# 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)26(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...

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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