幻灯片 1

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Chapter 9
Alcohols, Ethers and phenols
9.1 IUPAC Nomenclature of Alcohols,
Ethers and Phenols
9.1.1 Naming Alcohols
9.1.2 Naming Phenols
9.1.3 Naming Ethers
9.2 Preparation of alcohols,Ethers and
Phenols
9.2.1 Preparation of alcohols
A. Preparation of alcohols by
reduction of carbonyl compounds
(1) Hydrogenation of aldehydes and
ketones by catalysis of metals
(2) Reduction of carbonyl compounds
by metal hydrides
B. Preparation of diols
9.2.2 Preparation of Ethers
A. Ethers by intermolecular dehydration
of alcohols
B. Williamson Synthesis of Ethers
9.2.3 Preparation of phenols
A. Laboratory synthesis
B. Industrial synthesis
9.3 Reactions of Alcohols
The sites of reactions of a Alcohol
9.3.1 Acidity and Basicity of Alcohols
9.3.2 Conversion of alcohols to ethers
9.3.3 Oxidation of alcohols
A. Oxidation of primary alcohols
B. Oxidation of secondary alcohols
C. Oxidation of vicinal diols
9.4 Reactions of phenols
9.4.1 Acidity of Phenols
9.4.2 Electrophilic aromatic substitutions
9.4.3 Acylation of phenols
Fries rearrangement
9.4.4 Kolbe-Schmitt reaction
9.4.5 Preparation of aryl ethers
9.4.6 Cleavage of aryl ethers by hydrogen
halides
9.4.7 Claisen rearrangement of
allyl aryl ethers
9.4.8 Oxidation of phenols: Quinones
9.5 Reactions of Ethers
9.5.1 Acid-catalyzed cleavage of ethers
9.5.2 Preparation of epoxides
A.Epoxidation of alkenes by reaction
with peroxy acids
B. Conversion of vicinal halodrins
to epoxides
9.5.3 Reactions of Epoxides
A. Base-catalyzed ring opening
B. Acid-catalyzed ring opening
Compounds with O-containing
functional groups O
ROH
ROR'
ArOH
R C H
O
R C R'
Alcohol Ether Phenol Aldehyde Ketone
醇
醚
O
R C OH
酚
O
X,
R C Y
Carboxylic Carboxylic acid
acid
derivatives Y
羧酸
醛
羧酸衍生物
OR,
酮
Acetyl halides
酰卤
Esters
酯
O Carboxylic acid
C R anhydrides
酸酐
The interplay of these
Amides
NR'
2
compounds is fundamental
酰胺
to organic chemistry and biochemistry
Compounds that have hydroxyl
C OH group bonded to a saturated,
sp3-C atom-Alcohols.
Compounds
that
have
hydroxyl
OH
group bonded to a aromatic
ring-Phenols.
Compounds that have a oxygen
R O R' atom bonded to two carbon atom
-Ethers
Class of Ethers:
Class of Alcohols: R''
RCH2OH
RCHR'
OH
RCR' C
OH
Primary Secondary Tertiary
alcohols alcohols alcohols
O C
R O R'Ethers
CH2
H2C
O
Epoxides
9.1 IUPAC Nomenclature of Alcohols,
Ethers and Phenols
P252,8.1
9.1.1 Naming Alcohols
Common name: Alkyl + alcohol
Substitutive name: Suffix: e ol
CH3
• Number: begin at the end nearer
the hydroxyl group.
CH3COH
CH2OH
Benzyl alcohol
(苄醇)
H2C
CHCH2OH
Allyl alcohol
(烯丙醇)
2-Propen-1-ol
Phenyl methanol (2-丙烯-1-醇)
(苯甲醇)
CH3
tert-Butylalcohol
(叔丁醇)
2-Metyl-2-propanol
(2-甲基-2-丙醇)
HOCH2CH2OH HOCH2CHCH2OH ClCH CH CH OH
2
2
2
Ethyl glycol
OH
3-Chloro-1-propanol
(乙二醇)
1,2-Ethanediol
Glycerol(甘油)
OH
(3-氯-1-丙醇)
1,2,3-Propanetriol (CH ) C
C(CH )
9.1.2 Naming Phenols
Phenol is the base name:
o-, m-, p-: substitutent
OH
CH3
4-Methylphenol
p-Methylphenol
p-Cresol(甲酚) Cl
OH
OH
CH3
BHT
OH
OH
OH
1,2-Benzenediol
Catechol 1,3-Benzenediol
Resorcinol
(儿茶酚)
(邻苯二酚)
(间苯二酚)
3 3
3 3
CH3
OH
5-Chloro2-methylphenol
(2-甲基-5-氯
苯酚)
OH
1,4-Benzenediol
Hydroquinone
(对苯二酚)
(氢醌)
OH
OH
OH
OH
HO
OH
Pyrogallol
1,3,5-benzenetriol
(连苯三酚)
OH
(均苯三酚)
OH
1-Naphthol
α- Naphthol
2-Naphthol
β- Naphthol
(1-萘酚)
(2-萘酚)
9.1.3 Naming of Ethers
Functional class IUPAC names
Diethyl ether
P253
Tetrahydrofuran
Anisole
(THF)
phenyl ether
(乙醚)
(四氢呋喃) Methyl
(茴香醚)
CH3CH2OCH3
CH3
(苯甲醚)
Ethyl methyl ether C6H5O C CH3
(甲乙醚)
Symmetrical ethers (单醚) CH3
Unsymmetrical
(Mixed) ethers (混醚)
tert-Butyl
phenyl ether
(苯叔丁基醚)
Substitutive IUPAC
CH3CHCH2CH2CH3
OCH3
Alkoxy (烷氧基)
CH3
CH3CH2O
1-Ethoxy-4-methylbenzene
2-Methoxypentane
(4-甲基-1-乙氧基苯)
(2-甲氧基戊烷)
Suffix:yl oxy
Cyclic ethers:
O
O
O
1,4-Dioxane
Oxane 1,4-二氧六环
烷
二
烷
9.2 Preparation of alcohols, Ethers and
Phenols
9.2.1 Preparation of Alcohols
Transformation of the several functional
groups to alcohols:
C
ROH
P258,8.4
C
RX
O
C R'(H)
A. Preparation of Alcohols by
Reduction of Carbonyl Compounds
O
C
Reducing agent
C OH
(1) Hydrogenation of aldehydes and
ketones by Catalysis of metals
O
RC H + H2
Aldehydes
O
RC R' + H2
Ketones
CH3O
Pt, Pd, Ni, or Ru
RCH2OH
Primary alcohols
RCHR'
Pt, Pd, Ni, or Ru
OH
Secondary alcohols
O
H2, Pt
C H EtOH CH3O
H
C
H
OH
p-Methoxybenzaldehyde
p-Methoxybenzyl
alcohol(92%)
(2) Reduction of carbonyl compounds
by metal hydrides P259,
8.5
Metal hydrides:
H
Na
+
H B H
H
Li+
H
H Al H
H
Sodium
borohydride
NaBH4
Lithium aluminum
hydride
LiAlH4(LAH)
(硼氢化钠)
(四氢铝锂)
•Reaction of NaBH4 with aldehydes
and ketones
O
O
CH
CH33CH
CH22CH
CH22CH
CH
Butanal
NaBH
NaBH44
H
H22O
O
CH
CH33CH
CH22CH
CH22CH
CH22OH
OH
O
1-Butanol (87%)
OH
NaBH4
CH3CCH2C(CH3)3
EtOH
4,4-Dimethyl2-pentanone
O
NaBH4
H2O
CH3CHCH2C(CH3)3
4,4-Dimethyl2-pentanol(85%)
OH
An aqueous or
alcoholic solution
•Reaction of LiAlH4 with Aldehydes
and Ketones
(1) LiAlH4 / Et2O
(CH3)3CCHCH3
(2) H2O
OH
O
3,3-Dimethyl-2-butanone 3,3-Dimethyl-2-butanol
(CH3)3CCCH3
•Reaction of LiAlH4 with carboxylic acids
and esters
4 RCO2H + 3 LiAlH4
Et2O
[(RCH2O)4Al]Li + 4 H2 + 2 LiAlO2
H2O
O
C OH
1. LiAlH4 / Et2O
2. H2O
4 RCH2OH + Al (OH)3 + LiOH
CH2OH
Cyclopropanecarboxylic Cyclopropylmethanol
(环丙基甲醇)(78%)
Acid (环丙基甲酸)
O
RC OR'
1. LiAlH4 / Et2O
2. H2O
O
1. LiAlH4 / Et2O
COC2H5
2. H2O
RCH2OH + R'OH
CH2OH + C2H5OH
Ethyl benzoate
Benzyl alcohol
(苯甲酸乙酯)
(苄醇)(90%)
RCOOH
RCOOR'
1°Alcohols
Characteristics of reactions:
• Selective reduction:
NaBH4 does not reduce C=C, C C
and -COOH, -COOR。
LiAlH4 does not reduce C=C, C C
Reduced by LiAlH4
Reduced by NaBH4
O
O
O
O
O
RC O < RC OH < RC OR' < RC R' < RC H
Ease of reduction
O
O
COC2H5
O
NaBH4
H3+O
CH3OH
1. LiAlH4,ether
CH3CH2CH CHCOCH3
2. H3O+
H
OH
COOC2H5
CH3CH2CH CHCH2OH
+ CH3OH
Methyl 2-pentenoate
2-Penten-1-ol(91%)
• Solvents:
NaBH4
Solvents: H2O, ROH
LiAlH4
Et2O, THF
LiAlH4 reacts violently with water.
B. Preparation of diols
Vicinal diols
CH2CH2
OH OH
CH3CHCH2
OHOH
1,2-Ethanediol
Ethylene glycol
1,2-Propanediol
Propylene glycol
1,2-乙二醇(甘醇)
1,2-丙二醇
CH3
H3C C O OH
CH3
, OsO4(Cat)
RCHCH2
OH, OH
OH
HO
OsO4
Alkaline
Osmium tetraoxide tert-butyl hydroperoxide (碱性)
RCH CH2
(四氧化锇)
(叔丁基氢过氧化物)
HO
(CH3)3COOH, OsO4 (Cat)
(CH3)3COH, HO
Hydroxylation
Syn-addition
HO
H
H
KMnO4 / OH-
(cold)
9.2.2 Preparation of Ethers
A. Ethers by intermolecular dehydration
of alcohols
Substrate: Primary alcohols
Acid-catalyzed
Products: symmetric ethers
P261,
B. The Williamson Synthesis of Ethers 8.6
Sodium alkoxide,Alkyl halide and derivatives
Mixed ethers
R O Na + R' L
R O R' + Na L
L: Br, I, OSO2R'' or OSO2OR''
CH3CH2CH2OH + Na
Propyl alcohol
CH3CH2CH2O Na + 1/2 H2
Sodium propoxide
CH3CH2I
CH3CH2CH2OCH2CH3 + Na I
Ethyl propyl ether
(70%)
The reaction characteristic:
1. SN2 reaction
2. The best substrate is primary alkyl halide
(CH3)2CHONa +
CH2Cl
(CH3)2CHOCH2
CH2ONa + (CH3)3CHCl
+ NaCl
Alexander W. Williamson
(1824-1904)
Alexander W. Williamson was Born in London, England,
and received his Ph.D. at the University of Giessen in
1846.His ability to work in laboratory was hampered
by a childhood injury that caused the loss of an arm.
From 1849,utill 1887, he was professor of Chemistry
at University College, London.
Bonding in organic compounds at that time was thought to be of either the
water type, as in alcohols, ROH, or of the radical type, as in ethers which
would be given the formula RO. But Williamson, by his ether synthesis,
showed that mixed ethers, with two different alkyl groups, could be prepared.
Ethers thus has to have the water-type formula ROR', and oxygen had the
equivalent weight of 8 but the atomic weight of 16. By this type of argument
he established and rationalised the structures of many of the families of
simple organic compounds. Thus, in 1850 he predicted the existence of acetic
anhydride, which was prepared in 1851.We still have some examples of his
early apparatus, and his copper pelicans, in which he prepared ether, are
shown at right. When you realise the scale on which these reactions were
carried out, and the fact that the pelican was heated over a charcoal brazier,
it is remarkable that we do not seem to have records of catastrophic accidents
taking place.
Later on Williamson, again with people such as Liebig, was responsible for
the introduction of much of the glassware which we are familiar with today,
except that it was usually fitted together with corks rather than ground
glass joints. Standard joints, blown in a mould, as we know them today
did not come into use until the middle of the last (20th) century.
Towards the end of his period as Head of Department, Williamson became
very much involved in College and University politics, and his research
suffered. This was the period when the other London colleges - Kings,
Birkbeck, Queen Mary, what is now Imperial College, and so on were
combined into a federal university, and presumably Williamson felt
the need to fight the University College corner.
9.2.3 Preparation of phenols
From aniline:
A. Laboratory synthesis
N2+
NH2
OH
H3+O£¬¡÷
NaNO2, H2SO4
NO2
0~5¡æ
NO2
NO2
(80%)
B. Industrial synthesis
(1) Reaction of benzenesulfonic acid with NaOH
SO3H
SO3
H2SO4
CH3
Toluene
OH
1. NaOH, 300¡æ
2. H3+O
CH3
CH3
p-Toluenesulfonic p-methylphenol
acid
(72%)
碱熔法
(2) Hydrolysis of chlorobenzene
Cl
1. NaOH, H2O, 370¡æ
+
2. H
3. From cumene(枯烯)
+
CH3CH
无水 AlCl3
CH2 85 ~ 95 ¡æ
Friedel-Crafts alkylation
CH3
CH + O2
CH3
OH
卤苯水解
CH3
CH
CH3
Cumene
枯烯
CH3
95 ~ 135 ¡æ
C O OH
CH3
Cumene hydroperxide
(氢过氧化枯烯)
Cumene is oxidized to cumene hydroperoxide
CH3
C O OH
CH3
O
10% H2SO4
OH
~ 90¡æ
异丙苯法
9.3. Reactions of Alcohols
+ CH3CCH3
•The sites of reactions of a Alcohol:
H
C O H
Nucleophilic
substitution
H C
O
C C
Elimination
H
Nu:
C
H
C
Oxidation
O
Weak
basicity
Protonation
H A
H
H
O
H
Weak acidity
9.3.1 Acidity and Basicity of Alcohols
Like water, alcohols are both weakly
basic and weakly acidic. P256,8.3
As a weak base:
Reversible protonated by strong acids
to yield oxonium ions( 离子):
H
O H+H A
R
O H + A
R
An alcohol
An oxonium ion
As a weak acid:
H
H
R O + H O
O H + O
R
H
An alcohol
An
Alkoxide
Hydronium
H
ion(烷氧负离子) ion(水合离子)
Acid
(base) conjugate
conjugate
base
acid
TABLE. pKa Values for In any proton-transfer
some weak acids process:
ACID
CH3OH
H 2O
CH3CH2OH
(CH3)3COH
HC CH
H2
NH3
CH3CH3
P257, Table 8.1
K>1
Stroger
Stroger
+
pKa
acid
base
Weaker + Weaker
15.5
acid
base
15.74
16.0
18.0
25
35
38
50
Relative acidity:
H2O > ROH > RC C H
> H2 > NH3 > RH
Relative basicity:
R- > NH2- > H- >
C
C
>
RO
>
OH
R
2 CH3CH2OH + 2 Na
2 CH3CH2O Na + H2
CH3
CH3
2 H3 C C OH + 2 K
2 H3 C C O K + H2
CH3
CH3
NaH, NaNH2
P263.8.7
9.3.2 Conversion of Alcohols to Ethers
H2SO4
180 C
2 CH 2=CH 2 + 2H2O
H2SO4
140 C
CH3CH2-O-CH2CH3 + H2O
2CH3CH2OH
2 CH3CH2CH2CH2OH
H+
¡÷
Dehydration
CH3CH2CH2CH2OCH2CH2CH2CH3
+ H2O
Characteristics of the reaction:
1. Condensation(缩合反应)
2. Only for primary alcohols
3. The temperature of condensation is
lower than elimination.
4. SN2 mechanism
HOCH2CH2CH2CH2CH2OH
H2SO4
¡÷
O
1,5-Pentanediol
(1,5-戊二醇)
+ H2O
Oxane
(
烷)(76%)
9.3.3 Oxidation of alcohols
A. Oxidation of primary alcohols
O
R-CH2OH
[O]
FCH2CH2CH2OH
RCH2OH
PCC
CrO3 + HCl +
K2Cr2O7
H2SO4,H2O
O
R C H
N
O
R-C-H
3-Fluoro-1-propanol
(3-氟-1-丙醇)
P 263
[O]
R-C-OH
O
FCH2CH2 C OH
3-Fluoropropanoic acid
(3-氟丙酸) (74%)
PCC reagent is
soluble in CH2Cl2
N H CrO3Cl
Pyridinium chlorochromate ( PCC)
CH3
(C2H5)2C CH2OH + PCC
CH2Cl2
25 C
CH3 O
(C2H5)2C C
PCC doesn’t attack C=C bond
O
PCC
CH2OH CH Cl
2 2
C H
Citronellol
Citronellal (82%)
(香茅醇)
(香茅醛)
B. Oxidation of secondary alcohols
Secondary [O]
ketones
alcohols
RCHR'
OH
K2Cr2O7
H2SO4,H2O
RCR'
O
Chromic acid
H2CrO4
H
R
OH
O R' C
Na2 Cr2O7
H2SO4,H2O
Cyclohexanol
OH
[O]
No rection
R"
Cyclohexanone(85%)
AgIO3
C. Oxidation of vicinal diols
Vicinal diols react with HIO4, the
C-C bond is broken to form carbonyl
compounds
Ch.P225,(3)
O
RCHOH
+ O I OH
R'CHOH
O
-H2O
OH
O
RCH O
I
OH
R'CH O
OH
RCHO + HIO
3
R'CHO
AgNO3 is added to identify the vicinal diols
9.4 Reactions of phenols
The sites of reactions
Acylation
Acidity
Formation
of aryl ethers
Aromatic
Electrophilic
substitution
9.4.1 Acidity of Phenols P256,8.3
O
OH
pKa = 18
OH
CH3C OH
pKa = 9.89
pKa = 4.74
TABLE 1 The acidity constants of phenols
pKa (25℃)
Substimptuents o-
-H
-CH3
-Cl
-NO2
-OCH3
9.89
10.20
8.11
7.17
9.98
9.89
10.01
8.80
8.28
9.65
Substituents
9.89 2,4-Dinitro
10.17
2,4,6-Trinitro
9.20 (picric acid)
(苦味酸)
7.15
10.21
pKa (25℃)
3.96
0.38
Substituted phenols:
Electron - releasing group
Substuents
Acidity is decreased
Electron – withdrawing
on the position
group
o- or pAcidity is increased
O
H
O
+ H
pka = 10
Electron delocalization in phenoxide ion:
O
O
O
O
O
9.4.2 Electrophilic aromatic P266;
Ch.P322,(2)
substitutions
A hydroxyl group is a very powerful
activating substituent:
Bromination:
OH
OH
H2O
+ 3 Br2
Br (white) + 3HBr
Br
Br
(100%)
Sulfonation:
OH
25¡æ
OH
(concd)H2SO4
SO3H
OH
Rate control
100¡æ
100¡æ
SO3H
Equilibrium control
9.4.3 Acylation of phenols
Acylating agents: acyl halides and
carboxylic acid anhydrides Ch.P319(丙)
OH
+
CH3
H3C
OCOCH3
O
CH3CCl
pyridine
75£¥
H3C
Fries rearrangement:
O
OH
CC6H5
OH
O
OCC6H5
AlCl3
Phenol
benzoate
+ HCl
CH3
Phenolic
Esters
(酚酯)
Conversion of
aryl
esters
to
CC6H5
aryl ketones.
(9%)
O
p-hydroxylbenzopheone
+
(对-羟基二苯酮)(64%)
9.4.4 Kolbe-Schmitt reaction:
Carboxylaltion of phenols
Sodium phenoxide CO2
Heated under pressure
Salicylic acid
ONa
+ CO2
O
OCCH3
COOH
120¡æ
100 atm
Aspirin
(阿斯匹林)
(乙酰水杨酸)
Acidified
OH
H+
COONa
OH
COOH
Salicylic acid
(水杨酸)(79%)
9.4.5 Preparation of aryl ethers
Williamson Method
A Phenoxide anion A alkyl halide
Alkylation of hydroxyl oxygen a phenol
ArOH
NaOH
ArO Na
O Na
OH
+ NaOH
H2O
R X
(X = Cl, Br, I, ArOR
OSO2OR')
OCH3
CH3OSO2OCH3
Me2SO4-methylating agent
OCH3
+ Na+X
+ NaOSO2OCH3
(Anisole)
茴香醚
I + CH3ONa
Why?
9.4.6 Cleavage of aryl ethers by
hydrogen halides
Ar O
concd HX
¡÷
R
¡÷
Ar OH + RX
concd HX
Ar X + ROH
The bond of O-R was broken!
OCH3
OH
The bond of
HO
+ HBr
+ CH3Br C-O in phenols
has partial double
CH3
CH3
bond character
HBr
2
No reaction
9.4.7 Claisen rearrangement of
allyl aryl ethers
Intramolecular
Heating allyl aryl ether
reaction
The product is o-allylphenol
OCH2CH CH2
OH
200¡æ
CH2CH CH2
O
O
via
Transition state
Claisen was professor in Aachen in 1890,
Kiel in 1897 and Berlin in 1904.
Several syntheses especially condensation
reactions between aldehydes, ketones,
and esters (1881-1890) are connected with
Claisen´s name. He also carried out
research on tautomerism and
rearrangement reactions
(Umlagerungsreaktionen)
http://www.chemsoc.org/networks/enc/FECS/
Claisen.htm
19th Century
Claisen, Ludwig
Born: Köln (Germany), 1851
Died: Godesberg near Bonn
(Germany), 1930
9.4.8 Oxidation of phenols: Quinones
O P266
OH
(醌)
K2Cr2O7
H2SO4, H2O
OH
Hydroquionoe
The sructures
of quinones:
O
O
p-Benquinone
O
O
OH
- 2e
+ 2H
+ 2e
OH
O
O
O
O
O
CH3
CH3
CH2CH C(CH2CH2CH2CH)3CH3
CH3
Vitamin K
9.5 Reactions of Ethers
P267,8.9
9.5.1 Acid-catalyzed cleavage of ethers
CH3CH2OCH2CH3 + 2 HBr
2 CH3CH2Br + H2O
Mechanism of the reaction:
CH3CH2O CH2CH3 + Br
CH3CH2OCH2CH3 + HBr
CH3CH2O + CH3CH2Br
H
H
CH3CH2OH + HBr
Br
CH3CH2
+ CH3CH2 O H
H
Br + O H
H
9.5.2 Preparation of epoxides
A. Epoxidation of alkenes by reaction with
peroxy acids (过氧酸)
O
O
RHC CHR + R'C OH
O
O
RCH CHR + R'C O OH
Syn-addition
O
Peroxy acids: CH3COOH
C6H5COOH
Peroxyacetic acide Peroxybenzoic acide
(过氧乙酸)
(过氧苯甲酸)
B. Conversion of vicinal halohydrins (α-卤代醇)
to epoxides
X
R2C CR2
2
H2O
R2C CR2
HO X
HO
R2C CR2
O
Intramolecular Williamson ether synthesis:
R
HO
R
X
R C C
R
R
H O
HO H +
R
R
X
R C C
R
O
R
R
R C C R + X
O
R C C
R
O
R
H3C
H
C C
H
CH3
X
1. Br2/ H2O
2. HO
H3C
H
C C
H
CH
3
O
1. Anti-addition, 2. Inversion of configuration
9.5.3 Reactions of epoxides
A. Base-catalyzed ring opening
CH3CH2O + H2C CHCH3
O
CH3CH2OH
CH3CH2OCH2CHCH3
O
CH3CH2OCH2CHCH3 + CH3CH2O
OH
To the unsymmetric epoxide, in basecatalyzed ring-opening, attack by nucleophile
occurs at less substituted carbon atom.
B. Acid-catalyzed ring opening
CH3
CH3OH + CH3 C CH2
O
H
CH3
CH3
C CH2OH
OCH3
In the acid-catalyzed ring opening, the
nucleophile attacks primarily at theAntimore
hydroxylation
substituted carbon atom.
CH3
¦Ä
CH3
CH3OH + CH3 C CH2
O ¦Ä
H
CH3
C CH2OH
OCH3
H
SN2 reaction With inversion of configuration
O
+ CH3COOH
H
O + H3O
H
H
O + CH3COOH
H2O
H
OH
H
H
OH2
+
H
H
OH
H
OH
H
OH
H
Problems to Chapter 9
P276
8.24 (c), (d)
8.25 (b), (c)
8.28
8.31(a),(b)
8.33(a), (c), (e)
8.35(a),(d)
8.36(b), (e)
8.37(b)
8.38(b), (c)
8.40
8.41
8.43
8.46
8.48
8.51
8.53
8.54(b)
8.55
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