Research: Science & Education
Metal Complexes of EDTA: An Exercise in Data Interpretation Philip C. H. Mitchell Department of Chemistry, University of Reading, Reading, RG6 6AD, UK
Developing the ability to discern patterns and trends in chemical data and to build them into a model is, for the chemist, a skill as important as problem solving. Textbooks include large numbers of practice problems; instructors hold problem-solving classes; and problem-solving features regularly in this Journal (1, 2)—but data interpretation is less practiced. Much of one’s working life as a chemist is devoted to interpreting data from experiment and calculation or from the literature. Here my concern is not statistical analysis—most chemists know the standard mathematical techniques—but the next stage: recognizing patterns and trying to understand them, quantitatively or qualitatively, with the help of some general theory. In other words, developing a model. To illustrate this theme I describe in this paper how the stability constants of metal complexes of ethylenediamine-N,N,N′,N′-tetraacetate, EDTA 4{, may be interpreted through theories of metal–ligand bonding.
[M(H2O)6]2+ (aq) + EDTA4{ (aq) → [M(EDTA)]2{ (aq) + 6H2O
(1)
The stability constant, K, of the complex is the equilibrium constant for the complex-forming reaction (eq 2, charges omitted): K = [complex]/ [cation][EDTA]
(2)
Here [M(EDTA)]2{ is the complex and [M(H2O)6 ]2+ the cation. The logarithm of the stability constant is proportional to the Gibbs free energy change of the reaction (eq 3): ∆G = {RT lnK
(3)
Note that ln K measures the difference in free energy between the water complex and the EDTA complex. 1
The Experimental Data
EDTA Complexes The ligand EDTA 4{ (1) forms stable complexes with metal ions; it is sexadentate binding through four oxygens and two nitrogens. EDTA complexes are prepared by reacting cations with EDTA4{ in aqueous solution (e.g., eq 1). The reaction is substitution of coordinated water by EDTA 4{. O–
–O
C O
C CH2
CH2
Stability Constants of EDTA Complexes Values of K have been measured for many EDTA complexes (3). We wish to correlate trends in logK with properties of the metal ions and thence with the cation–EDTA bonding interaction. In Table 1 values of log K for selected EDTA complexes are listed according to the position of the central metal in the periodic table and the charge on the cation. Trends in Values of log K: Correlation with Properties of the Metals
O
NCH2CH2N CH2
O C –
CH2
In developing a model we must first assume that values of logK are not random. With what underlying properties of the metals do the trends in the values of log K correlate? Consider the position of the metal in the periodic table and properties that vary periodically—sizes, ionization energies, electronegativities.
O
C O–
O
EDTA4{ (1)
Table 1. Log K 's of EDTA Complexes According to Position of Central Atom in Periodic Tablea Group 1 Group 2 Group 3
Transition metals
Group 12 Group 14
Li + 2.79 Na+ 1.7
Mg2+ 8.64
K+ 0
Ca2+ 10.6
Al3+ 16.1 V2+ 12.7
Cr2+ 13.6 Cr3+ 24
Sr2+ 8.53 Ba2+ 7.63 aAt
Mn2+ 14.0
Fe2+ 14.3
Co2+ 16.3
Fe3+ 25.1
Co3+ 36
Ni2+ 18.6
Cu2+ 18.8
Zn2+ 16.5
Ag+ 7.32
Cd2+ 16.5 Hg2+ 21.8
Pb2+ 18.0
20 or 25 °C and 0.1 M ionic strength.
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Research: Science & Education
12
(a) 10
For groups 1 and 2, logK decreases down the group; for group 12, logK increases with increasing atomic number (the vertical trend of groups 1 and 2 is reversed).
Cation Charge
(b)
The bonding in compounds of metals is often described by an ionic model that may be modified to incorporate some covalency. This description is sensible because the characteristic property of the metallic elements is ionization to positive ions. The primary bonding interaction in metal complexes in the ionic model is coulombic, the attraction between unlike charges (the positive cation and the negative charge or dipole of the ligand). Thus with a coulombic model the interaction energy will increase with the charge on the cation. This is the trend we observe. However, the cation charge cannot be the only determinant of the interaction energy, since for ions of a given charge there is a wide variation of values of logK. If the dimensions of the EDTA ligand are approximately con-
1236
Li 5x1/r Na
4
log K K
2
5x1/r
0
10
20
30 atomic number
40
50
60
20 log K
log(K/l mol ) or 10x1/(r/A)
18
16
-1
oxide radii
14 Pauling radii 12
10
22
V
Cr
23
24
Mn 25
Fe
Co
26 27 atomic number
Ni 28
Zn
Cu
29
30
31
25
(c)
log K
23 21 19 17 15
-1
log(K/l mol ) or 10x1/(r/A)
The Ionic Model
Sr Ba
6
-2
Pretransition Metals. For group 1 (Fig. 1a) logK decreases with increasing atomic number, correlating with the decrease of 1/r. For group 2 the trend is similar, but Mg2+ is out of line (see later). First Transition Series. Correlation of log K with 1/r (Fig. 1b) is less satisfactory than for groups 1 and 2— certainly for the elements before iron. Group 12. Here (Fig. 1c) there is an inverse correlation between log K and 1/r; logK increases as the ions get bigger.
Interpreting Trends in Stability Constants
Mg
0
The trend in logK’s (Table 1) is 1+ < 2+ ≤ 3+.
Ionization Energies and Electronegativities In Figure 2, logK’s of EDTA complexes of the divalent transition metal cations are plotted against the sums of the first and second ionization energies (I1 + I2) and the Pauling electronegativities (5, 7). For the transition metals values of logK correlate with ionization energies better than with electronegativities. However, for the posttransition metals of group 12 (Fig. 3) logK correlates with Pauling electronegativities rather better than with ionization energies.
8
-1
pretransition < transition < posttransition
Atomic and Cationic Radii The trends in atomic and cationic radii are well known: values increase down groups 1 and 2 and decrease across the first transition series—the reverse of trends in logK. Evidently logK decreases as the cation radius increases. To visualize the relationships we plot log K’s and the reciprocals of the cation radii (1/r, see above) against atomic number for Groups 1 and 2 (Fig. 1a), the first transition series (Fig. 1b), and groups 12 and 14 (Fig. 1c). The radii are from R. D. Shannon (4).
Ca log K
log(K/l mol ) or 5x1/(r/A)
Position in the Periodic Table From the horizontal trends in the values of logK (Table 1) we see that the EDTA complexes with the smallest values of log K are those of groups 1 and 2 (the pretransition or A metals), and group 1 values are smaller than group 2 values. Log K increases across the first transition series and is larger for the posttransition metals (groups 12 and 14, the B metals) and also for Ag+ than for group 1. The horizontal pattern is
13 Zn
11
10x1/r Cd
9
Hg Pb
7 5
25
35
45
55 atomic number
65
75
85
Figure 1. Plots of log K (solid symbols) for EDTA complexes and reciprocals of the ionic radii (1/ r ) (open symbols) vs. atomic number for (a) pretransition metals (M + group 1, M 2+ group 2); (b) transition metals (M 2+); (c) posttransition metals (M2+).
Journal of Chemical Education • Vol. 74 No. 10 October 1997
Research: Science & Education 30
30 (ionisation energy/kJ)/100
28 logK or electronegativity or ionisation energy
logK or electronegativity or ionisation energy
28 26 24 22
10x(Pauling electronegativity)
20 18 16 14
log K
12 V 10
22
23
Cr 24
Mn 25
(ionisation energy/kJ)/100
26 24 22
logK
20 18 16 14
10x(Pauling electronegativity)
12 Fe
Co
26 27 atomic number
Ni 28
Cu 29
30
31
10
Cd
Zn
Zn
25
35
45
55 atomic number
Hg Pb 65
75
85
Figure 2. Values of logK for EDTA complexes, sums of the first and second ionization energies and Pauling electronegativities plotted against atomic number for the transition metals.
Figure 3. Values of logK for EDTA complexes, sums of the first and second ionization energies and Pauling electronegativities plotted against atomic number for the posttransition metals.
stant, then trends in the distances r are equivalent to trends in the cation radii; the interaction energies should therefore get smaller as the ions get bigger. Clearly, for groups 1 and 2 where logK is proportional to 1/r (see Fig. 1a), the cation–EDTA interaction is predominantly coulombic. For EDTA (and other) complexes of these electropositive elements an ionic model of the bonding is thus appropriate; it is less so for the transition metals and posttransition metals (see Figs. 1b and 1c). Indeed, in group 12, log K increases as the ionic radii increase (Zn to Hg).
The Problem of Magnesium—Entropy
Ligand Polarization and Covalency For the transition metals and posttransition metals, log K for the EDTA complexes correlates better with ionization energies and electronegativities (see Figs. 2 and 3) than with radii. To understand this, first recall that for metal cations as we move from left to right across the periodic table (e.g., K to Zn to Pb) the binding interaction with the less electronegative, more polarizable, nonmetals increases: the cations exhibit more B-character. To interpret these observations we modify our ionic model by introducing a covalent contribution, which increases as the cations become more polarizing and the ligands less electronegative (N vs. O). Thus the increase of stability of the EDTA complexes, relative to aqua complexes, across the transition series can be attributed to an increase of the covalent contribution to the bonding—a trend confirmed by recent ab initio calculations on the transition metal aqua ions (9).
Table 2. Values of ∆H and ∆S for Group 2 EDTA Complexesa Element
∆H (kJ mol{1)
∆S (J mol{1 deg{1)
Mg
14.6
21 0
Ca
{27.4
110
Sr
{17.1
110
Ba
{20.6
80
Data from ref 3. At 20 or 25 °C and 0.1 M ionic strength.
a
The value of logK for Mg-EDTA (see Fig. 1a) is anomalously low. To account for this, first recall that log K is proportional to the free energy (∆G) of complex formation and that ∆G is the net value of an enthalpy (∆H) and entropy (∆S) term (eq 8). ∆G = ∆H – T∆S
(4)
Strictly, the metal–ligand binding interaction is measured by ∆H. Therefore, implicit in our correlation of log K with binding in EDTA complexes is the assumption that trends in log K (equivalent to ∆G ) follow ∆H: that is, the entropy term (T∆S) is not dominant. Generally this is true for EDTA complexes (3), but magnesium is an exception (see Table 2): ∆H for Mg-EDTA is positive (endothermic) (possibly because of strain in the EDTA molecule when bound to the small Mg2+ ion) and the favorable logK is due to the entropy term (increase of translational entropy of water molecules due to charge neutralization when the complexes form, and consequent less solvent ordering). Note 1. Stability constant values are listed, in this paper and generally, as log10 K, or simply log K; ln K = 2.303 log K.
Literature Cited 1. Nakhleh, M. B.; Mitchell, R. C. J. Chem. Educ. 1993, 70, 190–192. 2. Asieba, F. O.; Egbugara, O. U. J. Chem. Educ. 1993, 70, 38–39. 3. Martell, A. E.; Smith, R. M. Critical Stability Constants; Plenum: London, 1974; Vol. 1, pp 204–211. 4. Shannon, R. D. Acta Crystallogr. 1976, A32, 751. 5. Pauling, L. The Nature of the Chemical Bond, 2nd ed.; Cornell University: Ithaca, NY, 1948; pp 58–75. 6. Phillips, C. S. G.; Williams, R. J. P. Inorganic Chemistry; Clarendon: Oxford, 1965; Vol. 1, p 114. 7. Coulson, C. A. Valence, 2nd ed.; Oxford University: Oxford, 1961; pp 136–142. 8. Laidler, K. J.; Meiser, J. H. Physical Chemistry, 2nd ed.; Houghton Mifflin: Boston, 1995; p 808. 9. Akesson, R.; Peterssonn, L. G. M.; Sandstrom, M.; Siegbahn, P. E. M. J. Am. Chem. Soc. 1994, 96, 10773–10779.
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