those uauallv eneonolered so it is sueeested ,... W I ~ K . h~.i~lalim, III lhxt i t i d SIIR.~?. approp I I h 1 f i e in I I to r x p c ~ re student I,, vrrliy at#alytwall) the pmposed procedure of maintaining the constancy of ionic strength and to investigate whether the method is valid when the stoichiometric concentrations of chloride and silver differ. Chapters 3-6 present some general ideas about acid-base equilibria, and s. detailed consideration of the titration of diprotie as Equilibria in Solution protic acid, H A , by a strong monoacidic well as monoprotic acids. In addition, base; the solubility of lead chloride; the George M . Fleck, Smith College, Northacid-base titmtions in nonaqueous solvents effect. of complexation equilibria an the ampton, Massachusetts. Holt, Rineare briefly discussed snd exemplified by the titration of chloride with silver; EDTA hart, and Winston, Inc., New York, tiaration of pyridine with perchloric acid in titrtstions; and the alanine-nickel(I1) sys1966. xvi 217 pp. Figs. and tables. glacial acetic acid. I t is gratifying to see tem. 16 X 23.5 cm. $9.95. manoprotic strong acids treated as s. speIn Section I, the first chapter provides a cial ease of monoprotie aeids in general so brief review of the concept of chemical Professor Fleck's book admirably fulfills that the demarcation between the two is equilibrium and the relationship between its goal of presenting a systematic developnot as rigid as is sometimes implied. The the thermadvnamies which describe the ment of those algebraic relationships relatdissociation constant,s for strong acids are ing to directly measurable experimental thus realized to be large hut finite. variables which may be derived upon the The determination of the apparent (i.e., concentration units which arise from a basis of postulated chemical equilibria in concentration) dissociation constant is disvariety of experimental techniques. Insolution. The equilibria, considered are cussed and a distinction is correctly made cluded is a concise exposition of the apthe four traditional categories of i a i c between the location of the point at which pmaeh to equilibrium as conveniently r e p equilibria: solubility, acid-base, redox, the fraction titrsted is O.&the "halfresented by use of deDonder's degree of adand complex ion. From experience, the way" point-and the point a t which the vancement variable. author recommends the text for juniors concentration of hydrogen ion is numers. rather der The reaond c h a ~ t e oresents and this reviewer heartily concurs, hut ically equal to the value of the dissociation tailed di-c>wion prw;pitatiov~Ulralim parenthetioally suggests its use would be constant. At the half-way point, which HS ~ ' ~ r m l ~ l by i f irhr ~ l tltmt~tm111 chloride extremely valuable in the development of Professor Fleck chooses to denote the wnh S L I V P ~ . The appmacl. is rat her dillcradditional insight and interest even for "macroscopic definition of the halfent than commonly encountered because someone who already m y have studied equivdelence paint," the concentration of the equilibrium concentration of C1- or this subject in some depth. hydrogen ion is explicitly shown to he Agf is considered to be the independent equal to that of the dissocistion constant The hook is formally divided into two primary variable and consequently, the only when the letter is numerically equal to sections: Section I is a methodological volume of titrant to be the dependent one. the square root of the ion product of water. presentation of fundamental principles and 9 1 1 dvantaee of this orocedure is the ..~ the desirability of designating Section I1 is a "case study" approach to J ~ s ~ ~ ~ a t i r d c ~ o1 h~11c rh* ~ n~q1191i011' s t ~ ~ ~ i ~ ~However, ~~ the point at which the concentration of H demonstrate how these methods have been ~ I pCl ~ y & ~ l lmcmir.~ful y only , f a pwv~piis equal to K'HA as the "microscopic applied to some particular systems conI i c . Ir i;. yrxtiiwtlg I O r e the taining multiple equilibria.. Both sections r c w w u ~ i wd the dmro~ed w ~ skl ~ % g t h definition of half-equivalence" may be seriously disputed. The designation "equivare chmxterized by s. thorough formulaahidl irwurdurii6gnillration of KC1 wirh alence" pertains to a particularly simple tion of the procedures required to obtain .4aSO,, c w n aloe!. thrv are originnlls . . horh relationship existing between the stoichionumerical values for the various equilihequimolar. m e t r i o a n d not the equilihrium-cnncenrium constants. The problems at the end of this chapter trations of acid and base at an unique locanz well as the others are well selected and In Section 11, the equilibria. selected ttre tion during the titsation. those pertaining to the titration of a. polyvery often commendably different from Also discussed is the location of the inflection point (corresponding to the maximum slope of the titration curve) which -Reviewed in this Issue cannot coincide with--but must always precede-the equivalence point even for the titration of a strong acid by a strong George M . Fleck, Equilibria in Solution base when the dilution occurring during Allen J. Bard, Chemical Equilibrium the titration is not neglected. Concisely described are the concepts of buffer capach a r d K. Nash, Stoichiometry: Atomic Keights, Molecular Formulas, ity and index and the theory of the detecMicrocosmic Magnitudes tion of the endpoint with two-color indicators. The chapter ondiprotic acids proGlenn Tilbury, Problem Solving in Chemistry vides detailed consideration of the nat,nre F. W. MeLafferty, Interpretation of Mass Spectra of the titration ouwe and the relationships existing between the macroscopic and Charles Kittel, Introduction to Solid State Physics microscopio equilibrium constants. The titration of an amino acid, including the Leslie E. Orgel, An Introduction to Transition3letal Chemistry: Ligand Field consideration of the zwitter ion, is also Theory illustrated. The following chapter on Eduard Farber, editor, Milestones of Modern Chemistry complex ion equilibria contains a rigorous formulation of the titration to form a. oneBrian Mason,Principles of Geochemistry one complex and presents a detailed algebraic description of systems containing 0 t h Hahn, A Scientific Autohiogrsphy multiple ligand-metal complexes. Chapter 8 is an original and rigamus E. If. E. Pietsch and the Gmelin Institute, editors, Gmelins Hmdbuch der Anortreatment of oxidation-reduction equiganischen Chemie. 8. Auflage, System Piummer 57, Nickel. Teil B, Lieferlibria wherein account is taken of the inmg 3 completeness of the stoichiometric reaction New Volumes in Continuing Series used as the hasis of the titration. Each chapter in Seethn I, as well as Section 11, conelodes with a very excellent
BOOK
REVIEWS
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Journol o f Chemical Education
After these basic and rather abbreviated treatments of elementary calculations, there are chapters an activity coefficients, graphical methods, separations, and nnmerical and wmputer methods. Eqnilibrium quotients are obtained from thee modynamic values by application of the DebyeHuckel equation, and then more realistic cdculetians are performed with the corrected "wnstant." The chapter ommended not only because of its eomprehensive presentation hut also because it on graphical methods begins with the frequently provides an original approach conversation-stopper, "We know, in printo many equilibrium systems which are ciple, how to solve any equilibrium p r o b lem," and proceeds to a. well-done survey familiar hut all too often considered in s of logarithmic and distribution diagrams manner somewhat less than rigorous. with emphasis on the "master variable" as JAMES A. G O L D M . ~ propounded by Sillen and by Freiser and Pololyleehnic Institute of Brooklyn Fernando. Log diagrams are said to he Brooklyn, New York used because they "linearize our curves," whereas it would be more to the point to explain that they make curves visible over tremendous concentration ranges on one graph. Since the "alpha. function'' was developed emlier, it would have been Chemical Equilibrium worthwhile to use it in connection with the log diagrams. Separations are presented Allen J . Bard, University of Texas, as rather brief views of ion exchange, Austin. Harper and Row, Inc., New solvent distribution, and electrodeposition, York, 1966. 202 pp. Figures. 16 X providing simple introductions to these 24 cm. $7.50. topics. The chapter on calculations shows how iteration can be used to solve q u a ; After introducing the basis far the law tions, and suggests the importance of of chemical equilibrinm, via thermodynacomputer programming in equilibrium mio and kinetic arguments, the author calculations. provides a guided tour through the stanIn view of the brevity of the hook, it is dard types of calculstions on simple examespecially commendable that each chapter ples of acid-base, solubility, complex supplies referenoes which would be useful formation, and oxidation-reduction equito the interested student. Also, there are libria. The discussions are clear, though good selections of problems with each brief and unencumbered by difficulties chapter, with answers to some in an a p such as wmplicating sidereactions, acpendix. The reviewer found only a few tivity coefficients, and experimental realiopportunities for niGpicking, such as the ties. suggestion that equilibrium theory is The treatment of acids and bases makes applicable, including equilibrium constant correct and consistent use of the Brginsted expressions, to the case of steady state definitions, rit,h no mention of "hydrolkinetics as observed in nuclear decay ysis" or 'kmmonium hydroxide." There chains. Overall, the book is quite is no discussion of strnctural effects on acid worthy of consideration by teachers. I t strength, and there is little discussion of could be used at the freshman level, where buffer solutions and no explanation of parts would be omitted, and it could be ampholytes. In the solubility chapter used with sophomores provided the the usual and undue reliance is placed on instructor is prepared to supplement the the solubility product wnstmt, and the text with more detailed material. student is Led to hdieve that polyvalent mlts dissociate wmpletely, rather than in RICHARD W. RA\IBTI.E steps. A good, though short., treatment of Carleton College fractional precipitation is followed by a Northfield, Minnesota short discussion of the enhancement by acids of the solubility of salts such as sulfides. Tinder mmolex ion eauilibria selection of thoughtful problems and auggestians for expermental investigations. Throughout the book critical references are provided to pertinent journal articles and other books. .4ppendix I is an annotated wmoilstion of some selected eauilib-
proton-transfer tipd into systems of wmpeting equilibria. The systems used me illustrative rather than representative of actual experimental studies. EDTA is mentioned, and the "alpha" pH function is developed for polypratio ligands. The oxidation-reduction chapter uses reactions written slwrtys m reductions, with standard reduction potentials. Equilibrium constants are calculated via subtraction of couples. Spontaneous reactions are identified through inspeetion of potentials to see which couple has the "better eleotron puller." Cases for discussion are good examples of practical inorgsni~analyticd chemistry. There is no discussion of galvanic ells, and potentials are presented simply as numbers which indicate the tendency to "pull electrons."
Stoichiometry: Atomic Weights, Molecular Formulas, Microcosmic Magnitudes
~~~~~~dK. ,yosh, ~~~~~d university-. ~ d d i ~ publishing ~ ~ -co., ~ ~ ~ ~~ 1966. + 182 pp. ~ i ing, and tables. 16 X 23.5 cm. $3.95. "Stoichiometry" is a supplemental book written for college freshmen chemistry students and wvers those topics relating to weighing and numbering atoms and molecules. Acwrding to the author the primttry goal of this text is a systematic examination of haw-by assigning weights (or masses) to atoms and formulas to molecules-chemists become able to characterize the fundamental
entities of chemistry. The author has chosen the traditional approach to the subject of stoichiometry which he refers to as the "low road," rather than to introduce data, collected by the use of complex instruments and interpretable only with theaid of higher theory. The first four chapters deal with the familiar subjects related to stoichiometry: The Atomic-Molecular theory; The Kinetic-Molecular theory; The Systemstic Assignment of Atomic Weights; and The Systematic Assignment of Molecular Formulas. The fifth and last chapter brings together the ideas presented in the first four and confirms, extends, snd qualifies some of the results obtained. I n the last chapter the Phenomena of Association and Dissociation are presented to explain deviations in the gas laws. X-ray crystallography and the Boltzmann distribution law are studied to give experimental bases fur determining Avogadro's number. The mass spectrograph and its applications are used to study isotopes and establish the atomic weight scale. The hook is written in a narrative style which arouses the curiosity of the reader and makes whst might be considered dull topics very interesting. The material is presented in a logical way and is based on data. that can he obtained readily and easily. Frequent references m e made to material presented in earlier sections whiob helps to tie all of the chapters together and develops a, coherent mode of thought. I t is the opinion of the reviewer that this text belongs an the shelf of every serious chemistry student. The topics of this book are fundamental and too often we find that beginning and advanced chemistry students h e failed to master the wnstructions of chemical stoichiometry.
P. CALVINMAYBURY University of South Florida Tampa
Problem Solving in Chemistry: A Dimensional Approach
Glen Tilbury, Wisconsin Stste University, Platteville. Lyons and Carnaban (an affiliate of Meredith Publishing Co.), Chicago, 1967. 236 pp. Figs. and tables. 16 X 23 cm. $2.20. This is a revised edition of a problem book previously reviewed (THIS JOURNAL 41, AS32 D9641). Although approxiof the volume is a l~mately ~ d ~threequarters ~page-for-page ~ . reprint, some minor *Iterations have been made, and three new ideas x~~~. willnst,mtd The chanter -.. --. =~.- Gram-Atoms --.has been merged with the chapter Moles, short sections on finding squares and square roots of exponential numbers and with the slide rule have been added, and a few sections have been rewritten. A new chapter on Equilibrium treats gsseous mixtures (on the basis of molar concentratiom), acid-hase reactiorli, nnd w l u b ~ l ~ t y product. The ch.aprrr llenr and Chnngrs in \latter i.i Inon mtitkd 'l'hcrmochcmir Volume
44, Number 7, July 1967
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