Computation of Paramagnetic Susceptibility

After you run the NMR spectrum of your toluene/M(acac)3 solution, you will have three pieces of raw data:

If you run this on the Varian 360 spectrometer in GbAd414, the spectrometer frequency (n) is 60 MHz ( 6.000 x 107 Hz).
The mass susceptibility of toluene is -9.0 x 10-9 m3/kg.

You can use your worksheet to step through the calculation using either this page or the relevant section from Shoemaker, Garland and Nibler's "Experiments in Physical Chemistry."  (Chapter XIII, Experiment 33, pp. 369-377).

The first operation is to calculate the mass susceptibility of the sample.  The equation to use is:
 

(Note the correction to Eq. 13, p. 14 in the lab manual.)
Make sure your units are correct:  m is in kg/m3!

Next, you must convert this to a molar susceptibility.
 

Again, make sure the molecular weight of the complex M is expressed in SI units:  kg/mol!

Next, we will take into account the contribution of diamagnetism of the sample.  This is a function of the number and typw of atoms and bonds in the molecule.

Here, ci are Pascal's constants for each atom type in the molecule, ti is the number of each atom type, and li are certain bond corrections.  Take these values from SGN, p. 372, or from the table below.

Pascal's constants:  units are 10-11 m3mol-1

Co+2           -15 Br-            -45 C          -7.5 N  Monoamides  -1.94
Co+3           -13 CN-          -23 Cl        -25.3 N Diamides, imides  -2.65
Cr+2           -19 Cl-            -33 F          -7.9 O  Alcohol, ether   -5.79
Cr+3           -14 F-             -14 H         -3.68 O  Aldehyde, ketone  +2.17
Cu+2           -14 NO3-         -25 I          -56.0 O  Carboxylate   -4.22
Fe+2           -16 OH-           -15 P         -33.0  
Fe+3           -13 SO4-2        -50 S        -18.8  
K+              -16 B              -8.8 N open chain     -7.00  
Ni+2             -15 Br             -38.5 N  Ring              -5.79  

li Corrections for Bonds
 

C=C           +6.9 C=N       +10.3
CºC           +1.0 CºN        +1.0
C=C-C=C      +13.3 C in aromatic ring     -0.30

 

Now, multiply by temperature (in Kelvin!).

Finally, you use the following equation to find the effective magnetic moment:

meff = 797.8Ö(Tcmcorr)

The magnetic moment is important, because it is (theoretically) a fuction only of the number of unpaired electrons:

m =  Ö(n(n+2))

Here, n should be either the total number of valence electrons for the metal ion (for a high spin complex) or a smaller number based on occupation of the tg set (for a low-spin complex).

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 Last updated:  02/28/2005
Comments to K. Gable