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DIRECT CALORIMETRIC DETERMINATION OFHEATS OF FORMATION OF SOME
METAL CHELATES
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Authors Gutnikov, George, 1938-
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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
-
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
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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
-
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).
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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).
-
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
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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),
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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
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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
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65
Recently, a new family of general equilibrium equations was
devel
oped to represent the temperatur