Magnetic Susceptibility and Unpaired electrons

[ReidMerrill]

Homework Statement

I'm am trying to find out the magnetic susceptibility,X_M in order to calculate the number of unpaired electrons in Mn(acac)₃ via the Evans Method

Homework Equations

X_M = (477) Δv/(Qv₁C)
X_M= X'_m+ X_M(metal)+ X_M (ligands)
Where X'_M is the magnetic susceptibilty of just the unpaired electrons.
Δv is the frequency difference between the two chloroform peaks, 648.2 MHz (7.2722 ppm-5.6517 ppm)*400 MHz
Q=2 because a superconducting NMR was used
v₁ is the frequency of the NMR, 400MHz
and c is the molarity of the solution used, 0.0948M
X'_MT=(1/8)n(n+2) where n is number of unpaired electrons

The Attempt at a Solution

The X_M I calculated is 4179.1878. I have nothing to base the accuracy of this off of.
the X_M (metal) = 511. THis was for elemental Mn. I couldn't find anything for Mn(III) so this might be the problem. And from the lab manual the X_M(ligands) is 3*52
Solving for X'_M I got 3512.1878
This gives an unpaired electron count of of nearly 3,000 so this cannot be correct.


Any help is greatly appreciated.

 

[mjc123]

Δν > ν₁? Looks like you multiplied 1.6205*400. What about the "ppm"?

 

[ReidMerrill]

Δν > ν₁? Looks like you multiplied 1.6205*400. What about the "ppm"?

1.6205 is the ppm. That's what the lab manual says to do.

EDIT: I see. the ppm x 400 MHz= Hz. I wasn't reading carefully. I'll see if this fixes things