Environmental Earth Sciences

, Volume 59, Issue 7, pp 1601–1606 | Cite as

Erratum to: Prediction of the thermodynamic properties of metal–arsenate and metal–arsenite aqueous complexes to high temperatures and pressures and some geological consequences

Erratum

Erratum to: Environ Geol (2007) 52:1343–1363 DOI 10.1007/s00254-006-0578-5

Marini and Accornero (2007) evaluated the standard thermodynamic properties (\( \Updelta G_{\text{f}}^{\text{o}} \), \( \Updelta H_{\text{f}}^{\text{o}} \), So, \( C_{\text{P}}^{\text{o}} \), Vo, ω) of several aqueous complexes formed by dissolved metals and dihydrogenarsenate, monohydrogenarsenate, arsenate and dihydrogenarsenite ions at reference pressure, Pr = 1 bar, and reference temperature, Tr = 298.15 K, as well as the pressure- and temperature-independent coefficients of the revised Helgeson–Kirkham–Flowers (HKF) equations of state a1,ML, a2,ML, a3,ML, a4,ML, c1,ML, and c2,ML, where the subscript ML identifies a generic aqueous complex formed by metal M and ligand L.

Unfortunately, we recently realized that there is a wrong sign in the Eq. 37 of Sverjensky et al. (1997), corresponding to Eq. 48 of Marini and Accornero (2007), which was used to calculate the EOS coefficient c1,ML. In the correct equation:
$$ c_{{1,{\text{ML}}}} = 0.6087 \cdot C_{{P,{\text{ML,Pr,Tr}}}}^{\text{o}} - \omega_{\text{ML,Pr,Tr}} \cdot 298.15 \cdot X_{\text{Pr,Tr}} + 5.85 $$
(1)
the term containing the solvent Born function X must have a negative sign. This is easy inferable by solving the HKF equation of state (see Marini and Accornero 2007 for the explanation of symbols):
$$ C_{{P,{\text{ML,Pr,T}}}}^{\text{o}} = \omega_{\text{ML}} \cdot T \cdot X + 2 \cdot T \cdot Y\left( {{\frac{{\partial \omega_{\text{ML}} }}{\partial T}}} \right)_{P} - T\left( {{\frac{1}{\varepsilon }} - 1} \right) \cdot \left( {{\frac{{\partial^{2} \omega_{\text{ML}} }}{{\partial T^{2} }}}} \right)_{P} + c_{{1,{\text{ML}}}} + {\frac{{c_{{2,{\text{ML}}}} }}{{(T - \Uptheta )^{2} }}} , $$
(2)
for T = Tr and rearranging it as follows:
$$ c_{{1,{\text{ML}}}} = C_{{P,{\text{ML,Pr,}}T}}^{\text{o}} - \omega_{\rm ML} \cdot 298.15 \cdot X_{\text{Pr,Tr}} - {\frac{{c_{{2,{\text{ML}}}} }}{{(298.15 - \Uptheta )^{2} }}} . $$
(3)

The wrong values obtained by Marini and Accornero (2007) for the EOS coefficient c1,ML determine increasingly large errors in the thermodynamic properties of the aqueous complexes of interest at temperatures increasingly different from Tr and, consequently, in the log K of their destruction reactions.

To compute the correct values of the EOS coefficient c1,ML, Eq. 3 was used, in which the value of c2,ML is given by (Sverjensky et al. 1997):
$$ c_{{2,{\text{ML}}}} = 2037 \cdot C_{{P,{\text{ML,Pr,Tr}}}}^{\text{o}} - 30460 . $$
(4)
The calculated values of the EOS coefficient c1,ML are reported in Table 1, together with all other estimated standard partial molal thermodynamic properties, at Pr, Tr, for the metal–arsenate and metal–arsenite complexes of interest as well as the equation-of-state parameters for calculating the corresponding properties at high temperatures and pressures. In addition to the new values of the EOS coefficient c1,ML, little modifications in the \( \Updelta H_{\text{f}}^{\text{o}} \) and So of the complexes MgAsO4, CaAsO4, MnAsO4, AlAsO4o, and FeAsO4o were introduced.
Table 1

Estimated standard partial molal thermodynamic properties of metal–arsenate and metal–arsenite complexes at 25°C, 1 bar and estimated equation-of-state parameters for calculation of the corresponding properties at high temperatures and pressures

Complex

\( \Updelta G_{f}^{o}\,({\text {cal}}\; {\text{mol}}^{-1})\)

\( \Updelta H_{f}^{o} \, ({\text {cal}}\; {\text{mol}}^{-1}) \)

S° (cal mol−1 K−1)

CP° (cal mol−1 K−1)

V° (cm3 mol−1)

a1 × 10 (cal mol−1 bar−1)

a2 × 10−2 (cal mol−1)

a3 (cal K mol−1 bar−1)

a4 × 10−4 (cal K mol−1)

c1 (cal mol−1 K−1)

c2 × 10−4 (cal K mol−1)

ω × 10−5 (cal mol−1)

NaH2AsO4°

−240179

−272608

41.2

37.8

41.1

7.3772

10.2353

1.1421

−3.2022

27.9202

4.6622

−0.0380

KH2AsO4°

−244935

−274352

54.5

21.9

52.4

8.9277

14.0226

−0.4840

−3.3587

18.6125

1.4173

−0.0380

MgH2AsO4+

−290910

−332717

−10.4

50.7

18.3

4.5105

3.2335

4.1483

−2.9127

42.2650

7.2899

0.7009

CaH2AsO4+

−314170

−348007

18.5

45.8

22.2

4.8949

4.1724

3.7452

−2.9515

35.3597

6.2862

0.2639

SrH2AsO4+

−315896

−347841

27.3

40.1

22.9

4.9488

4.3041

3.6887

−2.9570

30.8142

5.1312

0.1301

MnH2AsO4+

−236482

−270828

14.5

53.5

23.3

5.0617

4.5799

3.5702

−2.9684

40.4264

7.8583

0.3244

FeH2AsO4+

−205693

−243719

1.0

44.9

17.6

4.3531

2.8490

4.3134

−2.8968

37.3097

6.1166

0.5283

CoH2AsO4+

−193388

−232357

−1.5

45.2

13.9

3.8628

1.6516

4.8275

−2.8473

37.7921

6.1625

0.5664

NiH2AsO4+

−193146

−233785

−7.1

36.4

10.0

3.3580

0.4185

5.3569

−2.7963

33.4496

4.3750

0.6516

CuH2AsO4+

−166866

−204382

4.1

49.9

14.9

3.9712

1.9164

4.7138

−2.8583

39.7683

7.1249

0.4813

ZnH2AsO4+

−215927

−255372

−0.3

50.7

15.3

4.0397

2.0836

4.6420

−2.8652

40.8741

7.2945

0.5485

PbH2AsO4+

−187896

−215577

44.7

34.1

25.0

5.1359

4.7611

3.4924

−2.9759

24.9084

3.9167

−0.1328

AlH2AsO42+

−299978

−350717

−57.0

34.9

−7.1

1.4490

−4.2440

7.3587

−2.6036

44.5413

4.0694

1.9507

FeH2AsO42+

−189949

−235535

−39.9

66.2

1.1

2.4901

−1.7013

6.2670

−2.7087

60.4374

10.4402

1.6926

NaHAsO4

−234026

−272938

19.4

11.0

16.4

4.4640

3.1200

4.1970

−2.9080

24.8601

−0.7900

1.3274

KHAsO4

−238754

−275247

30.7

3.9

26.1

5.7282

6.2078

2.8713

−3.0357

19.1455

−2.2322

1.1561

MgHAsO4°

−282655

−326456

−17.1

−3.4

−0.5

1.6885

−3.6591

7.1076

−2.6278

3.8675

−3.7233

−0.0380

CaHAsO4°

−306038

−344341

3.5

−5.6

2.0

2.0228

−2.8426

6.7570

−2.6615

2.5879

−4.1694

−0.0380

SrHAsO4°

−307750

−344917

9.8

−8.1

2.4

2.0851

−2.6905

6.6917

−2.6678

1.1155

−4.6827

−0.0380

MnHAsO4°

−229564

−268033

0.7

−2.1

2.7

2.1148

−2.6180

6.6606

−2.6708

4.5920

−3.4707

−0.0380

FeHAsO4°

−196961

−237958

−8.9

−5.9

−0.9

1.6263

−3.8112

7.1729

−2.6215

2.3717

−4.2448

−0.0380

CoHAsO4°

−187516

−229240

−10.7

−5.8

−3.2

1.3102

−4.5832

7.5044

−2.5896

2.4302

−4.2244

−0.0380

NiHAsO4°

−185083

−227995

−14.7

−9.7

−5.7

0.9749

−5.4021

7.8559

−2.5557

0.1514

−5.0188

−0.0380

CuHAsO4°

−160044

−200797

−6.7

−3.7

−2.6

1.3964

−4.3727

7.4140

−2.5983

3.6572

−3.7966

−0.0380

ZnHAsO4°

−209827

−252128

−9.9

−3.4

−2.4

1.4251

−4.3025

7.3838

−2.6012

3.8733

−3.7213

−0.0380

PbHAsO4°

−180119

−214509

22.2

−10.7

3.7

2.2585

−2.2670

6.5099

−2.6853

−0.4328

−5.2225

−0.0380

AlHAsO4+

−295884

−343378

−46.1

−37.3

−8.2

1.0572

−5.2011

7.7696

−2.5640

−4.1613

−10.6336

1.2420

FeHAsO4+

−188188

−232211

−34.7

−23.405

−4.91

1.4545

−4.2306

7.3530

−2.6042

2.3700

−7.8022

1.0694

NaAsO42−

−223700

−253943

48.5

−38.4

−17.0

0.2824

−7.0935

8.5822

−2.4858

6.8433

−10.8648

2.5085

KAsO42−

−228428

−249049

84.0

−45.5

−9.6

1.1121

−5.0669

7.7120

−2.5696

−2.2416

−12.3070

1.9714

MgAsO4

−271474

−307316

9.64

−55.0

−26.0

−1.2915

−10.9377

10.2326

−2.3269

−12.3300

−14.2311

1.4754

CaAsO4

−294913

−323114

37.4

−57.2

−25.5

−1.3678

−11.1242

10.3127

−2.3192

−17.4821

−14.6772

1.0550

SrAsO4

−296243

−323239

43.9

−59.7

−25.4

−1.3889

−11.1758

10.3349

−2.3170

−19.8655

−15.1905

0.9562

MnAsO4

−218289

−247805

30.7

−53.7

−25.4

−1.3158

−10.9970

10.2581

−2.3244

−14.5434

−13.9785

1.1565

FeAsO4

−186668

−218541

21.7

−57.5

−26.1

−1.3653

−11.1181

10.3101

−2.3194

−15.5040

−14.7525

1.2932

CoAsO4

−177190

−210481

17.6

−57.4

−26.5

−1.4073

−11.2205

10.3541

−2.3152

−14.8722

−14.7322

1.3555

NiAsO4

−176304

−211320

11.8

−61.3

−27.0

−1.4432

−11.3083

10.3918

−2.3116

−16.3404

−15.5266

1.4434

CuAsO4

−151743

−183607

23.1

−55.3

−26.4

−1.4178

−11.2463

10.3651

−2.3141

−14.4180

−14.3044

1.2716

ZnAsO4

−200121

−233853

18.9

−55.0

−26.36

−1.3907

−11.1799

10.3366

−2.3169

−13.6104

−14.2290

1.3358

PbAsO4

−169793

−194437

54.9

−62.3

−25.16

−1.4108

−11.2291

10.3577

−2.3148

−22.9414

−15.7303

0.7904

AlAsO4°

−285558

−330011

−35.9

−60.2

−9.75

0.4180

−6.7624

8.4400

−2.4995

−29.3427

−15.3014

−0.0380

FeAsO4°

−177862

−218546

−23.5

−84.8

−13.09

−0.0391

−7.8787

8.9193

−2.4533

−43.7161

−20.3124

−0.0380

NaH2AsO3°

−203270

−228832

39.7

28.4

32.7

6.2236

7.4178

2.3518

−3.0857

22.4338

2.7495

−0.0380

AgH2AsO3°

−123526

−147071

44.3

25.8

33.0

6.2709

7.5332

2.3022

−3.0905

20.9088

2.2178

−0.0380

MgH2AsO3+

−251410

−286183

−11.3

41.3

9.9

3.3617

0.4276

5.3530

−2.7967

36.9078

5.3772

0.7149

CaH2AsO3+

−274922

−301872

17.1

36.4

13.8

3.7486

1.3726

4.9473

−2.8358

30.0706

4.3735

0.2853

SrH2AsO3+

−275601

−300702

25.8

30.7

14.5

3.8032

1.5060

4.8900

−2.8413

25.5459

3.2185

0.1538

BaH2AsO3+

−276315

−297936

40.1

25.6

19.9

4.4634

3.1185

4.1977

−2.9080

20.5926

2.1872

−0.0628

CuH2AsO3+

−134368

−164924

3.0

40.5

6.5

2.8237

−0.8865

5.9172

−2.7424

34.4453

5.2122

0.4990

PbH2AsO3+

−153138

−174063

42.8

24.7

16.5

3.9918

1.9667

4.6922

−2.8603

19.6811

2.0039

−0.1047

AlH2AsO32+

−266611

−309612

−55.5

25.5

−15.6

0.2881

−7.0796

8.5762

−2.4864

38.8545

2.1567

1.9289

FeH2AsO32+

−154392

−192413

−39.1

56.8

−7.3

1.3321

−4.5296

7.4814

−2.5918

54.8314

8.5274

1.6796

The SUPCRT-generated logarithms of the thermodynamic constants of the reactions of destruction (consistent with the requirements of the software package EQ3/6) for all the considered aqueous complexes, at 1.013 bar and 0.01, 25, 60, 100°C and at saturation pressure and 150, 200, 250 and 300°C, are listed in Table 2.
Table 2

Logarithms of thermodynamic constants of the reactions of destruction (as required by the software package EQ3/6) of the aqueous complexes containing arsenate and arsenite ions at 1.013 bar and 0.01, 25, 60, 100°C and at saturation pressure and 150, 200, 250 and 300°C

Complex T(°C)

0.01

25

60

100

150

200

250

300

NaH2AsO4°

1.8911

1.7753

1.5746

1.3381

1.0408

0.7263

0.3609

−0.1285

KH2AsO4°

2.0939

1.8948

1.6188

1.3247

0.9791

0.6336

0.2515

−0.2405

MgH2AsO4+

−2.0823

−1.7555

−1.5109

−1.3987

−1.4183

−1.5750

−1.8676

−2.3445

CaH2AsO4+

−1.6054

−1.4953

−1.4931

−1.6081

−1.8662

−2.2289

−2.7076

−3.3615

SrH2AsO4+

−0.8157

−0.8254

−0.9536

−1.1756

−1.5231

−1.9423

−2.4564

−3.1350

MnH2AsO4+

−1.1024

−1.0057

−1.0288

−1.1704

−1.4554

−1.8397

−2.3362

−3.0039

FeH2AsO4+

−3.1387

−2.7950

−2.5235

−2.3856

−2.3830

−2.5271

−2.8156

−3.2959

CoH2AsO4+

−0.4066

−0.2771

−0.2519

−0.3392

−0.5585

−0.8781

−1.3089

−1.9068

NiH2AsO4+

−1.9243

−1.6390

−1.4238

−1.3272

−1.3545

−1.5123

−1.8031

−2.2769

CuH2AsO4+

−2.0928

−1.8552

−1.7041

−1.6723

−1.7697

−1.9895

−2.3379

−2.8673

ZnH2AsO4+

−0.6738

−0.5256

−0.4867

−0.5648

−0.7764

−1.0900

−1.5155

−2.1087

PbH2AsO4+

−1.5392

−1.5950

−1.7688

−2.0265

−2.4056

−2.8506

−3.3929

−4.1134

AlH2AsO42+

−3.6996

−3.1952

−2.7692

−2.5203

−2.4408

−2.5506

−2.8307

−3.3191

FeH2AsO42+

−4.7729

−4.2654

−3.8790

−3.7014

−3.7268

−3.9484

−4.3419

−4.9412

NaHAsO4

6.4042

6.2855

6.1432

6.0208

5.9138

5.8400

5.7834

5.7293

KHAsO4

6.5807

6.4255

6.2413

6.0729

5.9074

5.7738

5.6561

5.5387

MgHAsO4°

4.4413

4.2954

4.1210

3.9578

3.7683

3.5483

3.2417

2.7585

CaHAsO4°

4.6511

4.4655

4.2456

4.0314

3.7781

3.4977

3.1370

2.6054

SrHAsO4°

5.3989

5.1457

4.8481

4.5692

4.2636

3.9546

3.5832

3.0543

MnHAsO4°

4.2110

4.0653

3.8910

3.7235

3.5233

3.2902

2.9703

2.4738

FeHAsO4°

3.6994

3.6057

3.4911

3.3780

3.2308

3.0385

2.7505

2.2795

CoHAsO4°

4.1574

4.0271

3.8706

3.7190

3.5332

3.3093

2.9942

2.4994

NiHAsO4°

4.4199

4.2712

4.0936

3.9226

3.7174

3.4776

3.1491

2.6430

CuHAsO4°

3.2018

3.1453

3.0815

3.0242

2.9430

2.8122

2.5811

2.1629

ZnHAsO4°

4.0677

3.9458

3.7982

3.6578

3.4885

3.2835

2.9889

2.5154

PbHAsO4°

4.2770

4.1056

3.9019

3.7089

3.4889

3.2490

2.9358

2.4578

AlHAsO4+

−0.1355

−0.1942

−0.2499

−0.2963

−0.3667

−0.4902

−0.7164

−1.1323

FeHAsO4+

−3.1723

−2.9745

−2.7389

−2.5187

−2.3236

−2.2341

−2.2842

−2.5488

NaAsO42−

15.2959

13.8545

12.3070

11.0077

9.8650

9.0982

8.6152

8.3961

KAsO42−

15.9563

13.9946

11.8493

9.9950

8.2866

7.0479

6.1503

5.5400

MgAsO4

13.9719

12.4912

10.9025

9.5600

8.3426

7.4506

6.7551

6.1685

CaAsO4

14.2801

12.6202

10.8258

9.2842

7.8502

6.7640

5.8852

5.1099

SrAsO4

15.3375

13.5804

11.6743

10.0363

8.5174

7.3736

6.4551

5.6483

MnAsO4

13.8821

12.3299

10.6592

9.2359

7.9273

6.9486

6.1646

5.4783

FeAsO4

12.5967

11.1505

9.6014

8.2896

7.0926

6.2054

5.5017

4.8926

CoAsO4

13.0352

11.5962

10.0553

8.7512

7.5622

6.6823

5.9861

5.3868

NiAsO4

12.0239

10.7063

9.3049

8.1283

7.0660

6.2882

5.6784

5.1566

CuAsO4

10.4895

9.2300

7.9034

6.8041

5.8271

5.1223

4.5724

4.0949

ZnAsO4

12.4594

11.0603

9.5648

8.3049

7.1645

6.3281

5.6713

5.1075

PbAsO4

13.2428

11.6746

9.9854

8.5451

7.2187

6.2228

5.4162

4.6855

AlAsO4°

8.3525

7.3748

6.3161

5.3948

4.4910

3.7140

2.9406

2.0425

FeAsO4°

5.3733

4.5945

3.8490

3.2941

2.8374

2.4877

2.1196

1.6021

NaH2AsO3°

−0.3201

−0.2502

−0.2380

−0.2707

−0.3540

−0.4891

−0.7051

−1.0748

AgH2AsO3°

−1.3155

−1.1840

−1.0977

−1.0644

−1.0864

−1.1757

−1.3543

−1.6893

MgH2AsO3+

−2.2085

−1.8818

−1.6375

−1.5163

−1.5133

−1.6411

−1.9056

−2.3626

CaH2AsO3+

−1.9433

−1.8063

−1.7736

−1.8513

−2.0588

−2.3705

−2.8024

−3.4201

SrH2AsO3+

−0.3179

−0.3689

−0.5449

−0.8012

−1.1685

−1.5919

−2.1040

−2.7826

BaH2AsO3+

−1.3798

−1.4274

−1.5929

−1.8400

−2.2036

−2.6319

−3.1584

−3.8662

CuH2AsO3+

−7.8251

−7.1140

−6.4194

−5.8821

−5.4680

−5.2734

−5.2815

−5.5329

PbH2AsO3+

−5.4793

−5.1972

−4.9832

−4.8774

−4.8847

−5.0251

−5.3150

−5.8279

AlH2AsO32+

−8.6846

−7.8170

−6.9742

−6.3355

−5.8591

−5.6460

−5.6612

−5.9349

FeH2AsO32+

−8.0194

−7.2819

−6.6317

−6.2040

−5.9700

−5.9767

−6.1925

−6.6491

The reactions of destruction of the aqueous complexes are as follows:

\( \begin{aligned} {\text{MH}}_{ 2} {\text{AsO}}_{ 4}^{{( {{\text{n}} - 1} ) + }} = {\text{ M}}^{{{\text{n}} + }} + {\text{ H}}_{ 2} {\text{AsO}}_{ 4}^{ - } \\ \end{aligned} \)

\( \begin{aligned} {\text{MHAsO}}_{ 4}^{{( {{\text{n}} - 2} ) + }} + {\text{ H}}^{ + } = {\text{ M}}^{{{\text{n}} + }} + {\text{ H}}_{ 2} {\text{AsO}}_{ 4}^{ - } \\ \end{aligned} \)

\( \begin{aligned} {\text{MAsO}}_{ 4}^{{\left( {{\text{n}} - 3} \right) + }} + {\text{ 2H}}^{ + } = {\text{ M}}^{{{\text{n}} + }} + {\text{ H}}_{ 2} {\text{AsO}}_{ 4}^{ - } \\ \end{aligned} \)

\( \begin{aligned} {\text{MH}}_{ 2} {\text{AsO}}_{ 3}^{{( {{\text{n}} - 1}) + }} = {\text{ M}}^{{{\text{n}} + }} + {\text{ H}}_{ 2} {\text{AsO}}_{ 3}^{ - } \\ \end{aligned} \)

All the data reported in Tables 1 and 2 are also given in the electronic supplementary material 1 (which is a patch for supcrt) and electronic supplementary material 2 (which is a patch for eq3/6).

Supplementary material

12665_2009_369_MOESM1_ESM.dat (50 kb)
Supplementary Table 1 (DAT 50 kb)
12665_2009_369_MOESM2_ESM.dat (15 kb)
Supplementary Table 2 (DAT 15 kb)

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Laboratory of Geochemistry, Dip. Te. RisUniversity of GenovaGenovaItaly
  2. 2.D’Appolonia SpAGenovaItaly

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