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CHAPTER 15 523 
 
symmetry passing through both nitrogen atoms in the 
ring makes the CH2 groups on one half of the molecule 
equivalent to the corresponding CH2 groups on the other 
half of the molecule. Overall, BZP has two signals for 
the piperazine CH2 protons, as shown below: 
 
 
 
DBZP has an additional plane of symmetry (slicing top 
to bottom in the structure shown), so all eight CH2 
protons are equivalent, and only one signal is expected 
for these eight protons. 
 
 
 
 
15.5. 
(a) This compound has eight different kinds of protons 
(highlighted below), giving rise to eight signals. 
 
 
 
 
 
 
 
 
 
 
(b) This compound has four different kinds of protons 
(highlighted below), giving rise to four signals. 
 
 
 
 
 
(c) This compound has two different kinds of protons 
(highlighted below), giving rise to two signals. 
 
 
 
(d) This compound has three different kinds of protons 
(highlighted below), giving rise to three signals. 
 
CH3
These two protons can
be interchanged by
rotational symmetry,
so they are homotopic
These two methyl
groups can be
interchanged
by rotational
symmetry, so all
six protons are
homotopic
CH3
CH3
CH3
H
H
CH3
CH3H
H
These two protons can
be interchanged by
rotational symmetry,
so they are homotopic
 
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