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ISO
STANDARD 31-8
Third edition
1992-12-15
Quantities and units -
Part 8:
Physical chemistry and molecerlar physics
Grandeurs et unifes -
Partie 8: Chimie physique et physique mol&ulaire
Reference number
ISO 31-87 992(E)
- -
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ISO 31=8:1992(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide
federation of national Standards bodies (ISO member bodies). The work
of preparing International Standards is normally carried out through ISO
technical committees. Esch member body interested in a subject for
which a technical committee has been established has the right to be
represented on that committee. International organizations, governmental
and non-governmental, in liaison with ISO, also take patt in the work. ISO
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard ISO 31-8 was prepared by Technical Committee
lSO/TC 12, Quantities, units, Symbols, conversion factors.
*
This third edition cancels and replaces the second edition
(ISO 31-8:1980). Th e major technical changes from the second edition are
the following:
- the decision by the International Committee for Weights and Measures
(Comite International des Poids et Mesures, CIPM) in 1980 concerning
the Status of supplementary units has been incorporated;
- a number of new items have been added;
- a number of new Chemical elements have been added in annex A.
The scope of Technical Committee ISOnC 12 is standardization of units
and Symbols for quantities and units (and mathematical Symbols) used
within the different fields of science and technology, giving, where
necessary, definitions of these quantities and units. Standard conversion
factors for converting between the various units also come under the
scope of the TC. In fulfilment of this responsibility, lSO/TC 12 has pre-
pared ISO 31.
0 ISO 1992
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronie or mechanical, including photocopying and
microfilm, without Permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-l 211 Geneve 20 l Switzerland
Printed in Switzerland
ii
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ISO 31=8:1992(E)
0 ISO
ISO 31 consists of the following Parts, under the general title Quantities
and units:
- Part 0: General principles
- Part 1: Spate and time
- Part 2: Periodic and related phenomena
- Part 3: Mechanics
- Part 4: Heat
- Part 5: Electricity and magnetism
- Part 6: Light and rela ted electromagnetic radiations
- Part 7: Acoustics
- Part 8: Physical chemistry and molecular physics
- Part 9: Atomic and nuclear physics
- Part 70: Nuclear reactions and ionizing radiations
- Part 11: Mathematical signs and symbok for use in the physical
sciences and technology
- Part 12: Characteristic numbers
- Part 13) Solid state physics
and C form an integral part of this part of ISO 31.
Annexes A, B
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ISO 31=8:1992(E) 0 ISO
Introduction
0.1 Arrangement of the tables
The tables of quantities and units in ISO 31 are arranged so that the
quantities are presented on the left-hand pages and the units on the cor-
responding rig ht-hand pages.
All units between two full lines belong to the quantities between the cor-
responding full lines on the left-hand pages.
Where the numbering of an item has been changed in the revision of a
part of ISO 31, the number in the preceding edition is shown in parenth-
eses on the left-hand page under the new number for the quantity; a dash
is used to indicate that the item in question did not appear in the preceding
edition.
0.2 Tables of quantities
The most important quantities within the field of this document are given
together with their Symbols and, in most cases, definitions. These defi-
nitions are given merely for identification; they are not intended to be
complete.
The vectorial Character of some quantities is pointed out, especially when
this is needed for the definitions, but no attempt is made to be complete
or consistent.
In most cases only one name and only one Symbol for the quantity are
given; where two or more names or two or more Symbols are given for
one quantity and no special distinction is made, they are on an equal
footing. When two types of italic (sloping) letter exist (for example as with
9, 0; q, 4; g, g) only one of these is given. This does not mean that the
other is not equally acceptable. In general it is recommended that such
variants should not be given different meanings. A Symbol within par-
entheses implies *[hat it is a “reserve Symbol”, to be used when, in a
particular context, the main Symbol is in use with a different meaning.
0.3 Tables of units
0.3.1 General
Units for the corresponding quantities are given together with the inter-
national Symbols and the definitions. For further information, see ISO 31-0.
The units are arranged in the following way:
a) The names of the SI units are given in large print (larger than text size).
The SI units have been adopted by the General Conference on Weights
and Measures (Conference Generale des Poids et Mesures, CGPM).
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0 ISO
ISO 31=8:1992(E)
The SI units and their decimal multiples and sub-multiples are rec-
ommended, although the decimal multiples and sub-multiples are not
explicitly mentioned.
The names of non-SI units which may be used together with SI units
b)
because of their practical importante or because of their use in
specialized fields are given in normal print (text size).
These units are separated by a broken line from the SI units for the
quantities concerned.
The names of non-SI units which may be used temporarily together
c)
with SI units are given in small print (smaller than text size) in the
“Conversion factors and remarks” column.
The names of non-SI units which should not be combined with SI units
d
are given only in annexes in some Parts of ISO 31. These annexes are
informative and not integral Parts of the Standard. They are arranged in
three groups:
1) special names of units in the CGS System;
2) names of units based on the foot, pound and second and some
other related units;
3) names of other units.
0.3.2 Remark on units for quantities of dimension one
The coherent unit for any quantity of dimension one is the number one (1).
When the value of such a quantity is expressed, the unit 1 is generally not
written out explicitly. Prefixes shall not be used to form multiples or sub-
multiples of this unit. Instead of prefixes, powers of 10 may be used.
EXAMPLES
Refractive index IZ= 1,53 x 1 = 1,53
Reynolds number Re = 1,32 x 103
Considering that plane angle is generally expressed as the ratio between
two lengths, and solid angle as the ratio between an area and the Square
of a length, the CIPM specified in 1980 that, in the International System
of Units, the radian and steradian are dimensionless derived units. This
implies that the quantities plane angle and solid angle are considered as
dimensionless derived quantities. The units radian and steradian may be
used in expressions for derived units to facilitate distinction between
quantities of different nature but having the same dimension.
0.4 Numerital Statements
All numbers in the “Definition” column are exact.
When numbers in the “Conversion factors and remarks” column are ex-
act, the word “exactly” is added in parentheses after the number.
0.5 Special remarks
In this part of ISO 31, Symbols for substances are shown as subscripts,
for example Cs, Ws, ps.
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0 ISO
ISO 31=8:1992(E)
Generally it is advisable to put Symbols for substances and their states in
parentheses on the same line as the main Symbol, for example
c(H*so,> l
The superscript * is used to mean “pure”. The superscript ’ is used to
mean “Standard”.
EXAMPLES
Vm(K2S04, 0,l mol . dmm3 in H,O, 25 “C)
for molar volume.
C$,(H,O, g, 298,15 K) = 33,58 J . K- ’ . mol- ’
for Standard molar heat capacity at constant pressure.
ln an expression such as (ps = xBV~ B/CXAV~A, where qs denotes the vol-
ume fraction of a particular substance B in a mixture of substances A, B,
where XA denotes the mole fraction of the substance A and VcA the
C
m’oL& volume of the pure substance A, and where all the molar volumes
v’ v; B, v;C, . . . . are taken at the Same temperature and pressure, the
m,Al
summation on the right-hand side is that over all the substances A, B, C,
. . . . of which a mixture is composed, so that &A = 1.
The names and Symbols of the Chemical elements are given in annex A.
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INTERNATIONAL STANDARD 0 ISO ISO 31=8:1992(E)
Quantities and units -
Part 8:
Physical chemistry and molecular physics
possibility of applying the most recent editions of the
1 Scope
Standards indicated below. Members of IEC and ISO
maintain registers of currently valid International
This part of ISO 31 gives names and Symbols for
Standards.
quantities and units of physical chemistry and
Where appropriate, conversion
molecular physics.
ISO 31-411992, Quantities and units - Part 4: tieat.
factors are also given.
ISO 31-9: 1992, Quantities and units - Part 9: Atomic
2 Normative references
and nuclear ph ysics.
The following Standards contain provisions which,
through reference in this text, constitute provisions 3 Names and Symbols
of this patt of ISO 31. At the time of publication, the
editions indicated were valid. All Standards are subject The names and Symbols for quantities and units of
to revision, and Parties to agreements based on this physical chemistry and molecular physics are given
part of ISO 31 are encouraged to investigate the on the following pages.
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ISO 31=8:1992(E) 0 ISO
PHYSICAL CHEMISTRY AND MOLECULAR PHYSICS Quantities
Remarks
the mass of an atom of the y called atomic weight.
8-l .2 relative molecular IUr Ratio of the average mass per
Formerly called molecular
mass molecule or specified entity of weight.
a substance to l/12 of the The relative atomic or molecu-
mass of an atom of the nuclide lar mass depends on the
12
C nuclidic composition.
8-2 number of N Number of molecules or other
molecules or other elementary entities in a System
elementafy
entities
amount of Amount of substance is one of
8-3
nf (v>
substance the base quantities on which
the SI is based.
v may be used as an alternative
to n when n is used for number
density of particles (see
8-i 0.1).
Number of molecules divided NA = (6,022 136 7 +
8-4 Avogadro constant L, NA
0,000 003 6) x 1023-mol-1 ‘)
by amount of substance.
NA = N/n
1) CODATA Bulletin 63 (1986).
8-5 molar mass M Mass divided by amount of m is the mass of the substance.
substance.
M = min
molar volume Volume divided by amount of The molar volume of an ideal
8-6
vm
substance. gas at 273,15 K and
101,325 kPa is
= V/n
vm
V m,=(O,O22 414 10 +
0,ciOO 000 19) m3/mol”
1) CODATA Bulletin 63 (1986).
2
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0 ISO ISO 31=8:1992(E)
PHYSICAL CHEMISTRY AND MOLECULAR PHYSICS
Units
International
Item
Conversion factors andl remarks
Name of unit Symbol for Definition
No.
unit
See the introduction, subclause
8-l .a
one 1
0.3.2.
See the introduction, subclause
8-2.a
one 1
0.3.2.
The definition applies to unbound at-
The mole is the amount
8-3.a
mole mol
of substance of a System oms of carbon 12, at rest and in their
which contains as many ground state.
elementar-y entities as
there are atoms in 0,012
kilogram of carbon 12.
When the mole is used,
the elementary entities
must be specified and
may be atoms, mol-
ecules, ions, electrons,
other particles, or speci-
fied groups of such par-
ticles
8-4.a
reciprocal mole, mol-’
mole to the
power minus
one
M= 10-3M, kg/mol =
8-5.a kg/mol
kilogram per
Mr kg/kmol = M, g/mol
mole
where Mr is the relative molecular
mass of a substance of definite
Chemical composition.
8-6.a m3/mol
cubic metre per
mole
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ISO 31=8:1992(E) 0 ISO
PHYSICAL CHEMISTRY AND MOLECULAR PHYSICS (confinued) Quantities
Item
Definition
Quantity Symbol Remarks
No.
8-7 molar Thermodynamic energy divided This quantity is also called
um
thermodynamic by amount of substance. molar internal energy.
See ISO 31-4.
energy
= Uln
um Similar definitions apply to
other molar thermodynamic
functions, for example
ffml A,, G,.
Heat capacity divided by
molar heat capacity Cm See ISO 31-4.
amount of substance.
8-9 molar entropy Entropy divided by amount of See ISO 31-4.
sm
substance.
=
S
Sin
m
8-l 0.1 volumic number of n Number of molecules or par-
molecules (or ticles divided by volume.
particles),
=
n
NW
number density of
molecules (or
particles)
8-l 0.2 molecular Number of molecules of B div-
CB
concentration of B ided by the volume of the mix-
ture
Mass divided by volume
8-l 1 .l volumic mass,
e
mass density,
density
8-l 1.2 mass concentration @s Mass of B divided by the vol-
of B ume of the mixture
8-12 mass fraction of B Ws Ratio of the mass of B to the
mass of the mixture
Amount of substance of B div- In chemistry also indicated as
amount-of-substance
concentration of B
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0 ISO ISO 31=8:1992(E)
PHYSICAL CHEMISTRY AND MOLECULAR PHYSICS (continued)
Units
International
Item
Name of unit Symbol for Definition Conversion factors and remarks
No.
unit
For the various types of calorie, see
8-7.a
joule per mole J/mol
ISO 3141992, annex B.
8-8.a
joule per mole J/(mol . K)
kelvin
8-9.a
joule per mole J/(mol . K)
kelvin
8-l 0.a reciprocal cubic rne3
metre,
metre to the
power minus
three
8-l 1 .a
kilogram per
kW3
cubic metre
__----------- ---
---__------- -----------------
1 kg/1 = 103 kg/m3 = 1 kg/dm3
8-l 1 .b kilogram per litre
wl, kg/L
The Symbol L was adopted by the
CGPM (1979) as an alternative to I
for the litre.
See the introduction, subclause
8-l 2.a
one 1
0.3.2.
8-l 3.a
mole per cubic mol/m3
metre
~.~-~--------~~_
-----------------
-------
1 mol/1 = 1 O3 mol/m3 = 1 mol/dm3
mol/l,
8-13.b mole per litre
mol/L
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0 ISO
ISO 31=8:1992(E)
Quantities
PHYSICAL CHEMISTRY AND MOLECULAR PHYSICS (continued)
Item
Remarks
Quantity Symbol Definition
No.
Ratio of the amount of sub- Alternative names for these
8-14.1 mole fraction of B
xB~ (YB)
stance of B to the amount of quantities are “amount-of-
(8-15.1)
substance fraction” and
substance of the mixture
“amount-of-substance ratio”
respectively.
8-14.2 male ratio of solute $ Ratio of the amount of sub-
For a one-solute solution,
(8-15.2) B stance of B to the amount of
r =./(l 3)
substance of the solvent sub-
stance
An alternative definition in
vohme fraction of (ps For a mixture of substances,
8-15
which the molar volumes VzA
(8-14.1) B
xBv:,B
of the pure substances A are
PB =
cxAvtt,A
replaced by the partial molar
volumes (ilV/anA),,, of the
where the VtA are the molar
substances A is also ‘Üsed.
volumes of th’e pure sub-
stances A at the same tem-
perature and pressure and
where C denotes summation
over all the substances
Amount of substance of solute
molahty of solute B bs, mg
8-16
B in a Solution divided by the
mass of the solvent
For a pure substance,
For a mixture of substances B,
8-17 Chemical potential PB
p = G/n = G,,.,
C
of B
where G, is the molar Gibbs
Pi =(aG/anB)T,p,~,. function.
The Symbol p is also used for
where ng is the amount of sub-
the quantity G,/NA, where NA is
stance of B and G is the Gibbs
the Avogadro constant.
function
For R, see 8-36. T is the
absolute activity of 1s
8-18 AB = exP(&/RT)
thermodynamic temperature.
B
For a gaseous mixture,
partial pressure of Ps
8-19
B (in a gaseous
=xB’p
PB
mixture)
where p is the pressure
For a gaseous mixture, & is iB = AB ’ hm @@/AB)
fugacity of B (in a
8-20
FBl 63)
l-0
proportional to the absolute ac-
gaseous mixture)
tivity AB, the proportionality fac-
tor, which is a function of
temperature only, being deter-
mined by the condition that at
constant temperature and com-
Position &/pB tends to 1 for an
infinitely dilute gas
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0 ISO ISO 31=8:1992(E)
PHYSICAL CHEMISTRY AND MOLECULAR PHYSICS (contin
...