# 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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