Outline
Lecture 1:
• Some principles of chemical metrology
- the mole
- the proposed re-definition
• Gas metrology
- applications to ambient air and natural gas
Lecture 2:
• Gas metrology in the global environment
- climate change
Quantities used to measure composition
A quantity is intensive if it is the same for sub-samples as for the whole.
• fractions describe how much of the total
property of a sample is contributed by one of
its constituent substances;
• concentrations describe the ratio of one
extensive quantity of a single substance to the
total volume of the mixture; and
• contents describe the ratio of one extensive
quantity of a substance to the total mass of
the mixture.
• Molality describes the amount of solute
entities divided by the mass of the solvent.
Doing metrology with ratios
• The quantities used to express composition are ratios
• many are dimensionless (eg mol/mol)
• others (eg mol/kg) use conversion factors, such as relative molecular masses that are known with very good accuracy.
• Metrology with ratios has “pitfalls”, because the extensive quantity (or the unit) is often cancelled.
• the link with the SI is therefore obscured
• attention can be diverted from using “good metrological practice”
• Why bother with the mole?
• Why bother with amount of substance?
The concept “amount of substance”
Avogadro’s Law (1811)
“Equal volumes of ideal or perfect gases, at the same temperature and pressure, contain the same number of particles, or molecules.”
Law of Multiple Proportions– (Dalton 1803)
“when elements combine, they do so in a ratio of small whole numbers”
Boyle’s Law (1662)
“For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional”
Law of Definite Proportions (Proust 1806)
“a chemical compound always contains exactly the same proportion of elements by mass”
Stoichiometry (Lavoisier)
“the relationship between the amounts of substance that react together, and the products that are formed”
gramme-molecule - First used in English in the
Encyclopaedia Britannica (1893).
mole – First used in English in the translation of
Ostwald’s “Principles of Inorganic Chemistry” (1902).
Kilogrammolekuel and g-Molekuel used by Ostwald
and Nernst in their text books in 1893.
Abbreviation to Mol recorded by Nernst.
The gram-molecule
The gram-molecule in use “On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by
the Molecular Kinetic Theory of Heat” Einstein, 1905
• Van’t Hoff’s Law for the osmotic pressure P V = z R T
Where z gram-molecules is dissolved in a a volume V
Let z=n/N where
n suspended particles are present and
N signifies the actual number of molecules contained in a gram-molecule
• The Stokes-Sutherland-Einstein formula
D
RTaN A
6
The gram-molecule in use “On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by
the Molecular Kinetic Theory of Heat” Einstein, 1905
• Van’t Hoff’s Law for the osmotic pressure P V = z R T
Where z gram-molecules is dissolved in a a volume V
Let z=n/N where
n suspended particles are present and
N signifies the actual number of molecules contained in a gram-molecule
• The Stokes-Sutherland-Einstein formula
D
RTaN A
6
“A new determination of molecular dimensions” Einstein, 1906
• Calculate the change in viscosity when spheres of radius a are dissolved in a solvent of viscosity
The total volume of dissolved material per unit volume of solvent
)5.21(*
M
Na 3
3
4
Perrin (1909) “It has become customary to name as the gram-molecule of a substance, the mass of the substance which in the gaseous state occupies the same volume as 2 grams of hydrogen measured at the same temperature and pressure.
Avogadro's proposition is then equivalent to the following:
Any two gram-molecules contain the same number of molecules.
This invariable number N is a universal constant, which may appropriately be designated Avogadro's Constant."
J. B. Perrin, “Mouvement brownien et réalité moléculaire”,
Annales de chimie et de physiqe VIII 18, 5-114 (1909).
trans: F. Soddy “Brownian Movement and Molecular Reality”,
Taylor and Francis (London) 1910.
The gram-molecule defined
The “Mol” in use Stille (PTB) explained in 1955 that Mol was being used in two conceptually
different ways. • The ”chemical mass unit” for example
1 mol = 22.991 g of sodium, or
1 mol = 58.448 g of sodium chloride
• The ”number of moles” ( from Molzahl ) given by the equation:
l = n / L
• Stille advocated the use of the Molzahl as a dimensionless quantity rather than the use of the quantity Stoffmenge (literally “amount of substance”)
1 Mol is “the Stoffmenge that contains as many entities as Ar(O) g of atomic oxygen”.
Stille “Messen und Rechnen in der Physik” 1955
n = number of entities
L = {NA}
Amount of substance
Guggenheim
• ..”for special problems it may be advantageous to increase the number of fundamental quantities above the usual number. It can sometimes be useful in dimensional analysis to regard the number of atoms as having dimensions different from a pure number” – Guggenheim, E. A. 1942 Units and Dimensions
• Phil. Mag. 33 pp479-496.
• “This quantity was first named “Stoffmenge” in German and the English translation is amount of substance” – Guggenheim, E. A. 1961 The Mole and Related Quantities
• J Chem Ed 38 86-87.
The 1971 definition of the mole
– “The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogramme of carbon 12.
When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles”.
– 14th CGPM, 1971
McGlashan, Metrologia, 1995, 31, 447-455.
• resolved the confusion arising from the use of both
• g-mol and kg-mol
• 12C and 16O basis
• introduced dimensional analysis to chemistry.
The atomic mass scale
m(12C) mu m(X)
Ar(12C) Ar(X)
The N measured atomic masses are related by the N-1 ratios Ar(X)/Ar(Y).
So we fix the value of the Nth ratio Ar(12C).
Atomic masses and fundamental constants
atomic level
m(12C) me
Ar(e)/Ar(12C) mu
Ar(12C)
Mass Fixed value
the mole (present definition)
m(12C)
M(12C)
me mu
Mu
Ar(12C)
Ar(12C)
Fixed value
macroscopic
atomic level
Mass
10-3 kg mol-1
Ar(e)/Ar(12C)
the mole (present definition)
m(12C)
M(12C)
NA
me mu
Mu
Ar(12C)
Ar(12C)
NA
Fixed value
macroscopic
atomic level
Mass
Ar(e)/Ar(12C)
Why change the definition of the mole?
• There is very little initiative for any change from the communities of users of the mole. – there is momentum behind the proposal for a “new SI”
– which could include a fixed value for NA
A possible rationale for change
• The mole has been derived from the gramme-molecule
– the amount of substance of 12g of 12C.
– We know the exact mass of a mole (of 12C), but we do not know the exact number of entities NA has some uncertainty
Is this sufficient to motivate a change?
the mole (present definition)
m(12C)
M(12C)
NA
me mu
Mu
Ar(12C)
Ar(12C)
NA
Fixed value
macroscopic
atomic level
Mass
Ar(e)/Ar(12C)
the mole (new definition)
m(12C)
M(12C)
NA
me mu
Mu
NA
Fixed value
Fixing NA means that another quantity in this
system has to be determined experimentally.
Ar(12C)
Ar(12C)
macroscopic
atomic level
Mass
Ar(e)/Ar(12C)
• The proposed new definition would reverse the present definition
– specify the number of entities in one mole • equal to NA exactly.
– some uncertainty in the mass of one mole • one mole of carbon-12 = 12g +/- u(a2).
• The molar masses and the atomic masses will have the same (relative) uncertainties.
• A single entity will be an exact amount of substance.
• Both approaches will be the same in practice • to within +/- u(a2)
A new definition for the mole
Possible definition 201X ?
201X
– “The mole is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 14X 1023 when it is expressed in the unit mol -1.”
1971
– “The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogramme of carbon 12.
When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles”.
The debate about a new definition for the mole
• Many users are confused about the existing use of the mole.
• The mole has always been used in conceptually different, but equivalent ways
• Much of the discussion originates from authors who believe that one of these is correct to the exclusion of the others.
• Would a change in the definition put an end to this discussion?
n= m / Ar(X) Mu
l = n / {NA}
n= n / NA
“chemical mass unit” “number of moles” “amount of substance”
The Avogadro constant
Becker, Rep Prog Phys 2001
Invention of new physical methods: diffusion, Brownian
motion, oil drop
Improvement in X-ray wavelength measurements
Atomic weight and chemical purity problems with Silicon
U(MM) contributes 61% of the published uncertainty of the 2003 natural Si result
Summary
• The mole and the Avogadro constant • Emergence of ideas of stoichiometry and thermodynamic
ensemble (18th and 19th centuries)
• Accurate chemical measurement (21st century)
• The mole has been used in conceptually different ways
• chemical mass unit
• number of moles
• amount of substance
• At present, we know the mass of a mole (of 12C), but not the number of entities. – is there sufficient momentum behind proposals to change?
– where should u(a2) lie?
Using the mole
• There is no direct realisation of the mole • The definition does not tell us how to make measurements
with respect to “the number of entities in 12g of 12C”.
• So – how do we make measurement in mol? • “by use of the RMM” • by X-ray crystal diffraction of Silicon • .. other methods
• 1995 – formation of the CCQM • “Is a hierarchical measurement system for chemistry necessary? How do we make measurements expressed in mol?
Kaarls, Milton et al., Comptes Rendues de Physique, 2004, 5, 907.
– “A primary direct method can be used to make a measurement that is traceable to the SI without the use of an external reference of the same quantity (for example gravimetry or coulometry).”
The Grande Salle Metaphor
Primary method of measurement
A primary method of measurement is a method having the highest metrological properties, whose operation can be completely described and understood, for which a complete uncertainty statement can be written down in terms of SI units.
– A primary direct method: measures the value of an unknown without
reference to a standard of the same quantity.
– A primary ratio method: measures the value of a ratio of an unknown to a standard of the same quantity; its operation must be completely described by a measurement equation.
Milton and Quinn, Metrologia, 2001, 38, 289.
Practical implementation of primary methods
pure materials calibration
standards
real sample or
matrix reference
material
real samples
primary ratio methods
(e.g. IDMS)
‘secondary’ methods
SI system of units
primary direct methods
(e.g. gravimetry)
primary direct methods
(e.g. coulometry, FPD)
pure materials calibration
standards
real sample or
matrix reference
material
real samples
primary ratio methods
(e.g. IDMS)
‘secondary’ methods
SI system of units
primary direct methods
(e.g. gravimetry)
primary direct methods
(e.g. coulometry, FPD)
Brown and Milton, Chemical Science Reviews (2007).
Gas Metrology
Stable
Unstable
CO CO2 O2
propane
natural gas (CH4)
HCl NH3
ozone
formaldehyde
Partially stable
SO2 NO NO2
H2S VOCs
H2O
all of the above &
Gases
Stable
Unstable
CO CO2 O2
propane
natural gas (CH4)
HCl NH3
ozone
formaldehyde
Partially stable
SO2 NO NO2
H2S VOCs
H2O
Dynamic methods
Stable in cylinders
Stable in cylinders
at high concentration
Standards for gases
• Gases weigh more than you expect !
10 litre of nitrogen at 100 atmospheres 0.8 kg
adding 1% of carbon dioxide 20 g
in order to achieve an accuracy of
0.05% for the gas concentration
Target weighing uncertainty 10 mg
10 litre cylinder 10 kg
1 part in a million for gravimetry
• Is this really achievable ?
Milton et al , Metrologia, 2002, 39, 97-99.
Sources of uncertainty in gravimetry
• Accuracy of the weighing ++
• Purity of the gas +
• Buoyancy effects -
• Cylinder expansion effects --
• Uncertainty in the RMM. ---
j j
j
i
i
i
M
m
M
m
x
ISO 6142 – “Preparation of calibration gas mixtures – gravimetric method”
Milton et al , Metrologia, 2011 Metrologia 48 R1
Single step dilution of CO in N2
Smaller uncertainties can be achieved by a series of dilutions
Source of uncertainty in gravimetry
Analysis versus Gravimetric Reference Value
Standard deviation of residuals is 1mmol/mol (0.002% rel)- after
excluding two outliers
At 50,000 mmol/mol, the gravimetric values are very consistent
within their stated uncertainties.
-80
-60
-40
-20
0
20
40
60
BAM CENAM CSIRO IPQ KRISS LNE NIST NMIJ NPL
Resd
iual D
evia
tio
n (
um
ol/m
ol)
kk=2=2
CO in N2 at 50,000 mmol/mol
Milton et al , Metrologia, 2006, 43, L7-L10.
All laboratories send a standard to the pilot
laboratory
So what’s the problem ?
• Instrumental methods for analysing gases
• Optical. chemical, mass spectrometric…
• all highly sensitive to the species and concentration
• So, the range of possible calibration gases needed is extremely large …
• Organic and inorganic chemistry
have the same problem.
Hydrocarbons N2, CO2, He Calorific
Value X
Small errors in composition determination
can prove expensive…
Gross Calorific Value (STP) = 37.094 MJ m-3
If the measured concentration of hexane was
200ppm too high then:
Gross Calorific Value (STP) = 37.113 MJ m-3
S p e c ie s % m o l /m o l
M e th a n e 8 2 .8 1
N it ro g e n 5 .2 4 3
C O 2 5 .0 5 2
E th a n e 4 .0 2 5
P ro p a n e 1 .6 6 5
i -B u ta n e 0 .4 7 7 9
n -B u ta n e 0 .5 0 0 1
n e o -P e n ta n e 0 .0 4 2 3
i -P e n ta n e 0 .0 6 5 8
n -P e n ta n e 0 .0 6 5 2
H e x a n e 0 .0 5 3 7
Calorific value of natural gas
Correlation in measured data
Brown et al, J. Chromat. A, 1040 (2004) 215–225
Milton et al , Meas. Sci. Technol. 20 (2009) 025101
The data from analysis by gas chromatography has substantial correlation between components.
Analysis of 7 10-component standards on the same instrument.
• The normalisation constraint brings further information to the system. • Various minimisation methods can be used to solve the problem. • It’s a genuine “free lunch”.
The benefits of “normalisation”
qw
w
w
ii
x
xy
1
Species x i u (x i ) y i u(y i )
nitrogen 0.2083 0.0003 0.2126 0.0003
carbon dioxide 0.0504 0.0002 0.0514 0.0002
ethane 0.1018 0.0003 0.1039 0.0003
propane 0.0456 0.0001 0.0466 0.0002
iso-butane 0.3904 0.0003 0.3985 0.0002
n-butane 0.011 0.0001 0.0112 0.0001
neo-pentane 0.1572 0.0003 0.1604 0.0003
iso-pentane 0.1002 0.0012 0.1023 0.0012
n-pentane 0.2259 0.0015 0.2306 0.0015
n-hexane 0.3375 0.0002 0.3445 0.0001
methane 96.3401 0.0542 98.338 0.0021
Sum of all
components97.9684 100.00
Raw data Normalised data
qw
w
w
i
ii
i
i xuTx
xu
T
x
y
yu
1
2
22
2
2
2
)(1)(2
1)(
Summary - standard gases
• Standard gases available for selected species:
• Can do much better in special cases: • Ensemble values • Complete mixture methods
• But – that’s all for stable species.
Uncertainty of preparation <0.05%(relative)
Uncertainty of analysis ~0.5%
Precision of analysis 0.01%
CCQM GAWG (and RMO) Comparisons
CCQM-K1.a CO in N2 VSL 1998
C'MET.QM-K1.a VNIIM 2008
CCQM-K1.b CO2 in N2 VSL 1998
CCQM-K1.c NO in N2 VSL 1998
EURO.QM-K1.c VSL 2002
APMP.QM-K1.c KRISS 2005
CCQM-K1.d SO2 in N2 VSL 1998
APMP.QM-K1.d NMIJ 2005
CCQM-K3 CO, CO2, propane in N2 VSL 1998
APMP.QM-K3 KRISS 2000
EURO.QM-K3 VSL 2000
C'MET.QM-K3 VNIIM 2005
EURO.QM-S1 CEM
CCQM-K52 CO2 in air (360 - 400 µmol/mol) NMISA 2006
CCQM-K53 O2 in nitrogen- preparative capabilities KRISS 2006
APMP.QM-K53 KRISS 2011
CCQM-K101 O2 in nitrogen (10 µmol/mol) NIM
Extended core mixturesCCQM-K51 CO in nitrogen (5 µmol/mol) NMISA 2006
CCQM-P73 NO in nitrogen (50 µmol/mol) - Preparative BIPM 2006
CCQM-K76 Sulphur dioxide (100 µmol/mol) NIST 2010
C'MET.QM-K76 VNIIM 2011
Core mixtures
Global atmospheric monitoring
CCQM-P41 CO2 and CH4 at ambient levels NMi 2002
CCQM-K52 CO2 in air (360 - 400 µmol/mol) NMISA 2006
CCQM-K68 Nitrous oxide in air KRISS 2008
CCQM-K82 Methane in air BIPM
CCQM-K83 Halocarbons in air NIST
CCQM-K84 Carbon monoxide in air KRISS
CCQM-K90 Formaldehyde BIPM
CCQM-K94 DMS in nitrogen KRISS
Air quality and indoor air
BIPM.QM-K1 Ozone at ambient level BIPM 2006
CCQM-K26.a Reactive gases-ambient levels - NO in N2 NPL 2003
EURO.QM-K26.a NPL
CCQM-K26.b Reactive gases-ambient levels - SO2 in Air NPL 2003
CCQM-K10 BTX in N2 (low conc 10-30 ppb) NIST 2001
CCQM-P73 Nitogen monoxide in nitrogen - preparative BIPM 2006
EURO.QM-S3 30 VOCs in nitrogen NPL 2008
CCQM-K74 Nitrogen dioxide (10 µmol/mol) BIPM 2009
CCQM-K7 Benzene/toluene/xylene (BTX) in nitrogen NIST 1999
CCQM-K22 VOCs in nitrogen NMIJ 2003
CCQM-K1.e,f,g Natural gases (6-comp) (Types 1,2,3) VSL 1998
CCQM-K16.a Natural Gas (12-comp) (Type IV)) BAM/NMi 2001
EURO.QM-K16 VSL 2012
CCQM-K16.b Natural Gas (11-comp) (Type V)) BAM/NMi 2001
CCQM-K23.a Natural Gas (7-comp) Type 1 NMi 2004
CCQM-K23.b Natural Gas (7-comp) Type 2 NMi 2004
C'MET.QM-K16 VNIIM 2008
CCQM-K23.c Natural Gas (7-comp) Type 3 NMi 2004
CCQM-K54 n-Hexane in methane - Preparative NMi VSL 2006
CCQM-P87 7-component study - Preparative NPL 2006
CCQM-K65 Methyl and Ethyl-mercaptan in methane VNIIM 2008
CCQM-K66 Impurities in methane NMIJ 2009
CCQM-K77 Synthetic refinery gas VSL 2011
Energy gases
Emission gases
CCQM-K15 SF6, CFCs - emission levels KRISS 2003
CCQM-K41 H2S in Nitrogen NIST 2004
APMP.QM-K41 KRISS 2009
CCQM-K46 Ammonia in nitrogen NMi 2005
APMP.QM-K46 CERI 2011
CCQM-K71 Multi-component stack emission gases NMI-VSL 2008
Forensic
CCQM-K4 Ethanol in air NPL 1999
EURO.QM-K4 NPL 2000
APMP.QM-K4 NMIJ 2000
EURO.QM-K4.1 VSL 2009
APMP.QM-K4.1 NMIJ 2005
CCQM-K93 Ethanol in nitrogen - Preparative NPL 2012
Results of CCQM key comparisons of gases
1E-12
1E-11
1E-10
1E-09
1E-08
1E-07
1E-06
1E-05
1E-04
1E-03
1E-09 1E-08 1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01 1E+00
1992-2002
2003-2007
HorLne
HorLne/4
HorLne*4
HLF
Amount fraction
all natural gas species
-6%
-4%
-2%
0%
2%
4%
6%
100 1000 10000 100000 1000000
Amount fraction mmol/mol
Re
lati
ve
Do
E
K1(e-g) 18
K16 23
K23 21
Total 62
Natural Gas
CCQM – Gas Analysis Working Group - Key
Comparison Results
all "core" species
-6%
-4%
-2%
0%
2%
4%
6%
1 10 100 1000 10000 100000 1000000
Amount fraction mmol/mol
Re
lati
ve
Do
E
CO2
CO
SO2
C3H8
NO
SO2CO2
CO2
NO
CO2
CO
CO
CO
K1 (a-d) 10
K3 3
K52 1
Total 14
Core species
CCQM – Gas Analysis Working Group - Key
Comparison Results
0.5% between gridlines - offset applied to each set
1
Re
lati
ve
de
gre
e o
f e
qu
iva
len
ce
(D
oE
/x)
[%re
l]
NMI-VSL NPL NIST NMIJ KRISS NRCCRM VNIIM
Performance of 7 NMIs
in all “core” + natural gas (C3 and below) KCs
CCQM – Gas Analysis Working Group - Key
Comparison Results
Data compilation by Dave Duewer, CSTL, NIST.
Lecture 1 - Summary
Gases
Stable
Unstable
CO CO2 O2
propane
natural gas (CH4)
HCl NH3
ozone
formaldehyde
Partially stable
SO2 NO NO2
H2S VOCs
H2O
all of the above &
macroscopic
m(12C)
M(12C)
NA
me mu
Mu
NA
atomic level
Mass
A of S
Fixedvalue
Fixing NA would mean that another quantity in this system would have to be
determined experimentally. There are several possible
choices.
Ar(e)/Ar(12C)
Ar(12C)
Ar(12C)
Name Symbol Definition SI unit
Mass fraction w jii m/mw kg/kg
Volume fraction
jii V/V
m3/m
3
Amount fraction
x jii n/nx
mol/mol
Mass concentration
V/m ii
kg/m3
Volume concentration
V/Vii
m3/m
3
Amount concentration
c
V/nc ii
mol/m3
Molality
b
solvii m/nb
mol/kg
Volume content
m/Vii
m3/kg
Amount content
k
m/nk ii
mol/kg