DIRECT CALORIMETRIC DETERMINATION OFHEATS OF FORMATION OF SOME METAL CHELATES

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GUTNIKOV, George, 1938-DIRECT CALORIMETRIC DETERMINATION OF HEATS OF FORMATION OF SOME METAL CHELATES.

University of Arizona, Ph.D., 1967 Chemistry, analytical

University Microfilms, Inc., Ann Arbor, Michigan

DIRECT CALORIMETRIC DETERMINATION OF HEATS

OF FORMATION OF SOME METAL CHELATES

by

George Gutnikov

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF CHEMISTRY

In Partial Fulfillment of the Requirements For the Degree of

DOCTOR. OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

19 67

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

I hereby recommend that this dissertation prepared under my

direction by George Gutnikov

entitled Direct Calorimetric Determination of Heats

of Formation of Some Metal Chelates

be accepted as fulfilling the dissertation requirement of the

degree of Doctor of Philosophy

jk uAJJ I tati^n Dissertation Director Date

After inspection of the dissertation, the following members

of the Final Examination Committee concur in its approval and

recommend its acceptance:*

iLR.jJztt (Ljzi 3T

9- 1 1 - C L 1

3.1 kjjf" i

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED: !&4JTL̂ 2J

AC KNOWLED GM E N TS

The author expresses his gratitude to Dr. Henry Freiser for

his counsel throughout the experimental work and in the preparation

of this thesis.

Thanks are also due to Dr. Quintus Fernando for helpful

discussion and to Mr. Ted Carnavale for writing the computer pro

grams.

Financial support of this research by the U. S. Atomic

Energy Commission is gratefully acknowledged.

iii

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS v

LIST OF TABLES vi

ABSTRACT . x

INTRODUCTION 1

STATEMENT OF PROBLEM 33

EXPERIMENTAL 34 General Considerations 34 Titrimetric Apparatus 36 Titrimetric Procedure 37 Calorimetric Apparatus 38 Calorimetric Procedure 43 Reagents 47

CALCULATIONS 50 Acid Dissociation Constants 50 Chelate Formation Constants . . . . 51 Heats of Reaction 53 Heats of Reagent Dissociation 54 Heats of Chelation 54

ERRORS 59

DISCUSSION 64 Comparison of Methods 64 Comparison with Previous Results 70 Discussion of Present Results 77

APPENDIX A 91

LIST OF REFERENCES 108

iv

LIST OF ILLUSTRATIONS

Figure Page

1. Cross-sectional View of Calorimeter 39

2. Calorimeter Circuit 41

3. Typical Time-temperature Curve 55

v

LIST OF TABLES

Table Page

I. Thermodynamic Values for the Chelation Reactions of Ethylene diamine and Trimethylenediamine 10

II. Thermodynamic Values for the Chelation Reactions of Di ethyl en etri amine and 2, 2' 2" -Triamino-triethylamine- 12

III. Thermodynamic Values for the Chelation Reactions of Triethylenetetramine and N, N' N"-Tetrakis-(2-aminoethyl)-ethylenediamine 13

IV. Thermodynamic Values for the Chelation Reactions of 1, 10-Phenathroline and 2, 2'-Bipyridine 15

V. Thermodynamic Values for the Chelation Reactions of Iminodiacetic and N-Methyliminodiacetic acids 17

VI. Thermodynamic Values for the Chelation Reactions of Nitrilotriacetic and Ethylenediaminetetra-acetic acids 18

VII. Thermodynamic Values for the Chelation Reactions of trans-Cyclohexanediaminetetraacetic and Ethyleneglycol-(bis-/3 -aminoethyl ether)-N, N' -tetraacetic acids 23

VIII. Thermodynamic Values for the Chelation Reactions of Ethyletherdiaminetetraacetic and Ethylthio-etherdiaminetetraacetic acids 25

IX. Thermodynamic Values for the Chelation Reactions of N-Hydroxyethylethylenediaminetriacetic and Diethylenetriaminepentaacetic acids ' 26

X. Thermodynamic Values for the Chelation Reactions of 2, 4-Pentanedione and Tripolyphosphoric acid 31

vi

vii

LIST OF TABLES--(Continued)

Table Page

XI. Thermodynamic Values for Ligand Dissociation .... 72

XII. Thermodynamic Values for the Formation of the 8-Quinolinol Chelates 74

XIII. Thermodynamic Values for the Formation of the 2-Methyl-8-quinolinol Chelates 75

XIV. Thermodynamic Values for the Formation of the 4-Methyl-8-quinolinol Chelates 76

XV. Thermodynamic Values for the Formation of the 8-Quinolinol-5-sulfonic acid Chelates 80

XVI. Thermodynamic Values for the Formation of the Quinoline-8-thiol and 2-Methylquinoline-8-thiol Chelates 85

XVII. Thermodynamic Values for the Formation of the 2,4-Pentanedione Chelates 89

XVIII. Summary of Acid Dissociation Constants 91

XIX. Summary of Chelate Formation Constants 92

XX. Data for AH 93 w

XXI. Data for AH^H 94

XXII. Data for AH_TT and AHC 95 Uri oJti

XXIII. Data for Mn(II)-8-Quinolinol 96

XXIV. Data for Co(II)-8-Quinolinol 96

XXV. Data for Ni(II)-8-Quinolinol 96

XXVI. Data for Cu(II)-8-Quinolinol 97

XXVII. Data for Zn(II)-8-Quinolinol 97

viii

LIST OF TABLES--(continued)

Table Page

XXVIII. Data for Cd(II)-8-Quinolinol 97

XXIX. Data for Pb(II)-8-Quinolinol 98

XXX. Data for Mn(II)-2-Methyl-8-quinolinol 98

XXXI. Data for Co(II)-2-Methyl-8-quinolinol 98

XXXII. Data for Ni(II)-2-Methyl-8-quinolinol 99

XXXIII. Data for Cu(II)-2-Methyl-8-quinolinol 99

XXXIV. Data for Zn(II)-2-Methyl-8-quinolinol 99

XXXV. Data for Pb(II)-2-Methyl-8-quinolinol 99

XXXVI. Data for Mn(II)-4-Methyl-8-quinolinol 100

XXXVII. Data for Co(II)-4-Methyl-8-quinolinol 100

XXXVIII. Data for Ni(II)-4-Methyl-8-quinolinol 100

XXXIX. Data for Cu(II)-4-Methyl-8-quinolinol 101

XL. Data for Zn(II)-4-Methyl-8-quinolinol 101

XLI". Data for Pb(II)-4-Methyl-8-quinolinol 101

XLII. Data for Mn(II)-8-Quinolinol-5-sulfonic acid .... 102

XLIII. Data for Co(II)-8-Quinolinol-5-sulfonic acid .... 102

XLIV. Data for Ni(II)-8-Quinolinol-5-sulfonic acid .... 102

XLV. Data for Cu(II)-8-Quinolinol-5-sulfonic acid .... 103

XLVI. Data for Zn(II)-8-Quinolinol-5-sulfonic acid .... 103

XLVII. Data for Ni(II)-8-Quinolinol-5-sulfonic acid (in aqueous solution) 103

ix

LIST OF TABLES--(continued)

Table Page

XLVIII. Data for Cu(II)-8-Quinolinol-5-sulfonic acid (in aqueous solution) 104

XLIX. Data for Zn(II)-8-Quinolinol-5-sulfonic acid (in aqueous solution) 104

L. Data for Mn(II)-Quinoline-8-thiol 104

LI. Data for Co(II)-Quinoline-8-thiol 104

LII. Data for Ni(II)-Quinoline-8-thiol 104

LIII. Data for Cu(II)-Quinoline-8-thiol 105

LIV. Data for Zn(II)-Quinoline-8-thiol 105

LV. Data for Pb(II)-Quinoline-8-thiol 105

LVI. Data for Co(II)-2-Methylquinoline-8-thiol 105

LVII. Data for Ni(II)-2-Methylquinoline-8-thiol 106

LVIII. Data for Cu(II)-2-Methylquinoline-8-thiol 106

LIX. Data for Zn(II)-2-Methylquinoline-8-thiol 106

LX, Data for Mn(II)-2,4-Pentanedione 106

LXI. Data for Ni(II)-2, 4-Pentanedione 107

LXII. Data for Cu(II)-2, 4-Pentanedione 107

LXIII. Data for Zn(II)-2, 4-Pentanedione 107

ABSTRACT

A simple, twin-differential calorimeter capable of determining

the heats of chelation in highly dilute solutions was designed and con

structed. The heats of reactions of several chelating agents containing

oxygen and sulfur donor atoms with a number of transition and heavy

metal ions were obtained, and the corresponding formation constants

were calculated. The chelating agents studied were 8-quinolinol, 2-

methyl and 4-methyl-8-quinolinol, 8-quinolinol-5-sulfonic acid, quino-

line-8-thiol, 2-methylquinoline-8-thiol, and 2, 4-pentanedione; the

n | 2+ 2+ 2+ 2"4~ 24- 21 metal ions included Mn , Co , Ni , Cu , Zn , Cd , and Pb

Reactions were generally performed in an aqueous 50 volume %

dioxane-0. 1 M NaClO^ medium, or in aqueous 0. 1 M NaClO^.

In contrast to previous studies, considerable regularity was

found in the entropy changes of chelation for the 8-quinolinols. The

heats of chelation for the quinoline-8-thiols showed that the metal-

sulfur bonds are stronger than the metal-oxygen bonds. The reversal

of the usual stability order (Ni > Zn) is due to a more favorable entropy

change, which was attributed to the formation of a tetrahedral zinc

chelate.

INTRODUCTION

During the past half century the application of organic reagents

to the solution of analytical problems has yielded numerous fruitful

results. Much of the earlier work was encumbered by the lack of a

theoretical foundation, frequently requiring the expenditures of exces~

cise effort in order to achieve a satisfactory solution.

An important development in the study of organic chelating

agents came in 1941 when Bjerrum^ presented a method for the

determination of the successive stability constants of metal ammine

( 2 ) complexes. Following Calvin's . modification of the Bjerrum method

in 1945, which extended its utility to almost any organic ligand capable

of exchanging a hydrogen for a metal, this so-called Calvin-Bjerrum

potentiometric technique has evolved into the most reliable mearjs of

evaluating the formation constants of metal chelates.

(3) Today formation constant data abound in the literature. An

analysis of this mass of information provides certain criteria for

1. J. Bjerrum, Metal Ammine Formation in Aqueous Solutionf P. Haase and Son, Copenhagen, 1941.

2. M. Calvin and K. W. Wilson, J. Am. Chem. Soc. 67, 2003(1945),

3. L. G. Sillen and A. E. Martell (compilers), Stability pon-stants of Metal Ion Complexes, The Chemical Society, London, Specif Publication No. 17, 1964.

1

2

assessing the extent of chelate formation. The approximate chelate

stability can be predicted from certain properties of the ligand and

metal ion, as well as the specific effects of the solvent.

The important factors for the ligand include the nature of its

donor atoms and their basicity, steric hindrance, and the size and

number of the rings formed.

Ligands containing oxygen, nitrogen, and sulfur as donor atoms

have assumed the greatest analytical significance because of their

ability to coordinate very effectively with many metals. In a study

of the EDTA analogs, CH2CH2[YCH2CH2N(CH2COO~)2] in which

Y=NCH , S, or O, Schwarzenbach et al. ̂ elegantly demonstrated the

stability sequence 0>N>S for the alkaline earths and N>S>0 for the

transition metals with nearly filled d orbitals. Manganese (II), how-

( 2 ) ever, exhibits an enhanced stability with O over N ligands. A

distinct preference for Se over S by transition metal ions has been

reported. ^

1. G. Schwarzenbach, H. Senn, and G. Anderegg, Helv. Chim. Acta 40, 1886 (1957).

2. H. Irving and R. J. P. Williams, Nature, Lond. 1'62, 746 (1948); J. Chem. Soc. 3192 (1953).

3. G. Schwarzenbach, G. Anderegg, W. Schneider, and H. Senn, Helv. Chim. Acta 38, 1147 (1955).

4. E. Sekido, Q. Fernando, and H. Freiser, Anal, Chem. 37, 1556 (1965).

3

Care must be exercised in the above comparisons to match .

ligand basicities. Because both hydrogen and metal ions act as Lewis

acids toward ligands, it is reasonable to expect a linear correlation

between acid dissociation and stability constants. Although such

relations have been observed frequently, they have been shown to

deviate somewhat if the parent ligand is substituted by groups posses

sing substantial ir donor or acceptor properties. ̂

Such correlations fail when a bulky substituent near the coordi

nating atom interferes with the bonding of the much larger metal ions.

The decreased stability of 2-methyloxine chelates relative to a series

( 2 ) of similar unhindered oxine chelates illustrates this point convincingly.

Despite its greater basicity, trimethylenediamine forms less

(3) stable chelates than ethylenediamine. This has been attributed to

ring strain in the six-membered ring. The less exothermic heat of

formation of trimethylenediamine chelates is consistent with this hypo

thesis. Five-membered chelate rings are generally found to be most

stable.

1. J. G. Jones, J. B. Poole, J. C. Tomkinson, and R, J. P. Williams, J. Chem. Soc. 2001 (1958).

2. W. D. Johnston and H. Freiser, Anal. Chim. Acta 11, 201 (1954).

3. I. Poulsen and J. Bjerrum, Acta Chem. Scand. 1407 (1955).

4

Since the additional stability observed in the displacement of

monodentate ligands by a polydentate ligand derives chiefly from an

increase in the number of particles in solution (hence the entropy

change is positive), the formation of a larger number of rings should

be accompanied by an increase in stability. This postulate is valid

provided that no serious ring strain is incurred, and the coordination

number of the metal is not exceeded.

The coordination number of many metals is commonly six;

lead and copper (II) generally form only four strong bonds, although

in the case of copper two additional weak bonds are formed due to the

Jahn-Teller effect.

Another property of metal ions which has been correlated with

chelate stability is charge density. For a group of similar metal ions

of the same charge which form essentially ionic bonds, stability varies

inversely with ionic radius. Thus, for the alkaline earths the sequence

Mg>Ca>Sr>Ba is often noted. In the case of the transition metal ions,

whose ionic radii are very similar, significant stability differences

arise from differences in the ligand field energy. In general, the

sequence Mn

5

Plots of stability constants against ionization potentials or

electronegativity frequently approximate a straight line. The basis of

the explanation is the fact that both of these parameters are measures

of electron affinity and hence are related to the attraction of the metal

ion for the electrons of the ligand.

Apart from the special properties of the ligand and metal ion,

the solvent employed can profoundly influence the stabilities observed.

The background electrolyte will affect the stabilities in accordance

with its activity coefficient, but additional effects will be observed if

it complexes with the metal ion.

In mixed solvents ions may be selectively solvated by either

component. ̂ Thus, calcium and zinc ions are hydrated predomi

nately in CHgOH-HgO and CHgCN-HgO mixtures, respectively, but in

the latter mixture silver ion is preferentially solvated by CH^CN. In

addition, for uncharged chelates enhanced solvation by the organic

component might be anticipated. Therefore, a change in solvent may

drastically alter the nature and, consequently, the equilibrium constant

of a particular reaction.

If the mole fraction of the "inert" component is kept relatively

small so that hydration is the main mode of solvation, then stability

1. H. Strehlow, et al. Ber. Buns en Ges ell. Physik. Chem. 62, 373 (1958); 66, 309 (1962); 69, 674 (1965); Z. Physik. Chem., N. F., 49, 44 (1966).

6

varies inversely with the solvent dielectric constant. This is illustrat

ed by the increase in stabilities of various metal oxinates as increasing

amounts of dioxane are added. ^

The increased stability in lower dielectric constant media may

be due to changes in solvent interaction and bond strengths. The

determination of the heats and entropies of chelation could therefore

substantially illuminate this question. As yet., however, few such

( 2 ) studies have been published and one indicates that solvation effects

predominate.

For the previous cases as well as the vast majority of others,

stability constants alone fail to distinguish adequately between such

factors as bond strengths, configuration, steric hindrance, and solva

tion effects. This is true because the formation (stability) constant,

K^, which is directly related to the free energy change, AG, by the

relation

AG = -RT In Kj

reflects differences in the changes in both the enthalphy, AH, and the

entropy, AS, since

AG = AH - TAS

A single number written as a subscript with a thermodynamic function

1. H. Irving and H. Rosotti, Acta Chem. Scand. 10, 72 (1956).

2. N. C. Li, J. M. White, and R. L. Yost, J. Am. Chem. Soc. 78, 5218 (1956).

will refer to the corresponding stepwise reaction, whereas two num

bers will refer to the corresponding overall reaction.

In the past conclusions were drawn from stability constants

about structural features of chelates. This was based on the assump

tion that stability constants were proportional to the enthalpies, hence

that the entropies were similar for most metals, and that they remained

constant in a series of related compounds.

In fact, however, it is general for changes in enthalpy and

entropy to at least partially compensate each other in dissociation pro

cesses.^ For example, increases in the attractive forces between

particles resulting in a more rigid structure would lead to negative

changes in both AH and AS. Conversely, formation of a looser struc

ture, for instance, due to steric hindrance would result in positive

enthalpy and entropy changes. In chelate formation disruption of

solvent molecules from the metal ion and ligand consumes energy, but

this process is compensated by the increase in the number of particles.

Since stability constants alone do not completely explain solu

tion processes, the trend toward obtaining AH and AS data has been

progressing steadily. At first AH was calculated from the temperature

variation of formation constants since this involved minimal modifica

tions in the equipment used for the determinations.

1. D. J. G. Ives and P. D. 'Marsden, J. Chem. Soc. 649 (1965).

8

The convenience of this procedure was offset., however, by the

frequent, large discrepancies in the data reported by different investi-

(1) gators for the same system. Errors arising from the uncertainties

in the formation constants (about t 0.1.0 log unit) can introduce an

error of about 4 kcal./mole into AH when measurements are made over

a 10° range. Other factors which contribute to the error include the

variation_pf AH with temperature, differences in activity coefficients

at different temperatures, kinetic effects, and competing reactions,

Hence, because of the inadequacies in the temperature dependence

method, direct calorimetry is now preferred for the determination of

AH.

To date a number of calorimetric determinations of the heats

of chelation have been carried out with N-N and N-O ligands. For O-O

ligands and those containing sulfur the data are still sparse.

Among ligands containing only nitrogen donor atoms, the vari

ous aliphatic polyamines have been studied extensively. Of these,

(2,3 4] ethylenediamine (en) has received the greatest amount of attention, ' '

1. F.J. C. Rossotti, in Modern Coordination Chemistry, J'. Lewis andR. G. Wilkins, eds. Interscience Publishers, Inc. New York, 1960, p. 68.

2. T. Davies, S. S. Singer, and L. A. K. Staveley, J. Chem, Soc. 2304 (1954).

3. I. PoulsenandJ. Bjerrum, ActaChem. Scand,, £, 1407 (1955).

4. M. Ciampolini, P. Paoletti, and L. Sacconi, J. Chem. Soc. 4553 (1960).

9

For the en chelates of the transition metal ions a definite decrease in

the stepwise entropies but a slight increase in the enthalpies was

generally observed (Table I). This was attributed to a greater release

of water molecules and, consequently, the rupture of a larger number

of metal-water bonds in the first step than in succeeding ones. An

exception was provided by zinc for which the formation of the bis che

late from the mono was accompanied by a lower AH but a higher AS.

++ This was explained by the formation of a tetrahedral Zn(en)g chelate

with the release of additional waters of hydration. ̂

The effect of introducing alkyl substituents onto ethylenedia-

(2) mine was investigated by Basolo and Murman. ' Although the AH and

AS values for en and its N-methyl derivative (Meen) differ only slightly,

those for the N, N'-diethyl derivative (diEten) are both considerably

more positive, to the extent that they nearly compensate each other in

terms of the free energy. The respective -AH^ and AS^g values, in

kcal/mole and e.u., for Ni with en, Meen, and diEten are 16, 3 and 7,

17. 0 and 1, and 7. 8 and 27. This effect was ascribed to steric hind

rance by the bulky alkyl substituents.

1. M. Ciampolini, P. Paoletti, and L, Sacconi, J, Chem. Soc. 4553 (1960).

2. F. Basolo and R. K. Murman, J. Am. Chem. Socu 76, 211 (1954).

TABLE 1. - -Thermodynamic values for the chelation reactions of ethylenediamine and trimethylenediamine.

en tm -AG -AH AS -AG -AH AS kcal kcal kcal kcal

Cation Step mole~l mole~l (e.u. ) mole"! mole~l (e. u. )

H+ 1 13. 9 12. 2 5. 7 14. 5

Mn2+

2 10. 2 10. 6 -1. 5 12. 4

Mn2+ 1 3. 8 2. 8 3. 0 2 2. 9 3. 2 -1. 0

Pe2+

3 1. 2 5. 1 -9. 5

Pe2+ 1 5. 9 5. 1 3. 0 2 4. 6 5. 3 -3. 0

o

o CO

+ 3 2. 8 5. 5 -8. 5

o

o CO

+

1 8. 1 6. 9 4. 0 2 6. 5 7. 1 -2.0

*T-2 + NI

3 4. 1 8. 2 -10.0

*T-2 + NI 1 10. 5 8. 9 5. 5 8. 7 7. 8 3. 0 2 8. 7 9. 4 -2. 5 6. 0 7. 2 -4. 1

2+ Cu

3 5. 9 10. 1 -8. 5 1. 7 6. 3 -15. 5 2+

Cu 1 14. 7 13. 1 5. 5 2 11. 0 12. 3 -4. 5

Zn2+

1-2 23. 4 22. 8 2. 0

Zn2+ 1 8. 1 7.0 3. 5 2 7. 0 4. 9 7. 0

Cd2+ 3 2. 6 5. 2 -8. 5

Cd2+ 1 8. 0 7.0 3. 1 2 6. 5 6. 5 0. 2 3

11

Despite its greater basicity, trimethylenediamine, which

forms six-membered chelate rings, reacts less exothermically than

ethylenediamine. ̂ ' This behavior probably results from greater ring

strain in the larger chelate ring.

Several higher homologs of ethylenediamine have also been the

subjects of thermodynamic studies. They include diethylenetriamine

(dien), 2, 2", 2"-triaminotriethylamine (tren), triethylenetetramine

(trien), and N, N', N"-tetrakis-(2-aminoethyl.) ethylenediamine (penten).

The data are presented in Tables II and III. For a given metal ion the

heat of chelation per amino group is similar, but tends to decrease

somewhat with the increasing number of chelate rings formed. Accord-

( 2 ) ing to Ciampolini, et al. this was due to ring strain or to weaker

bonding between the metal ion and secondary and tertiary amino nitro-

( 3 ) gens than primary nitrogens. Reilley, et al. ' suggested that these

effects could also be accounted for by changes in the base strengths of

the remaining amino groups after the first had bonded, and a change

in the acidity of the metal ion after formation of the first metal-amino

bond.

1. I. PoulsenandJ. Bjerrum, ActaChem„ Scand. 9, 1407(1955).

2. M. Ciampolini, P. Paoletti, and L. Sacconi, in Advances in the Chemistry in the Coordination Compounds, S. Kirschner, ed. The Macmillan Co., New York, 1961, p„ 303„

3. D. L. Wright, J, H. Holloway, and C„ N„ Reilley, Anal. Chem. 37, 884 (1965).

12

TABLE II. - -Thermodynamic values for the chelation reactions of diethylenetriamine and 2, 2', 2"- triaminotriethylamine.

dien tren

-AG -AH- AS -AG -AH AS kcal ^ kcal _1

(e. u.) kcal ^ kcal

(e. u.) Cation Step mole mole (e. u.) mole mole (e. u.)

H+ 1 13. 4 11.2 7.2 13.8 11. 7 7. 1

2 12. 3 12. 0 1.0 12. 9 12. 8 0. 2

Mn2+

3 5. 8 7.2 -4.7 11.5 12, 2 -2. 3

Mn2+ 1 7.9 3. 0 16. 5

Fe2+ 1 11.8 6. 3 18. 5

Co2+ 1 10. 9 8.2 9. 0 17. 0 10. 7 22. 0

Ni2+

2 8. 0 10. 2 -7. 5

Ni2+ 1 14. 5 11.9 8. 5 20. 0 15. 2 16. 0

Cu2+

2 10. 9 13. 4 -8.5

Cu2+ 1 21. 6 18. 0 12.0 25. 8 20. 4 18. 0

Zn2+

2 7.1 8.2 -3.5

Zn2+ 1 12.0 6. 5 18. 5 19. 7 13. 9 19. 5

2 7.5 10.1 -9.1

13

TABLE III. --Thermodynamic values for the chelation reactions of triethylenetetramine and N, N', N" -tetrakis-(2 • amino-ethyl) -ethylenediamine.

trien penten -AG -AH AS -AG -AH AS kcal ^ kcal ^ kcal kcal ^

Cation Step mole mole (e. u. ) mole mole (e. u. )

H+ 1 13. 3 11. 0 7. 8 13. 7 11. 3 8. 1 2 12. 4 11. 3 3. 7 13. 0 11. 5 5. 3 3 8. 9 9. 5 -2. 0 12. 2 13. 2 -3. 1 4 4. 4 6. 8 -8. 1 11. 5 12. 0 -1. 8

Mn2+

5 1. 8 4. 5 -9. 0

Mn2+ 1 6. 7 2. 3 15. 0 12. 6 8. 9 12. 5 2+

Fe 1 10. 5 6. 1 15. 0 15. 2 9. 7 18. 5 2+

Co 1 14. 9 10. 7 14. 5 21. 2 14. 8 21. 5 .2+

NI 1 19. 3 13. 9 18. 0 26. 1 19. 7 21, 5 2+

Cu 1 27. 6 21. 4 21. 0 30. 2 24. 5 19. 0 2+

Zn 1 16. 3 8. 3 27. 0 22. 0 14. 5 25. 0 2+

Cd 1 14. 8 9. 2 19. 0

14

Although the aromatic diamines 1, 10-phenanthroline (phen)

and 2, 2'-bipyridine (dip) are much less basic than ethylene diamine

5 (by about 10 ), they generally form chelates of comparable stability

( 1 2 ) (Table IV). Calorimetric studies ' disclose a fairly similar pat

tern in the heats and entropies of chelation for the aromatic amines,

in that the stepwise -AH values are somewhat less and the stepwise

AS values increase somewhat, especially for phen. This behavior is

the reverse of that found for the en chelates and was attributed to the

greater hindrance provided by the rigidity of the aromatic residue.

The greater rigidity of phen relative to dip was manifest in the less

favorable entropies of chelation for the latter ligand, since rotational

freedom was lost on chelation. Primarily because of this entropy dif

ference the phen chelates are more stable than those of dip. The

tris-ferrous chelates of the aromatic diamines exhibit an exceptional

stability, which is particularly marked if the AH values are compared.

In this well-known case a change in configuration occurs from the para

magnetic hydrated ferrous ioh to the diamagnetic complex. Although

all of the chelates of the aromatic amines are enthalpy-stabilized,

ligand field stabilization was shown to account for only a small part of

1. G. Anderegg, Helv. Chim. Acta 46, 2813 (1963).

2. R. L, Davies and K. W. Dunning, J. Chem. Soc. 4168 (1965).

15

TABLE IV. --Thermodynamic values for the chelation reactions of 1, 10-phenathroline and 2, 2'-bipyridine.

Cation

H+

Mn2+

2~h Fe „ 2+ Co

Ni2+

Cu2+

~ 2+ Zn

Cd2+

phen dip -AG -AH AS -AG -AH AS kcal kcal kcal kcal

Step mole"! mole"! (e. u. ) mole" -1 mole"! (e. u.)

1 6. 6 4. 0 9. 2 6. 2 3. 7 8. 2

1 5. 5 3. 5 6. 8 3. 5 3. 5 0. 0 2 4. 7 3. 5 4. 1 3 3. 6 2. 0 -0. 5

1-3 28. Sr 33. 0 -15. 4 23. 4 31. 4 -27. 0

1 9. 7 9. 1 2. 1 8. 1 8. 2 -0. 4 2 9. 0 6. 7 7. 8 7. 2 7. 0 0. 7 3 8. 0 8. 0 0.0 6. 4 6. 1 1. o

1 11. 8 11. 2 2. 1 9. 6 9. 6 0. 0 2 U. 1 9. 3 6. 1 9. 2 9. 4 -0. 7 3 10. 4 9. 5 3. 0 8. 8 9. 2 -1. 4

1 12. 4 11. 7 2. 4 10. 7 11. 9 -4. 1 2 9. 1 6. 5 8. 8 7. 5 5. 4 7. 2 3 7. 1 8. 2 -3. 7 4. 7 6. 5 -6. 2

1 8. 8 7. 5 4. 4 7. 1 7. 1 0. 0 2 7. 8 7. 5 1. 1 6. 1 5. 4 2. 4 3 6. 9 4. 3 8. 8 5. 1 5. 0 0. 3

1 7. 7 6. 3 4. 8 5. 7 5. 1 2. 1 2 6. 8 6. 8 0. 0 4. 8 4. 3 1. 6 3 5. 5 3. 0 8. 5 3. 6 4. 6 -3. 4

16

this. The author therefore attributed this stabilization to steric

factors.^

A large number of N-O ligands of great variety have been

investigated calorimetrically. The aminopolycarboxylic acids, many

of which have found extensive application in analytical chemistry, have

received the greatest amount of attention. The simplest members of

( 2 ) this series are the terdentate iminodiacetic and N-methyliminodia-

(3) cetic acids (Table V ). . The N-methyl derivative generally forms

somewhat more stable compounds (by about one log unit for the 1:1

complex and about two log units for the 2:1 complex). This stabiliza

tion is predominantly derived from a more favorable entropy change.

This behavior was explained by the larger size of the methyl group

which forces the two carboxylate groups closer together, resulting in

greater localization of charge on the oxygens and producing greater

ordering of the surrounding water. The release of this water during

chelation accounts for the increased entropies observed.

The next higher analog of this series, the quadridentate nitri-

lotriacetic acid (NTA), forms mono-chelates of about 2 log units

greater stability than the above compounds (Table VI). However,

1. G. Anderegg, Helv. Chim. Acta 46, 2813 (1963).

2. G. Anderegg, Helv. Chim. Acta 47, 1801 (1964).

3. G. Anderegg, in Essays in Coordination Chemistry, Exper. Sup pi. 9, 75 (1964).

17

TABLE V. - -Thermodynamic values for the chelation reactions of iminodiacetic and N-methyliminodiacetic acids.

Cation

2+ H+

Mn

^ 2+ Co

Ni2+

„ 2+ Cu

2+ Zn

Cd2+

lm mim -AG -AH AS -AG -AH AS kcal kcal kc al kcal

Step mole"! mole"! (e. u.) mole ~ 1 mole"! (e. u.)

1 12. 7 8. 2 15. 4 13. 0 6. 9 20. 5

1 7. 2 •0. 6 26. 6 2 5. 6 0. 3 18. 0

1 9. 4 2. 1 24. 6 10. 2 1. 9 28. 6 2 6. 9 3. 9 11. 2 8. 5 3. 6 16. 4

1 11. 0 5. 1

o

o

18

TABLE VI. - -Thermodynamic values for the chelation reactions of nitrilotriacetic and ethylenediaminetetraacetic acids.

NTA EDTA -AG -AH AS -AG -AH AS kcal kcal kcal kcal

Cation Step mole"! mole-* (e. u.) mole ~ 1 mole~l (e. u.;

H+ 1 13. 1 4. 7 28. 4 13. 8 5. 7 28

Mn2+

2 8. 3 4. 3 13

Mn2+ 1 10. 0 -1. 4 38. 9 17. 2 4. 6 48

2+ Fe

2 4. 7 5. 5 -1. 7 2+

Fe 1 19. 3 4.0 51

Co2+ 1 13. 9 0. 1 47. 2 21. 4 4. 2 60

Ni2+

2 5. 4 4. 7 2. 1

Ni2+ 1 15. 5 2. 6 43. 9 25. 5 7. 6 59

„ 2+ Cu

2 6. 5 5. 5 7. 0 ' „ 2+ Cu 1 17. 4 1. 9 52. 8 25. 5 8. 2 58

2+ Zn

2 6. 0 7. 0 -3. 5 2+

Zn 1 14. 2 0. 9 45. 5 22. 3 4. 9 59 2 5. 0 2. 7 7. 4

,2+ Cd 1 13. 2 4. 0 31. 3 22. 3 9. 1 44

Pb2+

2 6. 4 5. 1 • 4. 7

Pb2+ 1 15. 3 3. 8 39. 1 23. 6 13. 2 38

19

( 1 2 ) about 2 kcal/mole less heat is evolved in this process. ' Evidently

these chelates are entropy-stabilized, probably due to the additional

water released from the third carboxylate group in the reaction.

In contrast to the high entropies of about 40-50 e. u. observed

for the 1:1 transition metal chelates, those for the addition of another

NTA molecule are all nearly zero. At the same time, the enthalpies

become more exothermic by about 3-7 kcal/mole. These data sug

gest that one of the rings of the mono-chelate is opened when a second

NTA molecule attaches itself, so that the bis-chelate contains two

uncoordinated -CHgCOO groups. The high charge density in the

quadruply negatively charged chelate orders a considerable number

of water molecules around the chelate and thereby reduces the en

tropy change. The more negative AH _ values result from bonding JL

to an additional nitrogen while breaking a metal-carboxylate bond

whose formation may have been endothermic.

The entropies of formation of Cu(NTA) * and Pb(NTA) * are

nearly equal to those for the formation of the EDTA complexes. Ap

parently six rather than four waters of hydration are lost because

these metals usually exhibit a coordination number of four.

1. G. Anderegg, in Essays in Coordination Chemistry, Exper. Suppl. 9, 75 (1964),

2. J. A. Hull, E. H, Davies, and-L. A. K. Staveley, J. Chem. Soc. 5422 (1964).

20

The parent compound of this series, EDTA, has been studied

u , • , (1,2,3,4,5) . (1) .. by numerous investigators. Charles was the first to

demonstrate that the EDTA chelates owe their stability to the very

(3) favorable entropy changes. Staveley and Randall found an inverse

(4) linear relationship between AS and the metal ion radius. Anderegg

showed that the heat of chelation was markedly influenced by the

(5) anion of the metal salt used. Reilley, £t al, compared the AH values

for the transition metal-EDTA chelates with those for en and con

cluded that the acetate groups of EDTA contribute little to the total

heat of reaction. Their entropy contribution, however, constituted

the major factor of the total stability in solution.

The formation constants of the cyclohexyl analog, trans-

cyclohexanediaminetetraacetic acid (CDTA), exceed those of the

parent compound by 2 - 3 log units. On the basis of these data alone,

1. R. G. Charles, J. Am. Chem. Soc. 76, 5854 (1954),

2. R. A. Care and L. A. K. Staveley, J. Chem. Soc. 4571 (1956).

3. L. A, K. Staveley and T. Randall, Disc. Faraday Soc. 2S, 157 (1958).

4. G. Anderegg, Helv. Chim. Acta 46, 1833 (1963).

5. D. L. Wright, J. H. Holloway, and C. N. Reilly, Anal. Chem. 37, 884 (1965).

21

Schwarzenbach, et al/1^ correctly deduced that this higher stability

resulted from greater entropy changes, for it seemed unlikely that

the same donor atoms could bind the metals with such different

strengths. Confirmation of this deduction came from calorimetric

(2 3) data. ' For CDTA the enhanced entropy changes were attributed

to the loss of more water which was ordered by the larger charge

localization as a result of the greater rigidity imposed by the

cyclohexyl ring.

The chelate effect, defined as the difference in log units be

tween the chelate stability of a poly functional and a corresponding

simple ligand, is a measure of the increased stability gained by ring

(4) formation. In order to examine this effect more closely, a series

of EDTA homologs was studied calorimetrically, in which n, the

number of -CH^~ links between the nitrogens, was varied from two

(4) (5) to eight. Iminodiacetic acid or N-methyliminodiacetic acid

1. G. Schwarzenbach, R. Gut, and G. Anderegg, Helv. Chim. Acta 37, 936 (1954).

2. G. Anderegg, Helv. Chim. Acta 46, 1833 (1963).

3. D. L. Wright, J, H. Holloway, and C. N. Reilley, Anal. Chem. 37, 884 (1965).

4. G. Anderegg, Helv. Chim. Acta 417, 1801 (1964).

5. G. Anderegg, Helv. Chim. Acta 48, 1718 (1965).

22

served as the simple ligand. The chelate effect was found to be pri

marily an entropy effect, confirming the earlier proposal of Schwar-

zenbach. ̂ The variation in the chelate effect with n resulted from

changes in the enthalpy rather than the entropy. Other variations in

the AH and AS values were numerous and complex, so that a detailed

analysis of all the data could not be given.

The derivative containing two ether oxygens and six carbons

between the nitrogens, ethyleneglycol-(bis-/3-aminoethyl ether)-N,N'-

(2 3 4) tetraacetic acid (EGTA), displays a similar behavior ' ' (Table

VII). Relative to the EDTA homo log with n = 8, AH and AS for the

manganese and cadmium chelates of this ligand are 9 kcal/mole and~

20 e.u. more negative. Parallel effects, however, were not observed

for copper, zinc, cobalt, and nickel. In fact, AH is more positive for

cobalt and especially for nickel, indicating a dependence on the ion

(4) size. The manganese and cadmium data suggest bonding by the

weakly solvated ether oxygens in place of two charged carboxylate

groups which retain their water of hydration and are restricted in

1. G. Schwarzenbach, Helv. Chim. Acta 35, 2344 (1952).

2. G. Anderegg, Helv. Chim. Acta 47, 1801 (1964).

3. S. Boyd, A. Bryson, G. H. Nancollas, and K. Torrance, J. Chem. Soc. 7353 (1965).

4. Dt C. Wright, J, H. Holloway, and C. N. Reilley, Anal. Chem. 37, 884 (1965).

23

TABLE VII. --Thermodynamic values for the chelation reactions of trans-cyclohexanediaminetetraacetic and ethyleneglycol-

(bis-j3-aminoethyl ether)-' N, N' -tetraacetic acids.

CDTA EGTA

Cation Step'

-AG kcal mole" 1

-AH kcal mole~l

AS

(e. u,)

-AG kcal mole-1

-£H kcal mole-1

AS

(e. u.)

H+ 1 2

16. 6 8. 2

6. 7 2. 1

34 21

12. 7 11. 9

5. 8 5. 8

23. 3 20. 8

Mn2+ 1 22. 7 4. 1 66 16. 7 8. 8 27

Fe2+ 1 24. 8 6. 6 61 16. 1 5. 2 37 ^ 2+ Co 1 25. 6 2. 8 80 16. 7 3.4 45

Ni 1 26. 4 5.4 63 18. 5 5. 0 45 2+

Cu 1 25. 4 8.2 58 24. 2 i0. 5 46

Zn2+ 1 25. 3 7.7 82 19. 7 3. 8 53

Cd2+ 1 26.0 7.4 66 22. 7 14. 1 29

Pb2+ 1 26. 5 11.4 54 19. 9 12. 5 25

24

rotation by their mutual repulsion. Similar structural implications

were derived from nmr data^ for the alkaline earth chelates.

The incorporation of an oxygen atom between two ethylene

bridges connecting the nitrogens leads to ethyletherdiaminetetraacetic

acid (EEDTA), Its chelates were compared to those of the EDTA

homolog with the same number of carbon atoms interposed between the

nitrogens, and to the thioether analog, ETDTA (Table VIII). The pro

nounced increase in -AH for the EEDTA chelates of manganese and

cadmium was taken as an indication of coordination through the ether

oxygen. In terms of AH, only nickel and mercury show a definite pre

ference for the sulfur ligand, whereas lead, copper, and cadmium

react about equally well with both. Zinc and especially manganese

distinctly prefer the oxygen ligand. The AS values are quite similar

for both the oxygen and sulfur compounds.

N-Hydroxyethylethylenediaminetriacetic acid (HEDTA), which

differs from EDTA by the presence of a hydroxymethyl group in place

of an acetate group, usually exhibits more negative heats and entro-

( 2 ) pies of chelation (up to 2 kcal/mole and 10-20 e.u. ) (Table IX). To

account for this the following explanations were proposed: Metals

form stronger bonds with the hydroxyethyl group than with the acetate

1. A. Bryson and G, H. Nancollas, Chem. and Ind. 654(1965).

2. D. C. Wright, J. H. Holloway, and C, N, Reilley, Anal. Chem. 37, 884 (1965).

25

TABLE Vffl> --Thermodynamic values for the chelation reactions of ethyletherdiaminetetraacetic and ethylthioetherdiamine -tetraacetic acids.

EEDTA ETDTA -AG -AH AS -AG -AH AS kcal kcal kcal kcal

Cation Step mole"! mole -1 (e. u.) mole " * mole"! (e. u.)

H+ 1 12. 7 6. 2 22. 1 12. 6 6. 7 20. 3

Mn2+

2 11. 9 7. 3 15. 7 11. 4 6. 6 16. 3

Mn2+ 1 18. 5 5. 9 45. 6 13. 5 1. 5 41. 9

Co2+ 1 20. 5 6. 4 48, 2 18. 8 4. 6 48. 2

Ni2+ 1 20. 2 4. 7 52. 8 21. 1 7. 7 45. 5

Cu2+ 1 24. 3 9. 8 49. 0 22. 2 9. 1 44. 7

Zn2+ 1 20. 5 6. 0 49. 6 18. 0 3. 7 48. 9

Cd2+ 1 21. 7 9. 4 42. 0 19. 3 8. 2 37. 8

Pb2+ 1 20. 2 13. 2 23. 9 18. 6 13.0 19. 1

Hg2+ 1 32. 0 20. 5 35. 7 31. 0 22. 8 31. 6

26

TABLE IX. - -Thermodynamic values for the chelation N-hydroxyethylethylenediaminetriacetic triaminepentaacetic acids.

reactions of and diethylene-

HEDTA DPTA -AG -AH AS -AG -AH AS kcal kcal kcal kcal

Cation Step mole"! mole"* (e. u. ) mole" 1 mole~l (e. u.)

H+ 1 13. 3 14. 2 8. 0 21 2 7. 3 11. 5 4. 3 18

Mn2+

3 5. 7 1. 7 14

Mn2+ 1 14. 7 5. 2 32 21. 1 7. 5 46 2+

Fe 1 15. 9 6. 0 33

Co2+ 1 19. 7 6. 5 44 26. 1 9. 5 56

Ni2+ 1 23. 3 10. 3 45 27. 3 11. 2 54

O

C

I CO

+

X 23. 8 9. 4 48 29. 1 13. 4 53

Zu 1 19. 7 8. 4 38 25. 6 10. 6 50

Cd2+ 1 17. 8 10. 3 25 25. 8 12. 4 45

Pb2+ 1 21. 1 12. 6 29 25. 3 18. 8 22

27

group; the heat of hydration for the hydroxyethyl group is smaller

than that for the acetate group; the hydroxyethyl group remains un

bonded, thus relieving strain and strengthening the other chelate

bonds; the lack of charge lessens electrostatic repulsion. The lower

entropy of formation can be accounted for, at least in part, by the

fewer water molecules released in chelation.

The octadentate ligand diethylenetriaminepentaacetic acid

(DTPA) chelates more exothermically than EDTA, especially with the

( 1 2 ) transition metal ions. ' The corresponding entropies are fre

quently somewhat smaller. These facts were explained by the

preferential coordination of the transition metal ions with the third

amino group of DTPA instead of a carboxylate group.

A strong metal-nitrogen bond is formed, but fewer water mol

ecules are released from this uncharged amino group.

Considerably fewer calorimetric data have been reported for

(3) other N-O ligands. Izatt, et al. found only a small variation in

AH^ and AS^ (-4. 6 to -6. 0 kcal/mole and 19 - 22 e.u. ) for the copper

(II) chelates of glycine, a-aminoisobutyric acid, threonine, and

1. D. C. Wright, J. H, Holloway, and Ct N. Reilley, Anal. Chem. 37, 884 (1965).

2. G. Anderegg, Helv. Chim. Acta 48, 1722 (1965).

3. R. M. Izatt, J. J. Christensen, and V. Kothari, Inorg. Chem. 3, 1565 (1964).

28

sarcosine. The corresponding AHg and AS^ values differ by about

-0. 5 kcal/mole and 8 to 10 e.u. In another paper^ similar data for

the copper (II)-alanine system were presented. Although compensation

between the AH and TAS terms was observed in all of these cases, the

magnitudes were apparently too small for meaningful discussion by

the authors.

The thermodynamic functions for the reactions of manganese,

cobalt, and nickel with glycine have been determined by a temperature

( 2 ) dependence method using a cell without a liquid junction. The AH^

values vary from -0. 3 to -4 kcal/mole, but the AS^ values are all

about 14 e.u. Such variation in AHJ^ was found to be in accordance

with the metal sequence reflecting the effect of ligand field stabili

zation.

In another temperature dependence study using a polaro-

(3) graphic method the thermodynamics of association between nickel

and glycine were determined in aqueous and 45% aqueous dioxane

media. The heats of formation of the neutral chelate were found to be

1. K. Pf Anderson, D. A. Newell, and R. M, Izatt, Inorg. Chem. 5, 62 (1966).

2. J. R. Brannan, H. S. Dunsmore, and G. H. Nancollas, J. Chem. Soc. 304 (1964).

3. N. C. Li, J, M. White, and R. L. Yost, J. Am. Chem. Soc. 78, 5218 (1956).

29

the same in both media, but the entropy of formation was 11 e.u.

larger in 45% dioxane. This entropy difference was attributed to sel

ective solvation of the nickel and glycinate ions by water, but to

mixed solvation of the neutral chelate.

8-Quinolinol (oxine) and its derivatives have been studied by

( 1 2 ) ( 3 ) the temperature dependence method ' and calorimetrically. A

comparison of the thermodynamics of chelation of 2-methyl and 4-

(4) methyloxines shows more positive AH and AS values for the former.

The difference in the AH values was ascribed to steric hindrance to

metal-nitrogen bonding for the 2-methyl derivative, whereas the in

crease in the AS values was thought to result from reduced solvation

due to shielding by the 2-methyl group. For a series of 7-substituted

( 2 ) oxine-5-sulfonic acids chelates Uusitalo observed a regular vari

ation in AH values but similar AS values for both the alkaline earth

and transition metals (14 to 21 e.u. ) and essentially equal AS values

for a particular metal with different ligands. In contradistinction to

this, virtually no variation in AH was found for the cobalt, nickel, and

1. W. D. Johnston and H. Freiser, Anal. Chim. Acta 11, 201 (1954).

2. E. Uusitalo, Ann. Sci. Fenn. A (87) (1957).

3. D. Fleischer and H. Freiser, J. Fhys. Chem. 63, 260 (1959).

30

copper chelates of oxine and its 4-methyl homolog. ̂ The corre

sponding AS values varied extensively. It should be noted that such

invariance in Afi had not been found in any of the other studies men

tioned in this survey.

At the present time very few thermodynamic data are avail

able for chelation by O-O ligands. Izatt, et al. ̂ reported data for

some acetylacetone chelates of transition and heavy metal ions, which

were obtained by the temperature dependence method (Table X). An

unusual feature of these data was a higher -AH value for the nickel

than the copper chelate. Apparently because of the substantial un

certainty in the data, the authors offered no explanation of this

phenomenon.

Calorimetric data for terdentate triphosphate chelates show

( 2 ) that they are entirely entropy-stabilized. The heats of formation

for both the alkaline earth and transition metal ions are endothermic,

anc1 those of cobalt, nickel, copper, and zinc are even more so than

that of manganese. These data can be partially explained by the lack

of any ligand field stabilization for the transition metal ions. Also

1. D. Fleischer and H. Freiser, J. Phys. Chem. 63, 260 (1959).'

2. G. Anderegg, Helv. Chim. Acta 48, 1712 (1965).

31

TABLE X. - -Thermodynamic values for the chelation reactions of acetylacetone and tripolyphosphoric acid.

Cation

2+ H+

Mn

„ 2+ Co

XT-2 + Ni

2+ Cu

2+ Zn

2+ Cd

acae TPP -AG -AH AS -AG -AH AS kcal kcal kcal kcal

Step mole-* mole" 1 (e.u.) mole-* mole"! (e. u.)

1 12. 3 2. 8 32 11. 8 0. 1 40. 0

1 5. 8 2. 5 11 10. 8 -2. 8 46. 4 2 4. 2 4. 7 -1. 8

1 7. 3 1. 2 21 10. 7 -4. 5 51. 7 2 5. 7 5. 0 2.4

1 8. 2 6. 7 12 10. 5 -5. 0 52. 7 2 6. 3 6. 3 0 3 3. 0 6. 7 -12

1 11. 3 4. 7 22 12. 5 -4. 9 59. 2 2 9. 3 6. 6 9

1 6. 9 1. 9 17 11. 2

CO

CD

I 59. 8

1 5. 2 1. 4 13 10. 9 -2. 7 46. 2

32

noted in the explanation was the fact that although zinc binds water

more tightly than manganese, the reverse is true for the triphosphate

ion. It was therefore inferred that a similar situation should exist

for the intermediate transition metals of this series. The observed

large entropies of formation are comparable to those observed for

EDTA and DPT A chelates.

McAuley and Nancollas^ compared calorimetric AH values

for manganese and cobalt malonates with values obtained by the tem-

(2) perature dependence method using cells without liquid junction.

Very good agreement was found. The heat of reaction for the cobalt

compound (2. 9 kcal/mole) is less endothermic than that for man

ganese (3. 7 kcal/mole) but the corresponding entropies are both

27 e. u.

Very few data are available for ligands containing sulfur donor

( 3 ) atoms. Some approximate data, obtained by the temperature de

pendence method, for the copper and nickel chelates of some poly-

amines containing thio ether linkages indicate that the metal-sulfur

bond is weaker than the metal-nitrogen bond, but stronger than the

metal-oxygen bond.

1. A. McAuley and G. H. Nancollas, J. Chem. Soc. 989(1963).

2. V. S. K. Nair and G. H. Nancollas, J. Chem. Soc. 4367(1961).

3. J. R. Lotz, B. P. Block, and W. C. Fernelius, J. Phys. Chem. 63, 541 (1959).

STATEMENT OF PROBLEM

Although numerous free energy of chelation values can be

found in the literature, relatively few heats and entropies of chelation

data have been reported. Many of the latter data have been obtained

by the less reliable temperature dependence method and therefore the

relative contributions of the heats and entropies to the free energies

are oftimes uncertain. Because the heats and entropies of chelation

provide a more detailed insight into the structural features of chelates

in solution than the free energy, it is highly desirable to examine

these parameters.

This work was undertaken to compare the chelation reactions

of ligands containing oxygen and sulfur donor atoms by determining

their heats of chelation, using the more reliable direct calorimetric

method. The ligands chosen were 8-quinolinol, 2-methyl and 4-

methyl-8-quinolinol, 8-quinolinol-5-sulfonic acid, quinoline-8-thiol,

2-methylquinoline-8-thiol and 2, 4-pentanedione. The metal ions

2+ 2+ 2+ 2+ 2+ 2+ of interest were Mn , Co , Ni , Zn , Cd , and Pb . Since

many of the chelates possess a low solubility, it was necessary to

construct and test a calorimeter capable of dealing with highly dilute

solutions.

33

EXPERIMENTAL

General Considerations

The thermodynamics of chelation reported in this study refer

to the following reactions:

M + nL ^ ML n

where M represents a divalent metal ion and L the ligand anion; n

can take the values of 1, 2, or 3. Charges and molecules of solvation

have been omitted for simplicity.

The ligands, Bronsted bases, were generally employed as the

conjugate acid forms in order to permit convenient determination of

the equilibrium constants of the above reactions by measuring the

amount of hydrogen ion displaced by the metal ion. Consequently,

these additional reactions must also be considered:

HL H + L (dissociation)

HL + H > HgL (protonation)

In order to distribute the measured heat among all of the

various chelate and ligand species, their solution concentrations must

first be established. Suitable equations involving the acid dissociation

constant of the ligand, the total concentrations of reactants, and the

34

35

measured hydrogen ion concentration, can be derived for the concentra

tions of all these species.

For the concentrations of the chelate species these equations

require the evaluation of the formation constants, K^, and ^3*

These constants need not be determined separately because data for

their evaluation can be obtained simultaneously with the measured heats

from a series of calorimetric runs in which the total ligand and metal

concentrations are known and are varied suitably, and in which the

hydrogen ion concentration is measured. With a knowledge of these

quantities and the acid dissociation constants, n andpL can be calcu

lated, as described in the Calculation section. The acid dissociation

constants, however, must be determined separately.

The low solubility of many chelates in water frequently required

the use of a 50 volume % aqueous dioxane reaction medium.

Because the activity coefficients of the pertinent species are

unknown, the constants reported are actually concentration quotients.

To minimize variation in the activity coefficients, a constant ionic

strength of 0. 1 was maintained with sodium perchlorate. Appropriate

corrections were applied to the measured hydrogen ion values to

convert them to concentrations. These corrections were an addition

36

of 0. 10 to the pH reading in 50% dioxane^ and an addition of 0. 11 in

water. (2)

Complications due to metal hydrolysis were avoided by working

(3) in a sufficiently low pH region for each metal.

Titrimetric Apparatus

Titrations for the determination of the ligand dissociation con

stants were performed in a jacketed beaker which was maintained at

constant temperature by circulating water thermostated by means of

a Wilkens-Anderson Lo-Temp bath. The beaker was covered with a

plastic cap containing holes to accommodate two five-milliliter micro-

burets, a pair of electrodes, a nitrogen inlet tube, and a 0-50°

thermometer. A Beckman Research pH meter with a glass-saturated

calomel electrode pair was used for all pH measurements. Stirring was

accomplished with a Teflon-covered bar in conjunction with a magnetic

stirrer.

Standard sodium hydroxide solution was stored in a one-gallon

tubulated polyethylene bottle and was forced into the buret through a

1. S. Takamoto, Q. Fernando, and H. Freiser, Anal. Chem. 3J7, 1249 (1965).

2. M. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, Reinhold Publishing Corp. , New York, 1950, p. 543.

3. H. Freiser, R. G. Charles and W. D. Johnston, J. Am. Chem. Soc. 74, 1383 (1952).

37

two-way Teflon stopcock by means of air which had first been passed

through Ascarite-packed towers. The nitrogen used to purge the system

of carbon dioxide and oxygen was passed through an Ascarite-packed

tower and a gas scrubber which was immersed in the water bath and

which contained the same solvent as employed in the titration.

Titrimetric Procedure

For the determination of the acid dissociation constants a weighed

amount of ligand was added to the titration vessel, followed by five

milliliters of standard 0. 1 N aqueous perchloric acid and an equal volume

of dioxane (when required), and 100 ml of solvent. After assembling the

titration apparatus, dissolution of the ligand was effected with the aid

of the magnetic stirrer while the solution was being purged with a

stream of nitrogen. Slow passage of nitrogen was maintained throughout

the experiment. Increments of standard 0. 1 N NaOH were added and the

pH was read after allowing one to two minutes for the reading to sta

bilize. When working in 50% dioxane, matching increments of dioxane

were added after each NaOH addition.

Although the majority of data used for the stability constant

determinations were obtained from calorimetric runs to be described

later, some points were derived from preliminary experiments designed

to establish the maximum concentrations of reagents for a given extent

of reaction which did not form a precipitate for a specified period of

38

time. The apparatus and procedure used were similar to those described

above. Here no titration was performed, but known quantities of ligand

and metal were mixed, the pH was read, and the time required for preci

pitation to start was noted.

Calorimetric Apparatus

A twin-differential calorimeter, based on the titration calori

meter described by Tyson, McCurdy, and Bricker, ^ was constructed

and employed for all enthalpy determinations. The apparatus consisted

of two 280 ml silvered Dewar vessels embedded into two 16" x 12" x 3"

Styrofoam blocks placed on top of each other. Covers of 3/8" poly

ethylene, mounted on the underside of another Styrofoam block, fitted

snugly into the mouths of the Dewars. For each Dewar, holes were

drilled through the block and cover to accommodate two pairs of ther

mistors, a solution bulb, a polyethylene stirrer, and a heater (Fig. 1).

Except for the stirrer, all these devices were firmly mounted through

the cover and block.

Thermistors (Type 51A1, Victory Engineering Co.), having a

resistance of about 100, 000 ohms at 2 5° and a temperature coefficient

of -4. 6%/° at 25°, were utilized as temperature-sensing elements.

To utilize the higher temperature coefficient of high-resistance

1. B. C. Tyson, Jr., W. H. McCurdy, Jr., and C. E. Bricker, Anal. Chem. 33, 1640 (1961).

39

? JOINT

PLUNGER

SYNCHRONOUS MOTOR

T-TUBE

SYRINGE

STYROFOAM BLOCK

POLYETHYLENE COVER

SOLUTION BULB

STYROFOAM BLOCK

THERMISTORS

BULB OPENING

HEATER

STIRRER

DEWAR VESSEL

STYROFOAM BLOCK

~ - Cross - sectional view of calorimeter.

40

thermistors and to distribute the temperature-sensors at different

points in the calorimeter, a set of four thermistors connected in

parallel was employed. The resistances and temperature coeffi

cients of about fifty thermistors were determined, and from them

four closely-matching pairs were selected. These pairs were then

split up in order to provide a nearly identical resistance-temperature

response on each side of the calorimeter. Due to the corrosive

nature of the solutions used, each pair of thermistors was sealed in

6 mm soft-glass tubing.

Thermistors follow an exponential relation between resis

tance and temperature of the form

X =t exp B(l/T - 1/T ) o o

where If is the thermistor resistance, B is a constant, and T is the

absolute temperature. For the thermistors described above^ B

was found to be 4018. 9 and value of x could be calculated from

log t = -1. 44168 + 1745. 4/T

Each set of thermistors was incorporporated into the arms of

a Wheatstone bridge circuit, as shown in Fig. 2. The magnitudes of

the other resistances in the circuit were chosen so as to produce

minimal deviation from linearity of the output voltage vs. temperature

change, in accordance with the detailed considerations presented. ^

1. B. C. Tyson, Jr., W. H. McCurdy, Jr., and C. E. Bricker, Anal. Chem. 33, 1640 (1961).

41

17 KA 5 KA 14.5 KJ1

1000 A *-,0-5Vi SKA

9 K A l O O O p f 5 K A 2.8 KANJ/

SENSING CIRCUIT

RECORDER

BUCKING CIRCUIT

Fig. 2. --Calorimeter circuit.

42

Because minute temperature differences between the contents of the

two Dewars are almost inevitable, a bucking circuit was employed

to adjust the initial base line to zero or some other desired value.

Initiation of the reaction by mixing the reactants resulted in a

change in temperature--and hence in the thermistor resistance, pro

ducing an imbalance potential which was fed into the recorder. The

latter was a 2. 5 mv full-span Brown recorder with a chart speed of

l" per minute. Increased sensitivity was attained by inserting a

Brown Range Change accessory which decreased the span to 1 mv.

In order to smooth out the noise, a 1000 /uf capacitor was connected

in parallel to the recorder.

A glass bulb with a small opening at the bottom, which was

sealed with beeswax, served to separate the reactants prior to re

action. A glass rod plunger for breaking the seal and a syringe for

forcing out the solution were attached to a T-tube which was connected

by means of a standard taper joint to the top of the solution bulb. For

improved thermal transfer the bulb wall had been thinned to about 0. 7

mm by immersion in concentrated hydrofluoric acid.

Effective and equal stirring in each vessel was accomplished

with polyethylene stirrers driven by two 200 rpm synchronous motors

(Model K-2, Bodine Electric Co. ) which could be switched on simul

taneously. The. stirrer was guided into the vessel through a hole in

43

the cover whose diameterwas about 0. 5 mm larger than that of the

shaft, thus providing the only opening to the outside.

The electrical heaters ( ~ 60 ohms) were made from No. 36

manganin wire wound on a threaded 3 mm polystyrene rod and fixed in

place by a very light coating of epoxy resin. The rod was inserted in

to tightly-fitting thin-walled polyethylene tubing and was fashioned

into a circular shape by softening in a glycerol bath at 110-120° and

wrapping around a round object of the desired diameter. The ends of

the manganin wire were soldered to No. 20 copper leads for con

nections outside the calorimeter. Resistances were measured with

a Wheatstone bridge (Leeds and Northrup, Model 4735) at regular in

tervals. The variation was negligible.

Known amounts of heat were generated by passing a constant

current from a Sargent Model IV Coulometric Current Source,

equipped with a built-in timer, through the heater for a measured

period of time. Leads from the Sargent instrument were connected

to the copper leads of the heater via a three-position switch which

allowed the passage of current through each heater separately or

through both in series.

Calorimetric Procedure

An important advantage of a differential calorimeter lies in

its ability to cancel the heqtt of dilution and thus to feed only the

44

signal due to the main reaction into the recorder. When two solutions

are mixed, two heats of dilution are produced simultaneously, only

one of which can be compensated on the blank side. It was therefore

expedient to arrange for the other dilution heat to be negligibly small.

For this reason the reactant most likely to produce the greatest

dilution heat was placed on both the reaction and blank sides of the

calorimeter. In a few cases separate determination of a dilution heat

was necessary.

Solutions of the reactants were thermostated at 2 5. 0± 0. 1

degrees for sufficient time to attain thermal equilibration. The time

required varied according to the size and thermal properties of the

vessel and contents. Appropriate amounts of reactant and solvent

were pipetted into each Dewar to bring the total volume to 225. 0 ml,

thereby leaving only about a 7 mm air gap above the solution. After

sealing their openings with beeswax, the bulbs were filled with 12. 00

ml of solution, the top of which would then be about 5 mm below the

solution level in the Dewar. The calorimeter was assembled and the

syringes, opened to one ml in excess of the volume of the solution in

the bulb, were attached to the T-tubes. The stirrers were turned on

for a few minutes to homogenize the Dewar solutions. The entire

apparatus was then allowed to thermally equilibrate for about two

hours.

45

At the end of this time the stirrers were switched on and the

bucking voltage was adjusted to obtain a suitable baseline on the

recorder. The damping capacitor was turned on and allowed to charge

up. The chart drive motor was then started and an initial period of

10-15 minutes was recorded. The wax seal of the bulb on the blank

side was pierced and the solution was expelled into the Dewar solu

tion by means of the attached syringe. After a few seconds the syringe

was removed temporarily to permit the mixed solutions to rise into

the emptied bulb. The other wax seal was pierced and the heater on

the blank side was turned on. The bulb solution was then forced out

at such rate as to maintain the recorder pen at the same position.

The heater was turned off and on as required in order to compensate

the heat of reaction as nearly as possible and hence to approximate

a continuation of the initial period. Subsequent to mixing, about 5-7

minutes was required to reach thermal equilibrium, after which a

final period was recorded for sufficient time to give a well-defined

straight line (~ 10-15 min. ). Immediately after opening the calori

meter glass-calomel electrodes were inserted into the reaction side

vessel and the pH was measured.

At appropriate intervals calibrations were performed to deter

mine the sensitivity, S, by generating a known amount of heat on the

blank side and measuring the displacement on the chart paper. Fre

quently the final period of a run served as the initial period of a

46

calibration. To determine the difference in response, Ar, between

the sets of thermistors on the blank and reaction sides current was

passed through both heaters connected in series. The distance

between the initial and final periods was measured and then divided

by the time of heat generation to give Ar.

In order to estimate the accuracy and precision of the calori

meter, the well-established heat of formation of water was measured.

At an ionic strength of 0. 1 the neutralization of perchloric acid with

an excess of sodium hydroxide yielded heats of -13. 48, 13. 48, -13. 48,

and - 13. 45 kcal/mole for an average of 13. 47 kcal/mole, with a

standard deviation of 0. 015. By applying the appropriate heats of

dilution, ^ a value of -13. 34 kcal/mole at infinite dilution was ob

tained, in excellent agreement with recently reported values of

(2) (3) -13. 336 and -13. 337 kcal/mole. Although the maximum sensi

tivity of the calorimeter was about 0.00003°/mm of chart paper,

fluctuations in the initial and final periods due to electronic noise

1. C. E. Vanderzee and J. A. Swanson, J. Phys. Chem. 67, 285 (1963).

2. C. E. Vanderzee and J. A. Swanson, J. Phys. Chem. 67, 2608 (1963).

3. J. D. Hale, R. M. Izatt, and J. J. Christensen, J. Phys. Chem. 67, 2605 (1963).

47

reduced the actual sensitivity to about 0. 0001°. Separate experiments

indicated that the heat capacity of the calorimeter parts could be

neglected when estimating temperature changes to one significant

figure.

Reagents

The 1, 4-dioxane (Union Carbide Co.) was purified by refluxing

over sodium for a few days and then fractionating through a four-foot

column packed with glass helices. The distillate collected boiled at

98-99° under 700 mm Hg pressure.

The metal perchlorates were reagent grade, obtained from

the G. F. Smith Chemical Co. Approximately 0. 3 M solutions were

prepared and standarized with EDTA, using the procedures described

in. ̂ For Cu, Ni, and Mn the indicator was pyrocatechol violet, for

Zn--Zincon, for Cd and Pb--Xylenol orange, for Co--NH4SCH-

( 2 ) PhgAsCl. Solutions of NaClO^ gave negative tests with AgNOg and

BaClg solutions.

Standard sodium hydroxide solutions were prepared by diluting

a 50% solution and were standardized against primary standard grade

1. G. Schwarzenbach and H. Flaschka, Die Komplexometrische Titration, 5. ed., Ferdinand Enke Verlag, Stuttgart, 1965.

2. A. J. Cameron and N. A. Gibson, Anal. Chim. Acta 25, 24 (1961).

48

potassium acid phthalate. Perchloric acid solutions were prepared

from G. F. Smith Chemical Co. reagent grade acid and were stan

dardized against the sodium hydroxide solution.

8-Q,uinolinol (oxine) and 2-methyl-8-quinolinol were Eastman

Kodak Co. white label grade and were recrystallized from aqueous

ethanol followed by sublimation. The respective melting points of the

purified compounds were 73.0-74.0° and 71. 5-73.0°. Reported 74-74°

n r , A ° and 74 .

8-Quinolinol-5-sulfonic acid (Eastman Kodak Co. , white label

grade) was twice recrystallized from boiling 5% HC1 and once from

boiling water. It was air-dried. Tests with AgNO^ indicated the

absence of Cl~. Standard solutions of the sodium salt were prepared

from the free acid by titration to the isoelectric pH with standard

NaOH.

4-Methyl-8-quinolinol was synthesized according to the pro

cedure of Phillips, Elbinger, and Merritt. ̂ After three recrystal-

lizations from aqueous ethanol the material was sublimed twice. M. p.

140.0-141. 5. Reported 141°.

Quinoline-8-thiol (thiooxine) and 2-methylquinoline-8-thiol

( 2 ) were synthesized according to Kealey and Freiser and were

1. J. P. Phillips, L. L. Elbinger and L. C. Merritt, J. Am. Chem. Soc. 71, 3986 (1949).

2. D. Kealey and H. Freiser, Talanta JJ3 (1966) (in press).

49

converted to their sodium salts. After preparing solutions of these

reagents, an aliquot was saved for assay by potentiometric titration

with silver ion!^ Since these reagents oxidize slowly in solution,

the assay was performed immediately after initiation of the reaction

in the calorimeter.

2, 4-Pentanedione (acetylacetone) (Eastman Kodak Practical

grade) was washed successively with NaHCOg solution and water, then

(2 ) dried over anhydrous sodium sulfate, and fractionally distilled.

o B. p. 134.5-135.5 under 700mm Hg pressure. Gas-chromatographic

analysis using a silicone rubber column indicated substantially less

than one per cent of impurities.

1. M. W. Tamele and L. B. Ryland, Anal. Chem. 8_, 16, (1936).

2. D. Dyrssen, Svensk. Kem. Tidskr. 64, 213 (1952).

CALCULATIONS

Acid Dissociation Constants

The acid dissociation constants of the 8-quinolinols can be

represented by

[H+] [HL] / [H2L+] = Knh (1)

[H+] [L"] / [HL] = Koh (2)

These equations apply to 8-quinolinol-5-sulfonic acid as well, for in

the pH range employed only one anionic form (the same as for the other

oxines) is important.

In the determination of the acid dissociation constants by

potentiometric titration, the following equations must be considered:

Mass balance

CL = [H2L+] + [HL] + [L~] (3)

Charge balance

[H2L+] + [H+] + [Na+] = [A~] + [OH] + [L~] (4)

Here CT refers to the total ligand concentration and [A ] is equal to J-F

the concentration of strong acid added, which in the case of the sulfona

ted ligand is provided by the free sulfonic acid. [Na+] is equal to the

concentration of NaOH titrant added.

Combination of these equations with the expressions for the

acid dissociation constant yields

50

51

„ _ [H+] {CL [A] - [Na+] - [H+]

[A] - [Na+] - [H+] (5)

K - [H+j - tA"] - [OH"]] (6)

OH CL " [tNa+] " [A" I"* [OH"] _J

The dissociation constant of acetylacetone in 0.1M NaClO^

has been reported in the literature. ̂

Chelate Formation Constants """"

The chelate formation constants may be evaluated from a

knowledge of two parameters, H, the average number of ligand mole

cules bound per metal ion, defined as

[ML+] + 2[MLj n = ( 7 )

M

and [L ], the ligand anion concentration. These parameters, in turn,

can be calculated from the acid dissociation constants and the following

expressions describing the composition of the mixed solutions of ligand

and metal:

1. J. Rydberg, Svensk. Kem. Tidskr. 67, 499 (1955).

52

Mass balance

CM = Cm2+] + [ML+] + [ML2] (8)

CL = [HGL4] +[HL] + [L_] + [ML+] + 2[ML2] (9)

[C10~] = [A"] +2Cm (10)

Charge balance

2[M2+]+[ML+]+[H2L+]+[H4'3+[Na+] = [L~]+[0H"]+[C10^ (11)

Appropriate combination of these equations gives

C C +[A"]-[H+]-,[Na+] ( K +[H+]

* = ^ < 1 2 >

and

r . - , K ^ - ^ ' ^ I V oh

t»*j I

For details of these derivations the work of Johnston^ should

be consulted.

Another expression for n in terms of formation constants and

[L ] can be derived by expanding the denominator of the defining equa

tion (8) and expressing [ML+] and [MLg] in terms of the formation

constants, = |> +]/[M2+] • [L~] andK12= [MLg]/[M2+] • [l"]2.

1. W. D. Johnston, Ph. D. Thesis, University of Pittsburgh (1953).

53

Then

K^L'I +2K12[L"]2 (14) n

I+KJL"] +K12[L"]2

This equation can be rearranged to give

n = K,JL~] — + K (15) [L"](l-n) 1 - n

A least squares plot of of n vs. [L ] 2-n yields a i L - j ( l - n ) — L J

straight line with a slope equal to and an intercept equal to K^.

The log Kg values for the nickel chelates of oxine- 5-sulfonic acid

in water and in 50% dioxane were obtained graphically from the pL

value at n = 2.5, since the separation between log Kg and log Kg was

greater than two log units.

Heats of Reaction

The heat Q generated by the passage of a steady current i for a

time t through a resistance E is given by

where 4.1840 is the factor for converting joules to defined calories.

By using a fixed resistance and the same current setting, Q becomes

only a function of time.

To find the experimental heat of reaction, Q^, the final period

is first extrapolated back to the end of the initial period when the

4.1840 ( 1 6 )

54

reactants were mixed, and the distance, d, (Fig. 3) between these

periods is measured. Qr is then calculated from the following equa

tion:

Qr = Q + (d + Ar • t)S (17)

where Ar is the difference in response, t, the time, and S, the sensi

tivity, as described previously.

Heats of Reagent Dissociation

For one-step reactions, such as protonation and dissociation,

where the desired reactions can be forced to proceed quantitatively by

the use of an excess of a reagent, calculation of the heat of reaction is

simple:

AH = Q IA (18) r

where A is the number of millimoles of the desired species undergoing

reaction. The heat of protonation, AH.m) is measured directly, but JNri

the heat of dissociation, AHQJJ, is obtained as the difference between

the heat of neutralization and the heat of dissociation of water:

HL + OH" —> L~ + H-O AH . (19) 2 neut

Ho0 —> H+ + OH" AH (20) 2 w

HL —> H+ + L" AHOH(SH) (21)

Heats of Chelation

The heats of chelation of the thiooxinates were determined

directly, _i. £., the reaction goes to completion, so that equation (18)

TIME

Fig. 3. --Typical t ime-temperatur

56

applies in this case as well.

In the determination of the heats of formation of the oxines, the

experimental heat of reaction, Q^, is a composite of these heats of

reactions:

HL — ->H + L AHOH (22)

M2+ + L~ — -> ML+ AHT (23)

2+ M + 2L — ̂ ML2 AH12 (24)

HL + H+ —> H2L+ AHNH (25)

Here L refers to the total ligand which becomes bonded to

metal, ji. e., L = ML+ + 2MLg. Consequently

Qr = ML+AH1+ML2AH12 + H2L+AHNH + (ML+ + 2ML2)AHOH (26)

AH^JJ and AHQJJ are determined separately and ML+, MLG,

and H2L+, which represent the number of millimoles formed of these

species, are calculated from

(ML+ + 2ML ) = V • C n (27)

+ V ' ( C L ~ C M S ) H2L = —i — — T ~ < 2 8 )

I [ H ] )

+ V'CM" M L * u + I/ (K2LL'J) )

57

where V is the total volume of solution. It should be noted that volume

shrinkage occurs on mixing dioxane and water, which 25° gives a cor

rection factor of 0. 982^

Substituting the known quantities, we obtain

M L + ' A H 1 + M L 2 ' A H 1 2 = Q c h e l ' ( 3 1 )

where %hel " Qr ' (ML+ + 2ML2» AHOH " H2L+ ' ^NH'

The heats of chelation, AH^ and AH^2< can then be evaluated

by solution of simultaneous equations obtained at low n (n < 1) with

those obtained at high n (n> 1).

For the acetylacetonates the calculations are based on each

separate step of chelate formation. Here is due to reactions (19)

and (23), the reverse of reaction (20), and the following:

ML+ + L~ —> ML2 AH2 (32)

In this case ML+ is obtained from

ML+ = V- CM • n/| 2 + (l/K2[L"])j (33)

+ + The millimoles of ML , MLg, OH , and H present initially

are subtracted from their final amounts. The differences thus obtained

are substituted in the following relation

ML+ • AHt + ML2 * AH2 = Qchel (34)

1. D. Fleischer, Ph.D. Thesis, University of Pittsburgh (1959).

58

where Q . = Q - H • AH - OH • AH ,. The appropriate sets chel r w neut r

of equations are then solved simultaneously for AH^ and AH2 in a

manner similar to that above.

Computer programs were written to perform the above

calculations.

ERRORS

The errors associated with the AH values reported in this

study stem mainly from two sources: uncertainties in the appropriate

equilibrium constants and in the experimental heats of reaction. In

the majority of cases the simultaneous formation of more than one

species is unavoidable, requiring a knowledge of the stepwise equilib

rium constants and thereby increasing substantially the overall

error. For most reagent heats of dissociation the essentially quan

titative conversion of the neutral ligand to its cationic or anionic

form with an excess of perchloric acid or sodium hydroxide obviated

the necessity for the use of dissociation constants. Furthermore,

the relatively high solubilities permitted temperature changes as high

as 0. 05 .to 0.1° to be attained. Based on the experimental data, the

uncertainties in the heats of dissociation of oxine, 2-methyloxine,

oxine-5-sulfonic acid, and acetylacetone.probably do not exceed 0. 05

kcal/mole. Due to a more sparing solubility in the case of 4-methyl-

oxine, the error is about 0. 1 kcal/mole. A similar magnitude of

error is expected for the heat of dissociation of the SH group of thio-

oxine and its 2-methyl derivative. The heats of protonation of these

compounds, however, depend on calculation of the extent of reaction

59

60

from the measured final pH and the spectrophotometrically deter

mined pKnvT„, so that the uncertainties may amount to 0. 3 kcal/mole. f NH j

The uncertainties in the dissociation constants should be less

than 0. 05 log unit, corresponding to about 0. 07 kcal/mole in the free

energy. The errors in the entropy values should be given by the sum

of the errors in the free energy and enthalpy values, multiplied by

3. 35 (since at 25° one kcal/mole corresponds to 3. 35 entropy units).

Except for the case of the thiooxinate chelates, errors in the

heats of chelation arise from the uncertainties in the formation con

stants and in the calorimetric determinations. Analogous to the

previous procedure involving reagent heats, a large excess of metal

ion converted the anionic form of the thiooxinates completely to the

ML+ species. The limited solubility of these chelates, however, re

stricted the temperature changes observed to only a few thousandths

of a degree, which resulted in a greater uncertainty in the AH^ values

(0. 5 to 1.0 kcal/mole), and precluded the determination of AH^ values.

For the remaining chelates determination of the formation

constants was necessary. Since these were determined from some

what fewer, but perhaps more reliable points, and with a greater

variation in the total concentrations of metal and ligand, only a

slightly larger uncertainty than that prevailing in the ordinary poten-

tiometric titration technique is to be expected. On the basis of the

61

formal error treatment presented by Fleischer, ̂ an error of about

0. 2 log units might be anticipated in this work. Judging from a com

parison of the values obtained in this study with those determined by

Mr. Ted Carnavale in this laboratory using potentiometric titration

under similar conditions, this assumption appears to be justified:

System log Kx log K2 log K12 l o g K x logK2 log K^2

Mn(II)- -2-methyloxine 6. 84 6. 46 13, 30 6. 81 6 . 2 9 13. 10

Mn(II)- -oxine-5-sulfonic acid

CO 5. 92 13. 05 7. 05 6 . 1 3 13. 18

Co(II)- - 2 - methyloxine

o

CO CO 8. 66 1 7 . 4 6 8 . 5 9 8 . 7 9 17. 38

Pb(II)-- 2 - methyloxine 9. 85 7. 10 16. 95 9. 97 7 . 2 1 17. 18

Pb(II)-- 2 - methyloxine 10. 01 7 . 2 8 1 7 . 2 9

The values for the Cu, Ni, and Zn chelates of oxine and 2 -

methyloxine generally agree with those reported for a 50% dioxane-

0. 3 M NaClO . medium at 20°. ̂ 4

The total amount of chelate and protonated ligand formed is

determined from the final pH, and independent of the formation con

stants. The relative amounts of the various chelate species formed,

however, is governed by the formation constants. Hence the errors

1. D. Fleischer, Ph. D. Thesis, University of Pittsburgh (1959).

2. H. Irving andH. S. Rossotti, J. Chem. Soc. 2910 (1954),

62

introduced into the AH values by inaccuracies in the formation con

stants result from uncertainties in the apportionment of the observed

heat of reaction among the species present, since an error in the

concentration of one chelate species affects the concentration of the

other in the opposite direction. Because the stepwise AH values are

usually rather similar, however, such uncertainties produces errors

of less than approximately 0. 5 kcal/mole per step. This is supported

by the following AH values obtained through the use of formation con

stants and those obtained from proton displacement or direct re

actions which could be forced to proceed quantitatively to only one

chelate species:

Method of Calculation System Dependent on Independent of

-AHRAH12-AHI3

Cu(II)--oxine 10.2 19.6 9,4 18.9 9 . 7 2 0 . 2

Cu(II)--oxine-5-sulfonic acid 18.6 18.6

Ni(II)--oxine-5-sulfonic acid 25.4 24.2

As in the case of the reagent heats of dissociation, that por

tion of error in the heat of chelation due to calorimetric errors will

be a function of the magnitude of the heat evolved, which, in turn,

will generally be determined by the solubility of the chelate. (The

term solubility is employed here in the sense of the tendency of the

chelate to remain in solution for the duration of a calorimetric

63

measurement, and does not necessarily indicate the equilibrium

solubility.) Consequently, for the soluble chelates of oxine-5-

sulfonic acid and acetylacetone the total error, chiefly derived from

uncertainties inK^, in AH^, AH^* and AH^g will be about 0. 5, 1. 0,

and 1. 5 kcal/mole. A similar magnitude should be valid for AH^ of

the oxinates and 2-methyloxinates. Their AH^ values, however,

probably deviate by 1.5 kcal/mole, especially for the Mn, Co, and

Zn chelates. The greater insolubilities of the 4-methyloxinates,

which limited the temperature changes to only 0. 0005° to 0. 0006° for

the high n runs of Mn, Co, and Zn, reduce the reliability of AH^ to

0. 5 to 0. 8 kcal/mole, and AH^ t° about 2. 0 kcal/mole.

The errors in the entropies of chelation can be found analo

gously to that described for the entropies of dissociation.

The errors in AH0 and AS„ are, of course, equal to the sum 4 &

of the errors in AH, and AHL 0 and in AS.. and AS. 9.

DISCUSSION

Comparison of Methods

Two methods are generally employed for the determination of

heats of reaction in solution: direct calorimetry and the variation of

the equilibrium constant with temperature. The latter method is

based on the van't Hoff equation

dink/ dT = AH/RT2

and hence a plot of log K vs. 1/T yields a straight line with a slope of

AH/2. 303R. The heat of reaction, however, is not independent of

temperature, but varies with changes in the heat capacities of the

system. An indication of the magnitude of this variation is provided

by the recent data of Izatt, et al. ^ for the heat of chelation between

copper (II) and alanine: the AH and AH values at 10, 25, and 40° 1 ltt

are 5. 38, 4. 50, and 3. 99 kcal/mole and 10. 85, 9, 75, and 9. 64 kcal/

mole, respectively. A similar variation was also observed in the

reagent heat of dissociation. If these data are typical, the error

resulting from the assumption of temperature independence of AH

over a short temperature range would be tolerable in many cases.

1. K. P. Anderson, D. A. Newell, and R. M. Izatt, Inorg. Chem. 5, 63 (1966).

64

65

Recently, a new family of general equilibrium equations was devel

oped to represent the temperatur