“the mole and gas metrology” - società italiana di...

“The Mole and Gas Metrology”

Martin J.T. Milton

NPL, Teddington, UK

Friday 20th July 2012

Varenna

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)


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?


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.

The Grande Salle Metaphor

sample result

Salon d’Horlorge at the French Foreign Ministry.

– “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)


(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


(e.g. gravimetry)


(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.

Components of natural gas

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


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


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


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


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


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


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

Acknowledgements

The mole

• Dr Bernd Güttler (PTB)

• Prof Ian Mills

Gas Metrology

• The Gas Metrology and Trace Analysis Group at NPL – Andrew Brown, Paul Brewer, Richard Brown and others

• The CCQM - GAWG

The National Measurement System is the

UK’s national infrastructure of measurement

“the mole and gas metrology” - società italiana di...

Documents