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: n.lebrasseur@qmul.ac.uk

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