DMET| 2013-09-24
METROLOGICAL COMPATIBILITY OF THE MEASURING RESULTS OF AQUEOUS SOLUTIONS MASS FRACTIONS BY DENSIMETRY AND REFRACTOMETRY
Joint IMEKO International TC8, TC23 and TC24 Symposium 2013
A. FURTADO, C. OLIVEIRA, O. PELLEGRINO, C. PEREIRA, C. MATEUS, A. QUEIRÓS, R. CONCEIÇÃO, E. FILIPE
Andreia Furtado| DMET| 2013-09-24
Basic principles governing quantities and units
Published by the BIPM
http://www.bipm.org/en/publications/guides/vim.html
No fundamental ≠ in the basic principles of measurement in several sciences:
physics, chemistry, medicine, biology, or engineering
An attempt has been made to meet conceptual needs of measurement in fields such as:
biochemistry, food science, forensic science, and molecular biology
VIM 3rd edition – International Vocabulary of Metrology (JCGM 200:2012)
I. Reviewing concepts…
Andreia Furtado| DMET| 2013-09-24
I. Reviewing concepts…
Measurand (VIM 2.3) - quantity intended to be measured (VIM 1.1)
property of a phenomenon, body, or substance, that can be
expressed as a number and a reference
measurement unit
measurement procedure
reference material
combination of such
May be generically divided into:
• base and derived
• ‘physical’, ‘chemical’, and ‘biological’
In chemistry - “analyte” sometimes used for ‘measurand’
however these terms do not refer to a quantity
Ex: length of a steel rod at 23 °C
Ex: one cannot measure glucose but can measure the glucose concentration -
"glucose" is the component and "concentration" is the measurable property
Andreia Furtado| DMET| 2013-09-24 4
I. Reviewing concepts…
Property of a set of measurement results for a specified measurand, such that the absolute value of the
difference of any pair of measured quantity values (yi, yj) from two different measurement results is
smaller than some chosen multiple (k) of the standard measurement uncertainty of that difference (uyi-yj)
For measurements results (yi, yj) completely uncorrelated:
the standard measurement uncertainty of their difference (uyi-yj) is equal to the root mean square sum of
their standard measurement uncertainties (uyi, uyj)
Metrological compatibility (of measurement results) (VIM 2.47)
Andreia Furtado| DMET| 2013-09-24
n – ratio of the speed of light in vacuum
(c0) by the speed of light in the
substance (c) *
II. Introduction
cn
C0
SI derived unit
1
http://www.bipm.org/en/si/si_brochure/
*According to ISO 80 000-7:2008(E) - Ligth
r - mass (m) per unit volume (V)*
*According to ISO 80 000-4:2006(E) - Mechanics
• Decimal multiples and submultiples of SI units: g/cm3 and g/dm3
• Non-SI units accepted for use with the SI: g/mL and g/L
SI derived unit
kg/m3
V
mr
Quantity of dimension one
or
dimensionless quantity
Andreia Furtado| DMET| 2013-09-24
Refractive
index
Juices, soft drinks
and other sugary
compounds
Mass fraction
in sugar
BRIX
SI – cg sucrose/g sol.
Grape must Potencial
Volume Fraction
in alcohol
% vol.
SI – cL ethanol/L sol.
II. Introduction
Mass fraction
in sugar
Density
Mass fraction
in salts Seawater
Salinity (‰)
SI - g salt/kg sol.
Andreia Furtado| DMET| 2013-09-24
Reference
solutions
Density
Refractive
index
Xmglucose(n)
XmNaCl(r)
??? Mass fraction in:
Glucose
NaCl
II. Introduction
XmNaCl(n)
Xmglucose(r)
Andreia Furtado| DMET| 2013-09-24
Measuring Principle
Snell-Descartes Law
1. cell with the sample
2. LED = 589,3 nm
3. refraction in solution
4. measurement of critical angle with CCD
5. n determination
III. Experimental Methodologies
Measuring Principle
Law of Harmonic Oscillation
1. U-tube with a sample
2. electromagnetic force
3. measurement of vibration period (t)
4. rdetermination
C
mV
rt 2
Andreia Furtado| DMET| 2013-09-24
Features RE 50, Mettler
Toledo DMA 5 000, Anton Paar
1. Sample
Volume 2 ml 10 ml
Time 20 min 20 min
2. Quantities
Measuring
interval
Refractive index Density
1,320 00 a 1,580 00 (0,000 a 3 000,000) kg/m3
Resolution 0,000 01 0,001 kg/m3
3. Temperature
Measuring
interval (15,00 a 40,00) ºC (0,000 a 90,000) ºC
Resolution 0,01 ºC 0,001 ºC
III. Experimental methodologies
Andreia Furtado| DMET| 2013-09-24
r-PTB, NIST, GUM and H&D Fitzgerald
Densimetry
n -NIST and LGC Standards
Refractometry
t-Laboratory of Temperature - IPQ
t-Laboratory of Temperature - IPQ
III. Experimental methodologies
Andreia Furtado| DMET| 2013-09-24
8 solutions
Xm from 3 cg/g to 40 cg/g (ref. table)
III. Experimental methodologies
Glucose
Gravimetric preparation
4 solutions
Xm from 7 cg/g to 26 cg/g (sat.)
NaCl
Andreia Furtado| DMET| 2013-09-24
Reference data (ni, Xm(ni))
Linear regression
Xm(n) = a0 + a1 1
𝑗 𝑛𝑖
𝑗𝑛𝑖=1 +C
n
Official Journal of the European
Communities, L 272 de 1990-10-3, 1
Xm(n)
III. Experimental methodologies
Wolf, A. V., Aqueous Solutions and Body
Fluids, Hoeber, 1966
Glucose
NaCl
𝑛 =1
𝑗 𝑛𝑖
𝑗𝑛𝑖=1 +C
Andreia Furtado| DMET| 2013-09-24
Xm(r)
r
Reference data
(ri, Xm(ri))
Linear regression
Xm(r) = b0 + b1 1
𝑛 𝜌𝑖
𝑛𝜌
𝑖=1+C
Circular of the National Bureau of
Standards, C440, 632, 1942
III. Experimental methodologies
Söhnel, O., and Novotny, P., Densities of
Aqueous Solutions of Inorganic
Substances, Elsevier, Amsterdam, 1985
Glucose
NaCl
𝜌 =1
𝑛 𝜌𝑖
𝑛𝜌
𝑖=1+C
Andreia Furtado| DMET| 2013-09-24
uXm(n)
u t
u interpolation
u cal (RE 50)
u CRMs
u resolution
u dispersion
u dispersion
u t
u n
Sources of Uncertainty of Xm
IV. Uncertainty budget
Uncertainties calculated according to
ISO/IEC Guide 98-3:2008 Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)
u r
uXm(r)
u cal (DMA 5 000)
u linear regression
u reference data
Andreia Furtado| DMET| 2013-09-24
Solution
Mass fraction (cg/g) of glucose at 20 ºC
Xm ± U (k = 2)
Refractometry Densimetry
1 3,16 ± 0,10 3,23 ± 0,10 0,07 0,51
2 5,73 ± 0,10 5,79 ± 0,10 0,06 0,41
3 10,50 ± 0,10 10,43 ± 0,10 0,07 0,52
4 11,64 ± 0,10 11,66 ± 0,10 0,02 0,19
5 19,56 ± 0,10 19,56 ± 0,10 0,00 0,01
6 26,80 ± 0,10 26,78 ± 0,10 0,02 0,19
7 34,66 ± 0,10 34,65 ± 0,10 0,01 0,06
8 40,36 ± 0,10 40,28 ± 0,10 0,08 0,55
V. Results
Compatible results (VIM 2.47)
1
𝑿𝒎(𝒏) − 𝑿𝒎(𝝆) ≤ 𝟐 ∙ 𝒖𝟐𝑿𝒎(𝒏) + 𝒖𝟐
𝑿𝒎(𝝆)
∆𝑋𝑚 = 𝑋𝑚(𝑛) − 𝑋𝑚(𝜌)
∆𝑋𝑚
2 ∙ 𝑢2𝑋𝑚(𝑛) + 𝑢2
𝑋𝑚(𝜌)
Andreia Furtado| DMET| 2013-09-24
Solution
Mass fraction (cg/g) of NaCl at 20 ºC
Xm ± U (k = 2)
Refractometry Densimetry
1 7,0 ± 0,3 7,02 ± 0,01 0,01 0,03
2 12,9 ± 0,6 12,75 ± 0,01 0,18 0,29
3 19,6 ± 0,9 19,76 ± 0,01 0,14 0,15
4 24,1 ± 1,1 26,10 ± 0,01 2,03 1,77
V. Results
Compatible results (VIM 2.47)
1
𝑿𝒎(𝒏) − 𝑿𝒎(𝝆) ≤ 𝟐 ∙ 𝒖𝟐𝑿𝒎(𝒏) + 𝒖𝟐
𝑿𝒎(𝝆)
∆𝑋𝑚 = 𝑋𝑚(𝑛) − 𝑋𝑚(𝜌)
∆𝑋𝑚
2 ∙ 𝑢2𝑋𝑚(𝑛) + 𝑢2
𝑋𝑚(𝜌)
Non compatible results
> 1
Andreia Furtado| DMET| 2013-09-24
Values of Xm glucose compatible
with the input quantities r e n in
the range of [3; 40] cg/g
VI. Conclusions and Remarks
Glucose NaCl
Values of Xm NaCl compatible with the
input quantities r e n in the range of
[7; 20] cg/g
But not in the range of [21; 26] cg/g
Alternative methodologies for
Xm glucose determination?
Alternative methodologies for Xm NaCl
determination in the range of [7; 20] cg/g?
Why? More tests need to be performed…
Andreia Furtado| DMET| 2013-09-24
The metrological compatibility of the measuring results of glucose Xm
obtained by the two different methodologies (refractometry and densitometry)
was well established...
VI. Conclusions and Remarks
Were used the conversion tables adopted by the manufacturers of the measuring
instruments
Further studies – use the latest tables ICUMSA - 1998 forrand 2000 for n
(International Commission for Uniform Methods of Sugar Analysis)
Will the results remain compatibles?
Andreia Furtado| DMET| 2013-09-24
VI. Conclusions and Remarks
The metrological compatibility of measuring results of NaCl Xm above 21 cg/g
need to be studied…
Due to its interest for the food science, health science, and oceanography…
Speed of sound measurements of the salty solutions could be an alternative
methodology?
Andreia Furtado| DMET| 2013-09-24
VII. References
[1] A.Furtado, O.Pellegrino, S.Alves, I.Spohr, E.Filipe, Determinação da fracção mássica de soluções
aquosas de glucose por refratometria e densimetria de tubo vibrante, “Livro de Resumos da
CONFMET2010, Medições na Ciência e na Tecnologia”, SPMET, SPQ e RELACRE, 2010.
[2] Circular of the National Bureau of Standards, C440, 632, 1942.
[3] “International vocabulary of metrology-Basic and general concepts and associated terms” JCGM
200: 2012 3rd edition (2008 version with minor corrections).
[4] ISO/IEC Guide 98-3:2008 Uncertainty of measurement - Part 3: Guide to the expression of
uncertainty in measurement (GUM:1995).
[5] ISO 80 000-4:2006(E) - Quantities and units -- Part 4: Mechanics.
[6] ISO 80 000-7:2008(E) - Quantities and units -- Part 7: Light.
[7] Official Journal of the European Communities, L 272 de 1990-10-3, 1.
[8] Söhnel, O., and Novotny, P., Densities of Aqueous Solutions of Inorganic Substances, Elsevier,
Amsterdam, 1985.
[9] Wolf, A. V., Aqueous Solutions and Body Fluids, Hoeber, 1966.