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Chapter: 3 Chemistry
    Section: 3.9 Electrochemistry
        SubSection: 3.9.6 Activity coefficients

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3.9.6 Activity coefficients

Activity coefficients of some strong electrolytes in aqueous solution at 25 °C

The mean ionic activity coefficient γ± of an electrolyte, consisting of v+ cations R and v anions X, is related to the chemical potential μ of one mole of electrolyte by

    μ = μθ + v+RT ln mR + vRT ln mX + (v+ + v)RT ln γ±

where mR and mX denote the molalities of the cation R and anion X respectively while μ is independent of the composition of the solution and is chosen so that γ±→ 1 at infinite dilution.

In the following table of γ± for some typical 1–1 electrolytes at 25°C the values at molalities 0.1 upwards have been interpolated by a Debye–Hückel type of formula. All γ± values are considered to be accurate to within ±0.002.

Some 1-1 electrolytes at 25 °C

m/(mol kg - 1)

HCl

LiCl

NaCl

KCl

CsCl

LiNO3

NaNO3

KNO3

CsNO3

 

 

 

 

 

 

 

 

 

 

0.01     .    .    .

0.904

0.903

0.902

0.901

0.899

0.903

0.900

0.897

0.896

0.02     .    .    .

0.875

0.873

0.870

0.868

0.865

0.872

0.866

0.861

0.860

0.05     .    .    .

0.830

0.825

0.820

0.816

0.807

0.825

0.811

0.799

0.795

0.10     .    .    .

0.796

0.790

0.778

0.770

0.756

0.788

0.762

0.739

0.733

0.2        .    .    .

0.767

0.757

0.735

0.718

0.694

0.752

0.703

0.663

0.655

0.4       .    .    .

0.755

0.740

0.693

0.666

0.628

0.728

0.638

0.576

0.561

0.6       .    .    .

0.763

0.743

0.673

0.637

0.589

0.727

0.599

0.519

0.501

0.8       .    .    .

0.783

0.755

0.662

0.618

0.563

0.733

0.570

0.476

0.458

1.0       .    .    .

0.809

0.774

0.657

0.604

0.544

0.743

0.548

0.443

0.422

1.2       .    .    .

0.840

0.796

0.654

0.593

0.529

0.757

0.530

0.414

0.393

1.4       .    .    .

0.876

0.823

0.655

0.586

0.518

0.774

0.514

0.390

0.368

1.6       .    .    .

0.916

0.853

0.657

0.580

0.509

0.792

0.501

0.369

 

1.8       .    .    .

0.960

0.885

0.662

0.576

0.501

0.812

0.489

0.350

 

2.0       .    .    .

1.009

0.921

0.668

0.573

0.495

0.835

0.478

0.333

 

2.5       .    .    .

1.147

1.026

0.688

0.569

0.484

0.896

0.455

0.297

 

3.0       .    .    .

1.316

1.156

0.714

0.569

0.478

0.966

0.437

0.269

 

3.5       .    .    .

1.518

1.317

0.746

0.572

0.474

1.044

0.422

0.246

 

4.0       .    .    .

1.762

1.510

0.783

0.577

0.473

1.125

0.408

 

 

4.5       .    .    .

2.04  

1.741

0.826

0.583

0.473

1.215

0.396

 

5.0       .    .    .

2.38  

2.02  

0.874

 

0.474

1.310

0.386

 

 

 

 

 

 

 

 

 

 

 

 

The values of γ for typical 2–1 and 1–2 electrolytes in the following table are from Hamer and Wu (1972). They are principally derived from experimental values of relative water vapour pressures by use of the Gibbs–Duhem relation.


Some 21 and 12 electrolytes at 25 °C

m/(mol kg−1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

 

 

 

 

 

 

 

 

 

 

 

MgCl2   .    .

0.535

0.494

0.481

0.480

0.485

0.496

0.511

0.530

0.552

0.577

CaCl2    .    .

0.517

0.469

0.451

0.442

0.444

0.449

0.456

0.467

0.480

0.496

SrCl2     .    .

0.510

0.459

0.438

0.428

0.425

0.426

0.430

0.437

0.445

0.456

BaCl2    .    .

0.492

0.436

0.412

0.398

0.391

0.388

0.387

0.388

0.390

0.393

MnCl2    .   .   .

0.511

0.464

0.445

0.438

0.436

0.440

0.445

0.453

0.464

0.476

FeCl2     .   .   .

0.509

0.463

0.446

0.441

0.443

0.449

0.458

0.470

0.484

0.500

ZnCl2     .   .   .

0.499

0.447

0.419

0.400

0.384

0.371

0.359

0.348

0.339

0.330

CoCl2    .   .   .

0.529

0.483

0.467

0.463

0.465

0.472

0.482

0.496

0.513

0.532

NiCl2     .   .   .

0.527

0.482

0.466

0.462

0.465

0.473

0.484

0.499

0.517

0.538

CuCl2    .   .   .

0.495

0.441

0.418

0.407

0.407

0.398

0.398

0.399

0.402

0.405

MgBr2   .   .   .

0.540

0.512

0.511

0.522

0.540

0.565

0.595

0.629

0.669

0.715

CaBr2    .   .   .

0.540

0.502

0.491

0.492

0.500

0.513

0.530

0.551

0.576

0.604

SrBr2     .   .   .

0.535

0.492

0.477

0.473

0.476

0.483

0.494

0.508

0.525

0.545

BaBr2    .   .   .

0.512

0.463

0.444

0.437

0.436

0.438

0.443

0.451

0.460

0.471

Mg(NO3)2   .

0.526

0.484

0.470

0.467

0.471

0.479

0.491

0.508

0.521

0.540

Ca(NO3)2    .

0.494

0.433

0.402

0.382

0.369

0.359

0.352

0.348

0.344

0.342

Sr(NO3)2     .

0.482

0.414

0.376

0.350

0.331

0.316

0.304

0.294

0.285

0.278

Co(NO3)2   .

0.515

0.469

0.452

0.445

0.446

0.450

0.457

0.467

0.478

0.492

Cu(NO3)2   .

0.516

0.466

0.445

0.435

0.431

0.431

0.434

0.440

0.447

0.456

Li2SO4     .    .

0.469

0.400

0.364

0.341

0.325

0.312

0.303

0.296

0.289

0.285

Na2SO4   .    .

0.446

0.366

0.321

0.291

0.268

0.251

0.236

0.224

0.213

0.204

K2SO4     .    .

0.424

0.343

0.300

0.272

0.251

0.236

0.224

Rb2SO4   .    .

0.443

0.365

0.323

0.295

0.274

0.258

0.245

0.234

0.225

0.217

Cs2SO4   .    .

0.444

0.369

0.329

0.304

0.285

0.270

0.259

0.249

0.241

0.234

H2SO4     .    .

0.251

0.195

0.171

0.156

0.147

0.140

0.135

0.130

0.127

0.125

 

 

 

 

 

 

 

 

 

 

 


Values are compiled from NIST (formerly NBS) tabulations of Goldberg et al. (1977, 1978, 1979a, 1979b, 1981) and the computer compilation GAMPHI (Goldberg, 1985). Experimental values have also been compiled by Lobo (1989).

References

R. N. Goldberg and R. L. Nuttall (1977) J. Phys. Chem. Ref. Data, 6, 385.
R. N. Goldberg and R. L. Nuttall (1978) J. Phys. Chem. Ref. Data, 7, 263.
R. N. Goldberg, R. L. Nuttall and B. R. Staples (1979a) J. Phys. Chem. Ref. Data, 8, 923.
R. N. Goldberg (1979b) J. Phys. Chem. Ref. Data, 8, 1005.
R. N. Goldberg (1981) J. Phys. Chem. Ref. Data, 10, 1.
R. N. Goldberg (1985) GAMPHI—a Database of Activity and Osmotic Coefficients for Aqueous Electrolyte Solutions, NBS Technical Note 1206.
W. J. Hamer and Y.-C. Wu (1972) J. Phys. Chem. Ref. Data, 1, 1047.
V. M. M. Lobo (1989) Handbook of Electrolyte Solutions, Parts A & B, Elsevier, Amsterdam.

A.K. Covington

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