# Magnetic Susceptibility Of Different Compounds Biology Essay

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The response of an inorganic compound to a magnetic field depends on its electronic structure. If all the electrons are paired the substance will be weakly repelled by a magnetic field and it is said to be diamagnetic. However, if unpaired electrons are present in the substance it will be attracted into the magnetic field. The strength of this attraction depends on the number of unpaired electrons, and the substance is said to be paramagnetic.

The magnetic susceptibility of a compound can be measured by the Gouy Method. The apparatus is as shown in this figure:

The cryostat allows magnetic measurements to be made over a temperature range; if no cryostat is available measurements can only be made at room temperature.

A paramagnetic substance tends to concentrate lines of magnetic force in itself and will be pulled into a magnetic field. In the Gouy method of measuring magnetic susceptibility the force on a cylindrical sample of the substance suspended in a non-uniform magnetic field is measured. This along with the known coefficients is used to find out the molar susceptibility of the sample.

The molar susceptibility χM is given by:-

χM = [(2gw) / (yH2) x M] + DMC

Where:

w is the apparent increase in weight of the sample in the magnetic field.

y is the weight of the sample

H is the field between the pole faces

M is the molecular weight of the compound

DMC is the correction for the diamagnetic nature of tube.

## Procedure:-

(1) An empty Gouy tube was weighed and suspended from the balance so that its lower end was central between the magnet pole pieces. The tube was allowed to stand for 5 minutes to allow thermal equilibrium to be attained.

(2) The empty tube was weighed in and out of the field to find out the diamagnetic correction (DMC).

(3) The tube was then filled to a depth of 12 cm with mercury tetrathiocyanatocobaltate (II). It was ensured that the sample is uniformly packed by filling the tube portion-wise and tapping the tube to pack the solid evenly and firmly. The length of the sample was measured. The tube along with the sample was weighed to find the weight of the cobalt complex.

(4) The magnet was then brought forward to its stop. The current was turned on and the voltage was set to 7 V. The pull, i.e. the apparent difference in weight of the sample in and out of the field plus the DMC of the tube was measured.

(5) The same was repeated for field setting with voltage set at 10 volts. The weighing was carried out three times at each field-strength setting to estimate the error.

## Observations:-

DMC = weight inside magnetic field - weight outside magnetic field.

= 10.6 - 10.5

= 0.1 g

Using the following values:-

g = 9.8 m/s2

T = 298 K.

l = 0.12 m

k = 797.78 JK -1

w' = w - DMC

Sample

Weight of the sample taken (y)

Apparent Pull Weight in the field (w)

Apparent Weight (w')

CrCl3.6H2O

1.00 g

1.78 g

1.88 g

[Co(NH3)6]Cl3

1.00 g

1.409 g

1.509 g

Ni[C6H5)3P]2(NO3)2

1.00 g

1.15 g

1.25 g

## Calculations:-

## Calculated value of magnetic moment for [CrCl3.6H2O]

Cl- is a weak field ligand with d3 electronic configuration

Oxidation Number of Cr is III here

eg

Cr3+ - d3

Complex

1 1 1

t2g

No. of unpaired electrons = 3

µ=√ [n (n+2)]

In Cr3+, n=3 (unpaired electronic)

= √ [3*(3+2)]

= √15

= 3.87 BM

## Experimental value of magnetic moment for [CrCl3.6H2O]

DMC of atoms and groups = [Cr 3+ + 3Cl- +6H2O]

= (-138 x 10 -12) + (-3 x 294 x 10 -12) + (- 6 x 163 x 10 -12) BM

= - 1.998 x 10 -9 BM

## At 7 volts, (H = 28900 Am-1)

Χ'm(7) = Xm(7) + DMC of atoms and groups

= [(2gxw'xl)/(yH2)xM] + DMC of atoms and groups

= (2x1.88x10 -3x9.8x0.12x1346.33)/(1x10 -3x(289000)2 ) + (-1.998x10 -9)

= 7.133x10 -8 - 1.998x10 -9 BM

= 8.686x10 -8 BM

## At 10 volts, (H = 202300 Am-1)

Χ'm(10) = Xm(10) + DMC of atoms and groups

= [(2gxw'xl)/(yH2)xM] + DMC of atoms and groups

= (2x1.88x10 -3x9.8x0.12x1346.33)/(1x10-3x(202300)2) + (-1.998 x10-9)

= 7.6338x10-8 - 1.998x10-9 BM

= 7.434 x 10 -8 BM

Χ'm (av) = (Χ'm (7) + Χ'm (10)) / 2

= 8.0643x10 -8 BM

µ experimental = Kx(Χ'M (av)xT)½

= 797.78x(6.433x10-8 x298)½

= 3.910 BM.

## Calculated value of magnetic moment for [Co(NH3)6]Cl3

It has Cobalt in (III) oxidation state with d6 configuration. NH3 is a strong field ligand. Hence the complex will be high spin complex.

1 1

CO3+ d6

1L 1 1

No. of unpaired electrons (n) = 4

= √ [4x(4+2)]

= √24

= 4.89 BM

## Experimental value of magnetic moment for [CrCl3.6H2O

DMC of atoms and groups = [Co 3+ + 6 NH3 + 3Cl-]

= (-126x10-12) + (-6x226x10-12) + (-3x294x10-12) BM

= - 2.364x10-9 BM

## At 7 volts, (H = 28900 Am-1)

Χ'm7 = Xm7 + DMC of atoms and groups

= [(2gxw'xl)/(yH2)xM] + DMC of atoms and groups

=(2x1.509x10 -3x9.8x0.12x267.5)/(1x10-3x(289000)2) + (-2.364x10-9)

= 0.90032 x10-8 BM

## At 10 volts, (H = 202300 Am-1)

Χ'm (10) = Xm (10) + DMC of atoms and groups

= [(2gxw'xl)/(yH2)xM] + DMC of atoms and groups

= (2x1.509x10-3x9.8x0.12x267.5)/(1x10-3x(202300)2) + (-2.364 x10-9)

= 2.1x10-8 BM

Χ'M (av) = (Χ'M (7) + Χ'M (10)) / 2

= 1.5 x 10 -8 BM

µ experimental = K (Χ'M (av) x T ) ½

= 797.78 ( 1.5 x 10 -8 x 298) ½

= 4.67 BM.

## Calculated value of magnetic moment for [Ni (C6H5)3P](NO3)2

Here oxidation stat of Ni is +2. Its electronic configuration is d8. Phenylphosphine is a strong field ligand which gives a high spin complex.

1 1

Ni 2+ d8

1L 1L 1L

No. of unpaired electrons = 2

µ = √ [2x(2+2)]

= √8

= 2.828BM

## Experimental value of magnetic moment for [Ni (C6H5)3P](NO3)2

DMC of atoms and groups = [Ni2++ 2(Ph)3P+ 2NO3-]

= (-161x10-12) + (-2x2098x10-12) + (-2x326x10-12) BM

= - 5.009 x 10 -9 BM

## At 7 volts, (H = 28900 Am-1)

Χ'm(7) = Xm(7) + DMC of atoms and groups

= [(2gxw'xl)/(yH2)xM] + DMC of atoms and groups

= (2x1.25x10-3x9.8x0.12x707.3)/(1x10-3x(289000)2) + (- 5.009x10-9)

= 1.9881x10 -8 BM

## At 10 volts, (H = 202300 Am-1)

Χ'm (10) = Xm (10) + DMC of atoms and groups

= [(2gxw'xl)/(yH2)xM] + DMC of atoms and groups

= (2x1.25x10-3x9.8x0.12x707.3)/(1x10-3x(202300)2) + (-5.009x10-9)

= 4.5802x10-8 BM

Χ'M (av) = (Χ'M (7) + Χ'M (10)) / 2

= 3.284 x 10 -8 BM

µ experimental = Kx(Χ'M (av) x T ) ½

= 797.78 ( 3.284 x 10 -8 x 298) ½

= 2.495 BM.

## Result:-

For many complexes of the first row transition series the molar susceptibility is related to the magnetic moment µ by the expression

µeff = K (Χ'M x T) ½

Where

T is the absolute temperature

µ is the magnetic moment (usually independent of temperature)

K is a constant

But for some elements

μeff = [n(n + 2)]1/2

Where n is the number of unpaired electrons in the complex.

Thus, measuring the susceptibility leads directly to the number of unpaired electrons and hence the spin state of the ion. It is important to note however, that these simple expressions do not generally apply to complexes of the second and third transition series elements, nor to complexes of the first row transition elements in which spin orbit coupling can occur, or where there are metal-metal interactions.

## Report:-

The values of H at different field strength are:-

For field setting at 7 volts H is taken as 298000Am-1.

For field setting at 10 volts H is taken as 202300Am-1.

The chief source of error in this quantity is due to non uniform packing of the sample, non uniform density of the sample and backlash errors.

The diamagnetic correction is very important because the complex is not 100% paramagnetic and DMC can the affect the value of magnetic moment if not applied, that is why we add DMC to the magnetic moment.

The diamagnetic correction for each complex are:-

DMC of different atoms and groups are:-

DMC of atoms and groups = [Cr3+ + 3Cl- +6H2O]

= (-138 x 10 -12) + (-3 x 294 x 10 -12) + (- 6 x 163 x 10 -12) BM

= - 1.998 x 10 -9 BM

DMC of atoms and groups = [Co 3+ + 6 NH3 + 3Cl-]

= (-126x10-12) + (-6x226x10-12) + (-3x294x10-12) BM

= - 2.364x10-9 BM

DMC of atoms and groups = [Ni2++ 2(Ph)3P+ 2NO3-]

= (-161x10-12) + (-2x2098x10-12) + (-2x326x10-12) BM

= - 5.009 x 10 -9 BM

The corrected molar magnetic susceptibility for all the three compounds at both the field strength are:-

For field setting at 7 volts:-

## Sample

## Xm

## μ experimental

CrCl3.6H2O

8.686x10 -8 BM

4.058 BM

[Co(NH3)6]Cl3

0.90032 x10-8 BM

1.067 BM

Ni[C6H5)3P]2(NO3)2

1.9881x10 -8 BM

1.195 BM

For field setting at 10 volts:-

## Sample

## Xm

## μ experimental

CrCl3.6H2O

3.284 x 10 -8 BM

2.495 BM

[Co(NH3)6]Cl3

2.1x10-8 BM

4.85 BM

Ni[C6H5)3P]2(NO3)2

7.434 x 10 -8 BM

3.695

Comparison of the experimental and calculated values:-

## Sample

## μcalculated

## μ experimental

CrCl3.6H2O

3.87 BM

3.910 BM

[Co(NH3)6]Cl3

4.89 BM

4.67 BM

Ni[C6H5)3P]2(NO3)2

2.828BM

2.495 BM