Magnetic Moments
Lecture 4. CHEM1902 (C 10K) Coordination
Chemistry
Magnetic moments are often used in conjunction with electronic
spectra to gain information about the oxidation state and
stereochemistry of the central metal ion in coordination
complexes.
A common laboratory procedure for the determination of the
magnetic moment for a complex is the Gouy method which involves weighing
a sample of the complex in the presence and absence of a magnetic
field and observing the difference in weight. A template is
provided for the calculations involved.
For first row transition metal ions in the free ion state, i.e.
isolated ions in a vacuum, all 5 of the 3d orbitals are
degenerate.
A simple crystal field theory approach to the bonding in these
ions assumes that when they form octahedral complexes, the d
orbitals are no longer degenerate but are split such that two
orbitals, the dx2-y2 and the dz2
(eg subset) are at higher energy than the
dxy, dxz, dyz orbitals (the
t2g subset).
For ions with between 4 and 7 d electrons, this gives rise to 2
possible arrangements called either high spin-low spin or weak
field-strong field respectively. The energy gap is dependent on
the position of the coordinated ligands in the SPECTROCHEMICAL
SERIES. See an interactive JAVA
applet for examples.
Note: For C 10K, we assume that all Co(III),
d6 complexes are octahedral and LOW spin, i.e.
t2g6.
In tetrahedral complexes, the energy levels of the orbitals are
again split, such that two orbitals, the dx2-y2 and
the dz2 (e subset) are now at lower energy (more
favoured) than the remaining three dxy,
dxz, dyz (the t2 subset) which are
destabilised.
Tetrahedral complexes are ALL high spin since the
difference between the 2 subsets of orbitals is much smaller than
is found in octahedral complexes.
The usual relationship quoted between them is:
Δtet= 4/9 Δoct.
Square planar complexes are less commmon than tetrahedral and
for C 10K we will assume that the only ions forming
square planar complexes are d8 e.g. Ni(II).
Since the energy gap between the dxy and dx2-y2 is again Δoct
then these are considered low spin and are
all diamagnetic, μ=0 Bohr Magneton (B.M.)
The formula used to calculate the spin-only magnetic moment can
be written in two forms; the first based on the number of
unpaired electrons, n, and the second based on the electron spin
quantum number, S. Since for each unpaired electron, n=1 and
S=1/2 then the two formulae are obviously related.
μ= √n(n+2) B.M.
μ= √4S(S+1) B.M.
Comparison of calculated spin-only magnetic
moments with experimental data for some octahedral
complexes
| Ion |
Config |
μso / B.M. |
μobs / B.M. |
| Ti(III) |
d1 (t2g1) |
√3 = 1.73 |
1.6-1.7 |
| V(III) |
d2 (t2g2) |
√8 = 2.83 |
2.7-2.9 |
| Cr(III) |
d3 (t2g3) |
√15 = 3.88 |
3.7-3.9 |
| Cr(II) |
d4 high spin (t2g3 eg1) |
√24 = 4.90 |
4.7-4.9 |
| Cr(II) |
d4 low spin (t2g4) |
√8 = 2.83 |
3.2-3.3 |
| Mn(II)/ Fe(III) |
d5 high spin (t2g3 eg2) |
√35 = 5.92 |
5.6-6.1 |
| Mn(II)/ Fe(III) |
d5 low spin (t2g5) |
√3 = 1.73 |
1.8-2.1 |
| Fe(II) |
d6 high spin (t2g4 eg2) |
√24 = 4.90 |
5.1-5.7 |
| Co(III) |
d6 low spin (t2g6) |
0 |
0 |
| Co(II) |
d7 high spin (t2g5 eg2) |
√15 = 3.88 |
4.3-5.2 |
| Co(II) |
d7 low spin (t2g6 eg1) |
√3 = 1.73 |
1.8 |
| Ni(II) |
d8 (t2g6 eg2) |
√8 = 2.83 |
2.9-3.3 |
| Cu(II) |
d9 (t2g6 eg3) |
√3 = 1.73 |
1.7-2.2 |
Comparison of calculated spin-only magnetic
moments with experimental data for some tetahedral
complexes
| Ion |
Config |
μso / B.M. |
μobs / B.M. |
| Cr(V) |
d1 (e1) |
√3 = 1.73 |
1.7-1.8 |
| Cr(IV) / Mn(II) |
d2 (e2) |
√8 = 2.83 |
2.6 - 2.8 |
| Fe(V) |
d3 (e2 t21) |
√15 = 3.88 |
3.6-3.7 |
| - |
d4 (e2 t22) |
√24 = 4.90 |
- |
| Mn(II) |
d5 (e2 t23) |
√35 = 5.92 |
5.9-6.2 |
| Fe(II) |
d6 (e3 t23) |
√24 = 4.90 |
5.3-5.5 |
| Co(II) |
d7 (e4 t23) |
√15 = 3.88 |
4.2-4.8 |
| Ni(II) |
d8 (e4 t24) |
√8 = 2.83 |
3.7-4.0 |
| Cu(II) |
d9 (e4 t25) |
√3 = 1.73 |
- |
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The Department of Chemistry, University of the West Indies,
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