Section 2. General Information, Conversion Tables, and Mathematics

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SECTION2

GENERAL INFORMATION,

CONVERSION TABLES,AND

MATHEMATICS

2.1GENERAL INFORMATION AND CONVERSION TABLES 2.3

Table2.1Fundamental Physical Constants 2.3 Table2.2Physical and Chemical Symbols and De?nitions 2.6 Table2.3Mathematical Symbols and Abbreviations 2.23 Table2.4SI Pre?xes 2.24 Table2.5Greek Alphabet 2.25 Table2.6Abbreviations and Standard Letter Symbols 2.26 Table2.7Conversion Factors 2.35 Table2.8Temperature Conversion Table 2.54 2.1.1Conversion of Thermometer Scales 2.66 2.1.2Density and Speci?c Gravity 2.66 2.1.3Barometry and Barometric Corrections 2.70

Table2.9Barometer Temperature Correction—Metric Units 2.72 Table2.10Barometric Latitude-Gravity Table—Metric Units 2.75 Table2.11Barometric Correction for Gravity—Metric Units 2.77 Table2.12Reduction of the Barometer to Sea Level—Metric Units 2.78

Table2.13Viscosity Conversion Table 2.82 Table2.14Conversion of Weighings in Air to Weighings in Vacuo 2.83 Table2.15Hydrometer Conversion Table 2.85 Table2.16Pressure Conversion Chart 2.87 Table2.17Corrections to Be Added to Molar Values to Convert to Molal 2.88 Table2.18Molar Equivalent of One Liter of Gas at Various Temperatures and

Pressures 2.88 Table2.19Factors for Reducing Gas Volumes to Normal(Standard)

Temperature and Pressure(760mmHg) 2.91 Table2.20Values of Absorbance for Percent Absorption 2.96 Table2.21Transmittance-Absorbance Conversion Table 2.98 Table2.22Wavenumber/Wavelength Conversion Table 2.101 2.2MATHEMATICAL TABLES 2.102 2.2.1Logarithms 2.102

Table2.23Derivatives and Differentiation 2.104 Table2.24Integrals 2.105 2.2.2Surface Areas and Volumes 2.109 2.2.3Trigonometric Functions of an Angle? 2.113 2.2.4Expansion in Series 2.115

Table2.25Some Constants 2.117 2.3STATISTICS IN CHEMICAL ANALYSIS 2.117 2.3.1Introduction 2.117 2.3.2Errors in Quantitative Analysis 2.118 2.3.3Representation of Sets of Data 2.118 2.3.4The Normal Distribution of Measurements 2.119

Figure2.10The Normal Distribution Curve 2.119 Table2.26a Ordinates(Y)of the Normal Distribution Curve at Values of z 2.121 Table2.26b Areas Under the Normal Distribution Curve from0to z 2.122 2.3.5Standard Deviation as a Measure of Dispersion 2.121

2.1

2.2SECTION2

2.3.6Student’s Distribution or t Test 2.123

Table2.27Percentile Values for Student t Distribution 2.124 2.3.7Hypotheses About Means 2.126 2.3.8The Chi-square(?2)Distribution 2.128

Table2.28Percentile Values for the Chi-square(?2)Distribution 2.129 2.3.9The F Statistic 2.130

Table2.29F Distribution 2.131 2.3.10Curve Fitting 2.133 2.3.11Control Charts 2.137

Bibliography 2.138

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.3 2.1GENERAL INFORMATION AND CONVERSION

TABLES

TABLE2.1Fundamental Physical Constants

E.R.Cohen and B.N.Taylor,CODATA Bull.63:1–49(1986);J.Res.Nat.Bur.Standards,92:85(1987).

A.De?ned values

Physical quantity Name of

SI unit

Symbol for

SI unit De?nition

1.Base SI units

Amount of substance mole mol Amount of substance which contains as many

speci?ed entities as there are atoms of car-

bon-12in exactly0.012kg of that nuclide.

The elementary entities must be speci?ed

and may be atoms,molecules,ions,elec-

trons,other particles,or speci?ed groups

of such particles.

Electric current ampere A Magnitude of the current that,when?owing

through each of two straight parallel con-

ductors of in?nite length,of negligible

cross-section,separated by1meter in a

vacuum,results in a force between the two

wires of2?10

?7newton per meter of

length.

Length meter m Distance light travels in a vacuum during

1/299792458of a second.

Luminous intensity candela cd Luminous intensity,in a given direction,of a

source that emits monochromatic radiation

of frequency540?1012hertz and that has

a radiant intensity in that direction of

1/683watt per steradian.

Mass kilogram kg Mass of a cylinder of platinum-iridium alloy

kept at Paris.

Temperature kelvin K De?ned as the fraction1/273.16of the ther-

modynamic temperature of the triple point

of water.

Time second s Duration of9192631770periods of the ra-

diation corresponding to the transition be-

tween the two hyper?ne levels of the

ground state of the cesium-133atom.

2.Supplementary SI units

Plane angle radian rad The plane angle between two radii of a circle

which cut off on the circumference an arc

equal in length to the radius.

Solid angle steradian sr The solid angle which,having its vertex in

the center of a sphere,cuts off an area of

the surface of the sphere equal to that of a

square with sides of length equal to the ra-

dius of the sphere.

2.4SECTION 2

TABLE 2.1

Fundamental Physical Constants (Continued )

B.Derived SI units

Physical quantity Name of SI unit Symbol for SI unit Expression in terms of SI base units

Absorbed dose (of radiation)gray

Gy J ·kg ?1Activity (radioactive)becquerel Bq s ?1?m 2·s ?2

Capacitance (electric)farad FC ·V ?1?m ?2·kg ?1·s 4·A 2Charge (electric)

coulomb C A ·s Conductance (electric)siemens S ??1?m ?2·kg ?1·s 3·A 2Dose equivalent (radiation)sievert Sv J ·kg ?1?m 2·s ?2Energy,work,heat joule J N ·m ?m 2·kg ·s ?2Force newton N m ·kg ·s ?2Frequency hertz Hz s ?1Illuminance lux lx cd ·sr ·m ?2Inductance henry H V ·A ?1·s ?m 2·kg ·s ?2·A ?2Luminous ?ux lumen Lm cd ·sr Magnetic ?ux

weber Wb V ·s ?m 2·kg ·s ?2·A ?1Magnetic ?ux density tesla T V ·s ·m ?2?kg ·s ?2·A ?1Potential,electric

(electromotive force)volt V J ·C ?1?m 2·kg ·s ?3·A ?1Power,radiant ?ux watt W J ·s ?1?m 2·kg ·s ?3

Pressure,stress pascal Pa N ·m ?2?m ?1·kg ·s ?2

Resistance,electric ohm ?V ·A ?1?m 2·kg ·s ?3·A ?2Temperature,Celsius

degree

Celsius

?C ?(K ?273.15)

C.Recommended consistent values of constants

Quantity

Symbol

Value*

Anomalous electron moment correction ?e ?10.001159615(15)

Atomic mass constant m u ?1u 1.6605402(10)?10?27kg Avogadro constant

L ,N A 6.0221367(36)?1023mol ?1Bohr magneton (?eh /4?m e )?B 9.2740154(31)?10?24J ·T ?1Bohr radius

a 0 5.29177249(24)?10?11m Boltzmann constant

k 1.380658(12)?10?23J ·K ?1Charge-to-mass ratio for electron e/m e 1.758805(5)?10?11C ·kg ?1Compton wavelength of electron ?c 2.426309(4)?10?12m Compton wavelength of neutron ?c ,n 1.319591(2)?10?15m Compton wavelength of proton

?c ,p

1.321410(2)?10?15m Diamagnetic shielding factor,spherical water molecule

1??(H 2O) 1.00002564(7)

Electron magnetic moment ?e 9.2847701(31)?10?24J ·T ?1Electron radius (classical)r e 2.817938(7)?10?15m Electron rest mass m e 9.1093897(54)?10?31kg Elementary charge e

1.60217733(49)?10?19C Energy equivalents:1electron mass 0.5110034(14)MeV 1electronvolt 1eV/k 1.160450(36)?104K 1eV/hc 8.065479(21)?103cm ?11eV/h

2.417970(6)?1014Hz 1neutron mass 939.5731(27)MeV 1proton mass

938.2796(27)MeV

*The digits in parentheses following a numerical value represent the standard deviation of that value in terms of the ?nal listed digits.

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.5

TABLE 2.1Fundamental Physical Constants (Continued )

C.Recommended consistent values of constants (continued )Quantity

Symbol

Value*

931.5016(26)MeV

Faraday constant

F 96485.309(29)C ·mol ?1Fine structure constant

?0.00729735308(33)??1137.0359895(61)

First radiation constant c 1 3.7417749(22)?10?16W ·m 2Gas constant

R 8.314510(70)J ·K ?1·mol ?1g factor (Lande)for free electron g e 2.002319304386(20)

Gravitational constant G 6.67259(85)?10?11m 3·kg ?1·s ?2Hartree energy

E h 4.3597482(26)?10?18J Josephson frequency-voltage ratio 4.835939(13)?1014Hz ·V ?1Magnetic ?ux quantum

2.067851(5)?10?15Wb Magnetic moment of protons in water ?p /?B 1.520993129(17)?10?3Molar volume,ideal gas,p ?1bar,??0?C

22.71108(19)L ·mol ?1

Neutron rest mass m n 1.6749286(10)?10?27kg Nuclear magneton

?N 5.0507866(17)?10?27J ·T ?1Permeability of vacuum ?04??10?7H ·m ?1exactly Permittivity of vacuum

8.854187816?10?12F ·m ?1??h /2? 1.05457266(63)?10?34J ·s Planck constant

h 6.6260.755(40)?10?34J ·s Proton magnetic moment ?

p 1.41060761(47)?10?26J ·T ?1Proton magnetogyric ratio

?p 2.67522128(81)?108s ?1·T ?1Proton resonance frequency per ?eld in H 2O ??/2?p 42.576375(13)MHz ·T ?1Proton rest mass

m p 1.6726231(10)?10?27kg Quantum-charge ratio

h /e 4.135701(11)?10?15J ·Hz ?1·C ?1

Quantum of circulation

h /m e 7.27389(1)?10?4J ·s ·kg ?1Ratio,electron-to-proton magnetic moments ?e /?p 6.58210688(7)?102

Rydberg constant

R ? 1.0973731534(13)?107m ?1Second radiation constant c 2 1.438769(12)?10?2m ·K Speed of light in vacuum

c 029*******m ·s ?1exactly Standar

d acceleration of fre

e fall g n 9.80665m ·s ?2exactly Standard atmosphere

atm 101325Pa exactly

Stefan-Boltzmann constant ? 5.67051(19)?10?8W ·m ?2·K ?4Thomson cross section

?e 6.652448(33)?10?29m 2Wien displacement constant b 0.28978(4)cm ·K

Zeeman splitting constant

?B /hc

4.66858(4)?10?5cm ?1·G ?1

D.Units in use together with SI units

Physical quantity Name of unit Symbol for unit Value in SI units Area barn

10?28m

Energy electronvolt

eV (e ?V)?1.60218?10?19J megaelectronvolt 1MeV Length a ?ngstro ¨m 2A ?10?10m;0.1nm Mass

tonne

103kg;Mg

*The digits in parentheses following a numerical value represent the standard deviation of that value in terms of the ?nal listed digits.

The term million electronvolts is frequently used in place of megaelectronvolts.2

The a ?ngstro ¨m and bar are approved for temporary use with SI units;however,they should not be introduced if not used at present.

2.6SECTION 2

TABLE 2.1

Fundamental Physical Constants (Continued )

D.Units in use together with SI units (continued )

Physical quantity Name of unit Symbol for unit Value in SI units uni?ed atomic mass unit u[?m a (12C)/12]?1.66054?10?27kg dalton 3Da Plane angle degree ?(?/180)rad minute ?(?/10800)rad second ?(?/648000)rad Pressure bar 2bar 105Pa ?105N m ?2Time minute min 60s hour h 3600s day

d 86400s

Volume

liter (litre)L,l dm 3?10?3m 3milliliter

mL,ml

cm 3?10?6m 3

The a ?ngstro ¨m and bar are approved for temporary use with SI units;however,they should not be introduced if not used at present.

The name dalton and symbol Da have not been approved although they are often used for large molecules.

TABLE 2.2Physical and Chemical Symbols and De?nitions

Symbols separated by commas represent equivalent recommendations.Symbols for physical and chemical quan-tities should be printed in italic type.Subscripts and superscripts which are themselves symbols for physical

quantities should be italicized;all others should be in Roman type.Vectors and matrices should be printed in boldface italic type,e.g.,B,b.Symbols for units should be printed in Roman type and should remain unaltered in the plural,and should not be followed by a full stop except at the end of a sentence.References:International Union of Pure and Applied Chemistry,Quantities,Units and Symbols in Physical Chemistry,Blackwell,Oxford,1988;“Manual of Symbols and Terminology for Physicochemical Quantities and Units,”Pure Applied Chem.31:577–638(1972),37:499–516(1974),46:71–90(1976),51:1–41,1213–1218(1979);53:753–771(1981),54:1239–1250(1982),55:931–941(1983);IUPAP-SUN,“Symbols,Units and Nomenclature in Physics,”Phys-ica 93A:1–60(1978).

A.Atoms and molecules

Name

Symbol SI unit De?nition Activity (radioactivity)A Bq A ??dN B /dt Atomic mass constant m u kg m u ?m a (12C)/12Bohr magneton ?B J ·T ?1?B ?eh /4?m e Bohr radius

a 0m a 0?2?0h 2/m e e 2Decay (rate)constant ?s ?1A ??N B

Dissociation energy D ,E d J From ground state

D 0J From the potential minimum

D e J Electric dipole moment of a molecule p ,?C ·m

E p ??p ?E Electric ?eld gradient

V ·m ?2q ?

????2V /????Electric polarizability of a molecule ?C ·m 2·V ?1p (induced)??E

Electron af?nity E ea J Electron rest mass

m e kg Elementary charge,proton charge e C

Fine structure constant ???e 2/2?0hc

g factor

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.7

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

A.Atoms and molecules (continued )

Name

Symbol SI unit De?nition Hartree energy E h J E h ?h 2/4?2m e a 20

Ionization energy

E i J Larmor circular frequency ?L s ?1?L ?(e /2m )B Larmor frequency

?L Hz ?L ??L /2?Longitudinal relaxation time T 1s

Magnetogyric ratio

?C ·kg ?1???/L

Magnetic dipole moment of a molecule m,?J ·T ?1E p ??m ?B Magnetizability of a molecule ?J ·T ?2m ??B

Mass of atom,atomic mass m ,m a kg Neutron number N N ?A ?Z Nuclear magneton

?N J ·T ?1?N ?(m e /m p )?B Nucleon number,mass number A Planck constant h J ·s Planck constant/2?

?J ·s ??h /2?Principal quantum number (H atom)n E ??hcR /n 2

Proton number,atomic number Z Quadrupole interaction

??eQq ????Quadrupole moment of a molecule Q ;?C ·m 2E p ?0.5Q :V ???V ?1?3Quadrupole moment eQ C ·m 2eQ ?2??zz ?Rydberg constant

?m ?1R ?E /2hc

Transverse relaxation time

T 2

B.Chemical reactions

Name

Symbol SI unit De?nition Amount (of substance)n mol n B ?N B /L Atomic mass

m ,m a kg Atomic mass constant a m u kg m u ?m a (12C)/12Avogadro constant

L ,N A mol ?1

Concentration,amount (concentration)c mol ·m ?3c B ?n B /V

Degree of dissociation ?Density (mass)

?,?kg ·m ?3??m B /V Extent of reaction,advancement ?mol ????n B /?B B

Mass (molecular or formula unit)m ,m f kg Mass fraction

w w B ?m B /?m i Molality (of a solute)m mol ·kg ?1

m B ?n B /m A Molar mass M kg ·mol ?1M B ?m /n B Molar volume

V m m 3·mol ?1V m,B ?V /n B Molecular weight (relative molar mass)M r M r,B ?m B /m u Mole fraction b ,number fraction x ,y x B ?n B /?n i Number concentration

C ,n m ?3C B ?N B /V Number of entities (e.g.,molecules,atoms,ions,formula units)N Pressure (partial)p B Pa p B ?y B p Pressure (total)p ,P Pa

Solubility

mol ·m ?3

s B ?c B (saturated solution)

a In biochemistry this unit is called the dalton,with symbol Da.

For condensed phases x is used,and for gaseous mixtures y may be used.

2.8SECTION 2

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

B.Chemical reactions (continued )

Name

Symbol

SI unit

De?nition

Stoichiometric number ?Surface concentration ?mol ·m ?2

?B ?n B /A Volume fraction

?B ?V B /?V i

Symbols for particles and nuclear reactions:

Alpha particle

?Muon,positive ??Beta particle ??,??Neutron n,n 0Deuteron d,2H Photon ?Electron e,e ?Proton p,p ?Helion h Triton

t,3H

Muon,negative ??

The meaning of the symbolic expression indicating a nuclear reaction:

initial incoming particles outgoing particles

?nal

nuclide or quanta or quanta

nuclide

Examples:14N(?,p)17O,23Na(?,3n)20Na States of aggregation:

am amorphous solid cd

condensed phase (solid or liquid)aq aqueous solution cr crystalline

as,?aqueous solution at

??uid phase (gas or liquid)in?nite dilution

lc liquid crystal

g gas vit vitreous substance l liquid mon monomeric form s solid pol polymeric form

sln solution

ads

species adsorbed on a substance

C.Chromatography

Name

Symbol De?nition

Adjusted retention time t ?R t ??t ?t R R M Adjusted retention volume V ?R V ??V ?V R R M Average linear gas velocity ???L /t M

Band variance ?2Bed volume

V g Capacity,volume Q v Capacity,weight Q w Column length

L Column temperature ?Column volume

V col V col ??Dd 2/4

c Concentration at peak maximum C max Concentration of solute in mobile phase

C M Concentration of solute in sta-tionary phase

C S

Density of liquid phase

Diffusion coef?cient,liquid ?lm D f Diffusion coef?cient,mobile phase

D M

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.9TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

C.Chromatography (continued )

Name

Symbol De?nition Diffusion coef?cient,stationary

phase

D S Distribution ratio D c ?[A ?]S /[A ?]M

3amount of A per cm stationary phase 3amount of A per cm of mobile phase D g

?amount A per gram dry stationary phase 3amount A per cm of mobile phase D v

?3amount A,stationary phase per cm bed volume 3amount A per cm of mobile phase D S

?2amount of A per m of surface 3amount of A per cm of mobile phase Elution volume,exclusion chro-

matography

V e Flow rate,column

F c F c ?(?d 2/4)(?)(L /t )c tot M Gas/liquid volume ratio

?Inner column volume

V i Interstitial (outer)volume

V o Kovats retention indices

Matrix volume

V g Net retention volume

V N V ?jV ?N R Obstruction factor

?Packing uniformity factor

?Particle diameter

d p d p ?L /Nh Partition coef?cient

K K ?C S /C M ?(V R ?V M )/V S Partition ratio

k ?k ??C S V S /C M V M ?K (V S /V M )Peak asymmetry factor

AFRatio of peak half-widths at 10%peak height Peak resolution

Rs Rs ?(t R ,2?t R ,1)/0.5(W 2?W 1)Plate height

H H ?L /N eff Plate number

N eff 22N ?L /H ?16(t ?/W )?5.54(t ?/W )eff R b R 1/2Porosity,column

?Pressure,column inlet

p i Presure,column outlet

P o Pressure drop

?P Pressure-gradient correction

j 23[(p /p )?1]i o j ?32[(p /p )?1]i o Recovery factor

R n R n ?1?(rD c ?1)?n ;r ?V org /V aq Reduced column length

???L /d p Reduced plate height

h h ?H /d p Reduced velocity

v v ??d p /D M ?Kd p /t M D M Relative retention ratio

???(k ?/k ?)21Retardation factor c

R f R f ?d solute /d mobile phase Retention time

t R t R ?t M (1?k ?)?L /?Retention volume

V R V R ?t R F c Selectivity coef?cient d

k A,B k A,B ?[A ?]r [B ?]/[B ?]r [A ?]Separation factor

?A/B ?A/B ?(D c )A /(D c )B c

The distance d corresponds to the movement of solute and mobile phase from the starting (sample spotting)line.d Subscript “r ”represents an ion-exchange resin phase.Two immiscible liquid phases might be represented similarly using subscripts “1”and “2.”

TABLE2.2Physical and Chemical Symbols and De?nitions(Continued)

C.Chromatography(continued)

Name Symbol De?nition

Speci?c retention volume V?

V??273R/(p?Mw)

g L

Thickness(effective)of station-

ary phase

Total bed volume V

tot

Transit time of nonretained

solute

Vapor pressure p

Volume liquid phase in column V

Volume mobile phase in column V

Weight of liquid phase w

Zone width at baseline W

b?4

Zone width at peak height

1?2W1/2

D.Colloid and surface chemistry

Name Symbol SI unit De?nition

Adsorbed amount of B n s

mol

Area per molecule a,?m2a B?A/N?N

Area per molecule in a

?lled monolayer

m2a

m,B?A/N m,B Average molar masses:

Mass-average M

kg·mol?1M

m??n i M/?n i M i

Number-average M

kg·mol?1M

n??n i M i/?n i

Z-average M

kg·mol?1M

Z??n i M/?n i M

i i Contact angle?rad

Film tension?

N·m?1??f?2?f

Film thickness t,h,?m

Reciprocal thickness of the

double layer

?m?1??[2F2I c/?RT]1/2

Retarded van der Waals

constant

?,B J

Sedimentation coef?cient e s s s?v/a

Speci?c surface area a,s,a

m2/kg a?A/m

Surface coverage???N/N B

Surface excess of B n?

mol

Surface pressure?s,?N·m?1?s??0??

Surface tension,interfacial

tension

?,?J·m?2??(?G/?A s)T,p

Thickness of(surface or in-

terfacial)layer

?,?,t m

Total surface excess con-

centration

?mol·m?2????i

van der Waals constant?J

van der Waals-Hamaker

constant

e v is the velocity o

f sedimentation and a is the acceleration of free fall or centrifugation.

2.10SECTION2

TABLE2.2Physical and Chemical Symbols and De?nitions(Continued)

E.Electricity and magnetism

Name Symbol SI unit De?nition Admittance Y S Y?1/Z

Capacitance C F,C·V?1C?Q/U

Charge density?C·m?3??Q/V

Conductance G S G?1/R

Conductivity?S·m?1??1/?

Dielectric polarization(di-

pole moment per volume)

P C·m?2P?D??0E

Electrical resistance R?R?U/I??V/I

Electric current I A I?dQ/dt

Electric current density j,J A·m?2I?j dA

Electric dipole moment p,?C·m p?Qr

Electric displacement D C·m?2D??E

Electric?eld strength E V·m?1E?F/Q??grad V

Electric?ux?C??D d A

Electric potential V,?V,J·C?1V?dW/dQ

Electric potential difference U,?V V U?V

2?V1

Electric susceptibility?e?e??r?1

Electromotive force E V E?(F/Q)ds

Impedance Z?Z?R?iX

Loss angle f?rad??(?/2)??I??U

Magnetic dipole moment m,?A·m2E p??mB

Magnetic?eld strength H A·m?1B??H

Magnetic?ux?Wb??B d A

Magnetization(magnetic di-

pole moment per volume)

M A·m?1M?(B/?0)?H

Magnetic susceptibility?,????r?1

Magnetic vector potential A Wb·m?1B??A

Molar magnetic suscepti-

bility

?m n3/mol?m?V m?

Mutual inductance M,L

H E

1?L12(dI2/dt)

Permeability?H·m?1B??H

Permeability of vacuum?0H·m?1

Permittivity?F·m?1D??E

Permittivity of vacuum?0F·m?1?0??c

?1?2

Poynting vector S W·m?2S?E?H

Quantity of electricity,elec-

tric charge

Q C

Reactance X?X?(U/I)sin?

Relative permeability?r?r??/?0

Relative permittivity g?r?r??/?0

Resistivity??·m??E/j

Self-inductance L H E??L(dI/dt)

Susceptance B S Y?G?iB

f?I and?U are the phases of current and potential difference.

g This quantity was formerly called the dielectric constant.

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.11

2.12SECTION 2

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

F.Electrochemistry

Name

Symbol

SI unit De?nition

Charge density (surface)?C ·n ?2

??Q /A Charge number of an ion z z B ?Q B /e Charge number of electro-chemical cell reaction n ,(z )Conductivity (speci?c con-ductance)

S ·m ?1??j /E

Conductivity cell constant K cell m ?1

K cell ??R Current density (electric)j A ·m ?2j ?I /A

Diffusion rate constant,mass transfer coef?cient k d

m ·s ?1

k d,B ?|?B |I 1,B /nFcA Electric current I A

I ?dQ /dt Electric mobility

m 2·V ?1·s ?1?B ?v B /E Electric potential difference (of a galvanic cell)?V ,E ,U

V ?V ?V R ?V L

Electrochemical potential ??

J ·mol ?1?(?G /?n )

????B B Electrode reaction rate con-stant

(varies)n i

k ?I /nFA

ox a ?

Electrokinetic potential (zeta potential)

V Elementary charge (proton

charge)

e C

emf,electromotive force E V

E ?lim ?V

I :0

emf of the cell E V

E ?E ??(RT /n

F )???i ln a i Faraday constant

F C ·mol ?1F ?eL

Galvani potential difference ??V ???????

???Inner electrode potential ?V

????E Ionic conductivity ?S ·m 2·mol ?1?B ?|z B |Fu B

Ionic strength

I c ,I mol ·m ?3

I c ??c i z 21?2c

Mean ionic activity

a ?a ??m ???/m 0

Mean ionic activity coef?-cient

??(???)????????(?)(?)???

Mean ionic mobility

m ??1

mol ·kg (???)??????m ?(m )(m )???Molar conductivity (of an electrolyte)??2?1

S ·m mol ?B ??c B

?c (H )pH ??log

mol ·dm Outer electrode potential ?V ??Q /4??0r

Overpotential

?V ??E ?E ?IR I I ?0u Reciprocal radius of ionic atmosphere

?1m ??(2F 2I /?RT )1/2

Standard emf,standard po-tential of electrochemical cell reaction

E 0

V 00E ???G /nF ?(RT /nF )ln K

r Surface electric potential ?V ?????Thickness diffusion layer ?m

?B ?D B /k d,B Transfer coef?cient ?

?|?|RT ?ln|I |c ??

c nF ?E

Transport number

t t B ?j B /?j i Volta potential difference

????????

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.13

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

G.Electromagnetic radiation (continued )

Name

Symbol

SI unit

De?nition

Absorbance

????abs /?0

Absorbance (decaidic)A A ??log(1??i )Absorbance (napierian)B

B ??ln(1??i )

Absorption coef?cient:Linear (decaidic)a ,K ?1m a ?A /l Linear (napierian)??1

m ??B /l

Molar (decaidic)?2?1m ·mol ??a /d ?A /cl Molar (napierian)?2?1m ·mol ???/c ?B /cl Absorption index

k k ??/4??

?Angle of optical rotation ?rad

Circular frequency

??1?1s ,rad ·s ??2??Complex refractive index n ?n ????ik

Concentration,amount of substance

mol ·m 3Concentration,mass

kg ·m 3Einstein transition probabil-ities:

Spontaneous emission A nm

s dN n /dt ??A nm N n Stimulated absorption B mn ?1s ·kg dN /dt ??(??)B N n ??nm mn m Stimulated emission B nm ?1s ·kg dN /dt ??v ?(??)B N n nm mn m

Emittance

???M /M bb By blackbody

M bb First radiation constant c 1W ·m 22c ?2?hc 10Frequency

?Hz

??c /?Irradiance (radiant ?ux re-ceived)E ,(I )?2W ·m E ?d ?/dA Molar refraction

R ,R m 3?1m ·mol 2(n ?1)

R ?

V m

2(n ?2)

Path length (absorbing)l m Optical rotatory power ?[?]?rad ?[?]??/?l ?Planck constant h J ·s Planck constant/2??J ·s ??h /2?

Radiant energy

Q ,W J

Radiant energy density ?,w J ·m ?3??Q /V

Radiant exitance,emitted radiant ?ux M ?2W ·m M ?d ?/dA source

Radiant intensity

I ?1W ·sr I ?d ?/d ?Radiant power,radiant en-ergy per time ?,P W

??dQ /dt Refractive index n n ?c 0/c Re?ectance

????re?/?0Second radiation constant c 2

K ·m c 2?hc 0/k

Spectral radiant energy density:

In terms of frequency ??,w ?J ·m ·Hz ?3?1???d ?/d ?In terms of wavelength ??,w ?J ·m ?4???d ?/d ?In terms of wavenumber

?,w ????J ·m ?2

??d ?/d ?

???

2.14SECTION 2

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

G.Electromagnetic radiation (continued )

Name

Symbol

SI unit

De?nition

Speed of light:In a medium c m ·s ?1c ?c 0/n In vacuum

c 0m ·s ?1

Stefan-Boltzmann constant ?W ·m ·K ?2?4M bb ??T 4Transmittance ?,T ???tr /?0

Wavelength ?

m Wavenumber:In a medium ?m ?1??1/?

In vacuum

??m ?1

????/c ?1/n ?

0H.Kinetics

Name

Symbol SI unit De?nition

Activation energy

E a ,E J ·mol ?1

E a ?RT 2d ln k /dT

Boltzmann constant k ,k B J ·K ?1Collision cross section ?m 2?AB ??d 2AB Collision diameter d m d AB ?r A ?r B

Collision frequency

Z A

s ?1

Collision frequency factor z

AB ,z AA m 3·mol ·s ?1?1z AB ?Z AB /Lc A c B Collision number Z AB ,Z AA m ·s ?3?1Half-life

t 1/2s

c (t 1/2)?c 0/2Overall order of reaction n n ??n B

Partial order of reaction n B n B v ?k ?c B

Pre-exponential factor

A (mol ·m 3)n ·s ?1?1?1k ?A exp(?E a /RT )Quantum yield,photochem-ical yield

?Rate of change of quantity X

X ˙(varies)X

˙?dX /dt Rate of concentration change (chemical reac-tion)

r B ,v B mol ·m ·s ?3?1r B ?dc B /dt

Rate constant,rate coef?-cient

k (mol ·m 3)n ·s ?1?1?1n B v ?k ?c B

Rate of conversion change due to chemical reaction ˙??1mol ·s ˙?

?d ?/dt Rate of reaction (based on concentration)v

mol ·m ·s ?3?1?1v ??/V ??dc /dt

B B Relaxation time

??1/(k 1?k )

?1Standard enthalpy of acti-vation

?H ??

J ·mol ?1Standard entropy of activa-tion

?S ??J ·mol ·K ?1?1Standard Gibbs energy of activation

?G ??J ·mol ?1Volume of activation

??m 3·mol ?1

?V ??RT (?ln k /?p )T

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.15

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

I.Mechanics

Name

Symbol

SI unit

De?nition

Acoustic factors:Absorption ?a ?a ?1??Dissipation ????a ??Re?ection ???P r /P 0Transmission ???P tr /P 0Angular momentum

L J ·s L ?r ?p

Bulk modulus,compression modulus

K Pa K ??V 0(dp /dV )Density,mass density ?kg ·m ?3??m /V Energy

E J

Fluidity,kinematic vis-cosity ?

m ·kg ·s ?1??1/?

Force

F N

F ?d p /dt ?m a Friction coef?cient ?,(f )F frict ??F norm Gravitational constant

G N ·m 2·kg ?2F ?Gm 1m 2/r 2

Hamilton function H J

H (q ,p )?T (q ,p )?V (q )Kinematic viscosity ?m 2·s ?1???/?Kinetic energy E k J E k ?mv 21?2Lagrange function

L J L (q ,q ˙)?T (q ,q ˙)?V (q )Linear strain,relative elon-

gation ?,e ???l /l Mass

m kg Modulus of elasticity,Young’s modulus E Pa E ??/?Moment of inertia I ,J kg ·m 2

I ??m i 2r i Momentum p kg ·m ·s ?1p ?m ?Normal stress ?Pa ??F /A Potential energy

E p

E ?

?F ·ds

p Power P W

P ?dW /dt Pressure

p ,P Pa,N ·m ?2p ?F /A

Reduced mass ?kg ??m 1m 2/(m 1?m 2)Relative density d d ??/?0Shear modulus G Pa

G ??/?Shear strain ????x /d Shear stress

?Pa ??F /A Sound energy ?ux P ,P a W

P ?dE /dt Speci?c volume ?m 3·kg ?1??V /??1/?Surface density ?A ,?S kg ·m ?2

?A ?m /A Surface tension

?,?N ·m ,J ·m ?1?2??dW /dA Torque,moment of a force T ,(M )N ·m T ?r ?F Viscosity (dynamic)?,?Pa ·s ?x,z ??(d ?x /dz )Volume (or bulk)strain ?

???V /V 0Weight G,(W,P)N G ?m ·g Work

W ,w

W ?

F ?ds

2.16SECTION 2

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

J.Solid state

Name

Symbol SI unit De?nition

Acceptor ionization energy E a J Bragg angle ?rad n ??2d sin ?

Bloch function u k (r )?3/2m ?(r )?u k (r )exp(ik ·r )

Burgers vector

b m

Charge density of electrons ?C ·m ?3?(r )??e ?*(r )?(r )

Circular wave vector:For particles (k )k ,q

m ?1k ?2?/?

For phonons (q )Conductivity tensor ?ik S ·m ?1????1

Curie temperature

T C K Debye circular frequency ?D s ?1Debye circular wavenumber q D m ?1Debye-Waller factor B ,D Density of states

N E J ·m ?1?3N E ?dN (E )/dE Density of vibrational modes (spectral)N ?,g

s ·m ?3N ??dN (?)/d ?Diffusion coef?cient D m 2·s ?1dN /dt ??DA dn /dx Diffusion length

L m L ?(D ?)1/2Displacement vector of an ion

u m u ?R ?R 0

Donor ionization energy E d J Effective mass

m *kg Equilibrium position vector of an ion R 0m Fermi energy E F J Gap energy E g Gru ¨neisen parameter ?,????V /?C V

Hall coef?cient

A H ,R H m 3·C ?1E ???j ?R H (

B ?j )

Lattice plane spacing d m Lattice vector R ,R 0m

Lorenz coef?cient L

V 2·K ?2

L ??/?T Madelung constant ?2?N z z e A ??E ?

coul 4??R 00

Mobility

?m 2·V ·s ?1?1???drift /E Mobility ratio b b ??n /?p

Neel temperature

T N K Number density,number concentration n

m ?3

Order parameters:Long range s Short range ?Order of re?ection

n Particle position vector:Electron r m Ion position R j m Peltier coef?cient

?V Reciprocal lattice vector (circular)

m ?1

G ?R ?2?m

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.17

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

J.Solid state (continued )

Name

Symbol

SI unit De?nition

Relaxation time ?s ??1/?F

Residual resistivity ?R m Resistivity tensor ??·m E ???j Temperature

Thermal conductivity tensor ?W ·m ·K ?1?1J q ????grad T Thermoelectric force E V

Thomson coef?cient

V ·K ?1Translation vectors for the reciprocal lattice (circu-lar)

b ;b ;b 123a *;b *;

c *

m ?1a i ?b k ?2??ik

Translation vectors for crystal lattice a 1;a 2;a 3a ;b ;c m R ?n a ?n a ?n a 112233Work function

??E ?E ?F

K.Space and time

Name

Symbol SI unit De?nition Acceleration a ,(g )m ·s ?2

a ?d ?/dt Angular velocity ?

rad ·s ,s ?1?1??d ?/dt

Area A ,A

s ,S m 2Breadth

b m Cartesian space coordinates x ,y ,z m

Circular frequency,angular frequency ?rad ·s ,s ?1?1??2??

Diameter d m Distance d m Frequency

?,f Hz ??1/T

Generalized coordinate q ,q i (varies)Height h m Length

l m Length of arc s m Path length s m Period

s T ?t /N Plane angle

?,?,?,?,?rad,l ??s /r Position vector r m r ?x i ?y j ?z k

Radius

r m Relaxation time,time con-stant ?,T

s ??|dt /d ln x |

Solid angle ?,?sr,l ??A /r 2Speed

?,u ,w ,c m ·s ?1??|?|

Spherical polar coordinates r ,?,?m,l,l Thickness d ,?m Time t

s Velocity ?,u ,w ,c m ·s ??d r /dt

Volume

V ,(?)

m 3

2.18SECTION 2

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

L.Spectroscopy

Name

Symbol

SI unit

De?nition

Asymmetry parameter

2B ?A ?C ??

A ?C

Centrifugal distortion con-stants:

A reduction ?J ?JK ?K ?J ?K m ?1

S reduction D J D JK D K d 1d 2Degeneracy,statistical weight

g ,d ,?Electric dipole moment of a molecule

p ,?C ·m

E p ??p ?E

Electron spin resonance (ESR),electron paramag-netic resonance (EPR):Hyper?ne coupling con-stant:In liquids a ,A Hz H ?hfs /h ?a S ??I In solids T Hz H ?hfs /h ?S ??T ?I g factor g h ??g ?B B Electronic term T e m ?1T e ?E e /hc Harmonic vibration wave-

number ?e ;?r

m ?1Inertial defect ?kg ·m 2??I C ?I A ?I B

Interatomic distances:Equilibrium distance r e m Ground state distance r 0m Substitution structure dis-tance

r s

m Zero-point average dis-tance

r z

m Longitudinal relaxation time

T 1

Nuclear magnetic resonance

(NMR),chemical shift,?scale

???106(???0)/?0

Coupling constant,direct (dipolar)

D AB

Hz Magnetogyric ratio ?C ·kg ?1??2??/Ih Shielding constant ?A B A ?(1??A )B Spin-spin coupling con-stant

J AB

Hz H /h ?J AB I A ·I B

Principal moments of iner-tia

I A ;I B ;I C

kg ·m 2I A ?I B ?I C Rotational constants:In frequency A ;B ;C

Hz A ?h /8?2I A In wavenumber A

?;B ?;C ?m ?1A

??h /8?2I A Rotational term F m ?1F ?E rot /hc

Spin orbit coupling constant A m ?1T s.o.?A ?L

?·S ??Total term T m ?1T ?E tot /hc Transition dipole moment of a molecule

M ,R

C ·m

M ?

??p ??d ?

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.19 TABLE2.2Physical and Chemical Symbols and De?nitions(Continued)

L.Spectroscopy(continued)

Name Symbol SI unit De?nition Transition frequency?Hz??(E??E?)/h

Transition wavenumber??,(?)m?1???T??T?

Transverse relaxation time T

Vibrational anharmonicity

constant

?e?e;?rs;

tt?

m?1

Vibrational coordinates:

Internal coordinates R

,?j,

etc.

Normal coordinates,di-

mensionless

Mass adjusted Q

Vibrational force constants:

Diatomic f,(k)J·m?2f??2V/?r2

Polyatomic

Dimensionless normal

coordinates

?rst...,

rst...

m?1

Internal coordinates f

(varies)f

ij??2V/?r i?r j Symmetry coordinates F

(varies)F

ij??2V/?S i?S j

Vibrational quantum num-

bers

Vibrational term G m?1G?E

vib

/hc

Angular momentum types

Operator

symbol

Quantum number symbol

Total Z axis z axis

Electron orbital?L L M

One electron only?l l m

Electron orbital?spin??

L?S?????

Electron spin?S S M

One electron only s?s m

Internal vibrational:

Spherical top?l l(l?)K l

Other j?,??l(l?)

Nuclear orbital(rotational)?R R K

Nuclear spin?I I M

Sum of J?I?F F M

Sum of N?S?J J M

K,k

Sum of R?L(?j)?N N K,k

M.Thermodynamics

Name Symbol SI unit De?nition

Absolute activity??B?exp(?B/RT)

Activity(referenced to

Henry’s law):

Concentration basis a

???*

B B

a?exp

c,B?

2.20SECTION 2

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

M.Thermodynamics (continued )

Name

Symbol SI unit

De?nition

Molality basis a m ???*B B a ?exp m,B ??RT

Mole fraction basis a x ???*B B a ?exp x,B ??RT

Activity (referenced to Raoult’s law)

???*B B a ?exp

B ?

Activity coef?cient (refer-enced to Henry’s law):Concentration basis ?c a c,B ??c,B c B /c 0Molality basis

?m a m,B ??m,B m B /m 0Mole fraction basis ?x a x,B ??x,B x B Activity coef?cient (refer-enced to Raoult’s law)f

f B ?a B /x B

Af?nity of reaction A J ·mol ?1A ??(?G /??)p,T

Celsius temperature ?,t ?C

?/?C ?T /K ?273.15Chemical potential ?

J ·mol ?1?B ?(?G /?n B )T ,p,n

Compressibility:Isentropic ?S Pa ?1?S ??(1/V )(?V /?p )S Isothermal

?T Pa ?1?T ??(1/V )(?V /?p )T

Compressibility factor

Z ?pV m /RT

Cubic expansion coef?cient ?,?V ,?K ?1??(1/V )(?V /?T )p Enthalpy H J

H ?U ?pV Entropy

S J ·K ?1

dS ?dq /T

Equilibrium constant K 0,K

K ??exp(??r G ?/RT )

Equilibrium constant:Concentration basis K c (mol ·m ???3)K c ??c ?Molality basis K m (mol ·m ???1)K m ??m ?Pressure basis K p Pa ??K p ??p ?

Fugacity

Pa f ??lim (p /?)B B B B T

p :0

Fugacity coef?cient ??B ?f B /p B Gibbs energy G J G ?H ?TS

Heat

q ,Q

J Heat capacity:

At constant pressure C p J ·K ?1C p ?(?H /?T )p At constant volume C V J ·K ?1C V ?(?U /?T )V Helmholtz energy A J A ?U ?TS Internal energy U ?U ?q ?w

Ionic strength:

Concentration basis I c ,I mol ·kg ?3I c ?2

1?2?m z B B Molality basis

I m ,I mol ·kg ?121I ??2?m z m B B Joule-Thomson coef?cient ?,?JT K ·Pa ?1??(?T /?p )H Linear expansion coef?-cient

?1K ?1?1?(l/l )(?l /T )

Massieu function J J ·K ?1J ??A /T Molar quantity X X m

(varies)

X m ?X /n

Osmotic coef?cient:Molality basis

?m ??(?*??)/(RTM ?m )m A A A B Mole fraction basis

?x ??(???*)/(RT ln x )

x A A A

GENERAL INFORMATION,CONVERSION TABLES,AND MATHEMATICS 2.21

TABLE 2.2Physical and Chemical Symbols and De?nitions (Continued )

M.Thermodynamics (continued )

Name

Symbol

SI unit

De?nition

Osmotic pressure (ideal di-lute solution)

?Pa ??c B RT Partial molar quantity X X B (varies)X ?(?X /?n B )T,p,n Planck function Y J ·K ?1Y ??G /T Pressure coef?cient ?Pa ·K ?1??(?P /?T )V Ratioo f heat capacities ???C p /C V

Relative pressure coef?-cient

?p K ?1

?p ?(1/p )(?p /?T )V

Second virial coef?cient B m 3·mo l ?1pV m ?RT (1?B /V m ?···)Speci?c quantity X

x (varies)x ?X /m Standard chemical potential ?0J ·mo l ?1Standard partial molar en-thalpy

H 0J ·mo l ?1H 0??0?TS Standard partial molar en-tropy

S 0J ·mo l ·K ?1?1S 0??(??0/?T )Standard reaction enthalpy ?r H 0J ·mo l ?1

?r H 0???H 0Standard reaction entropy ?r S 0J ·mo l ·K ?1?1?r S 0???S 0Standard reaction Gibbs en-ergy

?r G 0J ·mo l ?1?r G 0????0

Surface tension

?,?

J ·m ,?2N ·m ?1??(?G /?A s )T,p

Thermodynamic tempera-ture T K Work

w ,W

Symbols used as subscripts to denote a chemical reaction or process:

ads adsorption mix mixing of ?uids at atomization r reaction in general c combustion reaction sol solution of solute in solvent dil dilution of a solution sub sublimation (solid to gas)f formation reaction trs transition (two phases)fus melting,fusion (solid to liquid)Recommended superscripts:

activated complex,transition state ?

in?nite solution E excess quantity *pure substance id ideal

standard

N.Transport properties

Name

Symbol SI unit De?nition

Coef?cient of heat transfer h ,(k ,K )W ·m ·K ?2?1h ?J q /?T Diffusion coef?cient D m 2·s ?1D ?J n /(dc /dl )Flux (of a quantity X )J X ,J (varies)J X ?A dX /dt ?1Heat ?ow rate ?W

??dq /dt Heat ?ux

J q

W ·m ?2J q ??/A Mass ?ow rate

q m ,m kg ·s ?1q m ?dm /dt Mass transfer coef?cient k d m ·s ?1Thermal conductance G W ·K ?1

G ??/?T Thermal conductivity

?,k

W ·m ·K ?1?1

??J q /(dT /dl )

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