# CMR Lesson 7, Multiplet Line Pattern Shapes and Pascalâ€™s

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```					CMR Lesson 7, Multiplet Line Pattern Shapes and Pascal’s Triangle:
Another way to remember coupling patterns and their shapes (i.e., the relative heights of
lines as shown in Figures VII-1 and VII-2) by use of Pascal’s triangle, shown in Figure
VII-4 (next page). With Pascal’s triangle (which can be derived each time you need it)
you can generate the multiplicity (s, d, t, q) and peak shape (1:1, 1:2:1, 1:3:3:1) at the
same time. All you need to remember is how to draw out the triangle, and the n +1 rule.
The # of lines in a pattern predicted with the n +1 rule. Quick inspection of Pascal’s
triangle will reveal the additivity pattern used to generate the numbers. For example, 1 +
2 = 3, so the value derived by connections of points with values 1 and 2 will have a value
of 3.

pattern         shape

singlet            1
1

1              1                                 doublet           1:1

triplet          1:2:1
1              2              1

1              3              3               1                 quartet          1:3:3:1

4              6              4              1          quintet         1:4:6:4:1
1

sextet          ?:?:?:?:?:?
?              ?              ?              ?
?            ?

Figure VII-4. Pascal’s Triangle

Using Pascal’s triangle and the n + 1 rule, if the carbon is attached to two hydrogens (the
number of attached hydrogens = n), then the carbon coupled to hydrogen would appear as
a triplet and the inner peak of the triplet would be twice as high as the two outer peaks.
This is very useful tool for NMR spectroscopy.

Q51. (a) Using Pascal’s triangle, what line
shape would you expect for a quintet?
(b) What one organic compound could
have a quintet single in its off resonance
decoupled 13C NMR spectrum?
Q52. What is the line shape of a sextet?      A51. (a) 1:4:6:4:1

(b) Only one compound would have a
quintet signal for carbon, methane!

Q53. What multiplicity and line shapes are A52. 1:5:10:10:5:1
expected for carbon atoms numbered 1-5 in the
off resonance decoupled 13C NMR of the By logical extension of additivity pattern
compound 2,2,4-trimethylpentane?              demonstrated in Pascal’s triangle.

(CH3)3CCH2CH(CH3)2
1    23 4 5

Q54.      How many signals and of what A53. C1 = quartet, 1:3:3:1
multiplicity and line shape are expected for the C2 = singlet
off resonance decoupled 13C NMR of the           C3 = triplet, 1:2:1
compound 3-methylpentane?                        C4 = doublet, 1:1
C5 = quartet, 1:3:3:1

Q55.    How could you use off resonance A54. 4 signals, two quartets, one triplet, one
decoupled 13C NMR to differentiate between doublet. Correlated to the structure as follows:
pentane and 2,3-dimethylbutane?              CH3CH2CH(CH3)CH2CH3
1 2 3 4            2 1
C1 = quartet, 1:3:3:1
C2 = triplet, 1:2:1
C3 = doublet, 1:1
C4 = quartet, 1:3:3:1

A55. (a) By number of observed signals. 2,3-
dimethylbutane would have 2 carbon signals,
and pentane would have 3.

(b) By multiplicity of observed peaks in off
resonance decoupled 13C NMR spectra. 2,3-
dimethylbutane would have 1 quartet and 1
doublet in off resonance decoupled spectra.
Pentane would have 1 quartet, 2 triplets, and no
doublets.
(CH3)2CHCH(CH3)2 and (CH3CH2)2CH2
1     2 2 1               1 2        3

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