Accounting for the fine structure in a spectrum

Account for the fine structure in the H-NMR spectrum of the C-H protons of ethanol. 

Strategy Refer to Pascal s triangle to determine the effect of a group of N equivalent protons on a proton, or (equivalently) a group of protons, of interest. 

Solution The three protons of the CH3 group split the single resonance of the CH2 protons into a 1 3 3 1 quartet with a splitting /. Likewise, the two protons of the CH2 group split the single resonance of the CH3 protons into a 1 2 1 triplet. Each of these fines is split into a doublet to a small extent by the OH proton. 

The spin-spin coupling constant of two nuclei joined by N bonds is normally denoted /, with subscripts for the types of nuclei involved. Thus, /ch the 

The magnitude of 7hh depends on the dihedral angle, between the two C-H bonds (2). The variation is expressed quite well by the Karplus equation  

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