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