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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…






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


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)


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

http://www.bipm.org/en/si/si_brochure/


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.


Reference

solutions

Density

Refractive

index

Xmglucose(n)

XmNaCl(r)

??? Mass fraction in:

Glucose

NaCl

II. Introduction

XmNaCl(n)

Xmglucose(r)


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


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


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


http://images.google.pt/imgres?imgurl=http://88.157.45.33/mtbrandao/products/g/R_APA-73035_g.jpg&imgrefurl=http://www.mtbrandao.com/detail.ud121?oid=77149&from_zone=destaques_laterais&UDSID=%C2%A7%C2%A7%C2%A7%C2%A72008092814443800678524304%C2%A7%C2%A7%C2%A7%C2%A7&usg=__S0b3MWIY5h4jzgG0gXDL8NCOvZ4=&h=180&w=162&sz=6&hl=pt-PT&start=2&um=1&tbnid=ypNWvMOQ7bmzBM:&tbnh=101&tbnw=91&prev=/images?q=ckt+100&hl=pt-PT&um=1


8 solutions

Xm from 3 cg/g to 40 cg/g (ref. table)


Glucose

Gravimetric preparation

4 solutions

Xm from 7 cg/g to 26 cg/g (sat.)

NaCl


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)


Wolf, A. V., Aqueous Solutions and Body

Fluids, Hoeber, 1966

Glucose

NaCl

𝑛 =1

𝑗 𝑛𝑖

𝑗𝑛𝑖=1 +C


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


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


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


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)


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


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…


The metrological compatibility of the measuring results of glucose Xm

obtained by the two different methodologies (refractometry and densitometry)

was well established...


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?



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?


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.

Andreia Furtado| DMET| 2013-09-24 21

Thank you!

Andreia Furtado

[email protected]

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