paper. The results summarized below allow predictions of thermodynamic data for aqueous metal-acetate complexes to pressures of 5 kb and temperatures of lOOO”C, but it is ex- pected that these data will be most immediately useful in speciation, solubihty, and mass-transfer calculations for much lower pressures and temperatures. In addition, the compre- hensive study of metal-acetate complexes described below provides a basis for similar studies which will permit the in-

4899

4900 E. L. Shock and C. M. Koretsky

elusion of many other types of metal-organic complexes in theoretical investigations of geochemical processes.

The present study employs the revised Helgeson-Kirkham- Flowers (HKF) equations of state for aqueous species (HELGESON et al., 1981; TANGER and HELGESON, 1988; SHOCK et al., 1992 ). The standard state for aqueous species adopted in this study corresponds to unit activity of the solute

in a hypothetical one molal solution referenced to infinite dilution. The convention chosen for representing any standard partial molal thermodynamic property (z”) of the ,jth aqueous species is expressed by

e 0 = 5 0 abs -, -I

_ Zco+abs ,-+I 1 (1)

where E,O ah and Z, represent the corresponding absolute property and charge of the jth aqueous species, respectively, and zifbs stands for the absolute standard partial molal property of the hydrogen ion. It follows from Eqn. 1 that all

conventional standard state properties of H+ are equal to 0.0 at all temperatures and pressures. In the following discussion, regression results for high temperature equilibrium constants of metal-acetate complexes are described, correlations among standard partial molal entropies (s” ) are presented, standard state experimental data at 25°C and I bar from the literature are critiqued, and methods are developed and employed for estimating data which have not yet been measured experi- mentally. Taken together, the data and parameters provided below allow estimation of consistent equilibrium constants for 1 14 metal-acetate complexes, and values are tabulated for fifty seven of these in the Appendix.

REGRESSION OF EQUILIBRIUM CONSTANTS FOR METAL-ACETATE COMPLEXES AT

ELEVATED TEMPERATURES

Experimental data for acetate complexes of Fe+* and Zn +* were regressed by SVERJENSKY et al. ( 1993), with the revised

HKF equations of state, together with the correlation algorithm provided by SHOCK and HELGESON ( 1988) to obtain values of s” and the standard partial molal heat capacity (C?;,“) at 25°C and 1 bar for the complexes. Results of this regression analysis are summarized in Table 1, and depicted in Fig. I for the first and second acetate complexes of Fe+*

and first through third complexes of Zn +2. Note that complete dissociation constants, indicated by the symbol 8, are plotted in Fig. 1 and subsequent figures in this paper. The values of c,O in Table 1 obtained by SVERJENSKY et al. (1993) were crucial in their development of correlations which yield the

ligand dependence in methods for estimating c,” of aqueous complexes. This estimation scheme was adopted in the pres-

ent study to obtain values of c’,” for metal-acetate complexes. These estimates were used, together with the correlation algorithm provided by SHOCK and HELGESON ( 1988), to re- gress low-temperature (O-l 00°C) equilibrium constants for metal-acetate complex dissociation with the revised-HKF equations of state to evaluate s” at 25°C and 1 bar for the complexes.

Results of regression analysis of low temperature data for acetate complexes of Pb’“, Mg+*, and Ca+* are depicted in Fig. 2. The resulting standard state thermodynamic data at 25°C and 1 bar and equation of state parameters are listed in Table 2. In the case of the Pb’* complexes, only the data

reported by GIORDANO ( 1989) were used in the regression procedure. Data reported for Mgf2-acetate dissociation by COLMAN-PORTER and MONK ( 1952) were not included in the regression procedure, and in the case of Ca+*-acetate complexes. only those data reported by DANIELE et al. ( 1985 ) and FEIN ( 199 1 ) were used. Predictions at 500 bars and their comparison to data reported by SEEWALD and SEYFRIED

( I99 I ) are discussed below.

CORRELATION METHODS FOR ESTIMATING STANDARD PARTIAL MOLAL ENTROPIES AND

VOLUMES OF ACETATE COMPLEXES

Values of so obtained by regression of experimental data as described above, are plotted in Fig. 3 for Fe(Ac)+.

Zn(Ac)‘,Ca(Ac)+.Mg(Ac)+.andPb(Ac)+.whereAcrefers to the acetate ligand (CH,COO-). It can be seen in this figure that values of s” for all of the complexes except Zn(Ac)+ are closely consistent with the correlation line given by

J&s: = 0.33&T;? + 13.0, (2)

where A,?: refers to the association reaction to form the first acetate complex. Equation 2 is a specific statement for the first acetate complexes of divalent metals of the general so

Table 1. Standard partial molal thenncdynamic data for acetate complexes at 25°C and 1 bar, together with parameters to calculate the

same properties at elevated temperatures and pressures obtained by regression of experimental data ranging from 25°C to 300°C by

Sverjensky et al. (1993).

Species -- b AC, AFi”” ? C, V-Q a; x 10 a; x 10-z a’3 a;xlo-4 c; c; x Ma cla”x lo.5

Fe(Ac)+ -111900. -139060. -1.5 81.2 24.7 5.3406 5.2564 3.6889 -2.9962 59.0575 13.5058 0.5756

Fe(Ac), -201800. -259100. 11.5 184.2 77.0 12.2878 22.2237 -2.9884 -3.6976 113.8428 34.4869 -0.03M)

Zn(Ac)+ -125660. -155120. 9.4 86.2 22.4 4.9645 4.3385 4.0485 -2.9583 60.4333 14.5142 0.4100

ZNAc& -216450. -271500. 22.5 193.3 74.4 11.931 I 21.3486 -2.6358 -3.6615 119 1584 36.3345 -0.0300

%(Ac)~- -305740. -378900. 23.6 315.2 131.9 20.2983 41.7841 -10.6785 -4.5063 202.5945 61.1716 1.2701

a. cal mol.’ b. cal mol.’ h’ c. cm3 mol.’ d. cal mol.’ bar” e. cal K mol.’ bar -’ f. cal K mol.’ g. Estimated with vaalgoritbm

proposed by Sverjensky et al. (1993).

Thermodynamic properties of aqueous acetate complexes 4901

Zn+* acetate complexes

0

log p, Giordano and Drummond (1991)

log & Giordano and Drummond (1991)

log p3 Giordano and Drummond (1991)

log !3, Archer and Monk (1964)

log p, Yatsimirskii and Federova (1956)

log p, Bardhan and Aditya (1955b), sol method

log p, Bardhan and Adityr (1955b), EMF method I I I I I I I1 1 I1 1 I I I I1 I1

50 100 150 200 250 300 350

Temperature, “C

Fe+* acetate complexes 0 1,,1,11,1(,,1,(,,,,,,,,,,1,,,,,,1,

-2

-6

0 Palmer and

-8 0 Palmer and

0 Palmer and

0 Yatslmirskll

Drummond (1966)

Drummond (1966)

Hyde (1993)

and Federova (1956)

-10”~‘~“““““““~““~‘~““““’

0 50 100 150 200 250 300 350

Temperature, “C

FIG. 1. Equilibrium dissociation constants for Fe+* and Zn +* acetate complexes as functions of temperature at I’sAT. Symbols represent experimental data from the sources indicated, and curves represent the results of regression of these data with the revised HKF equation of state parameters consistent with the data and parameters in Table 1. Data for the cations from SHOCK and HELGESON ( 1988, 1989) and for acetate from SHUCK ( 1993a) were used in the regression procedure.

estimation procedure outlined by SVERJENSKY et al. ( 1993). This procedure allows estimates from values of sz+“zs and siabs without the need for other data.

It should be noted that Zn+2 appears to be an exception to the general trend for other divalent cation complexes. This behavior was noted by SVERJENSKY et al. ( 1993) for Zn- chloride complexes and by SHOCK et al. ( 1993) for Zn-hydroxide complexes. As in the other cases, the value of Asp

for Zn( AC)+ falls off the correlation by a value which is ap- proximately equal to so for Hz0 at 25’C and 1 bar. These departures were taken by SVERJENSKY et al. ( 1993) to indicate a change in coordination of Zn+’ upon complex formation. Therefore, all of the values of AS,” for acetate complexes obtained from regression of experimental data are consistent with the estimation equations and observations of SVERJEN- SKY et al. ( 1993), and serve, in part, to confirm the general


Pb+* acetate complexes

100 150 200 250

Temperature, “C

Mg+* acetate complexes

0 50 100 150 200 250 300 350

Temperature, “C

C a+ * acetate complexes 0 ,,,,(,,l,,l,,.,,,,,,l.ll,llll,ll,,

-2

-3

-4

-5

-6

0 log a, A.rsh.r and Monk (1964)

0 log 4 Colman-Portor and Monk (1964)

0 log a, Dml*l* .t aI. (1986)

h] log a, Nmcolh (1066)

+ log p, Adllya (lSS7)

Thermodynamic properties of aqueous acetate complexes

Table 2. Standard partial molal tlwmcdynamic data for acetate complexes at WC and 1 bar, together with parameters to calculate the

same properties at elevated tcmpxaturcs and pmsswcs. Values of s’obtaiocd by regression of experimental data ranging from 0” to

100°C.

4903

Species A-6”, Apf s ’ -bg Fpb.h -c,i a; x 10 4 x lo-2 4 a;x loa b

V c, c; x 10-4 r&x lo.5

Pb(Ac)+ -97250. -115880. 36.0 71.4 32.1 6.1543 7.2429 2.9082 -3.0783 48.0824 11.5161 0.0057

Pb(Ac)z -186890. -229460. 69.8 165.0 85.2 13.4090 24.9584 -4.0570 -3.8107 102.6053 30.5811 -0.0300

WAG+ -221660. -245620. 12.5 83.1 29.3 5.9002 6.6232 3.1505 -3.0527 58.1976 13.8857 0.3636

Mg(Ac)+ -198520. -229480. -13.1 88.0 25.4 5.4981 5.6424 3.5341 -3.0122 64.6297 14.8894 0.7483

a cal mol” b. cal mol.’ C’ c. cd mol.’ d. cal mol.’ bar.’ c. cal K mol.’ bar -’ f. cal K mole’ g. obtained from regression of low

tempemtme log K data (see text). h. &mated with cp algorithm proposed by Svejensky et al. (1993) i. estimated with 0’

alogorithm proposed by Sverjensky et al. (1993)

usefulness of their theoretical methods. Estimates of s“ for on the analysis of data and experimental methods employed acetate complexes other than those of Z~I+~ were made in by the original investigators. Note that a wide variety of the present study with the correlation algorithm provided by monatomic and polyatomic monovalent, divalent, and tri- SVERJENSKY et al. ( 1993 ) . valent ions are represented in Table 3.

Only one experimental value of the standard partial molal volume ( P o ) for an acetate complex was found in the present study. AMARI et al. (1988) report v” = 19.5 for Ni(Ac)+. This value was included with other v” data for metal complexes of monovalent ligands by SVERJENSKY et al. ( 1993) to estimate values of the standard partial molal volume of association ( A v,” ) which are not available from experimental measurements, and in turn, to estimate the values of v” for the complexes listed in the tables.

Values of log @ from Table 3 were used in this study to calculate values of the standard partial molal Gibbs free energy of formation at 25°C and 1 bar ( Ae&) for metal-acetate complexes from

where

AC” = AC” + AGO r.q r f,M+= + r(A@w), (3)

AG,” = -2.303 RT log /3,, (4)

SUMMARY OF EXPERIMENTAL DISSOCIATION CONSTANTS AT 25°C AND 1 BAR AND METHODS

USED TO ESTIMATE MISSING VALUES

There are extensive low-temperature experimental data on acetate complex stability constants reported in the literature, and many of these data are included in compilations ( BJER-

RUM et al., 1957; SILLEN and MARTELL, 1964; 1971; MAR-

TELL and SMITH, 1977, 1982; PERRIN, 1979; CHRISTENSEN

and IZATT, 1983; SMITH and MARTELL, 1989). A majority of the reports in the literature give equilibrium constants for association /dissociation reactions at single, finite ionic strengths. Although these measurements may be useful for specific applications, standard state data cannot be extracted from such studies without making several assumptions. In the present study standard state data were compiled directly from the original literature sources, and in most of these studies sufficient data were collected over a range of ionic strengths so that a well-founded extrapolation to the standard state was made by the original authors. These data are compiled as complete dissociation constants (8) in Table 3. In the case of multiple entries for a log /3 value, those which are underlined in Table 3 were chosen in the present study based

20 ““1”“1”“I”“I””

t PbAc+

1

-50 -40 -30 -20 -10 0

s”‘$ (cal mol” K-l) M+

FIG. 3. Correlation of the standard partial molal entropy of association at 25°C and 1 bar for acetate complexes of divalent metal cations as a function of the standard partial molal entropy of the aqueous cations at 25°C and 1 bar. Values of tip were calculated from values of ,!I? given in Tables 1 and 2, together with values of s” for the cations from SHOCK and HELGE~ON ( 1988, 1989) and for acetate from SHOCK (1993a).

FIG. 2. Equilibrium dissociation constants for Pb+*, Mg+‘, and Ca+* acetate complexes as functions of temperature at PSAT, and 500 bars in the case of Ca(Ac)+. Symbols represent experimental data from the sources indicated, but curves were calculated in this study using parameters from Table 2, together with data for the cations from SHOCK and HELCESON ( 1988) and for acetate from SHOCK ( 1993a). Values of so in Table 2 were obtained by regression of the low temperature ( < IOO’C) data depicted in the figure (see text).


Table 3. Standard state equilibrium dissociation constants for a&ate complexes a1 WC and 1 bar.

Metal log 81 log a, log 63 refs

Li+ -0.26 b

Nat z I:

K+ s Mg**

: b P

ca+2 i E

Ba+z

cc+2 M&

Fe’2 co+* Ni’*

Co”

pd::

@?

fjj+a Ag+

Tv Al”

-0.44

E -1.15 -1.80

z -1.20

1;::: +z

E -1.68 -1.57

E -1.81 -1.90 -4.29 ;24 -2.68 -2.11 -1.09

?z-! :0.64

+O.ll

zz

1::;: -2.84 -2.67

a.6

:2.91 ax

&

12.75

& -2.61 -3.55 -6.89 aI -4.08 -3.06 -1.81

?z -0.64

:0.55

&i

L2.86 -5.45

14.20

:4 12 -4.54 -4.80

a3

dd

6 b

:

Am*3

Ao10~‘~ Cm+3

-2.51

z -3.02 -3.31 -2.77 -2.98

1;:;: -2.68 -3.03 -6.7 1

-4.03

z -5.42 -4.72 -5.04 -5.51

:::g -5.03 -5.57

-7.24 -6.30 -6.58 -7.41

I$::;( -6.60 -7.25

c

Y c

c f c c c c i

Z&Hi:+* -6 18 I

a. Viadimirovaet al. (19731 b. Archer sod Monk (1964) c. Moskvin (1969) d. Robiison and Davies (1937) e. M~~og~l and Top01 (19.52) f. M~~~~ and Po&rson (1947) g. VesiIev et ai. (1988) h. Y~i~~ii sod Federova (1956) i. Giordano (1989) j. Tedesco and Martinez (1978) k. Daniele et af. (1985) 1. Ma&oogrdl and Allen (1942) m. Davies and Monk (1951) n. Coleman-Porter and Mook (1952) p. Gureev et al. (1965) q. Lloyd et al, (1951) r. Siddhanta and Banejee (1958) s. Nancollas (1956) 1. A&w and Mook (1966) u. Choudbary and Pm.& (1975) Y. Khokblova et al. (1982) of Nikol’skii et al. in Moskvin (1969

4

w. MacDougall(1942) x. Manning and Monk (1962) y. reported values

et al. (1976) cc. Palmer and Bell (19 3) z. Nakashima and Rabenstein (1983) 88. De Diego et al. (1984) bb. Fedomv

dd. Thomas et al. (1991)

R represents the gas constant, T designates temperature in K, and r stands for the number of acetate ligands liberated in the rth complete dissociation reaction. Values of (A(?&) for complexes not already compiled in Tables l-3 are listed in Table 4, together with values of so, c;,“, and v o at 25°C and 1 bar estimated with methods described above, and equation of state parameters obtained with the correlation algorithm proposed by SHOCK and HELGESON ( 1988). This algorithm has been shown to apply to neutral inorganic species ( SHCXK et al., 1989 ) , a wide variety of aqueous organic com~unds (SHUCK and HELGESON, 1990; SHOCK, 1992, 1993a,b,d), and to inorganic metal-&and complexes ( SVER-

JENSKY et al., 1993; SHOCK et al., 1993). The standard partial molal enthalpies of formation ( AI?$ ) for aqueous complexes listed in Table 4 were calculated from the values of (Ai? F and 3” in the table, and are consistent with values of S” of the elements from COX et al. ( 1989) and/or WAGMAN et al. (1982).

Thermodynamic data and parameters in Table 4, together with corresponding values for acetate from SHOCK ( 1992) and cations from SHOCK and HELGESON ( 1988) and SHOCK et al. ( 1993 ) can be used to estimate values of log /3 and other therm~ynamic properties of acetate complex dissociation reactions at elevated temperatures and pressures. Although


Table 4. Standard partial molal themmdynamic data for acetate complexes at 25OC and 1 bar. tog&x with parameters to calculate tbc some properties at clewted tempemN~~ and prcrsut’~s.

Unless othemise noted. values of A$ arc calculated from selected log !3 values in Table 3. tog&a with values of bE; of cations fmm Shock and Helgeson (1988) and Shock et al. (1993). and ffi>

of acetate tiom Shock (199311).

Li(Ac) -158610. -184240. 19.5 86.7 48.5 8.3880 12.6976 0.7639 -3.3038 56.6767 14.6175

Na(Ac) -150720. -173540. 34.2 75.1 48.2 8.3514 12.6125 0.7884 -3.3003 49.8989 12.2617

K(Ac) -155420. -175220. 47.6 59.2 .59.5 9.9020 16.3937 -0.6874 -3.4566 40.563 1 9.0167

Sr(Ac)+ -224510. -247220. 20.0 77.4 30.1 5.9602 6.7718 3.0884 -3.0588 53.8109 12.7307

Ba(Ac)+ -223650. -242850. 33.5 72.3 35.4 6.6253 8.3926 2.4574 -3.1259 48.9806 11.6995 Mn(Ac)’ -144430. -169560. 6.3 90.8 30.4 6.0776 7.0570 2.9786 -3.0706 63.5668 15.4577

Mn(Ac)z -233850. -287670. 24.2 202.8 83.3 13.1542 24.3405 -3.8236 -3.7851 124.7315 38.2716

CciAc)’ -103260. -132080. -6.5 82.5 22.3 5.0294 4.4992 3.9806 -2.9649 60.4543 13.7619

Ni(Ac)+ -101120. -131450. -11.7 73.7 17.1 4.3556 2.8512 4.6343 -2.8%8 56.0621 Il.9745

WAC)+ -75640. -103120. -1.3 87.2 22.0 4.9722 4.3620 4.0290 -2.9592 62.4950 14.7244

Cu(Ac)* -165820. -222690 14.2 195.8 74.0 11.8801 21.2264 -2.5925 -3.6564 120.6150 36.8408 Cd(Ac)+ -109460. -135920. 6.6 92.1 32.1 6.3043 7.6112 2.7593 -3.0935 64.3035 15.7327

Cd(Ac), -199400. -254520. 24.6 205.4 85.2 13.4090 24.9584 -4.0570 -3.8lW 126.2752 38.8081

Hg(Ac)+ -54760. -79390. 18.5 105.0 27.6 5.6341 5.9787 3.3935 -3.0261 70.1764 18.3452

Hg(Ac), -146580. -198780. 40.1 230.4 80.2 12.7295 23.3004 -3.4080 -3.7421 140.9402 43.9053

Ag(Ac) -70840. -91650. 38.9 72.5 48.6 8.3987 12.7257 0.7485 -3.3050 48.3694 11.7300

Ag(Ac),’ -158990. -210560. 49.9 164.9 103.5 16.2287 31.8418 -6.7592 -4.0952 110.8373 30.5473 Tl(Ac) -95860. -113350. 55.2 45.3 69.7 11.2955 19.8003 -2.0347 -3.5974 32.4138 6.1843 AI(Ac)+~ -207630. -249130. -66.1 72.2 -0.03 2.4559 -1.7874 6.4578 -2.7050 67.4039 11.6689 AI(A -298430. -372080. -59.8 168.7 49.4 9.0207 14.2473 0.1442 -3.3679 118.5029 31.3303

Bi(Ac)+’ -67750. -96420. -15.2 153.5 21.7 5.1690 4.8386 3.8508 -2.9789 107.9465 28.2236 Bi(Ac),+ -157070. -212380. 9.6 327.3 73.6 11.9760 21.4619 -2.6877 -3.6661 201.6950 63.6303 Eu(Ac)+’ -229390. -264280. -31.1 63.0 3.4 2.7500 -1.0666 6.1690 -2.7348 57.1309 9.7898 L~(Ac)+~ -255750. -288710. -29.6 61.6 6.4 3.1548 -0.0804 5.7863 -2.7756 56.1530 9.5148

LGAc)z+ -346160. -4cn330. -10.1 148.1 56.6 9.7487 16.0216 -0.5464 -3.4412 99.3%9 27.1273 Nd(Ac)+2 -252510. -285470. -26.1 48.1 1.4 2.4521 -1.7961 6.4594 -2.7046 47.7869 6.7648 Nd(Ac)*+ -343330. -404110. -5.3 121.7 51.0 8.9606 14.0990 0.2066 -3.3618 83.3168 21.7619 Sm(Ac)+* -251240. -284550. -27.8 47.9 2.7 2.6264 -1.3667 6.2827 -2.7224 47.8346 6.7190 Sm(Ac),+ -3421%. -403500. -7.6 121.3 52.4 9.1590 14.5839 0.0138 -3.3818 83.3717 21.6725 Yb(AQt2 -244760. -280040. -36.6 63.4 -0.1 2.2906 -2.1905 6.6154 -2.6883 58.1718 9.8814

WAc)z+ -335520. -399750. -19.6 151.6 49.3 a.7953 13.6959 0.3628 -3.3451 102.7868 27.8427 U(Ac)+’ -205480. -235460. -21.3 144.6 19.3 4.8662 4.1031 4.1308 -2.9485 103.6659 26.4274

U(Ac),+ -296950. -354230. 1.3 310.1 70.9 11.6455 20.6554 -2.3718 -3.6328 192.7896 60.1258

U(Ac), -387360. -4737%. 17.7 496.0 128.4 19.3290 39.4128 -9.7374 -4.4082 2%.5739 97.99% U02(Ac)+ -320100. -363520. -1.7 123.0 55.8 9.5990 15.6588 -0.4099 -3.4262 83.5297 22.0118

UO,(Ac), -411840. -484700. 13.7 265.6 111.7 17.0325 33.8044 -7.5309 -4.1764 61.5228 51.0592

UO,(Ach- -502400. -607960. 18.3 438.0 173.8 26.0101 55.7294 -16.1571 -5.0828 275.3211 86.1855

-0.0300

-0.0300 -0.0300 0.2482 0.0459 0.4555

-0.0300

0.6472 0.7287 0.5681 -0.0300 0.44%

-0.0300 0.2712 -0.0300 -0.0300 0.8741

-0.0300

2.0552 1.4616

1.2860 0.4046 1.5269

I.5067 0.7c.w 1.4574

0.6305 1.4769 0.6644 1.6113 0.8449

1.3823

0.5324

-0.0300 0.5756

-0.0300

1.3526

most of the higher temperature data were used to construct the correlations for so and c,O described above, there are a few examples of experimental data which can be compared with predicted log /3 values. Three examples are given in Fig. 4. In the cases of the Cde2-acetate complex dissociation constants depicted in Fig. 4a, the curves represent predictions made with all of the correlation algorithms described above. These curves are only tied to experimental values at 25°C and 1 bar where they pass through the values reported by ARCHER and MONK ( 1964) which were determined to be the most accurate in the present study. Nevertheless, it can be seen in Fig. 4a that in each case the temperature dependence of the predicted log p values for each Cd+2-acetate complex is nearly parallel to the trend established by the low- temperature study reported by CHOUDHARY and PRASAD ( 1975 ) . Experimental equilibrium constants for dissociation of AlAc+’ AI( are shown in Fig. 4b together with calculated curves. The values of AS,” at 25°C and 1 bar estimated with the correlation scheme proposed by SVERJENSKY et al. ( 1993) were adjusted by the equivalent of the entropy contribution from the release of two H20 dipoles from the inner hydration sphere of the A1+3 ion for each complex-forming reaction. The close agreement between the experimental values and those estimated in this manner suggests that large coordination changes may accompany Alf3-organic interactions in aqueous solutions. Predicted (curve) and experi-

mental (symbol) values of the dissociation constant for NaAc are depicted in Fig. 4c. In this case, the predicted values are not in close agreement with the three experimental values reported by OSCARSON et al. ( 1988). This is not surprising because the latter values are tied to measurements of HCl and acetic acid dissociation made in the same study, and those for HCl disagree with most other data at high temperature and PSAT.

Predicted dissociation constants of Ca(Ac)+ at 500 bars are shown in Fig. 2 where it can be seen that they are within kO.25 log units ofthose reported by SEEWALD and SEYFRIED ( 199 1). The agreement is probably within experimental uncertainty as the values reported by SEEWALD and SEYFXIED ( 199 1) are from portlandite solubility studies, and sources of uncertainty would include the data for the species involved in the overall process studied, as well as the speciation of acetic acid and Ca+’ in the experimental solution.

Methods for Estimating Log fl at 2S’C and 1 Bar

Pairs of log 8, and log p2 values from Table 3 are plotted in Fig. 5 where it can be seen that most of the pairs of values are closely consistent with the correlation line given by

log 82 = 1.83 log /3, + 0.30. (5)


Cd** acetate complexes (4 O , , , I

- 0 log B, Bardhan .“d Adltya (195E.a)

-7 k 0 log (3, Vasllsv et a,. (rses)

: . log e, varaev et a,. (1988)

0 50 100 150

Temperature, “C

200 250

(b) A1+3 acetate complexes o ,,/, ,,,, ,,,, ,,,, ,,,, ,,,, ,,

l log j3, Fein (1991)

-1 - 0 log 4 Fein (1991) i

-2 - n log p, Palmer and Ball (in press)

0 log 4 Palmer and Ball (in prenr)

. log (3,: Thomas 81 a,. (1991)

l log p,: castet et a,. (1992) at Cl.1 M

u

B

0 50 100 150 200 250 300 350

Temperature, “C

N a+ acetate complex 1 /,,,,,,,,(,,,,,,,,,/,,,,//,,,,,l,r

Or@ 0

-1 -

-2 -

-3 0 log p,oscarron (1909)

0 log !3, Archer and Monk (1964)

0 log p, Daliela et al. (I 995)

1

i -4"'. '1') j ” ” “I”” 1 ""'I ” 1”” i

0 50 100 150 200 250 300 350

Temperature, “C


Metal-acetate complexes

log P, FIG. 5. Correlation of standard state values of log & with log @,

for acetate complexes at 25°C and 1 bar. Circles represent data from Table 3, the square indicates values calculated in this study which are consistent with higher-temperature measurements, and the line is given by Eqn. IO.

Figure 6 contains a plot of all pairs of selected log ,!I, and log & values from Table 3 and it can again be seen that most of the pairs of values are consistent with the correlation line given by

log j3s= 2.46 log /3, + 0.60. (6)

Equations 5 and 6 are consistent with the log j?l estimation scheme described by SASSANI and SHOCK ( 1993bf, and were used in this study to estimate values of log j32 and log & at 25°C and 1 bar for many metal-acetate complexes for which experimental data are lacking. These values of log 82 and log ps were used to calculate values of AGT for the appropriate complexes which are listed in Table 5, together with other the~~ynamic data at 25°C and 1 bar and equation of state parameters estimated with methods described above.

There are many other elements of geochemical interest for which no experimental standard state stability constants for acetate complexes were found in the literature. In the absence ofexperimental data, values of AC?,0 for the first acetate complex of several cations were estimated in the present study using the approach outlined by SASSANI and SHOCK ( 1993b). The estimated values of log Pi calculated from these AeP values are listed in Table 6, and the correlations used are shown in Fig. 7. Data used in the construction of Fig. 7 were taken from Table 3 and values of ACfO for cations were taken from SHOCK and HELGESON ( 1988 ) or SHOCK et al. ( 1993 ).

The vertical bars through these data indicate a range of rt500 cal mol-’ and do not represent uncertainty in the experimental data. Rather, the error bars are shown to indicate that the correlation lines fall within a +500 cal mol-’ envelope defined by the aggregate of the experimental values. The correlation expressions are given by

A(?: = -0.00521 (A&,+) - 392.

for monovalent cations,

(7)

AC; = -0.0161 (A@,+z) - 3530.8 (8)

for the alkaline earths,

A@ = -0.0161 (Ac&+z) - 2601.1

for the divalent transition cations,

(9)

AC; = -0.03796( AC&+,) - 9864. (10)

for La+3, trivalent light rare earth and trivalent heavy actinide cations, and

AC,” = -0.00182( A&++>) - 3900. (11)

for trivalent heavy rare earth and trivalent light actinide cations. The subdivision of the trivalent cations follows proce- dures outlined by SASSANI and SHOCK ( 1993b). The lack of data for group IRA cations other than Alf3, and the trivalent transition cations, precludes construction of analogous

Metal-acetate complexes

-51

-6

-7 i

-61

-6 -5 -4 -3 -2 -1 0

log P, FIG. 6. Correlation of standard state values of log /3, with log &

for acetate complexes at 25°C and I bar. Circles represent data from Table 3, the square indicates values calculated in this study which are consistent with higher-temperature data, and the line is given by Eqn. 1 I.

FIG. 4. Comparison of predicted equilibrium dissociation constants for acetate complexes of Cd+*, A1”3 and Na+ as functions of temperature at P SAT (curves) with experimental data (symbols). See text for discussion.


Table 5. Standard partial molal themmdynamic data for acetate complexes at 25°C and 1 bar estimated in the present study. together with estimated equation of

state parameters required to calculate the same properties at high pressures and temperatures. Values of Act, are consistent with log p values estimated with

FQns. (5) and (6).

Li(Ac&

Na(Ach-

K(Ac),

Mg(Ac),

WA+

WAC),

BtiAch

Map-

WA+ COG-

Ni(Ac),

Ni(Ac),

CUE-

Cd(Ac);

%(Ac)j-

Pb(Ac)3-

TKAc),

Bi(Ac),

Eu(Ac)~+

WAC),

WA+

Nd(Ac),

WAC),

WAC),

-246810. -304670. 25.5 192.5 103.5 16.3412 32.1211 -6.8785 -4.1068 130.4373 36.1810 I .2422

-238470. -292400. 44.0 170.0 103.2 16.2062 3 1.7884 -6.7416 -4.0930 114.6437 31.5846 0.9633

-242990. -292900. 60.7 138.9 115.8 17.8481 35.7984 -8.3 193 -4.2588 94.0916 25.2533 0.7097

-287830. -349260. -1.2 197.3 77.8 12.3982 22.4898 -3.0853 -3.7086 121.5413 37.1627 -0.0300

-311570. -362650. 32.3 187.7 82.1 12.9911 23.9379 -3.6556 -3.7685 I IS.9068 35.2043 -0.0300

-313610. -363740. 42.2 176.7 82.9 13.101s 24.2102 -3.7685 -3.7797 109.4234 32.9508 -0.0300

-3 12620. -358010. 59.7 166.8 88.9 13.9186 26.2066 -4.5556 -3.8623 103.6344 30.9388 -0.0300

-322580. -408280. 31.5 331.9 142.3 21.6217 45.0124 -11.9409 -4.6397 211.3036 64.5717 1.1536

-192770. -2s 146Q. 7.5 186.5 74.2 11.9141 21.3120 -2.6321 -3.6599 115.2121 34.9629 -0.0300

-281890. -373730. 10.4 304.4 132.2 20.3474 4 I .a989 -10.7127 -4.51 IO l98.1420 58.9793 1.4714

-190610. -251280. 0.7 169.4 68.5 11.1327 19.4031 -1.8801 -3.5810 105.1782 31.4753 -0.0300

-279690. -374030. 1.9 275.5 125.8 19.5212 39.8827 -9.9226 -4.4271 I 82.3942 53.0847 1.6030

-2ssalo. -345320. la.9 320.0 131.9 20.2654 41.7019 -10.6422 -4.5029 206.0700 62.1534 1.3408

-288030. -376010. 31.9 336.3 144.3 21.9033 45.7036 -12.2199 -4.6683 213.8505 65.4786 1.1469

-239020. -321900. 51.4 378.6 138.8 2 1.0462 43.6061 -11.3861 -4.5816 235.9096 74.0939 0.8508

-277750. -348760. 88.6 268.1 144.3 21.6128 44.992 1 -11.9361 -4.6389 165.9232 51.5732 0.2871

-183600. -230620. 70.3 111.7 127.1 19.3516 39.472 1 -9.7684 -4.4107 76.8519 19.7269 0.5643

-245540. -329240. 28.6 525.1 131.5 19.7454 40.4309 -10.1406 -4.4503 313.6160 103.9230 -0.0300

-320420. -383670. -12.0 150.7 53.3 9.3029 14.9307 -0.1123 -3.3961 101.2917 27.6639 0.7384

-410690. -504320. 0.2 226.6 108.8 16.6413 32.8512 -7 1605 -4.1370 138.7162 43.1323 -0.0300

-436550. -527920. 2.8 222.2 112.5 17.1523 34.1020 -7.6583 -4.1887 136.1072 42.2254 -0.0300

-433560. -524090. 9.1 177.7 106.3 16.3006 32.0216 -6.8393 -4.1027 llO.OlS6 33.1567 -0.03lxl

-432630. -523910. 6.0 176.9 107.8 16.5088 32.5307 -7.0412 -4.1237 109.5807 33.0056 -0.0300

-425590. -520890. -9.7 228.1 104.4 16.0356 3 1.3743 -6.5843 -4.0759 139.5859 43.4346 -0.0300

a. cal mol-’ b. cal mot-’ K-’ c. cm3 mol.’ d. cal mol.’ bar-’ e. cal K mol.’ bar -’ f. cal K mol.’

correlations to estimate At;: for these species. Note that a Table 6. Values of log p, calculated from

subdivision of divalent cations defined by Zn+2, Cd+‘, and Hg+’ can be observed in Fig. 7c, consistent with trends observed for this family of cations by SASSANI and SHOCK

(1993b). Values of AC: estimated with Eqns. 7-l I together with

Eqn. 4 yield the values of log /3, listed in Table 6 which were used in the present study to estimate values of log p2 and log & with Eqns. 5 and 6. These log p values were employed to calculate AC S for the corresponding complexes as listed in Table 7. Also listed in this table are values of 3”. v O, C?,” . and AH: predicted with methods described above, as well as estimated parameters for the revised-HKF equations of state.

ESTIMATED EQUILIBRIUM CONSTANTS AT ELEVATED TEMPERATURES AND PRESSURES

The data and parameters summarized in Tables 1, 2, 4, 5, and 7 allow estimates of dissociation constanJs for a wide variety of metal-acetate complexes which may be involved in geochemical processes in soils, sedimentary basins, hydrothermal systems, and metamorphic environments. Before discussing the results of such predictions, it may be useful to summarize the extent to which the data and parameters obtained in the present study are tied to experimental measurements. It should be kept in mind that in every case except Ni( AC)+, values of v ’ at 25°C and 1 bar were estimated in the present study. It should also be emphasized that the other

AG”, for complex association reactions

estimated with correlations shown in Fig. 7

(see text).

Cation log P,

NH,+ -0.2 1

Rb+ -0.03

cs+ -0.02

CU+ -0.33

Au+ -0.44

Be+2 -1.64

Ra+2 -1.04

Scfl -3.33

Pr+’ -2.71

Ce+’ -2.73

Gd+3 -2.65

Tbi3 -2.65

DY+~ -2.65

Ho+~ -2.64

Er+3 -2.64

Tm+3 -2.64

LU+3 -2.65

Y+3 -2.64


(4 MAC” species for Monovalent Ions 1500 . , . . , , , . ( .

1000

500

0

Y- -500

-1000

-1500

-2000 1

Na’

p_

‘z Li+

-25OOf~~“‘~~‘~~~‘~~~‘.~~‘...~ -60000 -60000 -40000 -20000 0 20000 40000

b-J MAC’ species of Divalent Transition Metal Ions

-7000 “‘~‘~‘~“~~“‘~~~~‘~~~“~~~~‘~“~‘~~””””~~~~’~~. -60000 -40000 -20000 0 20000 40000

9

04 o MAC’ species of Dlvalent Ions

(4 MAC+* species for REE+3 and ACr3 -2000 1, ” I ” ” I ‘1 ” I ” ” I ” ”

-3000

.

9 -4000

-5000

-6000 -170000 -160000 -150000 -140000 -130000 -120000 -110000

BG,

FIG. 7. Linear free energy relations used in the present study to estimate the standard Gibbs free energy of the reaction to form the first acetate complex for several classes of metal cations at 25°C and 1 bar. Vertical bars represent the 2500 cal mol-’ range which is thought to be tolerable for such estimates (see text).

data and parameters in Table 1 were obtained by regression of high temperature experimental data and are, therefore, likely to be the least subject to uncertainty. Values of c,” listed in Table 2 are estimates, but values of so, and therefore AI?:, were obtained by regression of low-temperature experimental data. Estimated data and parameters in Table 4 are tied to the experimental values of log p at 25°C and 1 bar from Table 3. Therefore, estimates made with data and parameters in Table 4 reflect the accuracy of the correlation algorithms as well as the experimental data at 25°C and 1 bar. In contrast, data and parameters in Tables 5 and 7 were all estimated in the present study. Those in Table 5 are linked to experimental log /3, values from Table 3 through the correlations shown in Figs. 5 and 6, but those in Table 7 derive from values of log PI listed in Table 6 which were estimated in the present study with the correlations shown in Fig. 7.

With all of this in mind, it should be evident that the uncertainty in values of log B calculated with data and parameters obtained in this study increases with increasing table number. We estimate that values of log fi calculated with parameters in Tables 1 and 2 have associated uncertainties of +0.2 units as confirmed by the plots shown in Figs. 1 and 2. Those calculated with data and parameters listed in Table

4 probably have associated uncertainties of +0.3 units of log ,6. On the other hand, it is safe to assume that values of log /3 obtained with data and parameters from Tables 5 and 7 have uncertainties of at least +0.5 units.

Examples of predicted log fl values as functions of temperature from 0” to 500°C and pressures corresponding to vapor-liquid saturation of Ha0 (PSAT ), 500, 1000, and 2000 bars are depicted in Figs. 8-10. Monovalent cation-acetate complexes are represented by Na(Ac) and Na(Ac);, and alkaline earth-acetate complexes by Ca( AC)+ and Ca( Ac)r in Fig. 8. Divalent transition cation-acetate complexes are represented by Mn(Ac)+, Mn(Ac),, and Mn(Ac); in Fig. 9 which also includes examples of divalent oxycation complexes represented by UOa( AC)+, UOa( Ach, and UOa( AC);. The two groups of trivalent cations designated in the construction of Fig. 7d are represented in Fig. 10 by the Nd+‘-acetate and the U+3-acetate complexes. Note that it is almost universal that acetate complexes are less stable at 100°C than they are at 25 “C, but considerably more stable at 200”-350°C than at lower temperatures.

Recently, HARRISON and THYNE ( 1992) reported estimates of log Jo? values for several groups of metal-organic ligand complexes, including acetate, at temperatures up to 200°C.

Tab

le 7

. S

tan

dard

par

tial

mol

al t

berm

odyn

arm

c da

ta f

or

acet

ate

com

plex

es

at 2

5’C

an

d 1

bar

esti

mat

ed

in t

he

pres

ent

stu

dy,

toge

ther

w

ith

est

imat

ed

equ

atio

n

of

stat

e pa

ram

eter

s re

quir

ed

to c

alcu

late

th

e sa

me

prap

enle

s at

hig

h

pres

sure

s an

d te

lllp

er.%

t”rW

Spe

cies

_a

_*

a A

Ci

f A

Hj

_.b

s a

x 10

-z

a2

a”3

f x

10-a

=

4 c;

f

x 10

-d

c2

a x

10-5

%

Rbf

Ac)

Rb(

Ac&

WA

C)

Cs(

Ac)

2-

Cu

(Ac)

CU

E-

Au

(Ac)

Au

(Ac)

;

NH

4(A

c)

NH

,(A

c)*

Be(

Ac)

+

Be(

Ac)

, R

a(A

c)+

RN

A+

W

AC

)+*

Sc(

Ac)

i

WA

C),

P

r(A

c)+

*

WA

C),

+

WA

C),

C

~(A

C)+

~

Ce(

Ac)

*+

C~

(AC

)~

Gd(

Ac)

+*

Gd(

Ac)

*+

Gd(

Ac)

j T

b(A

c)+

*

Tb(

Ac)

*+

Tb(

Ac)

, D

y(A

c)+

*

Dy(

Ac)

*+

DY

(AQ

H

o(A

c)+

* H

OE

+

Ho(

Ac)

, E

r(A

c)+

*

E~

(Ac)

~+

WA

C),

T

m(A

c)+

*

Tm

(Ac)

*+

Tm

(Ac)

l L

u(A

c)+

~

LU

G+

Lu

(Ac)

Y(A

c)+

$

Y(A

c)*+

Y

(Ac)

,

-156

110.

~

-244

000.

b

-158

olo.

g

-245

900.

h

-767

70.9

-165

0D0.

b

-49a

7o.g

1382

40.b

-1

0755

O.E

-195

64O

.h

- 174

020.

’

-263

740.

h

-223

900.

’

-312

940.

b

-233

OlO

.J

-324

640.

b

-415

370.

k

-254

57O

.J

-345

500.

b

-435

690.

k

-253

590!

-3

4455

0.h

-434

760.

k

-250

490.

’

-341

350.

”

-431

490.

k

-251

390.

’

-342

250.

b

-432

390.

k

-250

590.

’

-341

450.

b

-431

590.

k

-253

270.

’ -3

4412

0.6

-434

250.

k

-251

770.

’

-342

620.

h

-432

750.

k

-251

770.

’

-342

620.

b

-432

750.

k

-251

290.

’

-342

150.

b

-432

290.

k

-255

670.

’

-346

520.

h

-436

650.

k

- 174

950.

53

.7

48.0

65

.3

10.6

948

18.3

352

-1.4

623

-3.5

369

33.9

961

6.73

43

-0.0

300

-292

490.

68

.3

117.

0 12

2.2

18.6

924

37.8

608

-9.1

318

-4.3

441

80.2

139

20.8

Gu

O

0.59

41

-176

320.

57

.5

40.6

73

.3

11.7

865

20.9

974

-2.5

020

-3.6

469

29.6

579

5.22

64

-0.0

300

-293

570.

73

.2

102.

6 13

1.1

19.8

839

40.7

670

-10.

2671

-4

.464

2 7

I .07

39

17.8

580

0.52

08

-999

70.

28.7

85

.5

40.5

7.

3009

10

.048

3 I .

7946

-3

.194

3 56

.017

5 14

.388

3 -0

.030

0

-219

740.

37

.0

190.

3 94

.6

15.0

715

29.0

205

-5.6

592

-3.9

786

127.

5564

35

.733

9 1.

0691

-683

10.

48.0

56

.1

61.8

10

.213

0 17

.157

6 -0

.996

9 -3

.488

2 38

.743

2 8.

3843

-0

.030

0

-186

750.

61

.3

132.

8 11

8.3

18.1

917

36.6

392

-8.6

534

-4.2

936

90.4

610

24.0

193

0.70

10

-147

230.

50

.7

90.1

69

.6

11.2

849

19.7

719

-2.0

187

-3.5

963

58.7

075

15.3

233

-0.0

3M

-265

200.

64

.7

199.

3 12

7.0

19.3

685

39.5

090

-9.7

736

-4.4

122

128.

9386

37

.558

1 0.

6495

-213

040.

-4

5.6

97.1

21

.1

5.07

95

4.62

38

3.92

64

-2.9

700

74.5

470

16.7

410

1.24

65

-336

230.

-4

3.8

215.

1 73

.0

I I .

7442

20

.896

1 -2

.466

1 -3

.642

7 13

1.93

55

40.7

754

-0.0

3cQ

-239

380.

48

.0

67.6

37

.6

6.85

54

8.95

66

2.23

15

-3.1

492

44.1

726

10.7

370

-0.1

754

-353

260.

78

.8

157.

6 91

.4

14.2

584

27.0

324

-4.8

725

-3.8

964

98.2

315

29.0

609

-0.0

300

-268

100.

-4

2.4

65.7

2.

8 2.

7175

-1

.143

7 6.

1937

-2

.731

6 60

.319

5 10

.339

8 1.

7013

-389

320.

-2

7.5

156.

0 52

.5

9.27

94

14.8

737

-0.0

899

-3.3

938

106.

5183

28

.737

0 0.

9706

-511

840.

-2

0.0

235.

6 10

8.0

16.5

277

32.5

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Na(Ac)= Na’ + Ad Na(Ac),- = Na+ + 2 AC- :

100 200 300 400 500 0 100 200 300 400 500

Temperature, “C Temperature, “C

100 200 300 400 500

Temperature, “C

100 200 300 400 500

Temperature, “C

FIG. 8. Examples of predicted equilibrium dissociation constants for acetate complexes of alkali and alkaline earth cations as functions of temperature at PsA= and elevated pressures.

Comparisons between their estimates and those obtained in this study for Ca(Ac)+, Pb(Ac)+, AI(Ac and UOz(Ac)+ are depicted in Fig. 11. The methods adopted by HARRISON and THYNE ( 1992 ) appear to require nearly straight lines in log B vs. temperature space for all complexes. In many cases this is not a severe problem because of the limits they place on temperature. This can be seen in the Pb( AC)+ comparison in Fig. 11 where the HARRISON and THYNE ( 1992) values are quite close to those obtained in the present study. This is not surprising as both sets of estimates are based on experimental data from 25’C to 90°C. In the case of UOz( AC)+, the values from HARRISON and THYNE ( 1992) underestimate the stability of the complex at T s 85°C and overestimate the stability from 85” to 200°C compared to the values obtained in this study. This stems in part from their use of a nonstandard state value at 25°C but, in general, the estimates represent something like an average of the values obtained in the present study. In the case of Ca(Ac)+, a similar conclusion can be reached by comparing the values estimated in this study with those which HARRISON and THYNE (1992) obtained from “measured” values. Those which HARRISON and THYNE ( 1992) provide which are consistent with AH data (calculated) are clearly inconsistent with values estimated in this study. The greatest difference between the estimation methods appears to be the magnitude and temperature dependence of Al( AC)+’ dissociation. Perhaps further experimental work will reveal which of these methods pro-

duces the more reliable Al-acetate data. In the interim, the estimates made in the present study which are consistent with data reported by PALMER and BELL ( 1993) are also consistent with an estimation procedure which takes into account the temperature and pressure dependence of dissociation constants for hundreds of complexes ( SVERJENSKY et al., 1993; SHOCK et al., 1993; SASSANI and SHOCK, 1993a), and should provide values which are useful in geochemical modelling calculations (e.g., KORETSKY and SHOCK, 1993 ).

INCORPORATION OF DATA FOR METAL-ACETATE COMPLEXES IN GEOCHEMICAL CALCULATIONS

There are numerous examples of the application of the data and parameters obtained in this study in geochemical calculations, and one of these is given here. In this example, the goal is to determine the effect of acetate complexes on the speciation of metal cations found in an oilfield brine. For the sake of discussion, it is assumed that the brine ( 1 .O molal NaCl) is in equilibrium at 125°C with the assemblage calcite- dolomite-albite-kaolinite-quartz-galena-sphale~te-pyrite- chalcopyrite, and contains 5 ppm Li+, 100 ppm K+, 0.5 ppm Rb+, 0.2 ppm Cs+, 500 ppm Ca+‘, 20 ppm Sr+2, 10 ppm Ba+*, 1 ppm Mn+‘, 1 ppm Ni+‘, 0.2 ppm Cd+2, 10 ppm NHr, 2 ppm total sulfur, and 400 ppm acetate. These concentrations were selected based on moderately-saline brine compositions reported by KHARAKA et al. ( 1977). The ox-

4912 E, L. Shock and C. M. Koretsky

0 -2

-1 -3

-2 -4

a. a. B -3 $ -5

-4 -6

-5 -7

-6 -8 0 100 200 300 400 500 0 100 200 300 400 500


-3,....,....,....,.. ,,I. ,,

.12i,"'~""'~~""'~""'~' 0 100 200 300 400 500

Temperature, “C

1

UO,(Ac), = UO,+’ + 2 AC- - -2

-4

-6

._ 0 100 200 300 400 500

Temperature, “C

-12 -17

-14 -19 0 100 200 300 400 500 0 100 200 300 400 600

Temperature, OC Temperature, “C

FIG. 9. Examples of predicted equilibrium dissociation constants for acetate complexes of’divalent transition metals and oxy-cations as functions of temperature at PSAT and elevated pressures.

idation state imposed on the calculation was evaluated from = -2.55). Data for minerals were taken from HELGESON et

metastable equilibrium among carboxylic acids typical of al. (1978), ions from SHOCK and HELGESON (1988), dis-

oilfield brines at 125°C as described by SHOCK ( 1988, 1989, solved gases from SHOCK et al. ( 1989), chloride, sulfate, bi-

1993c), and represented by the fugacity of Hz (log f% carbonate, and carbonate complexes from SVERJENSKY et


-2 -1 ..,*,,..,,,,,,,,.,,l,,,,

-3 -2 1 Nd(Ac)+2 = Nd+3 + Ad :

-4

cl a

$ -5 if

-6

-7

-6 -?',..,""""',""""',-

0 100 200 300 400 500 0 100 200 300 400 500


-16 F

100 200 300 400 500

Temperature, “C

-6

a

B

-9

-12 ~,~~',~~~'~~~~'~~~~'~~~~ 0 100 200 300 400 500

Temperature, “C

-4,..,, I, ,, ,.‘..,“.‘,,.‘., -3~....,....,....,....,....,

-9.5

0.

is -15

-20.5

-26

0 100 200 300 400 500

Temperature, “C

-15t,“““““““““““,i 0 100 200 300 400 500

Temperature, “C

FIG. 10. Examples of predicted equilibrium dissociation constants for acetate complexes of trivalent rare earth and actinide cations as functions of temperature at PSAT and elevated pressures.


0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350

Temperature, % Temperature, “C

Ca(Ac)+ = Ca*’ + AC‘ :

Pb(Ac) = Pb+‘+ AC’

d

0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350


FIG. 11, Plots of log /3, against temperature at P sAT showing comparisons between values estimated by HARRISON and THYNE ( 1992) and those obtained in the present study. See text for discussion.

al. ( 1993), and hydroxide complexes from SHOCK et al. ( 1993). Activity coefficients for ah aqueous species were calculated with equations summarized by HELGESON et al. ( 198 1). The speciation calculations conducted in this study were accomplished with a modified version of the EQ3NR program ( WOLERY, 1983).

The calculated speciation of this hypothetical oilfield brine is listed in Table 8, where the distribution of each cation is listed. Note that the percentages in Table 8 indicate the relative abundance of each form of the indicated cation. Also listed in Table 8 are the calculated distributions for the ligands including acetic acid. It should be evident from the results shown in Table 8 that acetate complexes do not contribute more than a few percent to the concentration of metals in this hypothetical brine. Note that the contribution of the acetate complexes to the total concentration of the alkalis, 0.1, Mn, Cd, Zn, Pb, and Al are less than 0.5% in each case. Acetate complexes contribute slightly more to the concentration of alkaline earths, Fe and Co, but not as much as 3%. On the other hand, Na( Ac) and Ca( AC)+ account for - 38% of the acetate in this hypothetical brine, which suggests that

major rock forming element complexes should be included in any budget for dissolved organic carbon in oilfield brines.

CONCLUDING REMARKS

The data and parameters summarized above allow a quantitative assessment of the impact of acetate complexes on the speciation of metals in geologic fluids. The oilfield brine example cited above is one of many possible apphca- tions of these data. Others include solubility studies for minerals in organic-rich groundwaters and speciation of metals in seawater. The approach taken in this study can be applied to other metal-organic complexes for which experimental data are available in the literature. Although it appears that acetate complexes can do little to enhance the concentration of metals in oilfield brines, the same conclusion may not be reached for other organic ligands. Similarly, it appears from this study that acetate complexes can not be called upon to enhance the solubility of minerals in basinal brines, but surface complexes involving acetate may enhance the rate of mineral dissoiution.


Teble 8. Celcoleted qecietion at 125OC of metals and ligends including acetic acid in tbe hypothetical oilftild brine decribed in tbe text given in terms of percentegec. Tbe pctcenteges listed are all those above 0.5% end sum to mote than 99% for each metal or ligand. Data for chloride, bicarbonate, carbonate end sulfate complexes were taken from Sverjensky et al., 1993; those. for hydroxide complexes from Shock et al. 1993; and those for acetate complexes from this study.

Acetate chloride Manganese

E‘r@ 55.07 34.00 Cl- NaCl 88.09 11.72 MK1+ Mn+z 83.77 15.15 CH,COOH 6.33 ceAc+ 4.01 cobalt

M&o, 0.68

co+2 59.83 Nickel Alominom coC1+ 39.14 NiCI+ 3.29 ‘wOH),‘ 95.72 CoAc+ 0.77 Ni+’ 95.75 ARCH), 4.28

Copper (H) Potassium Ammonia CuOH+ 69.57 K’ 98.07 NH; 96.13 cuc1+ 26.45 KC1 1.69 NH&@ 3.70 CuC12 2.97

cu+z 0.76 Rubidium Barium Rb+ 88.72 Ba” 78.24 Iron(R) RbCl 10.90 BaCl+ 19.44 Fee2 72.97 BaAc+ 2.24 Fe@ 25.06 Silicon

FeAc+ 1.80 8iO,(as) 99.88 Cadmium CdCl CdCl’

55 87 Lead Sodium 28.08

CdCI; 14.12 PbCl, 41.97 Na+ 88.05 PbC1,-2 18.23 NaCl 11.72

Cd+’ 1.85 ::;s-

17.85 16.96 Strontium

Calcium Ca+’ 84.12

;:+TH’+ 2.54 f&+2 71.83 1.83 srC1+ 26.38

CaCl+ 8.07 SrAc* 1.73 caHco,+ 3.25 Lithium

CaAc~ CaCl 2.18 2.32 LiCl Li+ 96.96 2.66 Sulfur B,S(aq) 72.76 HS- 27.24

Carbonate Magnesium H2CO3 73.68 Mg+’ 66.19 zinc

F$b3+ 2.11 24.15 MgHCO,+ MgCl+ 30.90 1.45 &ICI+ 56.26 16.83 MgAc+ 1.43 ::t42 15.92

Cesium 5.23 CS+ 84.55

Xl:- $<jH’+ 4.25

CsCl 15.08 1.24

Acknowledgments-We are. indebted to Dimitri Svetjensky for keep ing us up to date with the latest techniques for estimating therrno- dynamic data for aqueous complexes, and for allowing this study of metal-acetate complexes to influence his thinking on the general process of complex formation in geologic fluids. We would also like to thank Dave Sassani for sharing his techniques and expertise which allowed estimates for many acetate complexes, and Ed Drummond, Tom Giordano, Jeremy Fein, Don Palmer, Julie Bell, and Dave We- solowski for providing experimental data in advance of publication. Thanks are also due to Ken Jackson, Nick Rose, Robert Smith, Mitch Schulte, Marc Willis, Jill Pasteris, Tom McCollom, J. K. Bohlke, and Harold Helgeson for many helpful discussions, Allison Shock, Patty DuBois, Jennifer Thieme, and Michelle Morgan for technical assistance, and Laura Crossey, Wendy Harrison, and Frank Mango for reviewing the manuscript. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the ACS, for partial support of this research through grant #23870-AC8.

Editorial handling: G. Faure

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Appendix: Equilibrium dissociation constants for metal-acetate complexes calculated with the revised-HKF equations of state using data and parameters from Tables 1, 2, 4, 5 and 7, together with data for the cations from Shock and Helgeson (1988, 1989) and/or Shock et al. (1993), and for acetate from Shock (1993a).

PSAT

Temperature 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350

LiAc BeAc+ NaAc MgAc+ A~Ac+~ Add+ KfIc caAc+ ScAc+’ MllAC+

Mn(A& FeAc+

Fe(A+ CoAc+

Co(Ac);? NiAc+ Ni(Ac), CMC Cl&+

CUC), ZlL4Cf

Zn(+ RbAc &AC+ YAc+~

A& CdAc+

cd(Ac), CsAc BaAc+ LaAc+2 CeAcC2 PrAc+’ NdAC+2 smAc+2 E~Ac+~ GdAc+’ TbAC+2 D~Ac+~ HoAc+’ ErAc’2 TmAc+’ YbAc+2 LuAc+~ All4C HgAc+2

Hg(Ac)2+ nAc PbAc+

-0.47 -0.30 -0.25 -0.28 -0.35 -2.10 -1.65 -1.40 -1.28 -1.24 +0.04 +O.lO +0.06 -0.03 -0.14 -1.50 -1.28 -1.22 -1.26 -1.35 -2.56 -2.75 -3.06 -3.42 -3.81 -4.26 -4.60 -5.17 -5.84 -6.57 +0.29 +0.26 +0.16 0.00 -0.13 -0.99 -0.93 -1.00 -1.15 -1.35 -3.77 -3.33 -3.10 -2.99 -2.97 -1.36 -1.22 -1.24 -1.34 -1.50 -2.43 -2.06 -2.03 -2.20 -2.49 -1.43 -1.29 -1.30 -1.38 -1.52 -2.98 -2.49 -2.33 -2.38 -2.55 -1.68 -1.46 -1.40 -1.43 -1.52 -2.91 -2.37 -2.19 -2.21 -2.36 -1.67 -1.43 -1.34 -1.35 -1.41 -2.90 -2.32 -2.08 -2.04 -2.14 -0.46 -0.33 -0.32 -0.37 -0.46 -2.49 -2.23 -2.13 -2.13 -2.19 -4.23 -3.63 -3.40 -3.39 -3.51 -1.54 -1.61 -1.79 -2.03 -2.31 -3.81 -3.45 -3.43 -3.59 -3.88

-l%I -0.03 -0.13 -0.25 -0.39 -1.15 -1.23 -1.38 -1.57

-3.01 -2.64 -2.47 -2.41 -2.44 -0.84 -0.73 -0.72 -0.77 -0.86 -2.13 -1.93 -1.89 -1.95 -2.07 -3.62 -3.15 -3.04 -3.14 -3.38 +0.04 -0.02 -0.13 -0.26 -0.40 -0.95 -0.99 -1.14 -1.35 -1.59 -2.84 -2.55 -2.44 -2.44 -2.50 -3.01 -2.73 -2.63 -2.63 -2.70 -2.99 -2.71 -2.59 -2.57 -2.61 -2.95 -2.67 -2.57 -2.56 -2.62 -3.14 -2.84 -2.71 -2.69 -2.73 -3.12 -2.80 -2.67 -2.64 -2.69 -2.93 -2.65 -2.55 -2.56 -2.64 -2.96 -2.65 -2.52 -2.49 -2.53 -2.98 -2.65 -2.52 -2.50 -2.56 -2.96 -2.64 -2.51 -2.50 -2.56 -3.00 -2.64 -2.48 -2.44 -2.48 -3.00 -2.64 -2.48 -2.44 -2.48 -2.89 -2.56 -2.42 -2.38 -2.43 -3.05 -2.65 -2.46 -2.39 -2.41 -0.47 -0.44 -0.49 -0.57 -0.68 -4.65 -4.29 -4.13 -4.09 -4.12 -7.59 -6.89 -6.62 -6.60 -6.75 +0.17 +O.ll 0.00 -0.14 -0.29 .2.48 -2.40 -2.45 -2.57 -2.74

-0.45 -1.27 -0.28 -1.49 -4.23 -7.34 -0.30 -1.58 -3.02 -1.69 -2.88 -1.70 -2.82 -1.65 -2.62 -1.52 -2.33 -0.59 -2.29 -3.75 -2.61 -4.25 -0.54 -1.79 -2.52 -0.97 -2.23 -3.72 -0.55 -1.86 -2.63 -2.82 -2.70 -2.72 -2.82 -2.80 -2.78 -2.63 -2.68 -2.68 -2.57 -2.58 -2.53 -2.50 -0.81 -4.22 -7.02 -0.45 -2.94

-0.59 -0.75 -0.93 -1.14 -1.38 -1.65 -1.98 -2.41 -2.92 -1.35 -1.48 -1.65 -1.85 -2.10 -2.39 -2.75 -3.21 -3.75 -0.44 -0.62 -0.81 -1.02 -1.25 -1.52 -1.84 -2.25 -2.76 -1.67 -1.87 -2.10 -2.36 -2.65 -2.99 -3.37 -3.83 -4.33 -4.66 -5.11 -5.57 -6.04 -6.54 -7.06 -7.62 -8.22 -8.71 -8.15 -8.99 -9.85 -10.7 -11.7 -12.7 -13.8 -14.9 -16.0 -0.48 -0.67 -0.88 -1.10 -1.34 -1.61 -1.93 -2.34 -2.85 -1.84 -2.12 -2.43 -2.76 -3.12 -3.53 -3.98 -4.51 -3.12 -3.27 -3.45 -3.67 -3.93 -4.24 -4.61 -5.06 -1.92 -2.19 -2.47 -2.78 -3.12 -3.50 -3.93 -4.44 -4.96 -3.34 -3.86 -4.44 -5.06 -5.75 -6.53 -7.40 -8.44 -9.59 -1.91 -2.15 -2.41 -2.70 -3.01 -3.37 -3.78 -4.26 -4.76 -3.18 -3.60 -4.07 -4.61 -5.22 -5.90 -6.70 -7.67 -8.73 -1.82 -2.03 -2.26 -2.52 -2.82 -3.15 -3.54 -4.00 -4.50 -2.97 -3.38 -3.85 “4.38 -4.98 -5.67 -6.46 -7.42 -8.48 -1.67 -1.85 -2.05 -2.29 -2.56 -2.87 -3.24 -3.68 -4.16 -2.61 -2.97 -3.38 -3.85 -4.39 -5.03 -5.77 -6.68 -7.67 -0.74 -0.91 -1.11 -1.32 -1.56 -1.84 -2.18 -2.60 -3.13 -2.44 -2.62 -2.83 -3.07 -3.35 -3.67 -4.03 -4.48 -4.95 -4.07 -4.47 -4.92 -5.44 -6.03 -6.70 -7.48 -8.44 -9.49 -2.93 -3.27 -3.63 -4.00 -4.40 -4.84 -5.31 -5.86 -6.41 -4.69 -5.20 -5.76 -6.37 -7.04 -7.80 -8.65 -9.68 -10.8 -0.70 -0.88 -1.06 -1.25 -1.47 -1.71 -2.00 -2.38 -2.87 -2.04 -2.31 -2.60 -2.92 -3.26 -3.64 -4.07 -4.59 -5,14 -2.66 -2.83 -3.04 -3.28 -3.56 -3.88 -4.26 -4.73 -5.25 -1.10 -1.26 - 1.43 -1.62 -1.84 -2.10 -2.40 -2.80 -3.30 -2.43 -2.66 -2.92 -3.21 -3.53 -3.88 -4.30 -4.79 -5.32 -4.13 -4.62 -5.15 -5.75 -6.41 -7.15 -8.01 -9.03 -10.2 -0.70 -0.86 -1.02 -1.20 -1.40 -1.62 -1.89 -2.24 -2.71 -2.16 -2.47 -2.80 -3.15 -3.53 -3.95 -4.42 -4.98 -5.60 -2.79 -2.99 -3.22 -3.48 -3.77 -4.11 -4.50 -4.98 -5.52 -2.98 -3.19 -3.42 -3.68 -3.98 -4.31 -4.71 -5.18 -5.69 -2.83 -3.00 -3.19 -3.42 -3.68 -3.98 -4.34 -4.78 -5.26 -2.87 -3.06 -3.28 -3.52 -3.80 -4.12 -4.50 -4.96 -5.45 -2.96 -3.14 -3.34 -3.58 -3.85 -4.17 -4.54 -4.99 -5.46 -2.95 -3.14 -3.36 -3.62 -3.91 -4.25 -4.64 -5.11 -5.62 -2.96 -3.17 -3.42 -3.69 -4.01 -4.36 -4.77 -5.25 -5.75 -2.77 -2.95 -3.16 -3.41 -3.69 -4.01 -4.39 -4.85 -5.33 -2.84 -3.05 -3.29 -3.56 -3.87 -4.23 -4.63 -5.12 -5.65 -2.84 -3.05 -3.29 -3.56 -3.86 -4.22 -4.62 -5.11 -5.62 -2.72 -2.91 -3.13 -3.38 -3.67 -4.01 -4.40 -4.87 -5.39 -2.73 -2.92 -3.14 -3.39 -3.68 -4.02 -4.41 -4.89 -5.39 -2.68 -2.87 -3.09 -3.34 -3.63 -3.97 -4.36 -4.83 -5.32 -2.63 -2.81 -3.02 -3.27 -3.56 -3.89 -4.28 -4.76 -5.30 -0.95 -1.11 -1.28 -1.47 -1.68 -1.92 -2.21 -2.59 -3.08 -4.37 -4.56 -4.78 -5.04 -5.34 -5.68 -6.08 -6.57 -7,ll -7.39 -7.84 -8.35 -8.93 -9.58 -10.3 -11.2 -12.2 -13.4 -0.62 -0.79 -0.98 -1.17 -1.39 -1.64 -1.93 -2.31 -2.79 -3.17 -3.42 -3.70 -4.00 -4.33 -4.71 -5.14 -5.67 -6.23

-5.07 -5.54


Appendix: PSAT (continued).

Temperature 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350

-4.03 -4.48 -4.99 -5.53 -6.12 -6.73 -7.38 -8.08 -8.85 -9.71 -10.7 -11.9 -1.39 -1.71 -2.08 -2.49 -2.94 -3.41 -3.91 -4.45 -5.01 -5.63 -6.32 -7.00

RaAC+ -0.93 -1.05 -1.26 -1.51 -1.79 -2.09 -2.40 -2.73 -3.08 -3.44 -3.83 -4.26 -4.75 -5.99 UAc+’

-5.33 -2.98 -2.68 -2.63 -2.73 -2.92 -3.17 -3.48 -3.84 -4.22 -4.64 -5.10 -5.60 -6.15 -6.77 -7.41

Us; -5.67 -5.03 -4.94 -5.15 -5.56 -6.1 1 -6.78 -7.54 -8.37 -9.26 -10.2 -11.3 -12.4 -t3.8 -15.1 UOzAc -3.39 -3.03 -2.88 -2.87 -2.93 -3.07 -3.25 -3.48 -3.75 -4.04 -4.38 -4.77 -5.20 -5.72 -6.27 UO,(Ac), -6.41 -5.57 -5.23 -5.17 -5.31 -5.60 -6.00 -6.49 -7.06 -7.70 -8.43 -9.24 -10.2 -11.3 -12.5 NH,Ac -0.23 -0.21 -0.30 -0.44 -0.60 -0.80 -1.00 -1.23 -1.46 -1.72 -1.99 -2.30 -2.65 -3.09 -3.64

Appendix 500 bars

Temperature 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400

LiAc -0.43 BeAc+ -2.08 NaAc +O.lO MgAc+ -1.47 AIAc+’ -2.57 AI(A&+ KAC

caAc+ ScAc+’ MnAc+

Ma(A+ FeAc+

fWAc), CoAc+

‘X4d2 NiAc+ Ni(Ac), CUAC

CuAc+

WAC),! znAc+

Zn(A+ RbAc SrAcf Y AC+* AgAc CdAC' WAd, CsAc BaAc+ LaAc+2 CeAc+’ PrAc+2

NdAc+* smAc+2 EuAc+’ GdAc+’ TbAc+2 DyAc+’ HoAc+’ ErAcC2 TmAc+2 YbAc+2 LuAc+’ AUAC HgAc+’

Hg(Ac); TIAC

PbAc+* Pb(Acb+ BiAc+ RaAC+ UAc*’

-4.22 -4.52 +0.35 +0.33 -0.95 -0.88

-3.76 -3.31

-1.40

-1.32

-2.89

-2.32

-1.68 -2.84 -1.65 -2.82 -0.42 -2.47 -4.13 -1.52

-3.72 +0.06 -1.17 -3.00 -0.79 -2.13 -3.54 +o. 11 -0.89 -2.83 -3.00 -2.97

-2.93 -3.13 -3.12 -2.92 -2.96 -2.98 -2.96 -2.99 -2.99 -2.89 -3.05 -0.41 -4.62

-7.48 +0.23 -2.44 -3.28 -1.14 -0.90 -2.96

-0.23 -1.61 +0.17 -1.24 -2.73

-1.25

-1.17

-2.36 - 1.42

-1.92

-2.25 -1.40 -2.21 -0.28 -2.19 -3.51 -1.57 -3.33 +0.04 -1.11 -2.62 -0.67 - 1.89 -3.01 +0.06 -0.94 -2.53 -2.71 -2.69

-2.65 -2.82 -2.78 -2.63 -2.63 -2.63 -2.62 -2.62 -2.62 -2.54 -2.63 -2.43 -2.35 -2.36 -2.43 -2.54 -2.70 -2.88 -3.10 -3.34 -3.60 -3.90 -4.20 -4.53 -4.90 -5.28 -0.37 -0.41 -0.49 -0.59 -0.71 -0.84 -0.98 -1.13 -1.29 -1.47 -1.65 -1.87 -2.09 -2.34 -2.65 -3.01 -4.25 -4.08 -4.02 -4.05 -4.13 -4.26 -4.42 -4.62 -4.84 -5.09 -5.35 -5.66 -5.97 -6.30 -6.67 -7.04

-6.76 -6.47 -6.44 -6.57 -6.82 -7.15 -7.56 -8.02 -8.54 -9.11 -9.71 -10.4 -11.1 -11.8 -12.7 -13.6 +0.19 +0.08 -0.05 -0.19 -0.34 -0.50 -0.66 -0.83 -1.00 -1.18 -1.37 -1.58 -1.80 -2.05 -2.36 -2.72 -2.35 -2.40 -2.51 -2.66 -2.84 -3.05 -3.28 -3.52 -3.78 -4.06 -4.35 -4.69 -5.01 -5.35 -5.74 -6.12 -3.26 -3.50 -3.86 -4.29 -4.78 -5.29 -5.83 -6.40 -6.99 -7.61 -8.24 -8.93 -9.62 -10.4 -11.2 -12.1 -1.00 -1.10 -1.33 -1.63 -1.99 -2.38 -2.81 -3.25 -3.71 -4.20 -4.69 -5.22 -5.73 -6.24 -6.79 -7.30 -1.00 -1.20 -1.44 -1.71 -1.99 -2.28 -2.58 -2.89 -3.22 -3.55 -3.89 -4.27 -4.65 -5.04 -5.48 -5.94 -2.64 -2.59 -2.67 -2.85 -3.09 -3.38 -3.71 -4.06 -4.45 -4.86 -5.28 -5.74 -6.20 -6.66 -7.15 -7.63

-0.17 -0.19 -0.25 -0.34 -0.46 -0.601 -0.76 -0.94 -1.14 -1.35 -1.59 -1.84 -2.12 -2.45 -2.82 -1.35 -1.22 -1.17 -1.19 -1.26 -1.36 -1.50 -1.67 -1.87 -2.09 -2.35 -2.63 -2.93 -3.30 -3.70 +o. 13 +0,04 -0.07 -0.20 -0.34 -0.50 -0.67 -0.85 -1.04 -1.25 -1.48 -1.72 -1.99 -2.31 -2.69 -1.17 -1.20 -1.28 -1.41 -1.56 -1.74 -1.95 -2.17 -2.42 -2.68 -2.97 -3.26 -3.56 -3.91 -4.24 -3.02 -3.37 -3.75 -4.14 -4.55 -4.96 -5.39 -5.82 -6.27 -6.71 -7.19 -7.62 -8.03 -8.44 -8.72 -5.06 -5.71 -6.41 -7.15 -7.91 -8.69 -9.49 -10.3,-11.1 -12.0 -12.9 -13.7 -14.5 -15.3 -16.0 +0.24 +O. 1 1 -0.04 -0.20 -0.37 -0.55 -0.73 -0.92 -1.13 -1.34 -1.58 -1.83 -2.11 -2.44 -2.83 -0.95 -1.09 -1.28 -1.49 -1.73 -2.00 -2.27 -2.57 -2.88 -3.21 -3.57 -3.92 -4.28 -4.68 -5.07

-3.07 -2.95 -2.92 -2.95 -3.03 -3.15 -3.31 -3.49 -3.71 -3.94 -4.22 -4.49 -4.78 -5.12 -5.45 -1.18 -1.27 -1.42 -1.60 -1.81 -2.05 -2.30 -2.57 -2.87 -3.17 -3.51 -3.84 -4.18 -4.55 -4.90 -I .88 -2.03 -2.31 -2.67 -3.09 -3.57 -4.09 -4.65 -5.26 -5.89 -6.59 -7.28 -8.01 -8.83 -9.67 -1.25 -1.32 -1.45 -1.61 -1.80 -2.01 -2.25 -2.50 -2.77 -3.05 -3.37 -3.68 -4.00 -4.35 -4.68 -2.19 -2.21 -2.37 -2.62 -2.93 -3.31 -3.74 -4.20 -4.72 -5.26 -5.89 -6.50 -7.15 -7.90 -8.64 -1.34 -1.36 -1.43 -1.55 -1.71 -1.89 -2.09 -2.32 -2.57 -2.83 -3.13 -3.42 -3.72 -4.07 -4.40 -2.04 -2.04 -2.17 -2.41 -2.71 -3.08 -3.50 -3.96 -4.47 -5.01 -5.63 -6.25 -6.89 -7.64 -8.38 -1.30 -1.29 -1.34 -1.44 -1.57 -1.72 -1.90 -2.10 -2.33 -2.56 -2.84 -3.11 -3.40 -3.73 -4.05 -1.95 -1.89 -1.97 -2.14 -2.38 -2.69 -3.04 -3.45 -3.90 -4.39 -4.95 -5.51 -6.10 -6.79 -7.48 -0.26 -0.30 -0.39 -0.50 -0.64 -0.79 -0.96 -1.15 -1.35 -1.57 -1.81 -2.07 -2.36 -2.70 -3.09 -2.08 -2.07 -2.11 -2.21 -2.33 -2.49 -2.67 -2.87 -3.10 -3.34 -3.63 -3.90 -4.18 -4.50 -4.80 -3.26 -3.23 -3.34 -3.54 -3.83 -4.18 -4.58 -5.03 -5.53 -6.06 -6.67 -7.28 -7.91 -8.65 -9.38 -1.74 -1.97 -2.23 -2.52 -2.82 -3.13 -3.46 -3.79 -4.15 -4.50 -4.89 -5.26 -5.63 -6.03 -6.38

-3.29 -3.44 -3.70 -4.05 -4.46 -4.92 -5.42 -5.96 -6.55 -7.16 -7.84 -8.52 -9.22 -10.0 -10.8 -0.04 -0.16 -0.30 -0.44 -0.59 -0.74 -0.91 -1.07 -1.25 -1.44 -1.66 -1.88 -2.13 -2.43 -2.80 -1.18 -1.32 -1.50 -1.71 -1.93 -2.18 -2.44 -2.72 -3.02 -3.32 -3.66 -3.99 -4.33 -4.72 -5.10 -2.44 -2.37 -2.38 -2.45 -2.57 -2.72 -2.90 -3.10 -3.34 -3.59 -3.88 -4.17 -4.49 -4.85 -5.22 -0.65 -0.70 -0.78 -0.88 -1.00 -1.14 -1.29 -1.46 -1.64 -1.83 -2.05 -2.29 -2.55 -2.87 -3.25 -1.83 -1.87 -1.98 -2.12 -2.30 -2.51 -2.74 -2.99 -3.27 -3.55 -3.88 -4.20 -4.53 -4.90 -5.27 -2.88 -2.96 -3.18 -3.49 -3.87 -4.31 -4.80 -5.33 -5.91 -6.51 -7.19 -7.87 -8.59 -9.42 -10.3 -0.04 -0.17 -0.30 -0.44 -0.58 -0.73 -0.88 -1.03 -1.19 -1.36 -1.55 -1.75 -1.98 -2.27 -2.61 -1.09 -1.30 -1.53 -1.79 -2.06 -2.35 -2.65 -2.96 -3.29 -3.63 -4.00 -4.37 -4.75 -5.18 -5.61 -2.41 -2.39 -2.45 -2.56 -2.70 -2.88 -3.08 -3.30 -3.55 -3.82 -4.12 -4.43 -4.76 -5.13 -5.52 -2.59 -2.58 -2.64 -2.75 -2.89 -3.07 -3.27 -3.50 -3.75 -4.01 -4.32 -4.62 -4.93 -5.29 -5.64 -2.57 -2.53 -2.57 -2.64 -2.75 -2.89 -3.06 -3.25 -3.46 -3.69 -3.96 -4.22 -4.50 -4.82 -5.14

-2.54 -2.52 -2.57 -2.66 -2.79 -2.95 -3.14 -3.35 -3.58 -3.83 -4.12 -4.40 -4.70 -5.04 -5.36 -2.68 -2.64 -2.67 -2.75 -2.87 -3.02 -3.19 -3.39 -3.62 -3.86 -4.14 -4.42 -4.71 -5.04 -5.36 -2.63 -2.60 -2.63 -2.72 -2.86 -3.02 -3.22 -3.44 -3.68 -3.95 -4.25 -4.55 -4.86 -5.22 -5.56 -2.52 -2.52 -2.59 -2.70 -2.86 -3.05 -3.27 -3.51 -3.77 -4.05 -4.37 -4.68 -5.00 -5.36 -5.69 -2.48 -2.44 -2.47 -2.56 -2.68 -2.83 -3.02 -3.22 -3.46 -3.71 -4.00 -4.28 -4.58 -4.92 -5.24 -2.48 -2.45 -2.50 -2.60 -2.75 -2.93 -3.14 -3.38 -3.64 -3.92 -4.24 -4.56 -4.89 -5.26 -5.62 -2.48 -2.45 -2.50 -2.60 -2.75 -2.93 -3.14 -3.37 -3.63 -3.91 -4.23 -4.54 -4.86 -5.23 -5.57 -2.45 -2.40 -2.42 -2.50 -2.63 -2.79 -2.98 -3.20 -3.45 -3.71 -4.01 -4.31 -4.63 -4.99 -5.35 -2.45 -2.40 -2.43 -2.51 -2.64 -2.80 -2.99 -3.21 -3.46 -3.72 -4.02 -4.32 -4.64 -5.00 -5.34 -2.39 -2.34 -2.37 -2.46 -2.59 -2.75 -2.94 -3.16 -3.40 -3.66 -3.97 -4.26 -4.57 -4.92 -5.25


Appendix: 500 bars (continued).

Temperature 0 25 50 75 loo 125 150 175 200 225 250 275 300 325 350 375 400

WC),+ -5.58 -4.91 -4.80 -4.99 -5.38 -5.91 -6.54 -7.25 -8.02 -8.85 -9.73 -10.6 -11.6 -12.6 -13.6 -14.6 -15.7 UOzAc+ -3.41 -2.97 -2.79 -2.75 -2.80 -2.92 -3.09 -3.29 -3.53 -3.80 -4.09 -4.40 -4.76 -5.10 -5.41 -5.87 -6.26 U02(Ac)2 -6.32 -5.40 -5.01 -4.93 -5.05 -5.31 -5.68 -6.13 -6.65 -7.23 -7.87 -8.54 -9.30 -10.1 -10.9 -11.8 -12.7 NH,Ac -0.17 -0.13 -0.21 -0.34 -0.50 -0.68 -0.88 -1.09 -1.30 -1.53 -1.77 -2.02 -2.30 -2.58 -2.89 -3.26 -3.68

Appendix 1000 bars

Temperature 100 150 200 250 300 350 400 450 500 550 600

LiAc BeAc+ NaAc MgAc+ AlAc+* Al(Ac)*+ KAC

caAc+

ScAc+* MnAc+ Mn(Ac)* FeAc+ Fe(Ac)* CoAc+ Co(Ac)* NiAc+ Ni(Ac), Cu AC CuAc+ WAC), ZnAc+

Zn(Ac)* RbAc SrAc+ YAc+* AgAc GlAc+ Cd(Ac), CsAc BaAc+ LaAc+* CeAc+* PrAc+* NdAc+*

;zc:;*

GdAc+* TbAc+* Dy AC+* HoAc+* ErAc+* TmAc+* YbAc+* LuAc+* AuAc HgAc+*

Hg(Ac),+ TIAC

PbAc+ Pb(Acb BiAc+ RaAc+ UAc+* U(Ac)*+ U02Ac+ UG2(Ac)* NH4Ac

-0.17 -0.36 -0.63 -1.13 -1.18 -1.40 -0.01 -0.27 -0.57 -1.23 -1.49 -1.83 -3.70 -4.47 -5.26 -6.30 -7.73 -9.22

-0.95 -1.70 -0.89 -2.24 -6.07 -10.7 -0.98 -2.71 -3.54 -2.68 -4.89 -2.59 -4.35 -2.38 -4.09 -2.16 -3.54 -1.20 -2.92 -5.16 -3.96 -6.18 -1.10

-1.32

-3.63

-2.09 -1.24 -2.70

-1.82

-6.89 -12.3 -1.35 -3.29 -3.96 -3.23 -6.03 -3.09 -5.33 -2.84 -5.07 -2.58 -4.40 -1.58 -3.35 -6.11 -4.59 -7.29 -1.42 -3.38

-1.73 -2.21 -2.77 -3.38 -4.11 -2.55 -3.09 -3.73 -4.41 -5.23 -1.64 -2.09 -2.62 -3.22 -3.95 -3.20 -3.75 -4.35 -4.93 -5.55 -7.68 -8.47 -9.20 -9.75 -10.1 -13.8 -15.3 -16.8 -18.0 -19.0

-4.91 -6.16 -4.78 -6.20 -10.3 -19.7 -5.01 -7.40 -7.43 -6.94 -14.7

+0.03

-2.35

-2.88 -1.36 -2.16

-0.72

-1.23

-1.40 -2.24 -1.38 -2.04 -1.30 -1.84 -0.33 -2.07 -3.21 -2.18 -3.57 -0.22 -1.45

-2.97

-2.50

-0.29

-1.73 -2.90 -1.72

-0.92

-1.66

-2.75 -1.62 -2.52 -1.50 -2.21 -0.56 -2.26 -3.65 -2.74 -4.28 -0.50 -1.86

-3.20 -2.18

-0.62

-3.83 -2.13 -3.48

-2.16

-1.96 -3.23 -1.79 -2.80 -0.86 -2.55 -4.33 -3.33

-1.76 -2.23 -2.78 -3.39 -4.15 -3.91 -4.57 -5.27 -5.95 -6.66 -4.43 -3.80 -7.25 -3.63 -6.40

-4.97

-4.99

-4.42 -8.58 -4.21

-5.15

-7.58 -3.91 -7.31 -3.56 -6.43 -2.49 -4.33 -8.33 -5.93 -9.75 -2.20 -4.57 -4.70 -2.65 -4.75 -9.13 -2.02 -5.04

-5.57 -5.08

-5.65

-10.0 -4.83

-5.78

-8.88 -4.51 -8.61 -4.13 -7.63 -3.06 -4.89 -9.61 -6.63 -11.1 -2.69 -5.24 -5.34 -3.19 -5.41 -10.6 -2.47 -5.78

-6.15 -6.78 -5.69 -6.31 -11.5 -13.0 -5.41 -6.01 -6.62 -10.2 -11.6 -13.1

-3.35 -6.13 -3.04 -5.36 -2.00 -3.81 -7.16 -5.25 -8.47 -1.78 -3.95 -4.13 -2.21 -4.14 -7.82 -1.65

-5.09 -5.70 -6.32 -9.90

-8.82 -3.70 -5.42

-4.69

-10.9 -7.25 -12.5 -3.26 -5.89

-10.1

-11.3

-4.48 -5.96 -12.3

-5.30

-7.87 -14.0 -3.98 -6.59 -6.70 -4.55 -6.15 -13.7 -3.67 -7.32 -7.07 -7.05 -6.38 -6.67 -6.62 -6.98 -7.08 -6.55 -7.13 -7.02

-11.5 -5.35 -6.50

-12.8

-13.8 -8.45

-5.93

-15.6 -4.79 -7.33 -7.47 -5.40 -7.47 -15.4 -4.44 -8.17

-5.17 -0.79 -2.33 -2.80 -1.18 -2.61 -4.53 -0.77 -2.55 -2.98 -3.17 -2.96 -3.04

-3.18 -1.49

-2.84 -5.99 -3.80 -6.05 -12.0 -3.00

-3.02 -0.24

-1.91 -3.67 -0.50

-2.21 -5.53 -1.04

-3.07 -6.63 -1.33

-3.59

-1.50 -2.00 -2.41 -2.64 -2.60 -2.83 -2.54 -2.70 -2.54 -2.74

-3.12 -3.73 -4.36 -3.40 -3.88 -4.40 -3.58 -4.06 -4.58 -3.31 -3.70 -4.15 -3.42 -3.86 -4.35

-6.32 -6.40

-6.51 -7.88 -7.73 -7.01 -7.31 -7.23 -7.66 -7.69 -7.17 -7.82 -7.68 -7.52 -7.45 -7.25 -7.62 -5.03 -9.26 -19.1 -4.71 -8.32 -17.3 -10.6 -8.56 -10.6 -22.2 -8.29 -18.4 -6.14

-4.66 -5.22 -5.77 -4.89 -5.48 -6.06 -4.88 -5.46 -6.02 -5.08 -5.71 -6.32 -5.24 -5.87 -6.47

-2.64 -2.81 -3.09 -3.46 -3.88 -4.35 -2.60 -2.79 -3.12 -3.52 -3.99 -4.51 -2.55 -2.44 -2.46 -2.46 -2.39 -2.39 -2.34 -2.33 -0.52 -4.00

-2.80 -2.61 -2.69 -2.69 -2.57 -2.57 -2.53 -2.48 -0.75 -4.18 -6.97 -0.41 -2.96 -5.11 -2.31

-3.16 -3.60 -2.91 -3.29 -3.04 -3.48 -3.03 -3.47 -2.88 -3.29 -2.89 -3.29

-4.10 -4.65 -3.73

-3.96 -3.75 -3.76 -3.10 -3.65 -1.63

-3.98

-5.38

-4.51

-4.22

-4.28 -4.28 -4.22 -4.18 -1.99

-4.53

-5.91 -11.1 -1.71 -4.93

-4.77 -5.14 -5.11 -5.75

-5.50 -5.50

-5.36

-5.40 -5.43 -2.91 -7.16 -13.9

-5.80

-2.62 -6.20 -12.3 -7.84 -6.03 -8.07 -16.6 -6.10 -13.2 -3.70

-6.13 -6.12

-5.94 -6.45 -6.37

-4.86 -4.86 -4.79 -4.77 -2.41 -6.51 -12.4 -2.12 -5.54 -10.9 -6.85 -5.28 -7.16 -14.7 -5.39 -11.5 -3.08

-6.62

-6.81

-6.84

-15.5

-4.21

-6.77

-8.52

-9.68

-17.2 -3.90 -7.56

-2.84 -3.24 -2.79 -3.18

-6.00

-13.8

-6.10 -3.49

-8.76

-7.81 -15.5 -3.19 -6.85

-1.02 -4.50 -7.78 -0.71 -3.39 -6.15 -3.13

-1.31 -4.91

-6.43 -0.12

-8.76 -9.86 -1.02 -1.35

-6.78 -4.15 -1.59 -1.65 -2.80 -5.25 -2.71 -4.85 -0.42

-3.86 -4.38 -7.25 -8.40 -4.02 -4.94

-9.60 -5.88 -4.59 -6.29

-2.19 -2.76 -3.35 -3.96 -3.30 -3.95 -4.68 -5.47

-6.79 -7.64 -8.92 -9.79 -18.5 -20.3 -6.81 -7.54 -14.8 -16.5 -4.39 -5.21

-6.36 -1.76 -9.35 -11.0 -12.8 -2.96 -3.37 -3.87 -4.14 -4.74 -5.43 -6.33 -7.44 -8.68 -10.0 -0.78 -1.18 -1.61 -2.06 -2.54


Appendix 2000 Bars

Temperature 100 1.50 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

LiAc BeAc+

NaAc MgAc+ AlAc+*

AIM+ KAC

&AC+

&AC+2

MnAc+

Mn(Ac)* FeAc+

Fe(Ac), CoAc+

Co(Ac12 NiAc+

Ni(Ac), CuAc

CuAc+

Cu(AcIz znAc+

WAC);, RbAc

SrAc+ Y AC+’

AgAc CdAc+

CdW2 CsAc BaAc+ L&c+2 CeAcf2

PTAC+2 NdAc+2 SmAC+2 E~Ac+~

GdAc+2 TbAC+z DyAc+*

HoAc+~ E~Ac+~

TmAC+2 YbAc+2

LuAc+~ AUAC

H~Ac+~

Hg(Acj2+ TIAC PbAc+

Pb(Ac), BiAc+2 R&C+ UAC+~

U(Ac12+ UO*Ac+

UGz(Ac12 NH4Ac

-0.05 -0.21 -0.43 -0.70 -1.00 -1.32 -1.68 -2.07 -2.48 -2.88 -3.31 -3.76 -4.24 -4.75 -5.27 -5.80 -6.35 -6.89 -7.44 -1.08 -1.10 -1.26 -1.50 -1.81 -2.17 -2.58 -3.04 -3.53 -4.01 -4.51 -5.06 -5.63 -6.23 -6.85 -7.49 -8.14 -8.79 -9.44

+0.06 -0.17 -0.43 -0.70 -1.00 -1.29 -1.61 -1.97 -2.34 -2.71 -3.10 -3.51 -3.95 -4.41 -4.88 -5.36 -5.85 -6.33 -6.81 -1.18 -1.39 -1.69 -2.03 -2.41 -2.82 -3.25 -3.73 -4.21 -4.67 -5.15 -5.66 -6.19 -6.75 -7.33 -7.94 -8.57 -9.22 -9.87 -3.67 -4.38 -5.10 -5.83 -6.54 -7.26 -7.97 -8.69 -9.39 -10.0 -10.7 -11.3 -11.9 -12.6 -13.3 -14.1 -14.9 -15.8 -16.6

-6.18 -7.51 -8.87 -10.2 -11.6 -12.9 -14.3 -15.6 -17.0 -18.2 -19.4 -20.7 -22.0 -23.3 -24.7 -26.2 -27.7 -29.4 -31.1 +O.ll -0.18 -0.48 -0.79 -1.10 -1.42 -1.76 -2.13 -2.52 -2.89 -3.29 -3.71 -4.15 -4.60 -5.07 -5.55 -6.02 -6.48 -6.94

-1.18 -1.57 -2.02 -2.50 -3.00 -3.51 -4.06 -4.63 -5.21 -5.75 -6.32 -6.90 -7.51 -8.14 -8.80 -9.48 -10.2 -10.9 -11.6 -2.86 -2.90 -3.08 -3.35 -3.68 -4.06 -4.48 -4.96 -5.45 -5.92 -6.42 -6.95 -7.50 -8.08 -8.69 -9.33 -9.99 -10.7 -11.4

-1.30 -1.62 -2.02 -2.45 -2.91 -3.39 -3.90 -4.45 -5.00 -5.51 -6.05 -6.60 -7.18 -7.78 -8.42 -9.08 -9.77 -10.5 -11.2 -1.98 -2.65 -3.48 -4.41 -5.40 -6.44 -7.53 -8.69 -9.87 -11.0 -12.2 -13.4 -14.6 -15.9 -17.3 -18.6 -20.0 -21.4 -22.9

-1.34 -1.63 -1.98 -2.37 -2.79 -3.23 -3.70 -4.21 -4.72 -5.20 -5.70 -6.22 -6.77 -7.34 -7.94 -8.57 -9.23 -9.90 -10.6 -2.06 -2.51 -3.14 -3.89 -4.71 -5.59 -6.54 -7.57 -8.61 -9.62 -10.7 -11.8 -12.9 -14.1 -15.4 -16.7 -18.0 -19.3 -20.7 -1.32 -1.51 -1.80 -2.15 -2.53 -2.94 -3.39 -3.88 -4.37 -4.84 -5.33 -5.84 -6.38 -6.95 -7.54 -8.17 -8.81 -9.48 -10.1

-1.86 -2.27 -2.88 -3.61 -4.43 -5.31 -6.26 -7.29 -8.34 -9.35 -10.4 -11.5 -12.7 -13.9 -15.1 -16.4 -17.7 -19.1 -20.5 -1.26 -1.41 -1.65 -1.95 -2.29 -2.66 -3.07 -3.51 -3.97 -4.41 -4.87 -5.35 -5.86 -6.40 -6.97 -7.56 -8.18 -8.81 -9.45

-1.69 -1.98 -2.47 -3.08 -3.78 -4.56 -5.40 -6.33 -7.29 -8.21 -9.18 -10.2 -11.3 -12.4 -13.6 -14.8 -16.1 -17.4 -18.7 -0.26 -0.46 -0.72 -1.00 -1.31 -1.65 -2.01 -2.41 -2.82 -3.23 -3.66 -4.12 -4.60 -5.10 -5.62 -6.14 -6.67 -7.19 -7.71

-2.01 -2.16 -2.40 -2.70 -3.04 -3.42 -3.83 -4.28 -4.74 -5.17 -5.63 -6.11 -6.62 -7.17 -7.74 -8.34 -8.97 -9.63 -10.3 -3.04 -3.41 -3.99 -4.70 -5.49 -6.36 -7.29 -8.31 -9.35 -10.3 -11.4 -12.5 -13.6 -14.8 -16.1 -17.4 -18.7 -20.1 -21.4

-2.13 -2.64 -3.18 -3.72 -4.28 -4.83 -5.41 -6.00 -6.59 -7.14 -7.71 -8.28 -8.89 -9.51 -10.2 -10.8 -11.6 -12.3 -13.1 -3.40 -4.04 -4.84 -5.72 -6.67 -7.66 -8.72 -9.84 -11.0 -12.1 -13.2 -14.3 -15.6 -16.8 -18.1 -19.5 -20.8 -22.2 -23.6 -0.13 -0.38 -0.64 -0.90 -1.16 -1.44 -1.73 -2.05 -2.38 -2.71 -3.06 -3.44 -3.83 -4.25 -4.67 -5.10 -5.53 -5.95 -6.36

-1.41 -1.78 -2.19 -2.63 -3.09 -3.56 -4.06 -4.59 -5.12 -5.63 -6.15 -6.70 -7.27 -7.87 -8.50 -9.15 -9.82 -10.5 -11.2 -2.32 -2.44 -2.68 -2.99 -3.36 -3.77 -4.22 -4.72 -5.23 -5.72 -6.24 -6.79 -7.37 -7.96 -8.59 -9.23 -9.89 -10.6 -11.2

-0.64 -0.82 -1.04 -1.30 -1.57 -1.86 -2.19 -2.54 -2.92 -3.28 -3.68 -4.10 -4.54 -5.00 -5.47 -5.95 -6.43 -6.91 -7.37 -1.84 -2.09 -2.44 -2.83 -3.27 -3.73 -4.22 -4.75 -5.28 -5.80 -6.33 -6.88 -7.46 -8.07 -8.70 -9.35 -10.0 -10.7 -11.4

-2.82 -3.40 -4.17 -5.05 -6.00 -7.01 -8.07 -9.22 -10.4 -11.5 -12.7 -13.9 -15.1 -16.4 -17.8 -19.1 -20.5 -21.9 -23.3 -0.16 -0.39 -0.63 -0.86 -1.09 -1.32 -1.57 -1.85 -2.14 -2.43 -2.73 -3.07 -3.42 -3.79 -4.17 -4.56 -4.94 -5.32 -5.69 -1.49 -1.95 -2.44 -2.94 -3.46 -3.98 -4.53 -5.1 1 -5.69 -6.25 -6.82 -7.42 -8.04 -8.68 -9.35 -10.0 -10.8 -11.5 -12.2

-2.39 -2.57 -2.86 -3.22 -3.61 -4.05 -4.51 -5.02 -5.55 -6.05 -6.59 -7.14 -7.72 -8.32 -8.95 -9.59 -10.3 -10.9 -f1.6 -2.57 -2.76 -3.04 -3.39 -3.78 -4.21 -4.67 -5.17 -5.68 -6.18 -6.69 -7.23 -7.79 -8.38 -9.00 -9.64 -10.3 -11.0 -11.7

-2.52 -2.64 -2.85 -3.12 -3.44 -3.79 -4.19 -4.62 -5.06 -5.49 -5.95 -6.42 -6.93 -7.46 -8.03 -8.61 -9.22 -9.85 -10.5 -2.52 -2.68 -2.93 -3.24 -3.60 -3.99 -4.42 -4.88 -5.36 -5.82 -6.30 -6.81 -7.34 -7.91 -8.49 -9.11 -9.75 -10.4 -11.1

-2.61 -2.74 -2.97 -3.26 -3.60 -3.98 -4.40 -4.86 -5.33 -5.78 -6.26 -6.76 -7.29 -7.84 -8.43 -9.04 -9.67 -10.3 -11.0 -2.57 -2.72 -2.99 -3.33 -3.71 -4.14 -4.60 -5.10 -5.62 -6.11 -6.63 -7.17 -7.74 -8.33 -8.95 -9.60 -10.3 -11.0 -11.6

-2.52 -2.72 -3.03 -3.40 -3.82 -4.27 -4.75 -5.27 -5.81 -6.31 -6.84 -7.39 -7.96 -8.56 -9.19 -9.85 -10.5 -11.2 -12.0 -2.41 -2.54 -2.78 -3.09 -3.45 -3.85 -4.28 -4.76 -5.25 -5.72 -6.21 -6.72 -7.26 -7.83 -8.43 -9.06 -9.71 -10.4 -11.1 -2.44 -2.61 -2.91 -3.28 -3.70 -4.16 -4.66 -5.20 -5.74 -6.27 -6.82 -7.39 -7.99 -8.61 -9.26 -9.93 -10.6 -11.3 -12.1

-2.44 -2.61 -2.91 -3.27 -3.68 -4.13 -4.62 -5.15 -5.69 -6.20 -6.74 -7.30 -7.89 -8.50 -9.14 -9.80 -10.5 -11.2 -11.9 -2.36 -2.50 -2.76 -3.09 -3.48 -3.91 -4.38 -4.89 -5.41 -5.91 -6.44 -6.99 -7.57 -8.18 -8.81 -9.46 -10.1 -10.8 -11.5

-2.37 -2.50 -2.76 -3.10 -3.49 -3.92 -4.38 -4.89 -5.42 -5.92 -6.44 -6.99 -7.57 -8.17 -8.80 -9.46 -10.1 -10.8 -11.5 -2.32 -2.46 -2.72 -3.05 -3.43 -3.85 -4.30 -4.80 -5.32 -5.81 -6.32 -6.86 -7.42 -8.01 -8.63 -9.28 -9.95 -10.6 -11.3

-2.31 -2.42 -2.67 -3.00 -3.38 -3.82 -4.29 -4.81 -5.34 -5.86 -6.40 -6.97 -7.57 -8.19 -8.83 -9.50 -10.2 -10.9 -11.6 -0.43 -0.64 -0.87 -1.11 -1.37 -1.64 -1.94 -2.27 -2.61 -2.94 -3.30 -3.69 -4.10 -4.53 -4.96 -5.41 -5.85 -6.29 -6.72

-3.94 -4.08 -4.34 -4.68 -5.07 -5.51 -5.98 -6.50 -7.04 -7.55 -8.09 -8.66 -9.25 -9.87 -10.5 -11.2 -11.9 -12.6 -13.3 -6.26 -6.73 -7.45 -8.31 -9.26 -10.3 -11.4 -12.6 -13.8 -15.0 -16.2 -17.4 -18.8 -20.1 -21.5 -22.9 -24.4 -25.8 -27.2 -0.02 -0.28 -0.55 -0.82 -1.09 -1.36 -1.65 -1.97 -2.30 -2.63 -2.97 -3.35 -3.74 -4.15 -4.57 -4.99 -5.42 -5.83 -6.24

-2.54 -2.85 -3.22 -3.62 -4.04 -4.49 -4.96 -5.48 -6.00 -6.49 -7.01 -7.55 -8.12 -8.73 -9.36 -10.0 -10.7 -11.4 -12.1 -3.97 -4.86 -5.82 -6.80 -7.80 -8.82 -9.88 -11.0 -12.1 -13.2 -14.3 -15.4 -16.6 -17.8 -19.1 -20.3 -21.6 -22.9 -24.2 -1.54 -2.21 -2.98 -3.80 -4.63 -5.48 -6.34 -7.23 -8.10 -8.93 -9.77 -10.6 -11.5 -12.3 -13.2 -14.1 -15.1 -16.0 -17.0 -1.57 -2.07 -2.58 -3.10 -3.61 -4.13 -4.67 -5.24 -5.82 -6.37 -6.94 -7.53 -8.16 -8.81 -9.48 -10.2 -10.9 -11.6 -12.3 -2.75 -3.21 -3.80 -4.46 -5.17 -5.90 -6.66 -7.45 -8.25 -9.00 -9.77 -10.6 -11.4 -12.2 -13.0 -13.9 -14.8 -15.7 -16.6 -5.10 -6.12 -7.42 -8.87 -10.4 -12.0 -13.6 -15.3 -17.0 -18.7 -20.3 -22.0 -23.7 -25.5 -27.2 -29.1 -30.9 -32.8 -34.7 -2.59 -2.79 -3.14 -3.57 -4.07 -4.60 -5.17 -5.78 -6.40 -6.99 -7.61 -8.24 -8.90 -9.59 -10.3 -11.0 -11.8 -12.6 -13.3

-4.57 -5.07 -5.88 -6.87 -7.97 -9.15 -10.4 -11.8 -13.1 -14.4 -15.8 -17.2 -18.6 -20.1 -21.7 -23.2 -24.8 -26.4 -28.0 -0.30 -0.64 -1.01 -1.39 -1.78 -2.18 -2.59 -3.04 -3.49 -3.93 -4.40 -4.88 -5.38 -5.90 -6.42 -6.95 -7.47 -7.99 -8.49

metal-organic complexes in geochemical processes: temperature dependence of the standard...

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