ISO 14912:2003

Gas analysis — Conversion of gas mixture composition data

ISO 14912:2003 defines the following quantities commonly used to express the composition of gas mixtures: mole fraction, mass fraction and volume fraction, as well as mole concentration, mass concentration and volume concentration. Relating to these quantities of composition, ISO 14912:2003 provides methods for the conversion between different quantities and the conversion between different state conditions. Conversion between different quantities means calculating the numerical value of an analyte content in terms of one of the quantities listed above from the numerical value of the same analyte content, at the same pressure and temperature of the gas mixture, given in terms of another of these quantities. Conversion between different state conditions means calculating the numerical value of an analyte content, in terms of one of the quantities listed above, under one set of state conditions from the numerical value of the same quantity under another set of state conditions, i.e. pressure and temperature, of the gas mixture. Gas mixture composition can be converted simultaneously between different quantities of composition and different state conditions by combination of the two types of conversion. ISO 14912:2003 is only applicable to homogeneous and stable gas mixtures. Therefore any state conditions (pressure and temperature) considered need to be well outside from the condensation region of the gas mixture and that of each of the specified analytes.

Analyse des gaz — Conversion des données de composition de mélanges gazeux

General Information

• Status: Published
• Publication Date: 02-Mar-2003
• ICS: 71.040.40 - Chemical analysis
• Technical Committee: ISO/TC 158 - Analysis of gases
• Drafting Committee: ISO/TC 158 - Analysis of gases
• Current Stage: 9092 - International Standard to be revised
• Completion Date: 02-Sep-2022

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 14912
First edition
2003-03-15

Gas analysis — Conversion of gas
mixture composition data
Analyse des gaz — Conversion des données de composition de
mélanges gazeux




Reference number
ISO 14912:2003(E)
©
ISO 2003

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ISO 14912:2003(E)
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ISO 14912:2003(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Terms and definitions .1
3 Symbols and units .4
4 Basic principles.6
4.1 Expression of gas mixture composition.6
4.2 Conversion between different quantities.8
4.3 Conversion between different state conditions.9
5 Main procedures.10
5.1 Conversion between different quantities of composition.10
5.2 Conversion to reference conditions.13
6 Practical implementation.13
6.1 Conversion between quantities of composition .13
6.2 Conversion of single analyte contents .14
6.3 Conversion of complete compositions.15
6.4 Conversion between state conditions .15
6.5 Simple approximations applicable to conversion .15
7 Input quantities and their uncertainties.16
7.1 Pure gas data.16
7.2 Gas mixture data .19
7.3 Rough uncertainty estimates.22
8 Conversion uncertainty .22
8.1 General considerations .22
8.2 Conversion of single analyte contents .23
8.3 Conversion of complete compositions.24
8.4 Uncertainty calculation using numerical differentiation.26
8.5 Variances and covariances of input composition data.27
9 Application recommendations.29
Annex A (normative) Assessment of state conditions .30
Annex B (normative) Summation relations for the expression of mixture properties .33
Annex C (informative) Mixture component data .34
Annex D (informative) Examples.40
Annex E (informative) Computer implementation of recommended methods.55
Bibliography.57

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ISO 14912:2003(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. Each 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 part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. 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.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 14912 was prepared by Technical Committee ISO/TC 158, Analysis of gases.
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ISO 14912:2003(E)
Introduction
The objective of gas analysis is to determine the composition of gas mixtures. Gas mixture composition is
expressed qualitatively in terms of specified mixture components of interest, called analytes, and the
complementary gas. Gas mixture composition is expressed quantitatively by specifying the amount of every
analyte in the mixture and the composition of the complementary gas.
For the purpose of specifying the amount of an analyte in a gas mixture, different quantities are in use. This
diversity is due to the fact that in different applications different quantities have decisive advantages.
Therefore procedures for conversion between different quantities are required.
In cases where these quantities involve the volumes of the analytes or the gas mixture or both, they depend
on the state conditions, i.e. pressure and temperature, of the gas mixture. For each of these quantities,
procedures for conversion between different state conditions are required.
As a crude approximation, all of the conversions referred to above can be performed on the basis of the Ideal
Gas Law. In most cases, however, an accurate conversion has to take into account the real gas volumetric
behaviour of the analyte and of the gas mixture. In particular, many conversions require values of the
compression factor (or of the density) of the gas mixture.
This International Standard provides formally exact conversion procedures, based on fundamental principles,
which fully account for real gas behaviour of pure gases and gas mixtures. In addition to these, approximate
procedures for practical applications are described, designed for different levels of accuracy and available
data. These approximations are necessary because measured gas mixture compression factors (or densities)
are rarely available and therefore have to be estimated from component data. Uncertainty estimates are given
which result from combining approximations in the conversion procedures with the uncertainties of the input
data. Where conversions require real-gas volumetric data of pure gases or gas mixtures, these are expressed
by compression factors. As equivalents, density data could be converted into compression factor data.
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INTERNATIONAL STANDARD ISO 14912:2003(E)

Gas analysis — Conversion of gas mixture composition data
1 Scope
This International Standard defines the following quantities commonly used to express the composition of gas
mixtures:
 mole fraction,
 mass fraction,
 volume fraction,
and
 mole concentration,
 mass concentration,
 volume concentration.
For these quantities of composition, this International Standard provides methods for
 conversion between different quantities, and
 conversion between different state conditions.
Conversion between different quantities means calculating the numerical value of an analyte content in terms
of one of the quantities listed above from the numerical value of the same analyte content, at the same
pressure and temperature of the gas mixture, given in terms of another of these quantities. Conversion
between different state conditions means calculating the numerical value of an analyte content, in terms of
one of the quantities listed above, under one set of state conditions from the numerical value of the same
quantity under another set of state conditions, i.e. pressure and temperature, of the gas mixture. Gas mixture
composition can be converted simultaneously between different quantities of composition and different state
conditions by combination of the two types of conversion.
This International Standard is applicable only to homogeneous and stable gas mixtures. Therefore any state
conditions (pressure and temperature) considered need to be well outside the condensation region of the gas
mixture and that of each of the specified analytes (see Annex A).
2 Terms and definitions
For the purpose of this document, the following terms and definitions apply.
NOTE See also References [1] and [2] in the Bibliography.
2.1 Quantities for the expression of gas mixture composition
NOTE Further information concerning the terms defined in this subclause is given in 4.1.
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ISO 14912:2003(E)
2.1.1
mole fraction
amount-of-substance fraction
x
quotient of the amount of substance of a specified component and the sum of the amounts of substance of all
components of a gas mixture
NOTE The mole fraction is independent of the pressure and the temperature of the gas mixture.
2.1.2
mass fraction
w
quotient of the mass of a specified component and the sum of the masses of all components of a gas mixture
NOTE The mass fraction is independent of the pressure and the temperature of the gas mixture.
2.1.3
volume fraction
φ
quotient of the volume of a specified component and the sum of the volumes of all components of a gas
mixture before mixing, all volumes referring to the pressure and the temperature of the gas mixture
NOTE The volume fraction is not independent of the pressure and the temperature of the gas mixture. Therefore the
pressure and the temperature have to be specified.
2.1.4
mole concentration
amount-of-substance concentration
c
quotient of the amount of substance of a specified component and the volume of a gas mixture
NOTE The mole concentration is not independent of the pressure and the temperature of the gas mixture. Therefore
the pressure and the temperature have to be specified.
2.1.5
mass concentration
β
quotient of the mass of a specified component and the volume of a gas mixture
NOTE The mass concentration is not independent of the pressure and the temperature of the gas mixture. Therefore
the pressure and the temperature have to be specified.
2.1.6
volume concentration
σ
quotient of the volume of a specified component before mixing and the volume of a gas mixture, both volumes
referring to the same pressure and the same temperature
NOTE 1 The volume concentration is not independent of the pressure and the temperature of the gas mixture.
Therefore the pressure and the temperature have to be specified.
NOTE 2 The volume fraction (2.1.3) and volume concentration (2.1.6) take the same value if, at the same state
conditions, the sum of the component volumes before mixing and the volume of the mixture are equal. However, because
the mixing of two or more gases at the same state conditions is usually accompanied by a slight contraction or, less
frequently, a slight expansion, this is not generally the case.
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ISO 14912:2003(E)
2.2 Additional quantities involved in conversions of gas mixture composition
2.2.1
compression factor
Z
quotient of the volume of an arbitrary amount of gas at specified pressure and temperature and the volume of
the same amount of gas, at the same state conditions, as calculated from the ideal gas law
NOTE 1 This definition is applicable to pure gases and to gas mixtures, therefore the term “gas” is used as a general
term which covers pure gases as well as gas mixtures.
NOTE 2 By definition, the compression factor of an ideal gas is 1. At room temperature and atmospheric pressure, for
many gases the compression factor differs only moderately from 1.
2.2.2
mixing factor
f
quotient of the volume of an arbitrary amount of a gas mixture at specified pressure and temperature and the
sum of the volumes of all mixture components, before mixing, at the same state conditions
NOTE If the component volumes are strictly additive, i.e. if the sum of the component volumes before mixing is the
same as the volume after mixing, the mixing factor is 1. At room temperature and atmospheric pressure, for many gas
mixtures the mixing factor differs only slightly from 1.
2.2.3
density
ρ
quotient of the mass of an arbitrary amount of gas and its volume at specified pressure and temperature
NOTE This definition is applicable to pure gases and to gas mixtures, therefore the term “gas” is used as a general
term which covers pure gases as well as gas mixtures.
2.2.4
molar volume
V
mol
quotient of the volume of an arbitrary amount of gas at specified pressure and temperature and its amount of
substance
NOTE 1 This definition is applicable to pure gases and to gas mixtures, therefore the term “gas” is used as a general
term which covers pure gases as well as gas mixtures.
NOTE 2 The amount of substance of a mixture is given by the sum of the amounts of substance of the components.
2.2.5
virial coefficients
coefficients in the expansion of the compression factor in terms of powers of a quantity of state
NOTE In practice, only two virial expansions are used, where the quantity of state is either the pressure, p, or the
inverse molar volume, 1/V , as follows.
mol
BT() C()T
ZV ,1T =+ + + . (1)
()
mol
2
V
V
mol
mol
2
Zp,T =+1 B′′T p+C T p + . (2)
() () ()
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ISO 14912:2003(E)
2.2.5.1
second molar-volume virial coefficient
B
coefficient of 1/V in the expansion of the compression factor in terms of inverse powers of the molar
mol
volume, V
mol
2.2.5.2
third molar-volume virial coefficient
C
2
coefficient of 1/V in the expansion of the compression factor in terms of inverse powers of the molar
mol
volume, V
mol
2.2.5.3
second pressure virial coefficient
B′
coefficient of p in the expansion of the compression factor in terms of powers of the pressure p
2.2.5.4
third pressure virial coefficient
C′
2
coefficient of p in the expansion of the compression factor in terms of powers of the pressure p
3 Symbols and units
Symbol Quantity SI unit
3
abbreviation of p/(RT)
α
mol/m
3
B second molar-volume virial coefficient
m /mol
B′ second pressure virial coefficient 1/Pa
3
mass concentration
β kg/m
3
c mole concentration
mol/m
6 2
C third molar-volume virial coefficient
m /mol
2
C′ third pressure virial coefficient
1/Pa
D dilution factor 1
f mixing factor 1
volume fraction 1
φ
i
gas mixture components (i = 1, 2, …, N) —
j, k gas mixture components (from 1 to N) —
(where needed in addition to symbol i)
m mass kg
M molar mass kg/mol
n amount of substance mol
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ISO 14912:2003(E)
Symbol Quantity SI unit
N
number of gas mixture components —
p pressure Pa
p saturation vapour pressure Pa
vap
p dew pressure Pa
dew
R molar gas constant (8,314 510)
J/(mol⋅K)
3
density
ρ kg/m
S
(sample of) gas mixture —
3 3
volume concentration
σ m /m
t Celsius temperature °C
T thermodynamic temperature K
3
V volume
m
3
V molar volume
m /mol
mol
w mass fraction 1
W weight (of a gas cylinder) kg
x mole fraction 1
X reference value of state conditions (X = p, T) same as for X
ref
X critical component property (X = p, T, V, Z) same as for X
crit
X pseudo-critical mixture property (X = p, T) same as for X
pscrit
Z compression factor 1

In addition to the symbols specified above, the following symbols are used to denote objects of generic
mathematical expressions.
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ISO 14912:2003(E)
Symbol Quantity
F mathematical function expressing a conversion
I input quantity of composition
O output quantity of composition
Ω conversion factor
K,L,P,Q,Y general variables or quantities
∂F/∂P partial derivative (sensitivity coefficient)
r(P,Q) correlation coefficient of quantities P,Q
R correlation matrix
u(P) standard uncertainty of quantity P
2
u (P) variance of quantity P
u(P,Q) covariance of quantities P,Q
U variance/covariance matrix
v(P) relative standard uncertainty of quantity P
4 Basic principles
4.1 Expression of gas mixture composition
The generic term for the amount of a component in a mixture is “content”. This term is intended for use only in
a purely descriptive or qualitative sense, and is, without further qualification, inappropriate and insufficient to
express quantitatively the amount of a component.
Quantitative statements require the expression of content as a value (the product of a number and a unit) of a
“quantity of composition”.
For present purposes, six quantities of composition, subdivided into two distinct conceptual families, called
fractions and concentrations, are defined in 2.1. The terms “fraction” and “concentration” are themselves
incomplete, and cannot be used in quantitative statements of content without qualification by one of the
modifiers “mole”, “mass” or “volume”.
In quantitative expressions of gas mixture composition, the applicable quantity, for example the mole fraction
or the mass concentration, shall be used in conjunction with the name or the chemical symbol of the
component.
EXAMPLE 1 The hydrogen content in a hydrogen/nitrogen mixture, expressed by mole fraction, is x(H ) = 0,1.
2
EXAMPLE 2 The sulfur dioxide content in air at 101,325 kPa and 25 °C, expressed by mass concentration, is
3
β(SO ) = 1 mg/m .
2
Gas mixture composition may either relate to the preparation of gas mixtures or to the analysis of gas
mixtures. In the first case, the composition expresses the formulation of a prepared mixture. Here the
components are the parent gases that were mixed. These can be technically pure gases or specified gas
mixtures. In the second case, the composition expresses the results of analysis. Here the components are the
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ISO 14912:2003(E)
analytes (i.e. the distinct chemical substances determined quantitatively) and the matrix (i.e. the
complementary gas).
Fractions are often used in the expression of results of gas mixture preparation. If a gas mixture consists of N
components, 1, 2, ., N, and if the amounts of these components in the mixture are quantified by amount of
substance, n , n , ., n , the mole fraction x of any component i is given by
1 2 N i
n
i
x = (3)
i
n
k
∑
k
If the amounts of the mixture components are quantified by mass, m , m , ., m , the mass fraction w of any
1 2 N i
component i is given by
m
i
w = (4)
i
m
k
∑
k
If the amounts of the mixture components are quantified by volume, V , V , ., V , the volume fraction φ of
1 2 N i
any component i is given by
V
i
φ = (5)
i
V
k
∑
k
Concentrations are often used to express the results of mixture analysis. If the amount of a specified analyte,
i, found in the analysed sample is quantified by amount of substance, n , and if V is the sample volume at
i S
specified pressure and temperature, the mole concentration (amount-of-substance concentration) c is given
i
by
n
i
c = (6)
i
V
S
If the analyte amount is quantified by mass, m , the mass concentration β is given by
i i
m
i
β = (7)
i
V
S
If the analyte amount is quantified by volume, V , the volume concentration σ is given by
i i
V
i
σ = (8)
i
V
S
In all the above expressions, it has to be noted that the sample volume depends on pressure and
temperature. In the expression for the volume concentration, the analyte volume also depends on pressure
and temperature. For both volumes, the state conditions have to be the same.
The quantities of composition exhibit different behaviour concerning the dependence on pressure and
temperature, as follows:
 mole concentration and mass concentration depend strongly on state conditions,
 volume fraction and volume concentration depend weakly on state conditions,
 mole fraction and mass fraction are strictly independent of state conditions.
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ISO 14912:2003(E)
The quantities above are primarily intended for describing the composition of gas mixtures which are
homogeneous and stable. In a technical sense, they may also apply to both heterogeneous and unstable
mixtures but that is not their intended usage in this International Standard (see below).
Given the restriction to homogeneous gas mixtures, the main implication for this International Standard is that
the state conditions (pressure and temperature) shall be such that the mixture is completely gaseous. This
requirement applies to all the quantities. In addition,
a) the volume concentration is only applicable if the state conditions are such that the individual component
under consideration, before mixing, is completely gaseous, and
b) the volume fraction is only applicable if the state conditions are such that all components, before mixing,
are completely gaseous.
The expression “completely gaseous” means, for an individual component, that the pressure is well below the
saturation pressure at the given temperature or that the temperature is well above the critical temperature. For
a mixture, the equivalent condition is that the pressure is well below the dew pressure at the given
temperature or that the temperature is well above the cricondentherm. In other words, the state conditions are
to be well outside the relevant condensation regions. Methods for assessing whether, at specified state
conditions, gas mixtures and their components are completely gaseous are described in Annex A.
If the restriction to homogeneous and stable mixtures cannot be guaranteed, then the way forward is
inevitably complex. For instance, if the gas mixture is not stable at the relevant state conditions, i.e. if chemical
reactions between mixture components take place, then the composition depends upon time and shall be
described accordingly (either using time-averaged quantities or a functional dependence upon time).
Analogously, in the case of a heterogeneous gas mixture, either spatial distributions or spatial averages shall
be employed. Situations of this sort, however, are beyond the scope of this International Standard.
4.2 Conversion between different quantities
The conversion between different quantities of composition uses the basic relations between the following
quantities, which apply both to pure gases and to gas mixtures:
 amount of substance, n
 mass, m
 volume, V
The relation between amount of substance and mass is given by Equation (9)
m
n = (9)
M
where M is the molar mass of the gas or gas mixture.
The molar masses of pure gases are calculated from the molar masses of the elements (see 7.1.1). The molar
masses of gas mixtures are calculated from the composition and the molar masses of the components (see
7.2.1).
The relation between amount of substance and volume is given by Equation (10).
pV
n = (10)
ZRT
where
p is the pressure of the gas or gas mixture;
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ISO 14912:2003(E)
T is the temperature of the gas or gas mixture;
Z is the compression factor of the gas or gas mixture;
R is the molar gas constant.
Equation (10) is the general equation of state for real gases. The compression factors of pure gases can be
calculated approximately from tabulated virial coefficients (see 7.1.2). The compression factors of gas
mixtures can be calculated approximately from the composition and the virial coefficients of the components
(see 7.2.2).
The relation between mass and volume is given by Equation (11):
m = ρV (11)
where ρ is the density of the gas or gas mixture.
The three quantities M, Z and ρ can be related by combining Equations (9), (10) and (11) to give
Mp
ρZ = (12)
RT
Therefore, only two of these quantities are independent. In this International Standard, the conversion
between quantities of composition is based on known values of M and Z.
In addition to the equations above, conversions between fractions and concentrations require relations
between the amount of a gas mixture and the amounts of its components.
If a gas mixture sample S consists of N components, 1, 2, ., N, the amount of substance n of the gas mixture
S
sample is given by the sum of the amounts of substance of the components.
nn= (13)
Sk
∑
k
Analogously, the mass m of the gas mixture sample is given by the sum of the component masses.
S
mm= (14)
Sk
∑
k
While amounts of substance and masses of mixture components are strictly additive, for component volumes
additivity is only an approximation (though usually very good). The relation between the volume V of the gas
S
mixture sample and the component volumes at identical state conditions is as follows:
Vf= V (15)
SS ∑k
k
where f is the mixing factor of the gas mixture S.
S
In the majority of applications, the mixing factor can be taken as unity (see 7.2.3).
4.3 Conversion between different state conditions
If gas mixture composition is expressed in terms of quantities which depend on pressure and temperature,
reference conditions are necessary for comparison purposes. Therefore, procedures for converting any such
mixture composition from given state conditions to specified reference conditions are required. The basic
relation involved in these conversions is the relation between the volume V( p,T) of a sample of a gas or gas
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ISO 14912:2003(E)
mixture at given sta
...