APPENDICES
APPENDIX
Principles of some of the Physical Techniques used in the Laboratory
Magnetic Susceptibility
Infrared Spectrometry
Electronic Spectra of Transition Metal Ions
Nuclear Magnetic Resonance Spectrometry
Cyclic Voltammetry
Useful Text
E.A.V. Ebsworth, D.W.H. Rankine and S. Cradock, "Structural Methods in Inorganic Chemistry",
Blackwell Scientific Publ., Oxford, 1987.
Appendix 1
The Determination of Magnetic Susceptibility.
If a cylindrical sample of matter is suspended between the poles of a magnet such that one end of
the sample is in a region of high field intensity and the other end is in a region of low field intensity,
then the sample will experience a force along its length. The magnitude of this force (F) is given
by the following expression:
F = (k1 - k2) (H12 - H22)A
where k1 is the magnetic susceptibility per unit volume of the sample,
k2 is the magnetic susceptibility per unit volume of the surrounding atmosphere
H1 is the maximum field to which the sample is subjected
H2 is the minimum field to which the sample is subjected
and
A is the cross-sectional area of the sample
The magnetic susceptibility of a substance may be defined by reference to the following equation:
B = H + 4I
where B is the number of lines of (magnetic) force passing through a unit area of material, H is the
magnetic field acting on the material and I is the intensity of magnetisation (the magnetic moment
per unit volume) of the material. The equation may be rewritten:
B/H = 1 + 4I/H
The quantity B/H is defined as the permeability of the material, and the quantity I/H is defined as
the susceptibility of the material.
i.e.
 = I/H (susceptibility per unit volume)
The specific susceptibility is given by g = k/d where d is the density of the material.
The molar susceptibility M = g . molecular weight
The atomic susceptibility, A = g . atomic weight
The ionic susceptibility I = g . ionic weight
The molar susceptibility of a complex is related to the ionic and atomic susceptibilities in a simple
additive fashion.
e.g.
for [Cr(OH2)6]Cl3 the molar susceptibility can be equated to
(Cr3+) + 3(Cl-) + 6(H2O)
Thus, in order to calculate the ionic susceptibility for Cr3+ from the experimental results, it is
necessary to know the susceptibilities of the other atoms in the complex and to correct for them.
Classes of Magnetic Behaviour
The experimental determination of magnetic susceptibility for a large number of elements and
compounds has shown that there are four main classes of magnetic behaviour which can be
defined in terms of magnitude, sign, dependence on the field and dependence on the temperature
of the susceptibility.
Class
Magnitude of 
Sign of 
Field Dependence
Diamagnetic
Paramagnetic
Ferromagnetic
Antiferromagnetic
1 x 10-6
1-100 x 10-6
10-2 - 10-4
1-100 x 10-6
negative
positive
positive
positive
independent
independent
dependent
often dependent
The variation of with temperature is indicated in the diagram below

1
1. Ferromagnetic
2. Paramagnetic
3. Antiferromagnetic
2
Curie Point
3
Neel Point
T
Chemical Considerations
Diamagnetic behaviour can be associated with the full electron shells in atoms; paramagnetic,
ferromagnetic and antiferromagnetic behaviours are associated with the presence of unpaired
electrons.
The paramagnetic susceptibility can be linked with the effective magnetic moment of an atom (or
ion) by the following expression:
M = N(eff2/3kT + )
where N is the Avogadro number, eff is the effective magnetic moment, k is the Boltzmann
constant and T is the absolute temperature. The quantity N gives the temperature-independent
paramagnetism: for most of the transition metals this quantity can be neglected if the
measurements are made at room temperature or below.
Thus, a reasonable approximation for most cases is
eff = 2.84 (M.T)
where  is a unit called the Bohr Magneton = 0.927 x 10-20 erg/gauss, or
eff = 2.84 (M.T) B.M.
For the first-row transition metals this eff can be linked to the number of unpaired electrons by the
so-called 'spin only' formula,
eff = [4S(S+1)]
Where S is the resultant spin quantum number for the ion (or atom) in question. If 'n' represents
the number of unpaired electrons, then S = n/2 and the spin only formula reduces to
eff = [n(n+2)]
Procedure for Measurement of the Magnetic Susceptibility of a Substance Using the MSB1
Magnetic Susceptibility Balance.
The instrument should have been switched on by a technician at the beginning of each
laboratory session and should be ready to use. Make sure that the compound to be measured is
a dry powder.
1. Turn the RANGE knob to the x1 scale.
2. Set the reading on the balance to 000 by gently turning the ZERO knob. The reading will
probably fluctuate by approximately 2 in the last figure. This is normal.
3. Accurately record the weight of a dry, empty sample tube.
4. Place the sample tube EXTREMELY CAREFULLY into the tube guide (the small hole on the
top of the instrument next to the spirit level) and record the reading (this is Ro).
5. Pack the sample into the tube to a depth of between 2.5 and 3.5 cm, tapping the base of the
tube gently on the bench to ensure uniform packing. Carefully clean the outside of the tube with
dry tissue and place the tube in the tube guide. After about 30 seconds the sample should have
equilibrated and a fairly constant reading be obtained. Record the reading (this is R) and an
estimate of the error.
6. Remove the tube from the tube guide, gently tap base of the sample tube on the bench and
record the reading once more. Repeat this process until a constant value of R is obtained. This
process ensures the material is evenly packed in the tube.
7. Accurately weigh the packed sample tube and measure the length, l, of the sample in cm,
ensuring the top of the sample is level.
8. Finally, carefully wash out the sample tube with a suitable solvent, rinse with water and lastly
acetone before placing in the oven to dry.
You should now be able to calculate the magnetic susceptibility, g, for your sample using
the equation below.
g 
where
Cbal . l.  R  Ro 
109 . m
Cbal = Balance constant. The value of Cbal will be displayed near the balance.
l = sample length in cm
R = reading for sample + tube (see above)
Ro = reading for empty tube (see above)
m = sample mass, ie mass (sample + tube) - mass (empty tube)
The magnetic susceptibility must now be converted to the molar susceptibility, M, by
multiplying by the molecular weight of the complex
 M   g . MWt
At this point it is necessary to make a diamagnetic correction. This takes into account the
contribution to the magnetic susceptibility arising from electrons in closed shells in the compound,
in particular from the ligands. This gives the susceptibility per mole of the paramagnetic ion, A,
A = M - (Diamagnetic Corrections)
A listing of diamagnetic corrections for a range of groups is given in the table below.
Finally, A is converted to the effective magnetic moment, eff by the equation below:
eff = 2.84(A.T)
where T is the temperature in degrees Kelvin.
Report eff for your compound and estimate the error in the value obtained.
Some Useful Diamagnetic Susceptibilities
Anions x10-6 (c.g.s.)
F-9.1
Cl
-23.4
Br-36.6
I
-50.6
NO3-18.9
ClO3-30.2
ClO4
-32.0
BrO3-38.8
IO4
-51.9
IO3-51.4
CN
-13.0
NCS-31.0
SO42-40.1
2CO3
-29.5
OH-12.0
2C2O4
-4.0
BrO4-37.0
Cations x10-6 (c.g.s.)
Li+
-1.0
+
Na
-6.8
K+
-14.9
+
Rb
-22.5
Cs+
-35.0
Ti4+
-35.7
+
NH4
-13.3
Hg2+
-40.0
2+
Mg
-5.0
Zn2+
-15.0
2+
Pb
-32.0
Ca2+
-10.4
Cu2+
-12.8
2+
Co
-12.8
Ni2+
-12.8
2+
VO
-5.0
Ag+
-28.0
Species (x 10-6 c.g.s.)
H
-2.93
C
-6.00
C(ring)
-5.76
N
-5.57
S
-15.0
P
-26.3
Species (x 10-6 c.g.s.)
O(ROH; R2O)
O(Carboxyl)
F
Cl
Br
I
Ligands x10-6 (c.g.s.)
Water
-13.0
Dipyridyl
-105.0
NH3
-18.0
N2H4
-20.0
Ethylenediamine
-46.0
Propylenediamine
-58.0
Pyridine
-49.0
o-phenanthroline
-194.0
acetylacetonate
-55.0
Acetate
-30.0
Oxalate
-25.0
Cyclopentadienyl
-68.0
Benzene
-55.0
Urea
-34.0
Thiourea
-42.0
Phthalocyanine
-422.0
CO
-10.0
PPh3
-167
-4.61
-3.36
-6.3
-20.1
-30.6
-44.6
Bonds (x10-6 c.g.s)
C=C
+5.5
C=N
+8.2
N=N
+1.8
C=N
+0.8
Magnetic susceptibility of Hg[Co(NCS)4] = 16.44 x 10-6, eff = 4.43 B.M.
Appendix 2
Infrared Spectra
Molecules absorb radiation in the infrared region of the spectrum principally by changes of
vibrational energy of the molecules.
A molecule of N atoms has 3N degrees of freedom. For non-linear molecules, 3 degrees of
freedom are associated with rotations of the molecule, and 3 degrees of freedom are associated
with translation of the molecule. Thus, there are 3N-6 degrees of freedom associated with
vibrations of the molecule and are called the 'normal modes of vibration'.
If one (or more) of these modes is accompanied by a change in dipole moment of the molecule,
then infrared radiation can be absorbed at a fixed frequency (or frequencies). The frequency of a
given mode is determined by (1) the masses of the atoms involved and (2) the force constant
appropriate to the vibration.
A simple way to determine the infrared activity of the modes of vibration of a molecule is to assign
the normal modes to the various symmetry species of the point group to which the molecule
belongs.
For example, SiHCl3 belongs to point group C3v and has 9 normal modes of vibration, 3 of species
a1, and 3 of the doubly degenerate species e, all of which are infrared active.
Therefore, much information can be gained about the symmetry of a molecule from its vibrational
spectra.
The information on numbers of bands can be augmented by the study of band contours which
arise as a result of rotational fine structure, although normally gas-phase spectra are required to
obtain this information.
Other information on more complex molecules may require the application of local symmetry and
characteristic group frequencies. For example, an investigation of the C=O stretching region of a
disubstituted complex L2Mo(CO)4 should reveal different numbers of bands for cis-substitution
(molecule of C2v symmetry) than for trans-substitution (D4h symmetry). The numbers of N=O
bands in Roussin's black salt should be correlated with its C3v structure. It should be possible to
determine whether or not S4N4 has a planar (C4v) structure.
Useful information may be found in F.A. Cotton, 'Chemical Applications of Group Theory', and
Herzberg, 'Infrared and Raman Spectra of Polyatomic Molecules'.
Preparation of Nujol Mulls for Infrared Spectra
Place about 1-2 mg of the sample in the centre of a ground-glass plate and cover with a second
plate. Grind to a fine powder using small circular motions of the plates. Apply the smallest drop of
the mulling agent from the tip of a microspatula to the powder and re-grind the mixture. Using a
polythene strip, transfer the mull to a rock salt or potassium bromide plate in a thin line down the
centre, and cover with a second plate. Mount in the sample holder and place in the beam. If the
mull is too thick and absorbs too strongly, gently squeeze the two plates together or add a further
drop of mulling agent and squeeze.
Appendix 3
Electronic Spectra of Transition Metal Ions
In the laboratory electronic spectra are measured on the Philips UV-visible spectrometers which
operate in the wavelength range 850-200 nm (~12000-50000 cm-1). Since these energies are
greater than either rotational (~5 cm -1) or vibrational (100-4000 cm-1) energies, most absorption
processes observed are due to electronic excitations. In the case of molecular species these are
excitations from the highest filled molecular orbital to the lower energy unfilled molecular orbitals.
For many organic molecules (e.g. benzene) these transitions lie in the UV-region of the spectrum.
However for transition metal complex ions such transitions often fall in the visible region of the
spectrum (giving rise to coloured compounds). Absorption of two main classes are of interest in
transition metal complexes.
1. Charge Transfer Transitions
These occur when electrons are promoted to unfilled molecular orbitals which lie on a different
part of the molecule. There are three common types of charge transfer transitions. The first if
ligand to metal charge transfer (LMCT) in which an electron from a molecular orbital on the ligand
is transferred to a molecular orbital based predominantly on the metal. These are particularly
common in higher oxidation state complexes (e.g. MnO4-). The second type is metal to ligand
charge transfer (MLCT) in which an electron from a metal based orbital is transferred to a low
energy unoccupied orbital on the ligand, (e.g. in CuI pyridine complexes an electron is tranferred
into the pyridine -antibonding orbital). The third type is metal to metal charge transfer. This is
most commonly observed in mixed valence compounds and is often referred to as intervalence
charge transfer. A well known example is Prussian Blue, KFeIII[FeII(CN)6], the charge transfer
transition giving rise to the intense colour.
2. d-d Transitions
These arise from the transfer of electrons between molecular orbitals of predominantly dcharacter, and are potentially very informative. In particular they are dependent on the symmetry
and the d-orbital occupancy, thus giving information molecular geometries and oxidation states.
The intensity of these absorptions is also useful since it gives a measure of the efficiency of the
absorption process. From a knowledge of group theory it is possible to devise selection rules
which govern these processes. In summary these are:
1.
The Orbital (or Laporte) Selection Rule: l =  1
This implies that transitions between orbitals of different types are allowed (high intensity) and
transitions between orbitals of the same type are forbidden (low intensity).
2.
The Spin Selection Rule: S = 0
Only transitions to states having the same overall spin (multiplicity) are allowed.
3.
Parity Selection Rule
Only transitions between symmetric (g - g) and unsymmetric (u - u) states are allowed. The
consequences of these rules are described in the table below. (A = allowed, F = forbidden).
Selection Rule
Intensity
Examples
1
2
3
(dm3 mol-1 cm-1)
______________________________________________________________________________
A
A
A
104 - 105
Charge Transfer
F
A
A
102 - 103
Tetrahedral Complexes
F
A
F
~10 - 50
Octahedral Complexes
F
F
F
< 10
[Mn(OH2)6]2+
Appendix 4
Nuclear Magnetic Resonance Spectra
In inorganic chemistry, a large number of nuclei have been studied by NMR spectroscopy and the
technique has been useful in elucidating the structures of many compounds. In particular, the
magnetic properties of the fluorine-19 nucleus, the phosphorus-31 nucleus and the boron-11
nucleus render them satisfactory for study by 19F, 31P and 11B NMR spectroscopy, respectively.
As with compounds containing hydrogen (studied by 1H NMR spectroscopy), the two most
important parameters are the chemical shift, , (measured in parts per million from reference
standard) and the coupling constant, J (measured in Hz). However, the chemical shifts obtained
from analysis of the 19F, 31P and 11B spectra often tend to be much larger than those obtained in
1H spectra and the coupling constants in inorganic compounds tend to be more variable than
those found in organic compounds. By observing the fine structure obtained from such spectra
and calculating the chemical shifts and coupling constants, the structures of many simple
inorganic compounds can be deduced. Three simple examples involving 19F, 31P and 11B spectra
are given below:
(i) Phosphorus Pentachloride, PCl5
Phosphorus pentachloride slowly transforms to an ionic solid according to the equation.
2PCl5  [PCl4]+ + [PCl6]A 31P NMR investigation into the reaction would show the following spectrum (chemical shifts are
referenced to 85% H3PO4).
PCl4+
PCl6-
PCl5
+19
-78
-281
ppm
As the conversion to [PCl4]+[PCl6]- proceeded, the central peak would decrease in intensity and the
other two peaks would increase in intensity together. Since both [PCl4]+ and [PCl6]- contain one
phosphorus atom, the integration would show these two signals were in the ratio 1:1.
(ii)
Sulphur Tetrafluoride, SF4
This is one of the classical examples of the use of NMR spectroscopy in structure determination.
The 19F NMR spectrum at low temperature consisted of two triplets (chemical shifts referenced
from CFCl3) as shown below. The spectrum can be interpreted to show that the four fluorines in
sulphur tetrafluoride consist of two pairs of magnetically different fluorine atoms. The only
structure which satisfies these requirements is
F
F
S
F
F
-70
-117
ppm
Thus, the two axial fluorine atoms (Fa) are magnetically equivalent, as are the two equatorial
fluorine atoms (Fe) but, since the Fa atoms are not magnetically equivalent to the Fe atoms, two
signals would be observed in the ratio 2:2. However, coupling of the 2Fa atoms to the 2Fe atoms
would cause the signal from the Fe atoms to be a 1:2:1 triplet; and, similarly, the coupling of the
2Fa atoms with the 2Fe atoms would also cause the signal from the Fe atoms to be a 1:2:1 triplet.
Since the coupling constants J{Fa-Fe} (= 78Hz) would be expected to be the same, the spectrum
can be assigned, except for deciding which signal is due to Fa and which is due to Fe.
(iii)
Diborane, B2H6
The structure of diborane, B2H6, is
H
H
B
H
H
B
H
H
It can be seen that the two bridging hydrogens (Hb) are magnetically different to the four terminal
hydrogens (Ht). Thus, the 11B NMR spectrum (below) shows a signal (due to the two identical
boron atoms) coupled to the terminal hydrogen atoms and also to the bridge hydrogen atoms.
Since each boron atom is bonded to two terminal hydrogen atoms, the coupling (J{B-Hb} = 135 Hz)
produces a triplet. Further coupling to the two bridged hydrogen atoms (J{B-Ht} = 46 Hz) produces
a triplet of triplets, as shown above. The intensity ratios for a triplet of triplets are, 1:2:1, 2:4:2,
1:2:1. Note that J{B-Ht} in the 11B NMR is equivalent to J{Ht - B} in the 1H NMR spectrum.
J{B-H t}
J{B-H b}
-18
ppm
Appendix 5
Cyclic Voltammetry
Voltammetry is a technique in which the current passing between two electrodes is measured as a
function of the potential applied to one of them. The potential of the working electrode is
measured and adjusted with reference to a standard saturated calomel electrode by a
potentiostat, and is normally varied as a function of time. In cyclic voltammetry, the potential is
scanned between potential limits (Fig. 1).
vertex 2
E
initial
final
vertex 1
Time
In this experiment, the variation of potential with time is under the control of a PC and the current
is measured and recorded by the computer.
At the working electrode, the electrochemical process is:
-
[Fe(CN)6]3-
e
[Fe(CN)6]4-
and the potential of the working electrode is given by the Nernst equation:
E = Eo + (RT/nF)ln{[Fe(CN)6]3-}/{[Fe(CN)6]4-}
Where Eo is the formal potential, n is the number of electrons involved and the concentrations
refer to species at the surface of the electrode (hence subscript s) and NOT to the concentrations
in the bulk of the solution.
Initially if the current is zero, the surface and bulk concentrations of Fe(CN) 63- are the same and
the surface concentration of Fe(CN)64- is very small, with the result that the electrode potential E is
much more positive than Eo. When the potential is shifted more negative (close to Eo) some
current flows from the working electrode to the solution and it reduces part of the cyanoferrate(III)
to cyanoferrate(II). The magnitude of the current depends on the rate of reduction of
cyanoferrate(III). This in turn will depend on a number of factors, such as overpotential E-Eo, rate
of charge transfer ko, concentration of oxidised and reduced species at the electrode surface, and
rate of diffusion of material to the electrode surface.
If the scan rate, v, (variation of potential with time) is sufficiently slow compared with the rate of
diffusion, the current is limited by the rate of diffusion of new material to the surface and the form
of the voltammogram is given in Fig. 2.
The variation of current with time is:
it = nFADo(Co/x)x=0,t
Where
A is the electrode area
Do is the diffusion coefficient of species O
Co is the concentration of O
t is time
x is distance from the electrode
The limiting current is:
ilc = nFADo(Co-Co(s))/
i
ilc
E
where  is the ideal distance over which the concentration reduces to zero. When half of the
cyanoferrate(III) carried to the electrode by diffusion is reduced, the current will be half the limiting
current. The surface concentrations of the two active species will both be equal to one-half the
bulk cyanoferrate(III) concentration and the electrode potential will be Ro (i.e. 0.356 volt measured
against a hydrogen electrode or 0.110 volt measured against a saturated calomel electrode). This
potential is called the half-wave potential, E1/2.
At any of these stages, doubling the cyanoferrate(III) concentration in the bulk of the liquid would
double the amount brought to the electrode by diffusion and so would double the current. The
current is proportional to the bulk cyanoferrate(III) concentration.
If the scan rate, v, is fast compared with the rate of diffusion, the current increase exponentially at
first, but later decreases by a second exponential decay to the diffusion limit. The appearance of
the voltammogram is then given by Fig. 3.
The peak current is given by:
ip = 2.69 x 105(N3/2 A Do1/2 Co v1/2)
i
ip
ilc
E
After the potential has been scanned well beyond the formal potential Eo, essentially all the
species at the electrode surface are in the reduced form, at the concentration of the original
oxidised form. If the direction of the potential scan is now reversed, the species at the electrode
surface are then re-oxidised. Since the rate of potential scan is fast compared with the rate of
diffusion, the current is the reverse direction will be similar to that of the forward direction, except
that the peak potential will be shifted (Fig. 4).
The important parameters of the cyclic voltammogram are the magnitudes of the cathodic and
anodic peak currents (ipc, ipa), the cathodic and anodic peak potentials (Epc, Epa) and the difference
in the peak potentials (Epa-Epc).
For an electrochemically reversible process (one in which both the oxidised and reduced species
rapidly exchange electrons with the working electrode) the following conditions apply:
ipc / ipa = 1
Epc
i
ipc
ipa
Epa
E