OpenStax Organic Chemistry: A Tenth Edition Student Solutions Manual
Chapter 12 – Structure Determination: Mass Spectroscopy and Infrared
Spectroscopy
Solutions to Problems
12.1 If the isotopic masses of the atoms C, H, and O had integral values of 12 u, 1 u and 16 u,
many molecular formulas would correspond to a molecular weight of 288 u. Because
isotopic masses are not integral, however, only one molecular formula is associated with
a molecular ion at 288.2089 u.
To reduce the number of possible formulas, assume that the difference in molecular
weight between 288 and 288.2089 is due mainly to hydrogen. Divide 0.2089 by 0.00783,
the amount by which the atomic weight of one 1H atom differs from 1. The answer,
26.67, gives a “ballpark” estimate of the number of hydrogens in testosterone. Then,
divide 288 by 12, to determine the maximum number of carbons. Since 288 ÷ 12 = 24,
we know that testosterone can have no more than 22 carbons if it also includes hydrogen
and oxygen. Make a list of reasonable molecular formulas containing C, H and O whose
mass is 288 and which contain 20–30 hydrogens. Tabulate these, and calculate their exact
masses using the exact atomic mass values in the text. The only possible formula for
testosterone is C19H28O2.
Isotopic mass
Molecular Mass Mass Mass Mass of
formula of carbons of hydrogens of oxygens molecular ion
C20H32O 240.0000 u 32.2504 u 15.9949 u 288.2453 u
C19H28O2 228.0000 28.2191 31.9898 288.2089
C18H24O3 216.0000 24.1879 47.9847 288.1726
12.2
Fragmentation occurs to a greater extent at the weakest carbon–carbon bonds, producing
a relatively stable cation. Spectrum (a), which has a dominant peak at m/z = 69,
corresponds to 2-methyl-2-pentene, and spectrum (b), which has m/z = 55 as its base
peak, corresponds to 2-hexene.
12.3 In a mass spectrum, the molecular ion is both a cation and a radical. When it fragments,
two kinds of cleavage can occur. (1) Cleavage can form a radical and a cation (the
species observed in the mass spectrum). Alpha cleavage shows this type of pattern. (2)
Cleavage can form a neutral molecule and a different radical cation (the species observed
1 11/15/2023
, OpenStax Organic Chemistry: A Tenth Edition Student Solutions Manual
in the mass spectrum). Alcohol dehydration and the McLafferty rearrangement show this
cleavage pattern.
For each compound, calculate the mass of the molecular ion and identify the functional
groups present. Draw the fragmentation products and calculate their masses.
(a)
In theory, alpha cleavage can take place on either side of the carbonyl group to produce
cations with m/z = 43 and m/z = 71. In practice, cleavage occurs on the more substituted
side of the carbonyl group, and the first cation, with m/z = 43, is observed.
(b)
Dehydration of cyclohexanol produces a cation radical with m/z = 82.
(c)
The cation radical fragment resulting from McLafferty rearrangement has m/z = 58.
(d)
Alpha cleavage of triethylamine yields a cation with m/z = 86.
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12.4 Identify the functional groups present in the molecule and recall the kinds of
fragmentations those functional groups produce. 2-Methyl-2-pentanol produces
fragments that result from both dehydration and from alpha cleavage. Two different alpha
cleavage products are possible.
Peaks might appear at M+ = 102 (molecular ion), 87, 84, 59.
12.5 We know that: (1) energy increases as wavelength decreases, and (2) the wavelength of
X-radiation is smaller than the wavelength of infrared radiation. Thus, we estimate that
an X ray is of higher energy than an infrared ray.
= hv = hc/λ; h = 6.62 10−34 J s; c = 3.00 108 m/s
for λ = 110−6 m (infrared radiation):
(6.62 10−34 J s)(3.00 108 m/s)
= = 2.0 10 −19 J
1.0 10−6 m
for λ = 3.0 10−9 m (X radiation):
(6.62 10−34 J s)(3.00 108 m/s)
= −9
= 6.6 10 −17 J
3.0 10 m
Confirming our estimate, the calculation shows that an X ray is of higher energy than
infrared radiation.
Convert radiation in m to radiation in Hz by the equation:
c 3.00 108 m/s
v= = = 3.3 1013 Hz
λ 9.0 10−6 m
The equation ɛ = hν shows that the greater the value of ν, the greater the energy. Thus,
radiation with ν = 3.3 × 1013 Hz (λ= 9.0 × 10–6 m) is higher in energy than radiation with
ν = 4.0 × 109 Hz.
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Chapter 12 – Structure Determination: Mass Spectroscopy and Infrared
Spectroscopy
Solutions to Problems
12.1 If the isotopic masses of the atoms C, H, and O had integral values of 12 u, 1 u and 16 u,
many molecular formulas would correspond to a molecular weight of 288 u. Because
isotopic masses are not integral, however, only one molecular formula is associated with
a molecular ion at 288.2089 u.
To reduce the number of possible formulas, assume that the difference in molecular
weight between 288 and 288.2089 is due mainly to hydrogen. Divide 0.2089 by 0.00783,
the amount by which the atomic weight of one 1H atom differs from 1. The answer,
26.67, gives a “ballpark” estimate of the number of hydrogens in testosterone. Then,
divide 288 by 12, to determine the maximum number of carbons. Since 288 ÷ 12 = 24,
we know that testosterone can have no more than 22 carbons if it also includes hydrogen
and oxygen. Make a list of reasonable molecular formulas containing C, H and O whose
mass is 288 and which contain 20–30 hydrogens. Tabulate these, and calculate their exact
masses using the exact atomic mass values in the text. The only possible formula for
testosterone is C19H28O2.
Isotopic mass
Molecular Mass Mass Mass Mass of
formula of carbons of hydrogens of oxygens molecular ion
C20H32O 240.0000 u 32.2504 u 15.9949 u 288.2453 u
C19H28O2 228.0000 28.2191 31.9898 288.2089
C18H24O3 216.0000 24.1879 47.9847 288.1726
12.2
Fragmentation occurs to a greater extent at the weakest carbon–carbon bonds, producing
a relatively stable cation. Spectrum (a), which has a dominant peak at m/z = 69,
corresponds to 2-methyl-2-pentene, and spectrum (b), which has m/z = 55 as its base
peak, corresponds to 2-hexene.
12.3 In a mass spectrum, the molecular ion is both a cation and a radical. When it fragments,
two kinds of cleavage can occur. (1) Cleavage can form a radical and a cation (the
species observed in the mass spectrum). Alpha cleavage shows this type of pattern. (2)
Cleavage can form a neutral molecule and a different radical cation (the species observed
1 11/15/2023
, OpenStax Organic Chemistry: A Tenth Edition Student Solutions Manual
in the mass spectrum). Alcohol dehydration and the McLafferty rearrangement show this
cleavage pattern.
For each compound, calculate the mass of the molecular ion and identify the functional
groups present. Draw the fragmentation products and calculate their masses.
(a)
In theory, alpha cleavage can take place on either side of the carbonyl group to produce
cations with m/z = 43 and m/z = 71. In practice, cleavage occurs on the more substituted
side of the carbonyl group, and the first cation, with m/z = 43, is observed.
(b)
Dehydration of cyclohexanol produces a cation radical with m/z = 82.
(c)
The cation radical fragment resulting from McLafferty rearrangement has m/z = 58.
(d)
Alpha cleavage of triethylamine yields a cation with m/z = 86.
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12.4 Identify the functional groups present in the molecule and recall the kinds of
fragmentations those functional groups produce. 2-Methyl-2-pentanol produces
fragments that result from both dehydration and from alpha cleavage. Two different alpha
cleavage products are possible.
Peaks might appear at M+ = 102 (molecular ion), 87, 84, 59.
12.5 We know that: (1) energy increases as wavelength decreases, and (2) the wavelength of
X-radiation is smaller than the wavelength of infrared radiation. Thus, we estimate that
an X ray is of higher energy than an infrared ray.
= hv = hc/λ; h = 6.62 10−34 J s; c = 3.00 108 m/s
for λ = 110−6 m (infrared radiation):
(6.62 10−34 J s)(3.00 108 m/s)
= = 2.0 10 −19 J
1.0 10−6 m
for λ = 3.0 10−9 m (X radiation):
(6.62 10−34 J s)(3.00 108 m/s)
= −9
= 6.6 10 −17 J
3.0 10 m
Confirming our estimate, the calculation shows that an X ray is of higher energy than
infrared radiation.
Convert radiation in m to radiation in Hz by the equation:
c 3.00 108 m/s
v= = = 3.3 1013 Hz
λ 9.0 10−6 m
The equation ɛ = hν shows that the greater the value of ν, the greater the energy. Thus,
radiation with ν = 3.3 × 1013 Hz (λ= 9.0 × 10–6 m) is higher in energy than radiation with
ν = 4.0 × 109 Hz.
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