EXPERIMENT VI
MAGNETOCHEMISTRY
In this experiment you will measure the magnetic moments of a number of transition
metal complexes and use the values obtained to calculate the number of unpaired electrons in
each complex.
You will use a magnetic susceptibility balance in which the sample (held in a thin
glass tube) sits between the poles of a strong magnet which is free to move. If the sample is
paramagnetic there is an attraction between the sample and the magnet. Since the sample tube
cannot move, the magnet tries to move towards the sample. The force needed to hold the
magnet in its original position is measured accurately and the result displayed on the front of
the machine. Paramagnetic samples give a large, positive reading; diamagnetic samples give a
small, negative reading (since the magnet is repelled slightly from the sample).
Experimental
Materials Required:
Ø
Ø
Ø
Ø
Ø
HgCo(SCN)4
FeC2O4.2H2O
K3[Fe(C2O4)3].3H2O
K4[Fe(CN)6].3H2O
K3[Fe(CN)6]
(Standard)
(Prepared in experiment V)
(Prepared in experiment V)
(Supplied)
(Supplied)
Measurement of Magnetic Susceptibility
1.
The Magnetic Susceptibility (MS) balance must be turned on and allowed to warm up
for 30 minutes. (The instructor should have done this before the beginning of the
laboratory period.)
2.
Obtain a sample tube from the stockroom. Handle it carefully because it is easy to
break and costs quite a bit. Make sure the tube is clean and dry.
3.
Weigh the empty tube and record the weight.
4.
Make sure the MS balance is switched on, with the left-hand knob set to the ‘x1’ scale.
Carefully adjusting the zero knob, zero the MS balance with the right-hand knob and
allow a minute for the display to settle (it will always fluctuate a little as it is very
sensitive).
5.
Place the empty tube into the hole on top of the MS balance, allow the display to settle,
and read Ro on the digital meter. It will be negative (typically -40 or so) because the
glass is diamagnetic. Remove your sample tube.
6.
Using a mortar and pestle, carefully crush your sample to very fine particles. Crush
enough sample to fill the sample tube to a height of between 2.5 and 3.5 cm. Using the
tools provided, fill your sample tube to 3.0 + 0.5 cm. Tap the bottom of your sample
tube on the bench provided several times to assure good packing of your sample. Using
the analytical balance, measure the mass of your sample plus sample tube.
7.
Zero the MS balance. Place your tube now loaded with sample in the MS balance and
read R from the digital meter. Take your sample out of the MS balance and tap the
bottom of it on the mat several times. Place your sample back in the MS balance and
again read R. Continue this process until subsequent readings agree to within + 3 R
units
8.
Remove your sample tube and rezero the MS balance. Measure the length of the sample
in the tube with the accurate ruler provided and determine an estimate of the uncertainty
in your measurement.
9.
Measure R for the standard sample provided in a manner similar to that described in 7.
Remove the standard and rezero the MS balance. Record L, m, and Ro for the standard.
10.
Measure the room temperature from the thermometer in the room.
11.
Empty your sample tube into your product vial. Clean out the remaining sample in your
sample tube first with an appropriate solvent (usually water) to dissolve the sample.
Then rinse the sample tube with acetone. Dry the sample tube by running air through
the tube using the vacuum line, tubing and glass tube provided. Return the sample tube
to the stockroom.
Data Analysis
Calibration can be checked from time to time using standard substance. If the balance is to
be used mainly for solid samples, then a solid calibrant (preferably Mercury
tetrathiocyanatocobaltate (II), HgCo(SCN)4 is recommended since some of the systematic
errors in packing may cancel and this complex is easily prepared in pure form. It is suitable
and not hygroscopic. It has a high magnetic susceptibility. Its mass susceptibility, χg = 16.44
x 10-6 c.g.s. at 20 0C.
The gram-susceptibility of a sample χg (in ml g-1) is given by Equation 1.
(6.1)
Where
C
=
I
R
R0
=
=
=
m
=
calibration constant for the balance (written on top
of each balance)
sample length in cm (between 1.5 and 2.5)
susceptibility balance reading for full tube
susceptibility balance reading for empty tube (don’t forget
this is negative, so R-R0 > R)
mass of sample in grams.
Having calculated χg, you next determine the molar susceptibility χm (in ml mol-1) which is
given by Equation 2.
(6.2)
Where M = molecular weight
Then, the diamagnetic correction needs to be added. The weak diamagnetism of all of
the closed pairs of electrons in the sample tends to give a small negative reading, which
makes the initial measurement of paramagnetism appear a bit too small. Correction values for
all kinds of molecules and ions are calculated and published in standard tables; relevant
values are given in Table 6.1 and Appendix. This gives the corrected molar susceptibility,
χmcorr (in ml mol-1), Equation 6.3.
(6.3)
Table 6.1 Diamagnetic corrections for ions and ligands
Finally, the magnetic moment χobs (in Bohr magnetons) is given by Equation 6.4
(6.4)
Where T is the ambient temperature in Kelvin.
The Relationship between the Number of Unpaired Electrons & the Magnetic Moment
For a free, gaseous metal ion the magnetic moment is given by Equation 6.5
(6.5)
where S is the spin quantum number and L the orbital quantum number. Thus, for a gaseous
Ti3+ ion (d1) S = 1/2 and L = 2. However in complexes of metal ions the orbital angular
momentum is often wholly or partially quenched because free movement of the odd electrons
around the nucleus is prevented due to the electric fields of other atoms and molecules surrounding
the ion. As a result of this we can, to a reasonable approximation, assume that the magnetic moment
of a complex arises only from the electron spin. If we therefore put L = 0 in the above equation,
it reduces to Equation 6.6 where n is the number of unpaired electrons (because S = n/2).
(6.6)
This is the ‘spin-only’ formula for magnetic moments, and the magnetic moments that it predicts for
different numbers of unpaired electrons are given in Table 6.2.
For first row transition metal ions (such as you have examined) this approximation holds
reasonably well. In practice ‘real’ magnetic moments may be slightly different from these,
usually a little larger, either because the orbital electronic motion is not completely quenched, or
because ‘spin-orbit coupling’ occurs which allows orbital angular momentum of excited states to
‘mix’ with the ground state. These effects can be large for second and third row transition metal
complexes and in these cases the spin-only formula is not satisfactory.
Exercises
1. Rationalize the difference in magnetic moment between the iron (III) complexes
K3Fe(C2O4)3.2H2O and K3Fe(CN)6.
2. Use the electronic configurations to explain the difference between the magnetic moments of the
iron (II) and (III) complexes K3Fe(CN)6.3H2O and K3Fe(CN)6.
References
1. L.J. William, The Principles of Inorganic Chemistry, Mc-Graw Hill, New York, 1976.
2. G. Mazz and B.W. Rockett, Practical Inorganic Chemistry, Van Nostrand Reinhold, New York,
1972.
3. Manual Bulletin of the JMC Magnetic Susceptibility Balance, Johnson Matthey Catalytic
Systems. Division Equipment, York Way, Royston, Herts SG8 5HJ.
4. D.F., Evans, J. Phys. E; Sci Instr.., 1974, 7, 247.
5. D.H., Grant, J. Chem. Educ., 1995, 72, 39.
Appendix
Cations
Li+
Na+
K+
Rb+
Cs+
NH4+
Mg2+
Ca2+
Sr2+
Ba2+
Cu2+
Ag2+
Zn2+
Cd2+
Hg2+
Tl+
Pb2+
Mn3+
“TM core”
“RE core”
Diamagnetic Correction Constants (Pascal’s Constants)*
Anion
Molecules
-106χα
-106χα
1
9
FH2O
Cl7
23
NH3
Br15
34
en
I22
50
py
CH3COO
33
29
PPh3
C6H5COO13
71
CN4
13
CNO9
23
CNS16
34
ClO4
26
32
CO3215
28
C2O4227
28
HCO213
17
NO320
19
2O
36
6
OH36
11
S232
28
SO4210
38
S2O3213
46
acac
20
52
-106χα
13
16
47
49
167
*All values are -106χα in cgs units. Example: for Li+, χα = -1x10-6 erg.G2mol-1. Abbreviations: acac- =
acetylacetone; en = ethylenediamine; PPh = triphenylphosphine; py = pyridine. TM core is estimate for
transition metal ion if not listed. RE is rare earth core for 3+ ions