Thomas H. Cmwford1 and John Swanson
California Institute of Technology Pasadena, 91 109
I I
I
Temperature Dependent Magnetic Measurements and Structural Equilibria In Solution
The importance of structure in contemporary chemistry is clearly evidenced by the increasing number of papers which deal with this subject in both the solid state and in solution. While the solid crystalline material may be structurally characterized quite accurately by diffractiontechniques, the structure of complex molecules or ions in solution must be inferred from their spectral and magnetic properties. Magnetic behavior has long been recognized as a readily obtained physical property which is closely tied to the structure of the compound, as described a number of years ago by Pauling and more recently interpreted by others in terms of the ligand field and molecular orbital theories: Temperature studies of magnetic properties have been found especially useful in establishing the nature of the ground states for paramagnetic ions which is intimately related to the symmetry of the magnetic species. Recently, a number of transition met,al complexes have been reported to undergo structural changes in solution as the temperature is changed. These structural modifications are prominently reflected in the concomitmt changes of the magnetic moment of the solution. Several such complexes have been studied and the thermodynamics of the processes causing the changes in magnetic behavior determined. These systems seem to us to be very suitable for undergraduate investigations in as much as they provide experience in the area of synthesis, dynamics, and structure. One of the problems, however, is that doing temperature-dependent magnetic studies is often not possible in many undergraduate laborat,ories, since they are not equipped with the apparatus for making such measurements. We wish to bring to the attention of those interested in such experiments a very useful and simple way for making solution magnetic measurements. The method employs a nuclear magnetic resonance spectrometer, and was originally described by Evans in 1959 (1). However, in our discussions with many people it seems that the method is not as widely known or used as it deserves to be. We recognize that it is far less expensive to set up a variable temperature Gouy balance than to install an nmr spectrometer for making temperature-dependent magnetic susceptibility measurements and that this experiment may have some appearance of "overlcill." However, we also recognize that there may be many undergraduate laboratories Contribution No. 4008 of the Gates and Crellin Laboborstories Chemistry. ' Present address: Department of Chemistry, University of Louisville, Louisville, Ky. 40205. of
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which are equipped to do room and/or variable temperature nmr spectroscopy but ~vhichare not equipped with even a room temperature Gouy balance. The Evans method will immediately provide a method of obtaining reasonably accurate magnetic susceptibilities with no equipment in addition to the nmr spectrometer. We shall simply describe the method as presented by Evans and out,line the experimental approach we have taken and present some results obtained. A number of papers have appeared in recent years describing the Gouy method, the apparatus as well as the theory of magnetic moments as related to chemical structure (2-4) and the units of magnetism (5). The reader is referred to these papers for a more detailed discussion of such matters. During the preparation of this manuscript a description, to which we shall refer later, of another experiment using the Evans method, appeared in THIS JOURNAL (6). Theory
One of the parameters which proton nuclear magnetic resonance spectroscopy provides is called the chemical shift, which is a measurement of the separation of the magnetic resonance positions of differenttypes of protons. The chemical shift of a magnetic nucleus is a complex function of many variables and these have been discussed adequately in several excellent references dealing with the principles of nmr spectroscopy (7). However, one important factor in determining the resonance line position, of which we shall take advantage, is the magnetic susceptibility of the medium in which the resonating nuclei are immersed. Consider the chemical shift of a specific type of protons in a solvent and observe the change of this shift when the paramagnetic species to be examined is added. Let the difference in volume magnetic susceptibilities of the two systems be AK. The difference in the magnetic resonance absorption of the protons in the two solutions is then given by the relationship
Evans bas experimentally confirmed the validity of this expression by studying the proton magnetic resonance of CH2 groups in dioxane in the presence of small amounts of Mn2+ and Co2+ ions (1). Equation ( 1 ) may be restated in terms of the more commonly used frequency separation ( A j / j replacing A H / H ) and by converting to mass susceptibility to give the follo~ing relationship
where x, = ~ / mis the mass susceptibility of the dissolved paramagnetic substance, m is the concentration of the paramagnetic substance expressed in grams per milliliter; Af is the separation of the resonance positions for two identical protons in the two solutions, and f is the frequency of operation of the spectrometer, both expressed in hertz, and xo is the mass susceptibility of the pure solvent. A correction term has been suggested by Evans to take into account any differencein density of the pure solvent, do, and that of the solution, d,, yielding
The third term in eqn. (3) has been found to make only a small correction and in cases where the paramagnetism is large the correction is negligible (1). The determination of the mass susceptibility of a p a r e magnetic substance in solution is made, therefore, by measuring the difference in the chemical shift of some proton in the pure solvent and in a solution containing the paramagnetic substance of known concentration. The value of xo may be obtained by summing the atomic susceptibilities of the substituent atoms of the solvent (including contributions from any constituent effects, e.g., C=C) and dividing this sum by the molecular weight of the solvent. The atomic susceptibilities are available in various references (8, 9). The mass susceptibility, x,, which results from eqn. (2) may be converted into molar susceptibility, xM', by multiplying X , b't the molecular weight of the complex. Then xM' must he corrected for the presence of the diamagnetic contribution from the ligand atoms. This is done by simply summing the diamagnetic contrihution (8,9) of each ligand atom and groups of atoms and adding the sum to the susceptibility of the complex to give the corrected molar susceptibility xas. This is related directly to the magnetic moment by eqn. (4),as discussed in references (2-6). Table 1 includes the magnetic moments of several transition-metal complexes, measured a t -40°, the normal operating temperature of our nmr spectrometer. Details are given in the Experimental Section. Tempmature Study. Because variable temperatures are readily obtainable with many commercial nmr spectrometers, the Evans method becomes a very convenient way of measuring the temperature-dependent magnetic properties of substances in solution. There are numerous systems *hich exhibit such behavior and we wish to describe two of them which are particularly Table 1.
Comvound* Cr(aca~)~ Fe(acac)a Cu(acttc)p Co(awe)n Cu(sa1icyl). Ni(sali~yl)~
well suited for investigation in the undergraduate laboratory. One system involves the preparation of a Ni(I1) complex with the ligand first reported by Sacconi (10).
This complex exists in solution at room temperature as a mixture of the ~aramaeneticoctahedral form and a diamagnetic square planar form. As the temperature increases the equilibrium shifts in favor of the diamagnetic form as the piperidine nitrogens in the axial positions are cleaved from the coordination of the nickel ion. The other system involves an equilibrium between monomeric and dimeric forms of a complex of Fe(II1) with the ligand N-hydroxyethylenediaminetriacetic acid (HEDTA) ( I I).
-
HOCHnCHa
\
HOGCH,;NCH2CHnN' (HEDTA)
/
CHlC02H
'
CHICOZH
We shall discuss the Ni(I1) system first. Nickel(I1)-Schiff Base Complex. The Ni(I1) system is attractive because it involves the preparation of a transition-metal complex, an investigation of its magnetic properties and the structural implications thereof, and the energy associated with the change in geometry from octahedral to square planar. Sacconi, et al., have reported the magnetic and structural properties of several Schiff base complexes of Ni(I1) including the present one. The magnetic moments range from zero (no unpaired spins and square planar) to 3.3 B.M. (two unpaired spins and octahedral). Intermediate values of magnetic moment indicate a mixture of octahedral and square planar forms in equilibrium. The presence of a third structural form, a five-coordinate square pyramid is an additional possibility. However, in the solvent m-xyleue, Ni(I1) complexes of I show no spectral evidence of any of this form being present (10). For this reason all solution magnetic measurements were made in m-xylene. The percentage of diamagnetic substance present in the solution can be calculated from the solution magnetic moment, w, and the value of 3.3 B.M. for the pure octahedral complex according to the equation
(
O/, diamagnetic species = 100 1
-
J
'5'
Room Temperature Magnetic Moments Measured in Different Solvent Systems
Benzene
DMSO
Benzeneb
DMSOb
CHCI,
TMS
3.7 5.5 Insol. 4.6 1.8 3.0
3.7 5.5 Insol. 4.8 1.8 2.8
3.8 5.6 Insol. 4.7 1.8 3.0
3.8 5.6 Insol. 4.8 1.8 2.8
3.7 5.6c 1.8 Insol. Insol. Insol.
3.7 5.5( 1.8 Insol. Insol. Insol.
CHClP
TMSb
3.8
3.8 5.6* 1.8 Insol. Insol. Insol.
5.70
1.8 Insol. Insol. Insol.
Preparations of these six compounds are described in references (14-18). Weasurements made using external standard method. ' 0.0200 g solute/ml solvent. a
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The ratio p2/(3.3)%represents the fraction of paramagnetic species present. The squared terms are used since X, is proportional to r2 (see eqn. (5) and references (8-4)). Since the equilibrium is between these two species, the equilibrium constant for the process diamagnetic
Table 2. Magnetic and Equilibrium Data for the Ni-Sal Complex Octahedral-Sauare Planar Eauilibrium
%
diamsg.
loe K*.
paramagnetic
is KO,=
I% [Yopmmnsgnetic] diamagnetic]
Values of K,, may he evaluated from the magnetic measurements at several different temperatures and a plot of log K versus 1/T will give the enthalpy for the process. Calculations. A calculation of K,, is illustrated for a m-xylene solution containing 0.0300 g of Ni(I1) complex/ml at 9°C with an observed Af of 22.9 Hz
where the third term of eqn. (3) is neglected. 3(22.9 Hz) lo-' gg' 22(3.14)(60X 108He)(0.0300 g) + 0'73 x. = 6.81 X 10- g-1 x r ' = (xd(mo1 wt) = (6.81 X 10-$g-')(493 g mole-1) = 3.37 X lo-' mole-'
'"
The experimental and calculated results are presented in Table 2, and Figure 1 shows the linear relationship which exists between log Kc, and 1/T. AH for this octahedron-square planar conversion may be calculated from the slope of the curve in Figure 1 and has a value of 5.6 Kc8.l mole-'. Iron-HDETA Complex. The Fe-HEDTA complex provides an interesting example of dimer formation in solution. The dramatic difference in the maenetic properties of the monomer and the dimer affords an easily measured physical parameter upon which to base equilihrium calculations. The monomeric complex, Fe-HEDTA, is yellow and has a large magnetic moment of 5.79 B.M. (x = 14.3 X mole-'), characteristic of five unpaired electrons. The structure of Fe-HEDTA has been suggested to be
-
.,
Correct for ligaud diamagnetism to get the corrected XM
Substitute the corrected molar susceptibility into the usual equation relating this quantity to magnetic moment (8). e = 2.84 dxT~ = 2.844(3.65 X 10-8)(282) p = 2.88 B.M.
Substitution of this into eqn. (4) leads to % diamagnetic form K.,
=
100
=
76 a = 3.2
(2.9)'
lop Keq O'O/ 0.I
Figure 1. Plot of log K,, venur 1/T X 1 OJ for the Ni-Sol complex odahedmn-tetrahedron equilibrium.
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The complex dimer has been isolated as the hydrated salt [HINCHGH2NHa][(FeHEDTA)%O] .6H20. Available structural information indicates that the dimer is held together through a near linear (165') Fe-0-Fe bridging unit (18). The solid dimer is red and has a magnetic moment of 2.9 B.M. (xe,,.. = 3.5 X mole-'). Schugar, et al. (IS), have measured the temperature dependence of the magnetic properties of the dimer and conclude that each iron in the dimes has five unpaired electrons but that the low-spin results from antiferromagnetic coupling. The Fe-HEDTA system has been studied in aqueous solution and the effect of pH, ionic strength, HEDTA concentration, and temperature on the monomer-dimer equilibrium reported (11, 12). The equilihrium constants have been determined from optical spectra over the temperature range 20-50°C. Since the monomer and dimer have significantly different magnetic properties, it is possible'to calculate an equilihrium constant from the observed magnetic susceptibility of a mixture of these two species in solution. The observed susceptibility per mole iron (XF.) of the solution may be defined in terms of the susceptibility/mole of iron of the pure dimer (1.75 X the concentration of the dimer [Dl, the susceptibility/mole the concenof iron of the pure monomer (14.3 X
tration of the monomer [MI according to the relationship
The first term in the numerator of eqn. (6) gives the contribution of the dimer to the total susceptibility of the solution mixture. Since we are interested in the susceptibility/mole of iron, we multiply the concentration of the dimer [Dl by two to get the total concentration of iron. The second term in the numerator provides the contribution of the monomer to the susceptibility. Division of the sum of these two contributions by 2 [Dl [MI, which is equal to the total iron concentration, [Fe3+], yields the susceptibility/ mole of iron. Dimensionally we can see this from the following
+
Measurement of xp. leads to a value of [Dl in terms of [MI and from the experimentally known [Fea+],the values of [Dl and [MI may be determined. The equilibrium constant, K.,, for the process
the steps involved, including the units of the d i e r e n t quantities
+ 0.72 X 10xg = 8.82 X
lo-'
g-1
g-'
X'M = (x.)(mol. wt. dimer) 7.48 X lo--=mole-I = (8.82 X 10- g-')(848 g m male-')
The diamagnetic correction for the ligand raises this to 7.81 X mole-'. Since each mole of dimer has two mole Fe(III), the average susceptibility per mole of Fe is XFI =
7'81
lo-'
2
=
3.90 X 10-8 (male Fe)-1
Substituting XP. into eqn. (6)
Since the total Fe3+concentration is known [Fea+] = 6.90 X 10-1M = 2[D]
+ [MI
and
2M-D
[MI = 1.18 X [Dl = 2.86 X
is
lo-¶ lo-%
Therefore and may be calcnlated from the above magnetic measurements. The determination of K., over a desired temperature range leads to a plot of log K., versus 1/T and the thermodynamic parameters of the reaction AH, AS, and A F may be calcnlated. The data presented in Table 3 relate to a solution 0.0345 M in the dimer salt, [C2N2Hlo][(FeHEDTA)r 0].6Hs0, and therefore, approximately 0.07 M in Fe(II1) and HEDTA. Figure 2 shows the linear relationship between log K., and 1/T. Calculations. A calculation of K., from concentra tion of iron [Fe3+]and Af is shown to further illustrate Table 3. Temp
Magnetic and Equilibrium Data for the Fe-HEDTA Monomer-Dimer Equilibrium
(T)
29 39
Xas
3.9 X lo-' 4.1 X
% Dimer
log K.,
83 81
2.32 2.21
Results are shown in Table 3 and the Arrhenius plot is shown in Figure 2. As suggested earlier, this problem may be approached from two different starting points. Since the process involves an equilibrium state between two species of complex, it is reasonable to approach the equilibrium from either side. I n the above example the solution was prepared from the hydrated salt of the dimer and the molecular weight of the dimer was used in the calculation of Alternatively, we have also studied this equilibrium process starting, so to speak, from the monomer side by simply mixing equimolar amounts of FeCla and HEDTA with three equivalents of NaOH to neutralize the displaced hydrogen ions. The resultant pH of the solution is around 6, which is essentially thr1.t of the solution prepared from the salt of the dimer. Experimental
Figure 2. Plot of log K., dimer equilibrium.
vonw 1/T X 10Vw the Fe-HEDTA monomer-
Room Temperature. The complexes listed in Table 1 were prepared by the procedures given in the reference indicated in the table. Two solvent system were employed in the room temperature measurements, dimetbylsulfoxide:benzene (90: 10) and ehloroform:tetrametbylsilane (95:5). All solvents were spectroquality. All solutions contained 0.0400 g solute/ml of solvent, unless otherwise noted. When necessary, solutions were sealed in the nmr tubes and heated to 5&60°C to accomplish solution. Evans cautions that large concentrations in some cases may cause excmsive broadening of the nmr peaks ( 1 ) . The external standard (which is simply the solvent system without the paramagnetic subst,ance) is placed into a piece of 3 mm 0.d. soft glass tubing, frozen in dry ice and sealed. Its final length should be less than the nmr tube into which it will be placed. Add about 2.5 em of sample to an nmr tube, insert the external standard into the nmr tube and cap. I t has been suggested by Deutsch and Poling, that nmr coaxial tubes heused (6). These ere certeinly superior to the apparatus we have described;
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however, we have found that it is possible to obtain reproducible resnlts using the much less expensive 3-mm tubing inside of a standard nmr tube. We have also measured Af by comparing the posiaion of the reference peak of the pure solvent, measured in an nmr tuhe itself, with the reference peak of the paramagnetic solution measured in an nmr tube by itself. The variation of this method fram the external standard method resulted in a difference of about 1 0 . 1 B.M. Where temperature studies are concerned, it is better to use the external standard method to insure the same temperature for the reference and paramagnetic solutions. The room temperature samples were measured on a Varim A-60A Analytical NMR Spectrometer at 4 0 T =t1°C. The sweep width was varied as the magnitude of Af varied from sample to sample. Spinning side hands were an occasional problem but these cen he removed or dearly identified by ehanging the spin rate of the sample tube. Table 1gives our values in B.M. for the several samples studied in hoth solvent systems (where solubility allowed) and with and without external standard. Also values are given under hoth the solvent and the reference material to show that little difference in the magnetic moment resulted when Af is measured from either the solvent pezk or the reference peak. Paramagnetic broadening sometimes makes it desirable to use the larger solvent peak. Variable Temperalure, Ni(II) Complez. The Schiff base Ni(I1) complex was prepared by the method of Smconi, el al. (10). The techniques of sample prepw~rstionwere identical to those described earlier. The external standard method was used to measure Af values. Spectra were obtained from a Varian A-56/60 Analytical NMR Spectrometer with a variable temperalure probe. Temperatures were measured using the Varian temperature curves of ethylene glycol above 2 0 T and methanol below 20°C. Solubility a t low temperatures limited the concentration to 0.0300 g/ml. The solvent system was meta-xylene:tetramethylsilane (95:s). Prior to making high temperature measurements in the nmr probe, the nmr tuhe should be sealed with a. torch and inserted into a. small length of iron pipe or copper tuhing and placed in an oven at a temperature slightly higher than the expected probe temperature. This will help to prevent an explosion of a weak tube inside the probe. A convenient temperature range is fram 10" to SOT!. Variable Tempernlure Fe-HEDTA Complez. The Fe-HEDTA monomer-dimer equilibrium may he studied by either (a) preparing the complex dimer according to the procedure of Schugar, el al. (11) and placing it in s. solution of the desired pH or (b) simply mixing FeCla with s. small excess of HEDTA and adjusting the pH to the desired value with NaOH. These two alternate procedures are discussed below. Mebhad (a). The solution was prepared from the solid dimer in a concentration of 0.0295 g/ml (0.0345 14 in dimer) and the
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pH adjusted to 6.0. Sufficientt-butanol was added to make the solution 2% by volume in thutanol. The external standard method was used and the solution for this was also a 2y0 1-hutanol solution with pH = 6.0. The capillmy and the external nmr tubes were sealed. The results of this study over the temperature range 29 to 65'C are given in Table 3. Method (b). To a solution 0.069 M in FeCL is added a, slight excess of HEDTA. The HEDTA is deprotonated by addition of three equivalents of NaOH. The resultant pH is approximately the ssme as that of the solution prepared from the solid dimer The solution is made 2% (by volume) in 1-butanal. (-6.0). The quantity m in eqn. (3) may be calculated by assuming the Fe(II1) to be completely complexed in the presence of excess ligand and in the monomer form. In this experiment we ohtained the following m = (6.9 X 10' mole FeW/ml)(3.31 X 10%g/mole FeHEDTA) m = 2.29 X 10-%g/ml The calculat,ion from this concentration leading to &, and the thermodynamic parameters proceeds as illustrated in the earlier calculation on Fe-HEDTA.
Literature Cited (1) EVANS,D.F..J . Chem. Soc.. 2003 (1959). L. J.. AND STAPPORD. F. E.. J. CREW.EDUC..39, 574 (2) BROBAC~(ER. (1962). M. J.. A N D BERQMANN, J. G.. J. CHEM.EDDC.. (3) KIRBOHNEB.S..ALBINAK. 39,576 (1962). R. L., J. CHEI. EDUO., 43. 521 (1966). (4) CARLIN. (5) Boa. W. G . . A N D ABBGEB, T..J. C ~ ~ m . E n r r c44,438 ., (1967). . , 167 (1969). (6) Dmmscn, J. L., A N D POLING. 8. M., J. C ~ E M . E D U C46, , W.. FEENEY. J.. A N D SUTCLIFPE, L. H.. "High Resolution (7) E a s ~ s r J. Nudear Magnetic Resonance Speotroseopy:' Vole. I and 11, Pergamon Press, Elmsford. New York. 1965. (8) Fmam, B. N., hao Llwis, J.. "Modern Coordination Chemistry'' (Editors: L E W IAND ~ WILEINS).Inters~ienae.New York. 1960,Chap. 6. J. A,, S C X N ~ D E W. R .G., A N D UERNSTEIN, H. J.. "High Resolu(9) POPGE, tion Nuclear Magnetio Resonance," MoGrhw-Hill. New York, 1959, C ~ & P2.. ...NANNELLI. P.,NLRDI.N.. A N D C A M P ~ L U.. ~ I, ~ O IChem., B. (10) S ~ o c o a rL 4,943 (1965). ~ , W * m w a . C.. Jonea. R. B.. A N D GRAY,H . B., J . Amer. (11) S c ~ o a n H.. Chem. Soe.. 89,3712 (1967). R. L.. A N D MARTELL.A. E., J . P h w . Chem.. 67, 576 112) GOBTAFBON. (1963). (13) ScnucAn, H.I.. Rossnam, G. R., A N D GRAY,A. B., J . Amar. Chcm. Sac., 91,4564 (1969). (14) Fnmsrrus, W . C.,nwo BI.*NCH,J. E . , in Inow. Syn., V, 130 (1957), W . L.Jolly, Ed., MeGrsw-Hill, Nerv York. (15) CXAR'EB,R. G.,A N D P * W G I Y O ~ ~M. K I A,, , J . Phys. Chem., 62, 440 (1958). H.F.. JOXNBON, K.,AND H E N ~ E V E LF. D , W., J . Amer. (16) HOI.TZCLA~, Chcm. Soc., 74,3776 (1952). (17) ELLERN, I., AND RAOBDALE. R. 0.. in Inoro. Svn.,XI. 82 (19681,W. L. Jolly, Ed., McGiaw-Hill, New York. (18) T u s o ~G. , N., A N D Aonlas, S. C . , J . A m w . Chcm. Soc., 62, 1228 (1940).
