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Essay/Term paper: Magnetic susceptability

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Magnetic Susceptability


Michael J. Horan II

Abstract:
The change in weight induced by a magnetic field for three solutions of
complexes was recorded. The change in weight of a calibrating solution of 29.97%
(W/W) of NiCl2 was recorded to calculate the apparatus constant as 5.7538. cv
and cm for each solution was determined in order to calculate the number of
unpaired electrons for each paramagnetic complex. Fe(NH4)2(SO4)2€6(H20) had 4
unpaired electrons, KMnO4 had zero unpaired electrons, and K3[Fe(CN)6] had 1
unpaired electron. The apparent 1 unpaired electron in K3[Fe(CN)6] when there
should be five according to atomic orbital calculations arises from a strong
ligand field produced by CN-.

Introduction:
The magnetic susceptibility is a phenomena that arises when a magnetic
moment is induced in an object. This magnetic moment is induced by the presence
of an external magnetic field. This induced magnetic moment translates to a
change in the weight of the object when placed in the presence of an external
magnetic field. This induced moment may have two orientations: parallel to the
external magnetic field of or perpendicular to the external magnetic field. The
former is known as paramagnetism and the later is known as diamagnetism. The
physical effect of paramagnetism is an attraction to the source of magnetism
(increase in weight when measured by a Guoy balance) and the physical effect of
diamagnetism is a repulsion from the source of magnetic field (decrease in
weight when measured by a Guoy balance).
The observed magnetic moment is derived by the change in weight. This
observed magnetic moment arises from a combination of the orbital and spin
moments of the electrons in the sample with the spin component being the most
important source of the magnetic moment. This magnetic moment is caused by the
spinning of an electron around an axis acting like a tiny magnet. This spinning
of the ³magnet² results in the magnetic moment.
Paramagnetism results from the permanent magnetic moment of the atom.
These permanent magnetic moments arise from the presence of unpaired electrons.
These unpaired electrons result in unequal number of electrons in the two
possible spin states (+1/2. -1/2). When in the absence of an external magnetic
field, these spins tend to orient themselves randomly accordingly to statistics.
When they are placed in the presence of an external magnetic field, the moments
tend to align in directions anti parallel and parallel to the magnetic field.
According to statistics, more electrons will occupy the lower energy state then
the higher energy state. In the presence of a magnetic field, the lower energy
state is the state when the magnetic moments are aligned parallel to the
external field. This imbalance in the orientation favoring the parallel
orientation results in attraction to the source of the external magnetic field.
Diamagnetism is a property of substances that contain no unpaired
electrons and lack a permanent dipole moment. The magnetic moment induced by one
electron is canceled by the magnetic moment of an electron having the opposite
spin state. The force of diamagnetism results from the effect of the external
magnetic field on the orbital motion of the paired electrons. The susceptibility
is correlated to the radii of the electronic orbits and the precession of the
electronic orbits. The complex mathematical system describing this system is
beyond the scope of the experiment. It must be included that paramagnetic
substances do have a diamagnetic component to them but it is much smaller than
the paramagnetic component and therefore can be ignored. Calculation. cm (the
mass susceptibility)is found for a calibrating solution of NiCl2 using the
equation
(1) where p is the mass fraction (w/w)
of NiCl2 of the solution and T is the absolute temperature. cv (the volume
susceptibility)is determined using equation

(2) where r is the density of the solution. The apparatus constant
moH2A/2 is evaluated using equation

(3) With the apparatus constant known and W (mass(kg) x 9.8 m s-2) known, it
is possible to determine cv for each solution using the equation
(4) cM
(molar susceptibility) is calculated (in SI units) using the equation
(5) With cM determined, the
Curie Constant C is calculated by the equation:

(6) The small diamagnetic term can be neglected for paramagnetic compounds and
the equation becomes:

(7) The atomic moment µ can then be calculated using the equation:
(8) The number
of unpaired electrons can be found approximately by the equation:
(9) where n is
the number of unpaired electrons.

Experimental Method:
The method described in Experiments in Physical Chemistry was followed.
The density of all solutions were measured using a pycnometer.
A solution of NiCl2 was made with the following parameters (table one):
Table One: Parameters of NiCl2 Solution Concentration (M) Weight
Fraction Density (kg/m3) NiCl2 2.308 .016 0.2997 1.3552 .003x103
Three test solutions were prepared as follows (table two): Table Two: Parameters
of Solutions Solution Concentration (M) Density (kg/m3) Fe(NH4)2(SO4)2€
6(H20) 0.705 .016 1.1148 .003x103 KMnO4 0.377 .016 1.0201 .003x103
K3[Fe(CN)6] 0.498 .016 1.0834 .003x103

Measurements in the presence and absence of magnetic fields were made
using a Guoy balance as described in Experiments in Physical Chemistry and were
made in triplicate.

Results: All measurements were performed at 293K. Table Three: Mass (field on -
field off) Solution  Mass (g)
Run One Run Two Run 3 Average NiCl2 0.09349 0.0001
0.09381 0.0001 0.10427 0.0001 0.09719 0.0001 Fe(NH4)2(SO4)2€ 6(H20) 0.03548
0.0001 0.03665 0.0001 0.04785 0.0001 0.03999 0.0001 KMnO4 -0.00406
0.0001 -.00404 0.0001 -0.00399 0.0001 -0.00403 0.0001 K3[Fe(CN)6]
0.00252 0.0001 0.00258 0.0001 0.00386 0.0001 0.00299 0.0001

Table Four: Weight for Solutions Solution  Weight (N) NiCl2 9.5246 .
0098x10-4 Fe(NH4)2(SO4)2€6(H20) 3.9190 .0098x10-4 KMnO4 -3.948 .
098x10-5 K3[Fe(CN)6] 2.930 .098x10-5

The following parameters of NiCl2 were determined (table five) using equations
1 and 2: Table Five: Parameters of NiCl2 cm 1.22 .04x10-7 m3kg-1. cv
1.66 .06x10-4

The apparatus constant moH2A/2 was evaluated using equation 3 as 5.73 .02.

cv was calculated for each solution (table six) using equation 4. Table Six
Solution  Weight (N) cv Fe(NH4)2(SO4)2€6(H20) 3.9190 .0098x10-
4 6.831 .003x10-5 KMnO4 -3.948 .098x10-5 -6.88 .02x10-6
K3[Fe(CN)6] 2.930 .098x10-5 5.10 .02x10-6

cM is calculated (in SI units) using equation 5 (table seven): Table Seven
Solution cv cM Fe(NH4)2(SO4)2€6(H20) 6.831 .003x10-5
1.087 .007x10-7 KMnO4 -6.88 .02x10-6 4.79 .03x10-9 K3[Fe(CN)6] 5.10 .
02x10-6 2.69 .02x10-8

With cM determined, the Curie Constant C is calculated by equation 7 (table
eight): Table Eight Solution C Fe(NH4)2(SO4)2€6(H20) 3.18 .02x10-5
KMnO4 1.406 .008x10-6 K3[Fe(CN)6] 7.90 .06x10-6

The atomic moment was then be calculated using equation 8 (table nine): Table
Nine Solution µ (Bohr Magneton) Fe(NH4)2(SO4)2€6(H20) 4.5044 KMnO4
0.9462 K3[Fe(CN)6] 2.2428

The number of unpaired electrons was found approximately by the equation 9
(table ten): Table Ten Solution n # unpaired electrons
Fe(NH4)2(SO4)2€6(H20) 3.6141 4 KMnO4 0.3767 0 K3[Fe(CN)6] 1.4557
1

Discussion:
The number of unpaired electrons determined experimentally is correct as
compared to atomic orbital calculations except for K3[Fe(CN)6](table eleven):
Solution Experimental Determined A.O. Calculations Fe(NH4)2(SO4)2€
6(H20) 4 4 KMnO4 0 0 K3[Fe(CN)6] 1 5

The cause of the discrepancy of the K3[Fe(CN)6] complex is not
experimental error but is from the physical properties of transition metal
complexes such as K3[Fe(CN)6]. These properties are characterized by ligand
field theory.
The compound K3[Fe(CN)6] is characterized as a low spin case. A low spin
case causes the measured numbers of unpaired electrons to be considerably less
than that calculated theoretically. This is caused by splitting of the five
degenerate d- level electronic orbitals into two or more levels of different
energies by the fields put out by the ligand.
In the case of K3[Fe(CN)6], CN- exerts a strong ligand field. This
strong splitting field results in a greater energy difference between the
bonding and antibonding orbitals. (see picture one) making it more probable that
all 5 e- will occupy the lower energy bonding orbital.
Picture One: A diagram of the weak field and strong field effect on
electron arrangement in Fe+3

The strong ligand field produced by CN- results in spin moment cancellation of
four out of the five unpaired electrons. This results to the apparent 1 free
electron determine by the experiment.
The sources of error in this experiment are the solutions, density and 
mass. All confidence limits were determined using the method of partial
fractions just how all lab reports are done. Although we initially had trouble
with the scale, these problems were resolved prior to taking measurements.
Although more accurate results are not needed, a possible way to
increase accuracy is to use more volume of solutions. When we performed this
experiment, we had to cut the volume used in other years by 50% because the
weight exceeded the capacity of the balance. Using more solution would decrease
the significance of the error in mass.


References:

1. Shoemaker, Garland, and Nibler, Experiments in Physical Chemistry, Fifth
Edition, McGraw-Hill Company, New York, 1989.

2. Mulay, L.N., Magnetic Susceptibility,. Intersceince Publishers, New York,
1963

3. Adamson, Arthur W., A Textbook of Physical Chemistry,. Tjird Edition,
Academic Press College Division, Orlando, Flrida, 1986.

4. Barrow, Gordon M., Physical Chemistry,. Third Edition, McGraw-Hill Company,
New York, 1973.


 

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