R�gles IUPAC (Green Handbook) - Unit�s SI

Abbreviated list of quantities, units and symbols in physical chemistry

1. Base SI Units
2. SI Prefixes
3. Examples of SI Derived Units with Special Names and Symbols
4. Recommended Symbols for Commonly Used Physical Quantities

• 4.1 Space and Time
• 4.2 Mechanics
• 4.3 General Chemistry
• 4.4 Chemical Kinetics
• 4.5 Atoms, Molecules and Spectroscopy
• 4.6 Electricity and Magnetism
• 4.7 Thermodynamics and Statistics
• 4.8 Radiation
• 4.9 Electrochemistry
• 4.10 Transport Properties

5. Units Outside the SI

• 5.1 Units Used with the SI
• 5.2 Other Units

6. Values of Some Fundamental Constants
7. References

  1. Base SI units and physical quantities

A physical quantity is the product of a numerical value (a pure number) and a unit.

Physical quantities are organized in a dimensional system built upon seven base quantities. The International System of Units (SI) is based on the seven base units having the same dimensions as the associated physical quantities. Their names and symbols are as follows:

 

Base Physical Quantity	Symbol for Quantity	Name of SI Unit	Symbol for SI Unit
length	l	metre	m
mass	m	kilogram	kg
time	t	second	s
electric current	I	ampere	A
thermodynamic temperature	T	kelvin	K
amount of substance	n	mole	mol
luminous intensity	Iv	candela	cd

The symbol for a physical quantity is a single letter of the Latin or Greek alphabet printed in italic (sloping) type. It may be modified by subscripts and/or superscripts of specified meaning, or further characterized in particular cases through annotations in parenthesies put directly behind the symbol. The symbol for a unit is printed in roman (upright) type. Neither symbol should be followed by a full stop (period).

The physical quantity 'amount of substance' or 'chemical amount' is proportional to the number of elementary entities - specified by a chemical formula - of which the substance is composed. The proportionality factor is the reciprocal of the Avogadro constanct L (6.022 x 10²³ mol^-1). The amount of substance should no longer be called 'number of moles'.

Examples of relations between "amount of substance" and other physical quantities:

2 moles of N₂ contain 12.044-x-10²³ molecules of N₂, amount of N₂ = n(N₂) = number of N₂ molecules/L;

1.5 moles of Hg₂Cl₂ have a mass of 708.13 g;

1 mole of photons with frequency 10¹⁴ Hz has an energy of 39.90 kJ;

1 mole of electrons, e^-, contains 6.022-x-10²³ electrons, has a a mass of 5.468-x-10^-7 kg, and a charge of -96.49 kC.

Prefixes to form the names and symbols of the decimal multiples and submultiples of SI units.*

 

Multiple	Prefix	Symbol
10-24	yocto	y
10-21	zepto	z
10-18	atto	a
10-15	femto	f
10-12	pico	p
10-9	nano	n
10-6	micro	�
10-3	milli	m
10-2	centi	c
10-1	deci	d
10	deca	da
102	hecto	h
103	kilo	k
106	mega	M
109	giga	G
1012	tera	T
1015	peta	P
1018	exa	E
1021	zeta	Z
1024	yotta	Y

* Decimal multiple and submultiples of the unit of mass are formed by attaching prefixes to gram, examples: mg, not �kg; Mg, not kkg.

3. Examples of SI derived units with special names and symbols

 

Physical Quantity (for symbols see Sect. 4 )	Name of SI Unit	Symbol for SI Unit	Expression in Terms of SI Base Units
frequency	hertz	Hz	s-1
force	newton	N	m kg s-2
pressure, stress	pascal	Pa	m-1 kg s-2 (= N-m-2 )
energy, work, heat	joule	J	m2 kg s-2 (= N-m = Pa-m3 )
power	watt	W	m2 kg s-3 (= J-s-1)
electric charge	coulomb	C	s A
electric potential	volt	V	m2 kg s-3 A-1 (= J-C-1)
electric capacitance	farad	F	m-2 kg-1 s4 A2 (= C-V-1)
electric resistance	ohm	W	m2 kg s-3 A-2 (= V-A-1)
electric conductance	siemens	S	m-2 kg-1 s3 A2 (= W-1)
magnetic flux	weber	Wb	m2 kg s-2 A-1 (= V s)
magnetic flux density	tesla	T	kg s-2 A-1 (= V s m-2)
inductance	henry	H	m2 kg s-2 A-2 (= V A-1 s)
Celsius temperature*	degree Celsius	oC	K
plane angle	radian	rad	1 **	(rad and sr may be included or omitted in expressions for the derived units)
solid angle	steradian	sr	1 **

* The Celsius temperature is defined by q / ^oC = T / K-273.15

4.1 physical quantities: space and time

 

Physical Quantity	Symbol	SI Unit
Cartesian space coordinates	x, y, z	m
position vector	r	m
length	l	m
height	h	m
thickness, distance	d, d	m
radius	r	m
diameter	d	m
path, length of arc	s	m
area	A, As, S	m2
volume	V	m3
plane angle	a, b, g, q, f	1, rad
solid angle	w, W	1, sr
time	t	s
frequency	v, f	Hz
angular frequency (=2pv)	w	s-1, rad s-1
characteristic time interval, relaxation time, time constant	t, T	s
velocity	v , u , w , c	m s-1
acceleration	a	m s-2

4.2 physical quantities: mechanics

Physical Quantity	Symbol	SI Unit
mass	m	kg
reduced mass	�	kg
(mass) density	r	kg m-3
relative density	d	1
specific volume	v	m3 kg-1
moment of inertia	I	kg m2
momentum	p	kg m s-1
angular momentum	L	kg m2 s-1 rad (= J s)
force	F	N (= kg m s-2)
weight	G, W	N
pressure	p, P	Pa
surface tension	g, s	N m-1, J m-2
energy	E	J
potential energy	Ep , V, F	J
kinetic energy	Ek , T, K	J
work	w, W	J
Hamilton function	H	J
power	P	W

  4.3 physical quantities: general chemistry

 

Physical Quantity	Symbol	SI Unit
number of entities	N	1
amount of substance, chemical amount	n	mol
molar mass	M	kg mol-1
relative molecular mass, (molecular weight)	Mr	1
relative atomic mass, (atomic weight)	Ar	1
molar volume	Vm	m3 mol-1
mass fraction	w	1
volume fraction	f	1
mole fraction	x, y	1
partial pressure of substance B	p B	Pa
number concentration	C, n	m-3
amount (of substance) concentration of B or concentration of B	c B , [ B ]	mol m-3
molality	m	mol kg-1
mass concentration	r, g	kg m-3
surface concentration	G	mol m-2
stoichiometric number	v	1
extent of reaction	x	mol

4.4 physical quantities: chemical kinetics

 

Physical Quantity	Symbol	SI Unit
rate of conversion	x	mol s-1
rate of concentration change of substance B (through chemical reaction)	v B , r B	mol m-3 s-1
rate of reaction	v	mol m-3 s-1
overall order of reaction	n	1
rate constant, rate coefficient	k	(m3 mol-1)n-1 s-1
half life	t1/2	s
pre-exponential factor	A	(m3 mol-1)n-1 s-1
energy of activation	E, Ea	J mol-1
Gibbs energy of activation	D�G	J mol-1
collision cross section	s	m2
collision frequency(of A with A )	zA (A)	s-1
collision frequency factor	zAB	m3 mol-1 s-1
quantum yield, photochemical yield	f, F	1

4.5 physical quantities: atoms, molecules and spectroscopy

 

Physical Quantity	Symbol	SI Unit
nucleon number, mass number	A	1
proton number, atomic number	Z	1
neutron number	N	1
decay constant	l	s-1
ionization energy	Ei , I	J
dissociation energy	Ed , D	J
electron affinity	Eea	J
quantum numbers:
principal	n	1
electron orbital	l, L	1
-- component	ml , ML	1
electron spin	s, S	1
-- component	ms , MS	1
total angular momentum	j, J	1
-- component	mj , MJ	1
nuclear spin	I	1
-- component	MI	1
vibrational	v	1
magnetic moment of a particle	�, m	J T-1, A m2
magnetogyric ratio	g	C kg-1
g-factor	g	1
Larmor circular frequency	wL	s-1
quadrupole moment	Q,, Q, eQ	C m2
wavelength	l	m
wavelength in a vacuum		m-1
total term	T	m-1
electronic term	Te	m-1
vibrational term	G	m-1
rotational term	F	m-1
rotational constants	A, B, C	m-1

 

4.6 physical quantities: electricity and magnetism

 

Physical Quantity	Symbol	SI Unit
electric charge	Q	C
charge density	r	C m-3
electric current	I	A
electric current density	j	A m-2
electric potential	f, V	V
electric potential difference, voltage	U, Df, DV	V
electric field strength	E	V m-1
electric displacement	D	C m-2
capacitance	C	F
permittivity	e	F m-1
relative permittivity	er	1
dielectric polarization	P	C m-2
electric susceptibility	ce	1
polarizability (of a particle)	a	m2 C V-1
electric dipole moment	p, �	C m
magnetic flux	F	Wb
Magnetic flux density	B	T
magnetic field strength	H	A m-1
permeability	�	H m-1, N A-2
relative permeability	�r	1
magnetization	M	A m-1
magnetic susceptibility	c	1
molar magnetic susceptibility	cm	m3 mol-1
resistance	R	W
conductance	G	S
resistivity	r	W m
conductivity	k	S m-1
self-inductance	L	H

 

4.7 physical quantities: thermodynamics and statistics

 

Physical Quantity	Symbol	SI Unit
heat	q, Q	J
work	w, W	J
thermodynamic temperature	T	K
Celsius Temperature	q, t	oC
internal energy	U	J
enthalpy	H	J
standard reaction enthalpy	D r H	J mol-1
entropy	S	J K-1
Gibbs energy	G	J
Helmholtz energy	A	J
heat capacity	C	J K-1
ratio Cp / Cv	g, k	1
Joule-Thomson coefficient	�, �JT	K Pa-1
isothermal compressibility	k	Pa-1
cubic expansion coefficient	a	K-1
chemical potential	�	J mol-1
affinity of a reaction	A	J mol-1
fugacity	f,	Pa
(relative) activity	a	1
activity coeficient:
-- mixtures	f	1
-- solutes	g	1
osmotic coefficient	f	1
osmotic opressure	P	Pa
equilibrium constant	K, K	1
-- on a concentration basis	Kc	(mol m-3)Sv
-- on a pressure basis	Kp	PaSv
-- on a molality basis	Km	(mol kg-1)Sv
density of (energy) states	r(E)	J-1
statistical weight	g	1
partition function:
-- particle	q, z	1
-- canonical ensemble	Q, Z	1
-- microcanonical ensemble	W	1
symmetry number	s, s	1
charateristic temperature	Q	K

 

4.8 physical quantities: radiation

 

Physical Quantity	Symbol	SI Unit
radiant energy	Q, W	J
radiant intensity	I, Ie	W sr-1, W
emissivity, emittance	e	1
absorptance	a	1
reflectance	r	1
transmittance	t	1
absorption coefficient:
-- linear (decadic)	a	m-1
-- molar (decadic)	e	m2 mol-1
refractive index	n	1
molar refraction	Rm	m3 mol-1
angle of optical rotation	a	1, rad

 

4.9 Physical quantities: electrochemistry

 

Physical Quantity	Symbol	SI Unit
charge number of and ion	z	1
ionic strength	Ic	mol m-3
	Im	mol kg-1
electromotive force, electrode potential	E	V
electrochemical potential		J mol-1
overpotential	h	V
pH	pH	1
charge number of a cell reaction	n, z	1
electrokinetic potential	z	V
molar conductivity (of an electrolyte)	L	S m2 mol-1
molar conductivity (of an ion), ionic conductivity	l	S m2 mol-1
electric mobility	u	m2 V-1 s-1
transport number	t	1

 

4.10 physical quantities: transport properties

 

Physical Quantity	Symbol	SI Unit
flux of a quantity X	Jx , J	(varies)
mass flow rate	qm,	kg s-1
volume flow rate	qV,	m3 s-1
heat flow rate	F	W
thermal conductivity	k, l	W m-1 K-1
coefficient of heat transfer	h	W m-2 K-1
thermal diffusivity	a	m2 s-1
diffusion coefficient	D	m2 s-1
vicosity	h, �	Pa s
kinematic viscosity	v	m2 s-1

 

5.1 units outside the SI: units used with the SI

Physical Quantity	Unit	Symbol for the Unit	Value in SI Units	SI Unit
time	minute	min	60	s
time	hour	h	3600	s
time	day	d	86 400	s
plane angle	degree	o	(p/180)	rad
volume	litre	l, L	10-3	m3
mass	tonne	t	103	kg
length	angstrom	�	10-10	m
pressure	bar	bar	105	Pa
energy	electronvolt*	eV	1.60218	x 10-19 J
mass	unified atomic mass unit*	u	1.660 54	x 10-27 kg

 

5.2 Other Units

These units were used in older literature. They are given here for the purpose of identification and conversion to SI units.

 

Physical Quantity	Unit	Symbol for Unit	Value in SI Units	SI Units
force	dyne	dyn	10-5	N
pressure	standard atmosphere	atm	101325	Pa
	torr (mmHg)	Torr	133.322	Pa
energy	erg	erg	10-7	J
	thermochemcal calorie	calth	4.184	J
magnetic flux density	gauss	G	10-4	T
electric dipole moment	debye	D	3.335 64	x 10-30 Cm
viscosity	poise	P	10-1	N s m-2
kinematic viscosity	stokes	St	10-4	m2 s-1

 

6. Values of Some Fundamental Constants ^#

 

Physical Quantity	Symbol for Unit	Value in SI Units	Unit
permeability of vacuum*	�o	4p x 10-7	N A-2
speed of light in vacuum*	co	299 792 458	m s-1
permittivity of vacuum	eo	8.854 187 816 x 10-12	F m-1
elementary charge	e	1.602 177 33(49) x 10-19	C
Planck constant	h	6.626 0755(40) x 10-34	J s
Avogadro constant	L, NA	6.022 1367(36) x 1023	mol -1
rest mass of electron	me	9.109 3897(54) x 10-31	kg
rest mass of proton	mp	1.672 6231(10) x 10-27	kg
Faraday constant	F	9.648 5309(29) x 104	C mol-1
Hartree energy	Eh	4.359 7482(26) x 10-18	J
Bohr radius	ao	5.291 772 49(24) x 10-11	m
Bohr magneton	�B	9.274 0154(31) x 10-24	J T-1
nuclear magneton	�N	5.050 7866(17) x 10-27	J T-1
Rydberg constant	R	10 973 731.534(13)	m-1
gas constant	R	8.314 510(70)	J K-1 mol-1
Boltzmann constant	k, kB	1.380 658(12) x 10-23	J K-1
gravitational constant	G	6.672 59(85) x 10-11	m3 kg-1
standard acceleration due to gravity*	gn	9.806 65	m s-2
triple point of water*	Ttp(H20)	273.16	K
zero of Celsius scale*	T(0oC)	273.15	K
molar volume of ideal gas (at 1 bar and 273.15 K)	Vo	22.711 08(19)	L mol-1

#Cohen, E.R. and Taylor, B.N., J. Res. Nat. Bur. Stand. 92 (1987) 85-95.
  *These values are exact by definition

 

7. References

IUPAC - http://old.iupac.org/reports/1993/homann/index.html

Page last modified 12 June 2000.
Copyright � 2000 International Union of Pure and Applied Chemistry.

Mills., I., Cvitas, T., Homann, K., Kallay, N. and Kuchitsu, K., Quantities, Units and Symbols in Physical Chemistry , 2nd edn. Blackwell Scientific Publications, Oxford 1993. (ISBN 0-632-03583-8.)

ISO Standards Handbook 2, Quantites and Units, ISO, Geneva 1993.

Cohen, E.r. and Giacomo, P., Symbols, Units Nomenclature and Fundamental Constants in Physics, 1987 Revision, Physica 146A (1987) 1-68.

Bureau International des Poids et Mesures, Le Syst�me International d'Unit�s (SI), 6th French ad English Edition, BIPM, S�vres 1991.