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McGRAW.HILL INTERNATIONAL SERIES
IN THE EARTH AND PLANETARY SCIENCES
FRANK PRESS, Consulting Editor
EDITORIAL BOARD
Kenneth O. Emery, Woods Hole Oceonographic Institution
Albert E. J. Engel, University of California, San Diego
Konrad Krauskopf, Stanford University
Bruce Murray, California Institute of Technology
Raymond Siever, Harvard University
Ex officio members
Sverre Petterssen, emeritus—University of Chicago
AGER • Principles of Poleoecology
BROECKER and OVERSBY • Chemical Equilibria in the Earth
DE SITTER • Structural Geology
EWING, JARDETZKY, and PRESS • Elastic Waves in Layered Media
GRANT and WEST • Interpretation Theory In Applied Geophysics
GRIFFITHS • Scientific Method in Analysis of Sediments
GRIM • Applied Clay Mineralogy
GRIM • Cloy Mineralogy
HEISKANEN and VENING MEINESZ • The Earth and Its Gravity Field
HOWELL • Introduction to Geophysics
JACOBS, RUSSELL, and WILSON • Physics and Geology
KRAUSKOPF • Introduction to Geochemistry
KRUMBEIN and GRAYBILL • An Introduction to Statistical Models in Geology
LEG GET • Geology and Engineering
MENARD • Marine Geology of the Pacific
MILLER • Photogeology
OFFICER • Introduction to the Theory of Sound Transmission
RAMSAY • Folding and Fracturing of Rocks
SHAW • Time in Stratigraphy
SHROCK and TWENHOFEL • Principles of Invertebrate Paleontology
TURNER • Metomorphic Petrology
TURNER and VERHOOGEN • Igneous and Metomorphic Petrology
TURNER and WEISS • Structural Analysis of Metomorphic Tectonites
WHITE • Seismic Waves: Radiation, Transmission, and Attenuation
C H E M I C A L E Q U I L I B R I A I N T H E E A RT H
Wallace S. Broecker
Professor of Geology
Lamont Doherty Geological Observatory
of Columbia University
Virginia M. Oversby
Research Fellow, Department of Geophysics and Geochemistry
Research School of Physical Sciences
The Australian National University
McGraw-Hill Book Company
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Chemical Equilibria in the Earth
Copyright © 1971 by McGraw-Hill, Inc. All rights
reserved. Printed In the United States of America.
No part of this publication may be reproduced, stored in
a retrieval system, or transmitted, in any form or by any
means, electronic, mechanical, photocopying, record
ing, or otherwise, without the prior written permission
of the publisher.
Library of Congress Catalog Card Number 79-109246
07997
1234567890 M AM M 79876543210
This book was set in Modern by The Maple Press Com
pany, and printed on permanent paper and bound by
The Maple Press Company. The designer was Merrill
Haber; the drawings were done by B. Handelman Asso
ciates, Inc. The editors were Bradford Bayne and
James W. Bradley. Peter D. Guilmette supervised
production.
P r e f a c e
Applications of thermodynamic and kinetic arguments to chemical sys
tems in the earth sciences have become so widespread that no graduate
student can consider himself equipped for future professional work unless
he is able to understand them. This book is intended to be an introduc
tion to the subject within the grasp of the average undergraduate science
major.
The first five chapters provide an introduction to thermodynamic
logic, both from the macroscopic and atomic points of view. It is our
impression that the usual development of the subject is sufficiently
abstract to force all but the best student to a recipe approach when
attempting to apply his knowledge. It is our hope that our more direct
development will help to overcome this difl&culty. However, we cer
tainly do not wish to pass off our treatment as a substitute for a standard
thermodynamics text. Our coverage is clearly more limited and its
development considerably less rigorous. For students who plan to go
further into the subject, exposure to a standard thermodynamics text
is an absolute necessity. Since thermodynamics is one of those subjects
learned only by repetitive exposure, most students will find our intro-
V
vi PREFACE
duction to the subject a worthwhile supplement to other training in this
area. In any case, these five chapters provide the theory needed to
treat most of the applications we deem important.
The remaining seven chapters deal with the most common types of
chemical reactions encountered in the earth sciences. In each case at
least one common process taking place within our solar system is treated
as an example. Both equilibrium and kinetic aspects are considered.
Problems at the end of each chapter are designed both to "cement" the
understanding of the material covered and to broaden the scope of
application to earth phenomena.
Although our book is designed for a one-semester course, the course
could easily be expanded to a full year by using the supplementary read
ings given at the end of each chapter in conjunction with current journal
articles. (In the supplementary readings, as well as in the problems
sections, items of more than average complexity are marked with an
asterisk.) Our intent was to present the bare bones of the subject—not
to review the successes and failures of attempts to apply this approach
to furthering our knowledge of earth processes and earth history.
We have received the assistance of many people during the prepara
tion of the manuscript, people without whose assistance the work would
never have been finished. G. D. Garlick, H. Greenwood, P. W. Gast,
and many others made helpful suggestions on how the manuscript could
be improved. During classroom trials with earlier versions of the
manuscript a number of students spotted ambiguities and errors which
have (we hope) been successfully eliminated. H. C. Helgeson and
D. R. Waldbaum allowed us to use prepublication data which were vital
to the presentations in Chaps. II and 12. We are extremely grateful
for their generosity. Last, but certainly not least, we thank M. L.
Zickle, our long-suffering typist, for the miraculous conversion of illegible
notes into neat typescript, and T. Zimmerman for the drafting of the
figures.
Wallace S. Broecker
Virginia M. Oversby
C o n t e n t s
Preface v
Table of Constants and Conversion Factors fx
Chapter 1 Thermodynamics as a Geologic Tool 1
Chapter 2 Volume 10
Chapter 3 Energy 38
Chapter 4 Randomness and Entropy 64
Chapter 5 Equilibrium and Its Attainment 99
Chapter 6 Reactions in Natural Gases 130
Chapter 7 Distribution of Trace Isotopes between
Coexisting Phases 150
Chapter 8 Distribution of Trace Elements between
Coexisting Phases 171
Chapter 9 Solid-state Mineral Transformations 186
Chapter 10 Melting Phenomena 219
Chapter 11 Solid-soiution Phenomena 236
Chapter 12 Reactions in Natural Waters 261
Appendix I Thermodynamic Derivations 295
Appendix II List of Symbols 304
Index 311
vii
Table of Constants
and Conversion Factors
CONSTANTS
Avogadro's number N 6.023 X 1023 mole-i
Boltzmann's constant k 1.381 X 10~'® erg/deg
Planck's constant h 6.625 X 10-22 erg-sec
Gas constant R 1.987 cal/deg-mole
8.315 joules/deg-mole
82.06 cm3-atm/deg-mole
Speed of light c 2.998 X 10^° cm/sec
Absolute zero -273.15^0
Charge on the electron e 1.602 X 10-'® coulomb
Mass of the electron 9.109 X 10-28 g
Mass of the proton 1.673 X 10-2^ g
Mass of the neutron 1.675 X 10-24 g
Base of natural logarithm e 2.718
In 10 2.303
ix
X TABLE OF CONSTANTS AND CONVERSION FACTORS
CONVERSION FACTORS
Length
1 cm = 0.3937 in. = 0.0328 ft = 6.214 X 10-" mile
1 in. = 2.54 cm
1 mile = 1609 m
1 A (angstrom unit) = 10"® cm = 10"" micron
A r e a
1 m^ = 10.76 ft2 = 1550 in.^ = 2.471 X 10"" acre
Volume
1 m3 = 35.31 ft' = 1000 Uters = 6.102 X 10" in.'
Time
1 year = 365.24 days = 8.766 X 10' hr = 5.259 X 10® min
= 3.156 X 10^ sec
Velocity
1 m/sec = 3.281 ft/sec = 3.6 km/hr = 2.237 mile/hr
= 1.944 knots
Mass
1 kg = 2.205 lb = 1000 g
Pressure
1 bar = 0.9689 atm = 14.5 lb/in.' = 75.01 cmHg
= 401.5 in H2O = 1 X 10® dynes/cm'
Energy
1 joule = 0.2389 cal = 9.481 X 10"" Btu
= 0.7376 ft-lb = 10' ergs
1 liter-atm = 24.2rcal
1 cal = 4.184 joules
