I'll try to explain the source of my confusion as clear as possible:
(*) The methyl protons in toluene are decoupled because the C-C bond between the methyl group and benzene allows very fast rotation. Hence, on average, these protons will see the same environment.
It is said that the time scale for the rotation must be faster than the time scale of the instrument. For a 250 MHz apparatus this would be (1/250MHz)=4 nanoseconds.
(*) In impure solvent the methylene protons of ethanol don't couple to -OH, since fast exchange of the OH protons results in decoupling and the protons will see an average environment.
Here it is said that this occurs if the timescale of exchange must be faster than the coupling constant J for the coupling. This is typically around 5-10 Hz. So in this case, if the exchange is in the 100 millisecond timescale decoupling already occurs.
This utterly confuses me, in the first case averaging requires nanosecond timescales (related to the frequency of the instrument) and in the second case almost second timescales (related to the small difference in frequency between coupled peaks)? Why?
ALSO and maybe related to this, why do we see in the spectrum of ethanol peak broadening for the OH proton, but not for the methylene group?