# Activation energy from dynamic NMR

1. Apr 25, 2013

### Chickenpoxpie

1. The problem statement, all variables and given/known data

I need to calculate the activation energy (barrier of rotation) of an amide bond. I have NMR spectra at various temperatures. I know that once I have the rates I can do an Arrhenius plot to find the activation energy, but I'm having trouble with the finding the rates'' part.

I found some equations and I want to confirm that I am doing the right thing

2. Relevant equations

Slow exchange (defined peaks)

k = pi*(va - vo)

where va is the full width at half height of the peak that has experienced some widening due to exchange. vo is the initial full width at half height of a peak due to no exchange (essentially the FWHH of a peak at low temperatures).

intermediate exchange

k = (pi * (do^2 - da^2))/2^.5

where do is the difference between the peaks when no exchange occurs (again at low temps). da is the difference between the peaks in spectrum.

fast exchange

k = pi * do^2 /(2(va - vo))

3. The attempt at a solution

I went through and did the calculation and came up with an Ea of 18 kcal/mol which is reasonable considering the Ea of the very similar peptide bond is about 20 kcal/mol. The problem occurs in the frequency factor which is off the charts (e^32) so this is giving me reason to believe I might not be using the correct equations.

Any help is appreciated.