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School of Biological and Chemical Sciences (SBCS)
Chemistry Data Booklet
This booklet is issued at induction to new undergraduate students enrolling onto chemistry degree programmes. You should bring it along to all workshops and practical classes.
Version 1.26 (Aug 2018)
About this Data Booklet This data booklet aims to facilitate access to some of the data that is most commonly required during the first year of studies on chemistry degree programmes at Queen Mary. It is not intended to be comprehensive and you are referred to the additional data sources mentioned in section 9 for further information. This booklet has been compiled using data from a variety of sources including: Atkins' Physical Chemistry, P.W. Atkins and J. de Paula, Oxford University Press (9th edn, 2010)
WebElements (http://www.webelements.com/ ) M. Winter Tables for Group Theory P.W. Atkins, M.S. Child and C.S.G. Phillips, Oxford University Press (available from http://www.oup.com/uk/orc/bin/9780199206063/01student/group/ )
... as well as a range of other web-based resources. A copy of this data booklet is available in electronic format (printable at A4 size) from http://courses.sbcs.qmul.ac.uk/docs/chemdata1.pdf
Any errors or suggestions should be notified to: [email protected]
The School would like to acknowledge Dr Roger M Nix for the compilation of this booklet.
1
C O N T E N T S
Page
1. General Data & Constants 1.1 Physical constants 1.2 Useful conversion factors 1.3 Base SI units 1.4 Derived SI units 1.5 Prefixes for SI units 1.6 Common non-SI units 1.7 Common Greek symbols 1.8 Other symbols
2 2 2 3 3 3 4 4
2. Atomic Properties 2.1 Isotopic masses, abundances and nuclear spins of selected elements 2.2 Periodic table: atomic numbers and molar masses 2.3 Pauling electronegativities and first ionization energies (Z = 1 – 92)
5 6 7
3. Molecular Properties 3.1 Bond dissociation enthalpies in diatomic molecules 3.2 Bond dissociation enthalpies in polyatomic molecules 3.2 Common abbreviations
8 8 9
4. Equations of Physical & Inorganic Chemistry 4.1 Classical mechanics – 4.7 Gas properties / gas laws 4.8 Boltzmann distribution / spectroscopy / spectrometry – 4.14 Wave-particle duality / uncertainty relationships
10 10 11 11
5. Spectroscopic Data 5.1 Electromagnetic spectrum 5.2 Infrared (IR) spectroscopy 5.3
1H nmr spectroscopy
5.4 13
C nmr spectroscopy
12 12 14 15
6. Symmetry 6.1 Determining the molecular point group 6.2 Illustrative examples of point groups
16 17
7. Mathematical Relations 7.1 Standard derivatives and integrals 7.2 Definite integrals 7.3 Trigonometry and geometry 7.4 Other formulae and equations
19 19 19 19
8. Probability and Statistics 8.1 Useful equations 8.2 Critical t-values 8.3 Error propagation formulae
20 20 20
9. Other Sources of Information 9.1 Online sources of information 9.2 Reference texts
21 21
Chemistry Data Booklet 1. General Data & Constants
2
1. General Data and Constants
1.1 Physical constants The following values are given to 5 s.f. which is adequate for any calculations on your degree course.
Quantity Symbol Value Units
Speed of light c 2.9979 108 m s
–1
Elementary charge e 1.6022 10–19
C
Boltzmann constant k ( or kB ) 1.3807 10–23
J K–1
Ideal gas constant R ( = NAk ) 8.3145 J K–1
mol–1
Planck constant h 6.6261 10–34
J s
( = h / 2) 1.0546 10–34
J s
Avogadro constant NA 6.0221 1023
mol–1
Faraday constant F ( = NAe ) 9.6485 104 C mol
–1
Atomic mass unit u 1.6605 10–27
kg
Mass - electron me 9.1094 10–31
kg
- proton mp 1.6726 10–27
kg
- neutron mn 1.6749 10–27
kg
Vacuum permittivity 0 ( = 1/(c20) ) 8.8542 10
–12 J
–1 C
2 m
–1
40 1.1127 10–10
J–1
C2 m
–1
Vacuum permeability 0 4 10–7
J s2 C
–2 m
–1
Acceln due to gravity g 9.8067 m s
–2
Bohr radius a0 ( = 402/ mee
2 ) 5.2918 10
–11 m
1.2 Other constants and conversion factors
0.0C = 273.2 K
RH = 1.0974 105 cm
−1
Kw = 1.00 10–14
(at 298 K)
1.3 Base SI units
Physical Quantity Name of SI Unit Symbol for SI Unit
Length metre m
Mass kilogram kg
Time second s
Electric current ampere A
Temperature kelvin K
Amount of substance mole mol
Note - by convention, the abbreviations for units named after people (e.g. Ampere, Kelvin) begin with a capital letter.
Chemistry Data Booklet 1. General Data & Constants
3
1.4 Derived SI units
Physical Quantity Name of
SI unit
Symbol for
SI unit
Definition in Base Units
(alternative formulation)
Force newton N kg m s –2
Energy (work) joule J kg m2 s
–2
Electric charge coulomb C A s
Electric potential volt V kg m2 s
–3 A
–1
Frequency hertz Hz s–1
Pressure pascal Pa kg m–1
s–2
( = N m –2
)
Power watt W kg m2 s
–3 ( = J s
–1)
1.5 Prefixes for SI units
(i) Reducing prefixes
Factor 10–18
10–15
10–12
10–9
10–6
10–3
10–2
10–1
Prefix atto femto pico nano micro milli centi deci
Symbol a f p n m c d
(ii) Enhancing prefixes
Factor 103 10
6 10
9 10
12
Prefix kilo mega giga tera
Symbol k M G T
1.6 Common Non-SI units
1 eV = 1.6022 10–19
J ( = 1 e 1 V)
1 cal = 4.184 J
1 hartree (Ha) = 2625.5 kJ mol–1
1 cm–1
= 1.9864 10–23
J ( = ch ~ )
1 atm = 101325 Pa
1 bar = 100000 Pa
1 psi = 6894.8 Pa ( psig – psi gauge; relative to atmospheric pressure)
1 Torr = 1 mmHg = 133.32 Pa
1 L (= 1 l ) = 1 dm3
1 Å = 1 10–10
m
1 debye (D) = 3.3356 10–30
C m
1 dalton (Da) = 1 u = 1.6605 10–27
kg
Chemistry Data Booklet 1. General Data & Constants
4
1.7 Common Greek symbols The following list is not the full Greek alphabet: less commonly used characters have been omitted. The associations mentioned for each symbol are illustrative and not comprehensive.
Lower Case
Upper Case
Name Common Associations / Uses
alpha - polarizability, Coulomb integral
beta - resonance integral
chi - magnetic susceptibility
delta - small change, chemical shift: - large change
epsilon - molar absorption coefficient, dielectric constant
phi - atomic wavefunction, azimuthal angle
gamma - surface tension, activity coefficient
eta - viscosity
kappa - thermal and electrical conductivity
lambda - wavelength : - molar conductivity
mu - chemical potential, reduced mass, dipole moment
nu - frequency
pi = 3.14159.... : - product, osmotic pressure
theta - angle, temperature, surface coverage
rho - density
sigma - collision cross-section; - summation.
tau - period, time constant, lifetime
omega - angular frequency
psi - wavefunctions
1.8 Other symbols The following symbols are also commonly used in chemistry.
c~ - speed of light (specifically in units of cm s–1
; 2.9979 1010
cm s–1
)
~ - wavenumber (units of cm–1
)
( = h / 2)
Å - ångström (1 Å = 1 10–10
m)
- standard state (e.g. H , also occasionally written as H )
Chemistry Data Booklet 2. Atomic Properties
5
2. Atomic Properties 2.1 Isotopic masses, abundances and nuclear spin of selected elements
Element Isotope Mass / u Abundance / % Nuclear spin, I
H 1H 1.0078 99.985 ½
D 2H 2.0140 0.015 1
He 3He 3.0160 0.00013 ½
4He 4.0026 100 0
Li 6Li 6.0151 7.42 1
7Li 7.0160 92.58 3/2
B 10
B 10.0129 19.78 3
11
B 11.0093 80.22 3/2
C 12
C 12.0000 98.89 0
13
C 13.0034 1.11 ½
N 14
N 14.0031 99.63 1
15
N 15.0001 0.37 ½
O 16
O 15.9949 99.76 0
17
O 16.9991 0.037 5/2
18
O 17.9992 0.204 0
F 19
F 18.9984 100 ½
Ne 20
Ne
19.9924 90.48 0
21
Ne
20.9940 0.27 3/2
22
Ne
21.9914 9.25 0
Na 23
Na
22.9898 100 3/2
Mg 24
Mg
23.9850 78.99 0
25
Mg
24.9858 10.00 5/2
26
Mg
25.9826 11.01 0
Al 27
Al
26.9815 100 5/2
Si 28
Si
27.9769 92.23 0
29
Si
28.9765 4.67 ½
30
Si
29.9738 3.10 2
P 31
P
30.9738 100 ½
S 32
S
31.9721 94.93 0
33
S
32.9715 0.76 3/2
34
S
33.9679 4.29 0
36
S
35.9671 0.02 0
Cl 35
Cl 34.9688 75.53 3/2
37
Cl 36.9651 24.4 3/2
Br 79
Br 78.9183 50.54 3/2
81
Br 80.9163 49.46 3/2
I 127
I 126.9045 100 5/2
Chemistry Data Booklet 2. Atomic Properties
6
1
Peri
od
ic T
ab
le o
f th
e E
lem
en
ts
18
h
ydro
gen
1
H
1.0
079
2
Key:
13
14
15
16
17
hel
ium
2
He
4.0
026
lit
hiu
m
3
Li
6.9
41
ber
ylliu
m
4
Be
9.0
122
ele
men
t n
am
e
ato
mic
nu
mb
er
X
mola
r m
ass / g
mol–
1
b
oro
n
5
B
10.8
11
carb
on
6
C
12.0
11
nit
roge
n
7
N
14.0
07
oxy
gen
8
O
15.9
99
flu
ori
ne
9 F
18.9
98
neo
n
10
Ne
20.1
80
so
diu
m
11
Na
22.9
90
mag
nes
ium
12
Mg
24.3
05
3
4
5
6
7
8
9
10
11
12
alu
min
ium
13
Al
26.9
82
silic
on
14
Si
28.0
86
ph
osp
ho
rus
15
P
30.9
74
sulp
hu
r
16
S
32.0
65
chlo
rin
e
17
Cl
35.4
53
argo
n
18
Ar
39.9
84
p
ota
ssiu
m
19
K
39.0
98
calc
ium
20
Ca
40.0
78
scan
diu
m
21
Sc
44.9
56
tita
niu
m
22
Ti
47.8
67
van
adiu
m
23
V
50.9
42
chro
miu
m
24
Cr
51.9
96
man
gan
ese
25
Mn
54.9
38
iro
n
26
Fe
55.8
45
cob
alt
27
Co
58.9
33
nic
kel
28
Ni
58.6
93
cop
per
29
Cu
63.5
46
zin
c
30
Zn
65.4
09
galli
um
31
Ga
69.7
23
germ
aniu
m
32
Ge
72.6
4
arse
nic
33
As
74.9
22
sele
niu
m
34
Se
78.9
6
bro
min
e
35
Br
79.9
04
kryp
ton
36
Kr
83.7
98
ru
bid
ium
37
Rb
85.4
68
stro
nti
um
38
Sr
87.6
2
yttr
ium
39
Y
88.9
06
zirc
on
ium
40
Zr
91.2
25
nio
biu
m
41
Nb
92.9
06
mo
lybd
enum
42
Mo
95.9
4
tech
net
ium
43
Tc
[9
8]
ruth
en
ium
44
Ru
101
.07
rho
diu
m
45
Rh
102
.91
pal
lad
ium
46
Pd
106
.42
silv
er
47
Ag
107
.87
cad
miu
m
48
Cd
112
.41
ind
ium
49
In
114
.82
tin
50
Sn
118
.71
anti
mo
ny
51
Sb
121
.76
tellu
riu
m
52
Te
127
.60
iod
ine
53 I
126
.90
xen
on
54
Xe
131
.29
ca
esiu
m
55
Cs
132
.91
bar
ium
56
Ba
137
.33
lute
tiu
m
71
Lu
174
.97
haf
niu
m
72
Hf
178
.49
tan
talu
m
73
Ta
180
.95
tun
gste
n
74
W
183
.84
rhe
niu
m
75
Re
186
.21
osm
ium
76
Os
190
.23
irid
ium
77
Ir
192
.22
pla
tin
um
78
Pt
195
.08
gold
79
Au
196
.97
mer
cury
80
Hg
200
.59
thal
lium
81
Tl
204
.38
lead
82
Pb
207
.2
bis
mu
th
83
Bi
208
.98
po
lon
ium
84
Po
[2
09]
asta
tin
e
85
At
[21
0]
rad
on
86
Rn
[2
22]
fr
anci
um
87
Fr
[22
3]
rad
ium
88
Ra
[22
6]
law
ren
ciu
m
103
Lr
[26
2]
ruth
erfo
rdiu
m
104
Rf
[26
1]
du
bn
ium
105
Db
[2
62]
seab
org
ium
106
Sg
[2
66]
bo
hri
um
107
Bh
[2
64]
has
siu
m
108
Hs
[26
9]
mei
tne
riu
m
109
Mt
[26
8]
darm
stad
tium
110
Ds
[27
1]
roen
tgen
ium
111
Rg
[2
72]
cop
ern
iciu
m
112
Cn
[2
85]
la
nth
anu
m
57
La
138
.91
ceri
um
58
Ce
140
.11
pras
eody
miu
m
59
Pr
140
.91
neo
dym
ium
60
Nd
144
.24
pro
me
thiu
m
61
Pm
[1
45]
sam
ariu
m
62
Sm
150
.36
euro
piu
m
63
Eu
151
.96
gad
olin
ium
64
Gd
157
.25
terb
ium
65
Tb
158
.93
dysp
rosi
um
66
Dy
162
.50
ho
lmiu
m
67
Ho
164
.93
erb
ium
68
Er
167
.26
thu
lium
69
Tm
168
.93
ytte
rbiu
m
70
Yb
173
.04
ac
tin
ium
89
Ac
[2
27]
tho
riu
m
90
Th
232
.04
pro
tact
iniu
m
91
Pa
231
.04
ura
niu
m
92
U
238
.03
nep
tun
ium
93
Np
[2
37]
plu
ton
ium
94
Pu
[2
44]
amer
iciu
m
95
Am
[2
43]
curi
um
96
Cm
[2
47]
ber
keliu
m
97
Bk
[24
7]
calif
orn
ium
98
Cf
[25
1]
ein
ste
iniu
m
99
Es
[25
2]
ferm
ium
100
Fm
[2
57]
men
dele
vium
101
Md
[2
58]
no
bel
ium
102
No
[2
59]
N
ote
: th
e v
alu
es o
f m
ola
r m
ass in
this
perio
dic
table
are
giv
en t
o 5
s.f.
where
they a
re k
now
n t
o t
his
pre
cis
ion,
or
oth
erw
ise t
he m
ost accura
te v
alu
e a
vaila
ble
. E
lem
ents
with m
ola
r m
asses in s
quare
bra
ckets
have
no s
table
isoto
pes, and in
these insta
nces t
he a
ppro
xim
ate
mola
r m
ass g
iven is that
of th
e m
ost sta
ble
isoto
pe.
2.2 Periodic table: atomic numbers and molar masses
The values of molar mass in this periodic table are given to 5 s.f. where they are known to this precision, or otherwise the most accurate value available. Elements with molar masses in square brackets have no stable isotopes, and in these instances the approximate molar mass given is that of the most stable isotope.
Chemistry Data Booklet 2. Atomic Properties
7 1
18
1312
H
2.2
2
Key:
13
14
15
16
17
2372
He
520
Li
1.0
900
Be
1.6
F
irst I.E
. / kJ m
ol -
1
X
Ele
ctr
onegativity
801
B
2.0
1086
C
2.6
1402
N
3.0
1314
O
3.4
1681
F
4.0
2081
Ne
496
Na
0.9
738
Mg
1.3
3
4
5
6
7
8
9
10
11
12
578
Al
1.6
789
Si
1.9
1012
P
2.2
1000
S
2.6
1251
Cl
3.2
1521
Ar
419
K
0.8
590
Ca
1.0
631
Sc
1.4
658
Ti
1.5
650
V
1.6
653
Cr
1.7
717
Mn
1.6
759
Fe
1.8
758
Co
1.9
737
Ni
1.9
746
Cu
1.9
906
Zn
1.7
579
Ga
1.8
762
Ge
2.0
947
As
2.2
941
Se
2.6
1140
Br
3.0
1351
Kr
403
Rb
0.8
550
Sr
1.0
616
Y
1.2
660
Zr
1.3
664
Nb
1.6
685
Mo
2.2
702
Tc
2.1
711
Ru
2.2
720
Rh
2.3
805
Pd
2.2
731
Ag
1.9
868
Cd
1.7
558
In
1.8
709
Sn
2.0
834
Sb
2.1
869
Te
2.1
1008
I 2.7
1170
Xe
376
Cs
0.8
503
Ba
0.9
524
Lu
1.1
680
Hf
1.3
761
Ta
1.5
770
W
1.7
760
Re
1.9
840
Os
2.2
880
Ir
2.2
870
Pt
2.2
890
Au
2.4
1007
Hg
1.9
589
Tl
1.8
716
Pb
1.8
703
Bi
1.9
812
Po
2.0
920
At
2.2
1037
Rn
393
Fr
0.7
509
Ra
0.9
538
La
1.1
534
Ce
1.1
527
Pr
1.1
533
Nd
1.1
540
Pm
545
Sm
1.2
547
Eu
593
Gd
1.2
566
Tb
573
Dy
1.2
581
Ho
1.2
589
Er
1.2
597
Tm
1.3
603
Yb
499
Ac
1.1
587
Th
1.3
568
Pa
1.5
598
U
1.4
2.3 Pauling electronegativities and first ionization energies (Z = 1 – 92)
The electronegativity values given in this table are the Pauling values, given to 1 d.p.; the first ionization energy is given to the nearest integer value in kJ mol
-1 (based upon data sourced from WebElements). For successive
higher valence-level ionization energies (second, third, fourth etc.) see www.webelements.com .
Chemistry Data Booklet 3. Molecular Properties
8
3. Molecular Properties 3.1 Bond dissociation enthalpies in diatomic molecules
The following values are based upon spectroscopic determination of the bond dissociation energy D0 in the
most common isotopic variant of the relevant diatomic molecule, and are accurate to around 1 kJ mol–1
.
Homonuclear bond ΔH298 / kJ mol–1 Heteronuclear bond ΔH298 / kJ mol–1
H–H
N≡N
O=O
F–F
Cl–Cl
Br–Br
I–I
436
945
498
159
242
194
152
H–F
H–Cl
H–Br
H–I
C≡O
570
431
366
298
1076
3.2 Bond dissociation enthalpies in polyatomic molecules
The following values represent the typical amount of energy needed to break one bond of the indicated type in
a stable, neutral molecule. Values for single-bonds are based upon experimental measurements of homolytic
cleavage of the bond in a range of different molecules. Actual values are affected by the molecular
environment, and may show substantial variation ( 30 kJ mol–1
, or more) from the values listed below, as
illustrated by the values from several selected compounds. Bond dissociation enthalpies for multiple-bonds are
derived from thermodynamic data and are very approximate.
Homonuclear bond ΔH298 / kJ mol–1 Heteronuclear bond ΔH298 / kJ mol–1
C–C
C=C
C≡C
CC (aromatic)
Si–Si
N–N
N=N
P–P
O–O
S–S
347
612
838
505
226
158
410
198
144
266
C–H
C–H (in CH4)
N–H
N–H (in NH3)
O–H
O–H (in H2O)
Si–H
P–H
S–H
C–O
C=O
C–N
C=N
C≡N
C–F
C–Cl
C–Br
C–I
Si–O
413
435
391
450
464
497
318
321
364
358
746
286
615
887
476
352
296
234
466
Chemistry Data Booklet 3. Molecular Properties
9
3.3 Common abbreviations
Ac acetyl CH3CO
acac acetylacetonate (ion) [CH3COCHCOCH3]
Ar any aryl group (if not, argon!) e.g. meta-CH3.C6H4.
Boc / BOC t-butoxycarbonyl (CH3)3COCO
bipy / bpy 2,2'-dipyridyl (C5H4N)2
Bn / Bzl benzyl C6H5CH2
Bz benzoyl C6H5CO
Cp cyclopentadienyl (ion) C5H5
DME glyme; 1,2-dimethoxyethane CH3OCH2CH2OCH3
DMF N,N-dimethylformamide HCON(CH3)2
DMSO dimethyl sulphoxide (CH3)2SO
EDTA ethylenediaminetetraacetic acid (HOOCCH2)2NCH2CH2N(CH2COOH)2
en ethylene diamine H2NCH2CH2NH2
IPA i-propyl alcohol CH3CH(OH)CH3
LDA lithium diisopropylamide LiN(CH(CH3)2)2
mesyl methanesulphonyl CH3SO2
NBS N-bromosuccinimide C4H2O2NBr
ox oxalate (ion) C2O42
phen 1,10-phenanthroline (C5H3NCH)2
Ph phenyl C6H5
py pyridine C5H5N
R any alkyl group e.g. CH3 , C2H5
TFA trifluoroacetic acid CF3COOH
THF tetrahydrofuran C4H8O
TMS trimethylsilyl (CH3)3Si
or tetramethylsilane if NMR Si(CH3)4
Ts / tosyl para-toluenesulfonyl para-CH3.C6H4.SO2
Chemistry Data Booklet 4. Equations
10
4. Equations of Physical & Inorganic Chemistry
4.1 Classical mechanics
𝑣 =𝑑𝑥
𝑑𝑡 𝑎 =
𝑑𝑣
𝑑𝑡=
𝑑2𝑥
𝑑𝑡2 𝐹 = 𝑚𝑎
𝑝 = 𝑚𝑣 𝐸 =1
2 𝑚𝑣2 =
𝑝2
2𝑚 𝑊 = 𝐹𝑥 = 𝑃∆𝑉
A
FP 𝐸 =
1
2 𝐼𝜔2 =
𝐽2
2𝐼 𝜇 =
𝑚1𝑚2
𝑚1 + 𝑚2
4.2 Properties of matter
V
m
V
nc 𝑞 = 𝐶∆𝑇
4.3 Electromagnetic radiation / photons
𝑐 = 𝜈𝜆
1~ ; ( is in cm).
~~ch
hch
4.4 Rotational motion / energy levels
𝜀 = 𝐵𝐽( 𝐽 + 1) 𝐵 = ℎ2
8𝜋2𝐼 𝐼 = 𝜇𝑟2
4.5 Vibrational motion / energy levels
𝜀 = (𝜐 +1
2)ℎ𝜈 𝑉 =
1
2 𝑘𝑥2 𝜈 =
1
2𝜋√
𝑘
𝜇
𝐺𝜐 = (𝜐 +1
2) 𝜔𝑒 − (𝜐 +
1
2)
2
𝜔𝑒𝑥𝑒
k
ce ~2
1
4.6 Electrostatic interactions / intermolecular potential energy functions
𝐹 = 𝑞𝐸 𝐹 =𝑞1𝑞2
4𝜋𝜀0𝑟2 𝑉 =
𝑞1𝑞2
4𝜋𝜀0𝑟
𝑉 =−2𝜇1
2𝜇22
3(4𝜋𝜀0)2𝑘𝑇𝑟6 𝑉 = 4𝜀 [(
𝑟0
𝑟)
12
− ( 𝑟0
𝑟)
6
] 𝐸 =−𝑁𝐴|𝑧+||𝑧−|𝑒2𝑀
4𝜋𝜀0𝑟0(1 −
1
𝑛)
4.7 Gas properties / gas laws
𝑃𝑉 =1
3 𝑁𝑚𝑐2̅̅ ̅ NkTnRTPV nRTnbV
V
anP
2
2
Chemistry Data Booklet 4. Equations
11
4.8 Boltzmann distribution / spectroscopy / spectrometry
𝐴 = −log10 (𝐼
𝐼0) = 𝜀𝑐𝑙 kT
g
g
N
N elower
upper
lower
upper [𝛼]𝜆
𝑇 =𝛼
𝑙 𝜌 (or
𝛼
𝑙 𝑐)
4.9 Chemical thermodynamics
𝐻 = 𝑈 + 𝑃𝑉 𝐶𝑣 =𝑑𝑈
𝑑𝑇 𝐶𝑝 =
𝑑𝐻
𝑑𝑇
Δ𝑆 =𝑞𝑟𝑒𝑣
𝑇 𝑆 = 𝑘𝑙𝑛𝑊 Δ𝐺 = Δ𝐻 − 𝑇Δ𝑆
Δ𝐺° = −𝑅𝑇 ln 𝐾 𝑑 ln𝐾
𝑑𝑇=
Δ𝐻
𝑅𝑇2
4.10 Reaction kinetics
RT
Ea
Ak
e tk e][][ 0AA tk2
][
1
][
1
0
AA
4.11 Acidity / basicity
3-
3
10dm mol
]O[Hlog pH
][HA
][A]O[H 3
a
K p𝐾𝑎 = − log 𝐾𝑎
][HA
][Alogp pH 10aK
][B
][OH][HB b
K
4.12 Crystallography
1
𝑑ℎ𝑘𝑙2 =
ℎ2
𝑎2+
𝑘2
𝑏2+
𝑙2
𝑐2 (for orthorhombic systems)
4.13 Quantum mechanics
EH ˆ ),,(2
ˆ 22
zyxVm
H
2
~
n
RchE H
n
2
2
2
1
11~
nnRH
𝜓𝑛𝑙𝑚 = 𝑁. 𝑅𝑛𝑙(𝑟). 𝑌𝑙𝑚(𝜃, 𝜙)
4.14 Wave-particle duality / uncertainty relationships
𝜆 =ℎ
𝑝
2
xp
2~
E
Chemistry Data Booklet 5. Spectroscopic Data
12
wavelength / m
5. Spectroscopic Data 5.1 Electromagnetic (EM) spectrum The following figure indicates the nomenclature system applying to specific wavelength ranges of the electromagnetic spectrum (boundaries are approximate).
10–16 10–14 10–12 10–10 10–8 10–6 10–4 10–2 100 102 104 106 108
γ rays X rays UV IR microwaves radiowaves
V I B G Y O R
400 700 wavelength / nm
5.2 Infrared (IR) spectroscopy The following chart indicates some of the characteristic higher-wavenumber absorptions associated with the presence of commonly-occurring functional groups in organic compounds. The ranges of peaks which are extensively broadened by hydrogen-bonding are shown as hatched (rather than shaded) bars. The table on the following page provides a more comprehensive and detailed listing of the characteristic wavenumber absorptions associated with the presence of specific functional groups in organic compounds.
3800 3400 3000 2600 2200 1800 1400
wavenumber / cm–1
OH
NH
CH
CC
CN
C=C
C=N
C=O
alcohol,
carboxylic acid
amine, amide, imine
alkyne
nitrile
alkene
imine
various CH - see table below
various CO - see table below
3800 3400 3000 2600 2200 1800 1400
Chemistry Data Booklet 5. Spectroscopic Data
13
1. OH stretching
3650–3600 s sharp O–H stretch (free) alcohol, phenol
3600–3200 s broad O–H stretch (H–bonded) alcohol, phenol
3300–2500 m broad O–H stretch (H–bonded) carboxylic acid
2. NH stretching
3500–3400 (2 bands) m N–H stretch (asym/sym) primary amide
3500–3300 (2 bands) m N–H stretch (asym/sym) primary amine
3460–3400 m N–H stretch secondary amide
3450–3300 m N–H stretch secondary amine
3. CH stretching
3330–3270 s sharp C–H stretch alkyne (terminal)
3100–3000 s C–H stretch aromatics
3100–3000 m =C–H stretch alkene
3000–2850 m C–H stretch (multiple band) alkane
2860–2695 m –CHO: C–H stretch aldehyde
4. CC / CN stretch
2260–2210 v –CN stretch nitrile
2260–2100 w –CC– stretch alkyne
5. X=Y=Z stretch
~ 1950 m C=C=C stretch allene
2160–2120 s R–N=N+=N stretch azide
6. C=O (carbonyl) stretch (lowered by 10-40 cm–1
if aryl or ,-unsaturated)
1850–1800, 1790-1740 s C=O stretch anhydride
1815–1790 s C=O stretch acid chloride
1800–1750 s C=O stretch ester (of phenols/enols)
1780–1760 s C=O stretch ester (5-ring lactones)
1750–1735 (1)
s C=O stretch ester
1740–1720 s C=O stretch aldehyde
1725–1705 (1)
s C=O stretch ketone
1725–1700 s C=O stretch carboxylic acid
~ 1690 (2)
(~1600) s C=O str. (coupled with CN) primary amide
1700–1670 (2)
(~1530) s C=O str. (coupled with CN) secondary amide
~ 1670 (1)
s C=O stretch lactam
7. C=C stretch
1680–1600 (3)
m –C=C– stretch alkene
1600, 1580 m / w C–C stretch (in–ring) aromatics
~ 1500 m C–C stretch (in–ring) aromatics
8. C=N , N=O, N–H modes
1690–1640 v C=N stretch imine , oxime
1650–1580 m N–H bend primary amine
1550–1475, 1360–1290 s / m N–O stretches (asym/sym) nitro- compound
9. Fingerprint region (various C–X stretches, bending modes and deformation modes)
< 1500 v Various (for more advanced analysis only)
Intensity: s = strong, m = medium, w = weak, v = variable 1. raised in strained ring systems (by ~30 cm
–1 for 5-ring molecules; by ~60 cm
–1 for 4-ring molecules)
2. lowered by ~40 cm–1
in solid-phase 3. lowered by ~30 cm
–1 if conjugated
Chemistry Data Booklet 5. Spectroscopic Data
14
5.3 1H nmr spectroscopy
The following chart indicates the range of -values (relative to TMS = 0 ppm) over which particular types of proton typically give a peak in the
1H nmr spectrum. This figure relates only to common compounds of C, H, N
and O, and some halogenated compounds.
aldehyde (RCHO, ArCHO)
heterocyclic aromatic aryl
conjugated alkene isolated
CHX
halogen-
CH2X
CHO
oxygen-
CH2O, CH3O
nitrogen- CHnN...
carbonyl CHn(CO)
alkyne CCH
alkyl arene CHnAr
alkyl CHnR
ROH , RCOOH RNH2 , RNHR' RCONH2 , RCONHR'
Key:
R = alkyl
X = halogen
11 10 9 8 7 6 5 4 3 2 1 0
11 10 9 8 7 6 5 4 3 2 1 0
/ ppm
Exchangeable with D2O; often (very) broad; very variable
Chemistry Data Booklet 5. Spectroscopic Data
15
5.4 13C nmr spectroscopy
The following chart indicates the range of -values (relative to TMS = 0 ppm) over which particular types of carbon atoms typically give a peak in the
13C nmr spectrum. This figure relates only to common compounds of
C, H, N and O (it excludes, for example, halogenated carbon atoms).
aldehyde, ketone
acid, ester
anhydride COO
amide CON<
imine >C=N
aromatic (e.g. phenyl)
alkene >C=C<
nitrile CN
alkyne CC
alcohol, ether
ester CHnO
amine,
amide CHnN<
alkyl
chain CHnR
C=O
220 200 180 160 140 120 100 80 60 40 20 0
220 200 180 160 140 120 100 80 60 40 20 0
/ ppm
Chemistry Data Booklet 6. Symmetry
16
6. Symmetry
6.1 Determining the molecular point group
Yes
Yes
linear?
two or more unique C3
axes ?
No
No
No No
No
No
No
No
No
proper rotation axis (Cn ) ?
reflection plane ?
inversion centre ?
Yes
(identify the value of n )
Yes
Yes
Yes
Yes
Yes
n C2 axes perpendicular to
the Cn axis ?
n vertical reflection planes
v ?
2n-fold improper rotation axis ?
Cnh
Cnv
C s
Cn
S2n
C i
C1
Yes inversion centre ?
No
Dh
Cv
Yes
No
No
Yes
Yes
horizontal reflection plane
h ?
n dihedral reflection planes
d ?
Dnh
Dnd
Dn
horizontal reflection plane
h ?
two or more unique C5
axes ?
Yes
No No
No No
No No
inversion centre ?
Yes
Yes Yes
Yes Yes one or more
reflection planes ?
I h
I
O h
Td T
Th
O
inversion centre ?
inversion centre ?
two or more unique C4
axes ?
Chemistry Data Booklet 6. Symmetry
17
6.2 Illustrative examples of point groups
n = 2 3 4 5 6 Cn
Dn Cnv
(pyramid) (cone) Cnh Dnh (plane or bipyramid)
Dnd S2n
Chemistry Data Booklet 6. Symmetry
18
Other point groups Cs Ci Oh octahedron Ih dodecahedron (view down one C3 axis) (view down one C5 axis)
Td tetrahedron Ih icosahedron (view down one C3 axis) (view down one C5 axis)
Oh cube R3 sphere (view down one C3 axis)
A
A
B
B
C
C
Chemistry Data Booklet 7. Mathematical Relations
19
7. Mathematical Relations 7.1 Standard derivatives and integrals
1 nn mnxmxdx
d
(if n 0 )
Cn
mxdxmx
nn
1
1
(if n –1 )
Cxdx
x )ln(
1
)()( )(' xfxf exfedx
d
1a x a xe dx e Ca
xx
dx
d 1)ln( Cxxxdxx )ln()ln(
xxdx
dcossin Cxdxx cossin
xxdx
dsincos Cxdxx sincos
dx
du
du
dfuf
dx
d)( vduuvudv
dx
dvu
dx
duvuv
dx
d )()()(' afbfdxxf
b
a
dx
dvu
dx
duv
vv
u
dx
d2
1
7.2 Definite integrals
∫ 𝑥𝑛𝑒−𝑎𝑥𝑑𝑥∞
0
=𝑛!
𝑎𝑛+1 ∫ sin2 (
𝑛𝜋𝑥
𝐿) 𝑑𝑥
𝐿
0
=𝐿
2
7.3 Trigonometry and geometry
1sincos 22 cossin22sin
C
c
B
b
A
a
sinsinsin 2222 sin211cos2sincos2cos
Abccba cos2222 2222 )()()( zyxd
7.4 Other formulae and equations
Quadratic solution, a
acbbx
2
42 e𝑥 = 1 +
𝑥
1!+
𝑥2
2!+
𝑥3
3!+ ⋯ , −∞ < 𝑥 < ∞
Chemistry Data Booklet 8. Probability and Statistics
20
8. Probability and Statistics 8.1 Useful equations
!!
!
rrn
nCr
n
!
!
rn
nPr
n
Sample variance:
i
i xxn
s 22 )(1
1 Sample mean limits
n
stx
8.2 Critical t-values
Degrees of Freedom
Probability
0.1 0.05 0.01 0.001
1 6.31 12.71 63.66 636.62
2 2.92 4.30 9.93 31.60
3 2.35 3.18 5.84 12.92
4 2.13 2.78 4.60 8.61
5 2.02 2.57 4.03 6.87
6 1.94 2.45 3.71 5.96
7 1.90 2.37 3.50 5.41
8 1.86 2.31 3.36 5.04
9 1.83 2.26 3.25 4.78
10 1.81 2.23 3.17 4.58
20 1.73 2.09 2.85 3.85
(normal dist) 1.65 1.96 2.58 3.29
8.3 Error propagation formulae
Mathematical Manipulation Propagation of Errors
Z = c X (Z) = c (X)
Z = X Y (Z)2 = (X)
2 + (Y)
2
Z = X Y or Z = X/Y 222
)()()(
Y
Y
X
X
Z
Z
Z = X n
X
Xn
Z
Z )()(
Z = ln X X
XZ
)()(
Z = log10 X X
XZ
303.2
)()(
Z = exp (X) (Z) = Z (X)
Z = 10 X
(Z) = 2.303 Z (X)
Chemistry Data Booklet 9. Other Sources
21
9. Other Sources of Information As previously noted, this data booklet is not intended to be comprehensive and there are a number of reliable sources of information available in the library and online which you are recommended to refer to for additional data.
9.1 Online Sources of Information Recommended sources include:
Kaye & Laby : Tables of Physical & Chemical Constants An extensive set of physical and chemical data, ranging from atomic properties to molecular structural data and thermodynamic data. http://www.kayelaby.npl.co.uk/ WebElements Extensive data about the chemical and physical properties of the elements, and some data about their compounds http://www.webelements.com/ NIST Chemistry WebBook An extensive collection of thermodynamic data and spectroscopic data (searchable by chemical name and formula) http://webbook.nist.gov/chemistry/ NIST – Periodic Table A periodic table which includes ground-state electron configuration and first ionization energy data, in addition to atomic numbers and molar masses. http://www.nist.gov/pml/data/upload/periodic-table.pdf Tables for Group Theory All the key tables for group theory: including character tables, and tables for direct products, descent in symmetry and subgroups. http://www.oup.com/uk/orc/bin/9780199206063/01student/group/ Wikipedia A lot of useful scientific information is available on this “openly-editable encyclopedia”, but you should check that any data you intend to use is properly referenced to an original scientific source. http://en.wikipedia.org/
See also the various other links provided from the School's Chemistry Learning Resources on the Web page: http://courses.sbcs.qmul.ac.uk/info/home.htm
9.2 Reference Texts The recommended source for most quantitative chemical and physical information is:
CRC Handbook of Chemistry and Physics (CRC Press – currently available as the 92
nd edition, published 2011, ed. W.M. Haynes)
- available in Science reference section of QMUL Main Library.
For more detailed information on applications of spectroscopy for the identification of molecular structure you are advised to refer to:
Spectroscopic Methods in Organic Chemistry D.H. Williams and I. Fleming (6th edition, McGraw Hill, 2008). QD95 WIL