direct calorimetric determination of heats of ......the heats of reactions of several chelating...
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DIRECT CALORIMETRIC DETERMINATION OFHEATS OF FORMATION OF SOME METAL CHELATES
Item Type text; Dissertation-Reproduction (electronic)
Authors Gutnikov, George, 1938-
Publisher The University of Arizona.
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This dissertation has been microfilmed exactly as received 67-3956
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
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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
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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
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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
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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
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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
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LIST OF ILLUSTRATIONS
Figure Page
1. Cross-sectional View of Calorimeter 39
2. Calorimeter Circuit 41
3. Typical Time-temperature Curve 55
v
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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
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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
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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
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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
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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.
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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
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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).
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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).
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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
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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).
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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).
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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).
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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).
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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).
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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
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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).
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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
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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
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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).
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Recently, a new family of general equilibrium equations was devel
oped to represent the temperatur