Page 1 of 22
Key Comparison CCQM-K73
Amount Content of H+ in Hydrochloric Acid (0.1 mol·kg-1)

Final Report: 26 October 2012

Kenneth W. Pratt1,2
Jose Luis Ortiz-Aparicio, Francisco Javier Matehuala-Sanchez, Monika Pawlina, Władysław
Kozłowski, Paulo P. Borges, Wiler B. da Silva Junior, Mónica B. Borinsky, Ana Hernandez-
Mabel Puelles, Nadia Hatamleh, Osvaldo Acosta, João Nunes, M. J. Guiomar Lito, M.
Filomena Camões, Eduarda Filipe, Euijin Hwang, Youngran Lim, Wu Bing, Wang Qian, Wei
Chao, Akiharu Hioki, Toshiaki Asakai, Michal Máriássy, Zuzana Hanková, Sergey Nagibin,
Olexandra Manska, Vladimir Gavrilkin

Abstract
This key comparison (KC), CCQM-K73, was performed to demonstrate the capability of the
participating National Metrology Institutes (NMIs) to measure the amount content of H+, νH+,
in an HCl solution with a nominal νH+ of 0.1 mol·kg
-1. A parallel Pilot Study, CCQM-P19.2,
was performed for NMIs that did not desire to participate in the KC. The comparison was a
joint activity of the Electrochemical Working Group (EAWG) and Inorganic Analysis
Working Group (IAWG) of the CCQM and was coordinated by NIST (USA) and CENAM
(México).

The method of determination of νH+ was left to the individual participant. All participants
used either coulometry or titrimetry with potentiometric determination of the endpoint.

The agreement of the results was not commensurate with the claimed uncertainties of the
subset of participants that claimed small uncertainties for this determination. A workshop on
technical issues relating to the CCQM-K73 measurements was conducted at the joint IAWG-
EAWG meeting at the Bureau International des Poids et Mesures (BIPM), Paris (Sèvres) in
April 2010. Several possible sources of bias were investigated, but none could explain the
observed dispersion among the participants’ results.

In the absence of a specific cause for the dispersion, the IAWG and EAWG decided to assign
a Key Comparison Reference Value, KCRV, and standard uncertainty of the KCRV, uKCRV,
based on the DerSimonian-Laird statistical estimator. The uKCRV is dominated by the
between-laboratory scatter of results in CCQM-K73. The uncertainty estimates from the
participants with the lowest reported uncertainties remain unsupported by this KC.

Metrology Area
Amount of Substance

Branches
Electrochemistry, Inorganic Analysis

Subject
Determination of the amount content of H+ in hydrochloric acid solutions.


1 Study Coordinator
2 Organizational affiliations of all authors listed in Table 1.

Page 2 of 22
Time schedule
Dispatch of the samples: 26 June 2009
Deadline for receipt of the report: 30 September 2009
Discussion of results: EAWG/IAWG Joint meeting, 4 November 2009
Draft A Report December 2009

All dates in this Report are 2009, unless noted otherwise.

Participants
The list of participants is given in Table 1 for CCQM-K73. VNIIFTRI originally registered
for CCQM-K73 but withdrew after it proved impossible to ship the samples to them. DFM
originally registered for CCQM-K73 and received samples, but withdrew owing to equipment
difficulties.


Table 1. Table of participants, Key Comparison CCQM-K73.

Acronym Participant (NMI) Country Analyst(s)
CENAM Centro Nacional de Metrología México
Jose Luis Ortiz-Aparicio,
Francisco Javier Matehuala-
Sanchez
DFM Dansk fundamental metrology Denmark Pia Tønnes Jakobsen
GUM Główny urząd miar Poland
Monika Pawlina, Władysław
Kozłowski
INMETRO
Instituto Nacional de Metrologia,
Normalização e Qualidade Industrial
Brazil
Paulo P. Borges, Wiler B. da
Silva Junior
INTI
Instituto Nacional de Tecnología
Industrial
Argentina
Mónica B. Borinsky-Ana
Hernandez-Mabel Puelles-Nadia
Hatamleh-Osvaldo Acosta
IPQ
IPQ/UMCA-LCM, Instituto Português da
Qualidade - Scientific and Applied
Metrology Unit
Portugal
M. João Nunes, M.J. Guiomar
Lito, M. Filomena Camões,
Eduarda Filipe
KRISS
Korea Research Institute of Standards and
Science
Korea Euijin Hwang, Youngran Lim
NIM
National Institute of Metrology of P. R.
China
China
Wu Bing; Wang Qian; Wei
Chao
NIST
National Institute of Standards and
Technology
USA Kenneth W. Pratt
NMIJ National Metrology Institute of Japan Japan Akiharu Hioki, Toshiaki Asakai
SMU Slovenský metrologický ústav
Slovak
Republic
Michal Máriássy, Zuzana
Hanková
UMTS
Ukrainian State Research and Production
Center of Standardization Metrology,
Certification, and Consumers’ Rights
Protection
Ukraine
Sergey Nagibin, Olexandra
Manska, Vladimir Gavrilkin
VNIIFTRI
All-Russian Scientific Institute for
Physical-Technical and Radiological
Measurements
Russia Viatcheslav Kutovoy

Page 3 of 22
Coordinating Laboratories

National Institute of Standards and Technology
Analytical Chemistry Division
Gaithersburg, MD 20899-8391
USA

Centro Nacional de Metrología
Carretera a los Cués, km 4,5
El Marqués, Querétaro, C.P. 76246
MÉXICO

Study Coordinator: Kenneth W. Pratt
(Telefax: +1 301 869 0413; e-mail: kenneth.pratt@nist.gov)

A copy of the Technical Protocol distributed to all participants is attached as an Appendix to
this Report.


Sample preparation and bottling
The CCQM-K73/P19.2 solution was prepared from concentrated reagent-grade hydrochloric
acid (Mallinckrodt AR3, Lot H611 T13A01) and high-purity deionized water. The water had
an indicated electrolytic conductivity of 18.2 MΩ·cm at delivery. A 150 mL portion of this
acid was added to ≈18 L H2O and the solution was mixed by agitating and subsequently by
bubbling house N2 (mass fraction of CO2 < 1 µmol·mol
-1) through the solution for > 1 h.
Preliminary titration of this solution yielded νH+ ≈ 0.9958 mol·kg
-1. To permit a larger
number of bottles to be filled, a 2 L additional portion of solution was prepared from ≈ 2 L
H2O and 17 mL of the same reagent grade hydrochloric acid. This second portion was added
to the original batch to yield the final batch. The composite solution was thoroughly mixed
by agitation and bubbling with house N2 for 2 h. This final batch (the “CCQM-K73
solution”) had a volume of ≈ 20 L, with a nominal νH+ of 0.1 mol·kg
-1.

Sixty-four 250 mL high-density polyethylene (HDPE) bottles were cleaned by rinsing three
times in water and soaking in water for 3 h or longer. This cycle was performed a total of
three times. The bottles then were rinsed a final three times with water and were dried at
50 °C to 70 °C in an oven. The clean, dry bottles were filled with the CCQM-K73 solution
and numbered/labeled consecutively in filling order on 23 June. The caps of the filled bottles
were hand-torqued and allowed to sit overnight. They were re-torqued the following morning
and re-weighed. All masses remained constant within 0.010 g. Heat-shrink seals were then
applied to the necks of the re-torqued bottles. The sealed bottles were labeled, weighed, and
bagged in transparent polyethylene (PE) bags. Then, the PE-bagged, labeled bottles were
sealed in aluminized polyethylene terephthalate (PET) bags, which were numbered and
labeled identically to the bottles. Finally, the PET-bagged bottles were weighed. The PET-
bagged bottles were delivered to the NIST Shipping Department on 26 June, and were
shipped to participants from 26 June through 1 July. The first (1) and last (64) bottles were
retained at NIST for verification of homogeneity of the CCQM-K73 solution.



3 Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the
experimental procedure. Such identification does not imply recommendation or endorsement by the National
Institute of Standards and Technology, nor does it imply that the materials or equipment identified are
necessarily the best available for the purpose.

Page 4 of 22
Solution homogeneity and stability
Coulometric titrations of samples from bottles 1 and 64 were performed to verify the
homogeneity of the CCQM-K73 solution with respect to the set of bottles. Coulometric
titrations of solution directly taken from the carboy were also performed immediately before
and following this bottling step. Results of these titrations are shown in Table 2.

The sample was not deaerated after the main titration [1] in the preliminary titrations.
However, as the preliminary titrations were performed from deaerated solution (see details of
preparation, above), the solution may be assumed to be largely free from dissolved CO2. This
assumption was verified by noting that the maximum slope of the titration curve in the final
titration was only about 8 % lower than the maximum slope of the titration curve in the initial
titration (both slopes normalized to 1 L, to account for the increase in volume on addition of
the sample).


Table 2. Measurements of Homogeneity and Stability at Coordinating Laboratory (25 °C).

Source Date of titration νH+/(mol·kg
-1)
carboy (before filling bottles) 22-Jun 0.100 922 9
carboy (before filling bottles) 22-Jun 0.100 922 2
carboy (before filling bottles) 23-Jun 0.100 923 9
carboy (before filling bottles) a 23-Jun 0.100 916 6
carboy (after filling bottles) 23-Jun 0.100 916 8
CCQM-K73 Bottle 64 24-Jun 0.100 918 3
CCQM-K73 Bottle 1 24-Jun 0.100 917 6
CCQM-K73 Bottle 64 24-Jun 0.100 913 7
CCQM-K73 Bottle 1 24-Jun 0.100 914 4
Mean 0.100 918 5
Standard Deviation (SD) 0.000 003 7
SD of Mean 0.000 001 2

aCarboy was vigorously swirled prior to this titration to assure homogeneity of contents.


The data in Table 2 provide an evaluation of homogeneity and stability of the CCQM-K73
solution to the precision of the coulometric method as implemented at the preparing
laboratory (NIST). The agreement between the preliminary titrations of Bottles 1 and 64
indicates that the CCQM-K73 solution as bottled was homogeneous. The ≈ 0.007 % decrease
noted in the preliminary titrations of the carboy solution (prior to bottling) in Table 2 likely
resulted from the incorporation of condensate water in the carboy neck into the bulk solution
at the time of mixing. The agreement between the results of the titrations of Bottles 1 and 64
and the results of the carboy titrations indicate that no significant change in νH+ resulted from
the bottling procedure. Finally, the agreement between all these preliminary titrations
(performed in June) and the NIST CCQM-K73 titrations (performed at the end of September)
indicate that any drift that occurred over the entire designated period [2] of the CCQM-K73
measurements was < 0.007 % (cf. the reported mass changes documented in Table 3).

Page 5 of 22
Although the lack of sample deaeration in the preliminary titrations compromises this
assessment of drift to some extent, the fact that the preliminary titrations were performed on
substantially deaerated solution reduced the component of uncertainty for dissolved CO2 from
ca. 0.011 % (calculated for non-deaerated solution in equilibrium with atmospheric CO2) to
≈ 0.005 % for these preliminary titrations.


Sample delivery
The sample bottles were shipped from NIST on 26 June through 1 July. Each participant
received two or three 0.25 L HDPE numbered bottles, packaged as described above,
according to the quantity requested.

Following the initial shipment, VNIIFTRI reported that delivery of the CCQM-K73 samples
required two special licenses, as Russian regulations classify hydrochloric acid (of any
concentration) a precursor for narcotics. VNIIFTRI was not able to obtain these licenses in
the required time frame and requested to withdraw from CCQM-K73 on 3 August.


Verification of mass stability of shipped bottles
Participants were requested to measure the mass of the PET-bagged bottles soon after receipt
(storing at least overnight to assure temperature equilibrium with the weighing laboratory).
These masses are listed in Table 3 as mbag, along with the weighing dates
4.

Immediately before performing the measurement of νH+, participants were requested to
measure the mass of the bottle outside the bags (removed from the external PET and internal
PE bags). These masses are listed in Table 3 as mbottle, along with the weighing dates.

Participants also reported the balance reading, mW; the ambient pressure, p, and temperature,
T, at the time of each weighing. If the relative change in mass using the submitted mbag or
mbottle differed by > 0.02 % from the initial pre-shipment masses, m0,bag and m0,bottle, the
coordinating laboratory independently calculated separate values of mbag and mbottle from the
participant-supplied values of mW, p, and T using the formula used to calculate m0,bag and
m0,bottle. The coordinating laboratory then contacted the participant to verify the weighing and
calculation for buoyancy.

The data in Table 3 demonstrate that except for one value of mbag reported by IPQ, the bagged
bottles remained constant in mass to within 0.015%, relative, between the initial sealing in the
aluminized PET bags on 25 June and the respective date of measurement. The values of
mbottle outside the bags also remained constant to within 0.013 %, relative, although a small
loss in mass was evident in almost all cases.

The relative changes in mbag and mbottle listed in Table 3 are referenced to m0,bag and m0,bottle,
respectively. If the relative changes are referenced instead to the mass of solution, the values
of Δmbag/m0,bag and Δmbottle/m0,bottle in Table 3 should be multiplied by 1.11 and 1.12, respectively.


4 Masses of the PET-bagged bottles for NIST in Table 3 were measured immediately prior to opening the PET
bags.

Page 6 of 22
Table 3. Mass Changes on Shipping: PET-Bagged Bottles and Sample Bottles.

Sample information
Data Pertaining to Bagged Bottle Data Pertaining to Bottle outside Bags
25-Jun
pre-ship
mass,
m0,bag/g
Weighing
Date at
NMI
mbag/g
(NMI)
Relative
change in
mass
Δmbag/m0,bag
24-Jun
pre-ship
mass,
m0,bottle/g
Weighing
Date for
mbottle
(NMI)
mbottle/g
(NMI)
Relative change
in mass
Δmbottle/m0,bottle NMI
Bottle
No.
CENAM
4 314.553 3-Aug 314.552 -0.0003% 300.944 1-Sep 300.926 -0.0060%
44 308.011 3-Aug 307.997 -0.0044% 294.485 1-Sep 294.456 -0.0097%
49 309.536 3-Aug 309.531 -0.0015% 296.170 1-Sep 296.152 -0.0059%
DFM
20 313.624 2-Jul 313.635 0.0034% 300.158 --- --- ---
31 311.777 2-Jul 311.783 0.0018% 298.196 --- --- ---
GUM
25 312.708 14-Jul 312.710 0.0005% 299.083 8-Sep 299.071 -0.0040%
39 309.474 14-Jul 309.460 -0.0045% 295.896 15-Sep 295.886 -0.0033%
60 312.755 14-Jul 312.760 0.0015% 298.170 16-Sep 298.155 -0.0050%
INMETRO
21 311.778 27-Jul 311.775 -0.0011% 298.598 6-Aug 298.583 -0.0052%
56 307.128 27-Jul 307.119 -0.0027% 293.662 6-Aug 293.631 -0.0107%
INTI
19 312.102 6-Jul 312.120 0.0059% 298.342 5-Aug 298.340 -0.0007%
42 309.613 6-Jul 309.620 0.0022% 296.300 --- --- ---
53 312.035 6-Jul 312.050 0.0049% 298.325 20-Aug 298.310 -0.0051%
IPQ
8 304.238 3-Jul 304.380 0.0468% 290.943 29-Jul 290.938 -0.0015%
36 309.285 3-Jul 309.250 -0.0113% 295.654 14-Aug 295.634 -0.0069%
45 309.393 3-Jul 309.340 -0.0171% 295.835 17-Aug 295.815 -0.0065%
KRISS
10 312.968 7-Jul 312.986 0.0059% 299.435 15-Sep 299.408 -0.0090%
33 310.722 7-Jul 310.740 0.0056% 296.987 29-Sep 296.949 -0.0127%
NIM
9 309.891 6-Jul 309.894 0.0008% 296.477 23-Sep 296.461 -0.0055%
40 307.165 6-Jul 307.172 0.0024% 293.480 23-Sep 293.470 -0.0035%
NIST
3 309.554 24-Sep 309.562 0.0025% 295.818 25-Sep 295.809 -0.0027%
28 312.398 24-Sep 312.406 0.0025% 299.184 24-Sep 299.174 -0.0033%
57 310.558 24-Sep 310.569 0.0034% 296.981 28-Sep 296.969 -0.0040%
NMIJ
7 312.014 30-Jun 312.015 0.0003% 298.317 11-Aug 298.308 -0.0029%
27 314.019 30-Jun 314.020 0.0003% 300.207 --- --- ---
52 308.259 30-Jun 308.264 0.0016% 294.547 --- --- ---
SMÚ
6 306.600 7-Jul 306.606 0.0019% 293.054 23-Sep 293.042 -0.0040%
59 306.273 7-Jul 306.277 0.0015% 292.457 23-Sep 292.446 -0.0038%
UMTS
14 309.970 21-Jul 309.954 -0.0050% 296.607 25-Aug 296.583 -0.0082%
62 310.056 21-Jul 310.042 -0.0044% 296.026 25-Aug 295.999 -0.0090%


Timetable of Measurements and Submission of Reports
The dates of receipt of the samples, the dates of measurements, and reporting dates are given
in Table 4.

Page 7 of 22
Table 4. Dates of Sample Receipt, Measurement Period, and Report Date.

NMI Study Sample Received Measurement Period Report Received
CENAM K73 20-Jul 1-6 Sep 30-Sep
DFM K73 1-Jul --- ---
GUM K73 14-Jul 8, 16 Sep 30-Sep
INMETRO K73 24-Jul 24 Aug-18 Sep 24-Sep
INTI K73 1-Jul 5, 19 Aug 7-Oct
IPQ K73 2-Jul 29 Jul-25 Aug 30-Sep
KRISS K73 29-Jun 28-30 Sep 1-Oct
NIM K73 6-Jul 2-17 Sep 27-Sep
NIST K73 25-Jun 24-28 Sep 1-Oct
NMIJ K73 29-Jun 12-13 Sep 30-Sep
SMU K73 30-Jun 23-25 Sep 29-Sep
UMTS K73 9-Jul 26-27 Sep 30-Sep
VNIIFTRI K73 --- --- ---


All CCQM-K73 reports were received by the deadline, excepting INTI, who requested (and
was granted) an extension within the allotted timeframe. The results were distributed to all
participants on 20 October.


Correspondence with Participants
Each participant was contacted as the weighing and reported results were received by the
coordinator. One participant also received specific correspondence from the coordinator prior
to the report deadline as noted below.

CENAM requested advice regarding the correct procedure to follow if analysis is performed
using more than one method. On being advised that the selection of method(s) and whether to
combine results is left solely to the participant, CENAM elected to submit the coulometric
result as their CCQM-K73 result and to submit the separate titrimetric result as an information
value. CENAM was also advised to recheck the weighings of their bottles and did so. The
results in Table 3 reflect the revised mass values.

In none of the above cases was any information released or implied in any correspondence
regarding the value of νH+ for the CCQM-K73 solution, prior to the release of the summary of
results to all participants on 20 October.


Results and Discussion
The results are summarized in Table 5 for CCQM-K73. In addition to the official results,
several participants also reported “information only” values for the CCQM-K73 solution
based on other determinations. The information only results are listed in Table 6 for
comparison with the official results.

Page 8 of 22
Table 5. Results of Key Comparison CCQM-K73 Sorted by Value.

NMI
Amount Content of H+
νH+/(mol·kg
-1) U/(mol·kg-1)
IPQ 0.100 143 0.000 092
UMTS 0.100 42 0.000 48
INTI 0.100 87 0.000 30
CENAM 0.100 894 0.000 013
KRISS 0.100 906 0.000 018
NIM 0.100 917 0.000 080
NIST 0.100 922 4 0.000 004 5
SMÚ 0.100 936 7 0.000 007 8
NMIJ 0.100 941 5 0.000 005 8
INMETRO 0.100 974 1 0.000 004 9
GUM 0.101 04 0.000 26


Table 6. Results of “Information Only” Values for CCQM-K73 Solution Sorted by Value.

NMI Measurand j
Amount Content
νj/(mol·kg
-1) Uj/(mol·kg
-1)
CENAM H+ 0.100 884 0.000 038
NIM Cl– 0.100 922 0.000 102
NIM H+ 0.101 070 0.000 114


The above-tabulated values are presented in graphical form in Figures 1a and 1b, with the
results sorted by value within the given study. The Key Comparison Reference Value
(KCRV), calculated as described below, is shown in Figure 1a as a reference. Figure 1b is
identical to Figure 1a except that the y-axis is expanded by a factor of 10 around the KCRV.

Page 9 of 22
Figure 1a. Results of Key Comparison CCQM-K73 and Submitted “Information-Only”
Values. Error Bars Correspond to Standard Uncertainties (k = 1).




Figure 1b. 10-Fold Expansion of Figure 1a around KCRV.

Page 10 of 22
Measurement Techniques
Table 7 lists the methods used by the participants. Participants are listed in alphabetical order
within each set of results.


Table 7. Participant Methods.

Set of
Results
NMI
Method (for titrimetry – reference
compound)
CRMa (for titrimetry), Comments
(coulometry)
K73
CENAM coulometry – vertical
GUM titrimetry (Trisb) SMÚ A0701509
INMETRO coulometry – vertical
INTI titrimetry (KHPc) NIST 84j
IPQ titrimetry Cl− (KCl) NIST 999b
KRISS coulometry – horizontal, 2 IC
NIM coulometry – horizontal, 2 IC
NIST coulometry – horizontal, 2 IC
NMIJ coulometry – horizontal, 2 IC
SMÚ coulometry – vertical
UMTS coulometry – agar membrane, 1 IC
Info
values
CENAM – H+ titrimetry (Tris) NIST 723d
NIM – Cl– coulometry Cl – horizontal, 2 IC Result uncorrected for Br
NIM – H+ titrimetry (Na2CO3) NIM GBW06101A

a Certified reference material
b Tris(hydroxymethyl)aminomethane
c Potassium hydrogen phthalate

For participants who used coulometry, Table 7 notes the configuration of the coulometric cell
and the number of intermediate compartments (IC) used. Coulometric cells use two general
configurations: vertical and horizontal [3]. Vertical cells have the counter-electrode half-cell
(anode for titrations of H+) situated vertically along the center axis of the sample half-cell
(cathode for titrations of H+). An intermediate compartment (IC) along this same axis
connects the two half-cells. To avoid losses of sample or titrant, the IC usually is filled with
solution withdrawn from the sample cell prior to sample introduction and returned during the
course of the main titration. Horizontal cells have the counter-electrode half-cell and the
sample half-cell situated parallel (side-by-side), with one or (generally) two ICs connecting
the two half-cells near their bottoms. In both configurations, any sample or titrant that
diffuses into the IC(s) is returned to the sample cell by emptying and filling the IC(s)
pneumatically (piston burette or gas pressure/vacuum).

All participants that used coulometry used a silver anode in the coulometric cell. Anode
geometries varied. A silver anode has the advantage that the pH of the anolyte (electrolyte in
the anode compartment) remains virtually constant during the electrolysis, owing to the
absence of H+ in the anodic half-reaction:

Ag + Cl− → AgCl(s) + e−.

Participants that used titrimetry generally used gravimetric delivery of the major fraction of
the titrant, with volumetric additions near the end point.

Page 11 of 22

IPQ performed an argentimetric titration of Cl− in the CCQM-K73 sample. No correction was
performed for Br−. The reported value of νH+ was obtained via the assumption of equality
between the reported νH+ and the amount content of total halide (result of the Ag
+ titration) in
the HCl sample.


Traceability of Titrimetric Results
Titrimetric methods are (in principle) primary ratio methods [4]. A titrimetric method
compares an amount of analyte to a standard of the same quantity. Therefore, each titrimetric
result must be traceable to a reference compound. For each participant that used titrimetry,
Table 7 notes the reference compound that was used and the specific certified reference
material (CRM) that served as the acidimetric standard. Two exceptions are noted. The IPQ
result was not traceable to an acidimetric standard, but rather to a KCl standard.

Each CRM noted in Table 7 (other than the pH CRM with no certified assay) was certified by
coulometry. The Tris CRMs were certified using HCl as the excess added substance in a
coulometric back-titration. Hence, the issues discussed below with respect to the CCQM-K73
coulometric results apply indirectly to those participants that used Tris as the reference CRM.
Although an existing KC is available for KHP [5], certain problems associated with the
coulometric determination of νH+ in the CCQM-K73 solution apply also in the case of KHP.
The NIM Na2CO3 CRM was certified by coulometry with electrogenerated H
+ [6] and does
not involve the coulometric standardization of HCl in its certification.


Statistical Evaluation of the Results
A Birge analysis [7] of the CCQM-K73 results was performed. The weighted mean of the
participants’ results,
)H(R
, for CCQM-K73 was calculated using Eq 1:

n
i
iiw
1
R )H()H(
. (1)

The wi are given by Eq 2, where u(xi) is the reported standard uncertainty for participant i:


n
i i
i
i
u
u
w
1
2
2
)]H([
1
)]H([
1
. (2)

The uncertainty of the weighted mean for CCQM-K73 determined by the external consistency
method,
)]H([ REu
, was calculated at each temperature using Eq 3:


1
)H()H(
)]H([ 1
2
R
RE
n
w
u
n
i
ii. (3)

In Eq 3, n is the number of participants, wi is the normalized weight for participant i, and
)H(i
is the reported result for participant i.

Page 12 of 22
The uncertainty of the weighted mean for CCQM- K73 determined by the internal
consistency method,
)]H([ Rmu
, was also calculated. The value for
)]H([ Rmu
is given by
Eq 4:


n
i iu
u
1
2
Rm
)]H([
1
1
)]H([
. (4)

The Birge ratio, R = uE/um, was then calculated at each temperature. The result including all
CCQM-K73 participants was R = 7.923. The Birge ratio including all CCQM-K73
participants except IPQ was 6.024. Each of these R values indicate that in each case
(including or excluding IPQ), the external (between-participant) uncertainty greatly dominates
over the claimed uncertainties of the participants. The value compares to R values between
1.6 and 3.6 for pH KCs [10-15], in which the claimed uncertainties were far more consistent
with the between-participant scatter.

The CCQM-K73 results were subsequently submitted for statistical evaluation by S. Ellison,
LGC. His analysis (slightly rephrased from [8]) is as follows.

The χ2 on all the CCQM-K73 participants came out over 600. This value is far too large.
Usually, the problem goes away after eliminating the obvious outliers (in this case, IPQ).
Omitting IPQ, the χ2 is still ≈300. To accept the hypothesis of mutual consistency, the χ2 would
have to be not greater than about 20.

Other explorations make it clear that this is not down to any one or two labs. IPQ aside, it is
mostly a matter of substantive disagreement among the labs with the smallest uncertainties.

With such marked disagreement among those labs, there is no real point in seeking a KCRV at
all, unless the differences turn out to be attributable to test material inhomogeneity. Otherwise,
the participants with large uncertainties can mostly take some comfort from it – they mostly
agree with each other and with the participants with small uncertainties. On this evidence, the
participants with large uncertainties have no additional work to do. The participants in the
middle, particularly those with the four smallest uncertainties, need to work to find out what is
going on. In other words, about half the data set are in disagreement and the other half mostly
have such large uncertainties that they all agree with everyone.

[Ellison’s] recommendation is not to put a KCRV on CCQM-K73, and it is even more difficult
to assign an uncertainty to the KCRV. If an uncertainty is assigned to the KCRV, it would be
large.

[Ellison’s] current favorite estimator for this kind of situation (an MM-estimate, which is
uncertainty-respecting, very robust, and uses a Birge-like scale expansion) comes in at
0.100 928 2 mol·kg-1 with a standard deviation of the mean of 0.000 005 8 mol·kg-1. The only
CCQM-K73 participants that are heavily downweighted in this calculation are IPQ and
INMETRO.

Even if the MM-estimate model is used, [Ellison is] still not at all sure what should be used for
the uncertainties of the degrees of equivalence.

Calculation of the KCRV and Its Uncertainty
Calculations of candidate KCRVs, x, and corresponding combined standard uncertainties of
the candidate KCRVs, uKCRV, were performed using two data sets: (1), the set of nine
CCQM-K73 results (excluding IPQ and UMTS), n = 9; and (2), the central set of seven

Page 13 of 22
coulometric results from CENAM through INMETRO (see Table 5, Figures 1a and 1b), n = 7.
The n = 9 set contains titrimetric results from two participants: INTI and GUM. The n = 7 set
includes only the coulometric results.

Calculations were performed for each data set using the following statistical estimators:
mean (unweighted), median, Graybill-Deal, and DerSimonian-Laird. The results are shown
in Table 8 for the n = 9 set and Table 9 for the n = 7 set.


Table 8. Statistical Estimators for CCQM-K73 Results. IPQ and UMTS Excluded (n = 9).

Estimator
Candidate
Value,
x/(mol·kg-1)
u(Value)/(mol·kg-1)
Mean 0.100 933 6 0.000 016 4
Median 0.100 922 4 0.000 011 8
Graybill-Deal 0.100 941 1 0.000 001 4
DerSimonian-Laird 0.100 929 6 0.000 010 8


Table 9. Statistical Estimators for CCQM-K73 Results. Coulometric Results Only,
Excluding UMTS (n = 7).

Estimator Value/(mol·kg-1) u(Value)/(mol·kg-1)
Mean 0.100 927 5 0.000 009 9
Median 0.100 922 4 0.000 011 2
Graybill-Deal 0.100 940 9 0.000 001 4
DerSimonian-Laird 0.100 929 2 0.000 010 9

The best estimator for the present data should consider the degree of confidence in the
reported uncertainties of the participants. The mean and median each neglect the reported
uncertainties in obtaining the final value. The Graybill-Deal estimator overestimates the
effect of results with low uncertainties and is inappropriate for the present set of data.

Preliminary results were presented to the April 2011 joint IAWG-EAWG meeting of the
CCQM. At this meeting, it was felt that the uncertainties reflect the differences in the
procedures, yet many of the reported uncertainty intervals do not overlap. Accordingly, it
was decided to use the DerSimonian-Laird estimator for the KCRV and uKCRV for
CCQM-K73.

Based on the above analysis, the Degrees of Equivalence, di, and uncertainties of the Degrees
of Equivalence, u(di), were calculated for each participant. Values of di were calculated using
Eq 5, where the KCRV is given by the DerSimonian-Laird mean, xDL, and xi is the reported
result of participant i:


DLxxd ii
. (5)

Page 14 of 22
For the nine participants for which the results were used in calculating the KCRV, the u(di)
were calculated using Eq 6, where ui is the standard uncertainty reported by participant i, λ is
the interlaboratory variation, and u(xDL) is the standard uncertainty of xDL:


DL
22 xuudu ii
. (6)

For the two participants (IPQ and UMTS) whose results were not used in calculating the
KCRV, the u(di) were calculated using Eq 7:


DL
22 xuudu ii
. (7)

Table 10 gives the xKCRV = xDL, xi, uKCRV, di, u(di); and the corresponding relative quantities,
di/xKCRV, u(di)/xKCRV, for CCQM-K73. The u(di) for CCQM-K73 have a minimum value,
equal to
DL
2 xu
= 0.000 024 mol·kg-1, that is set by the between-laboratory scatter of
results. This circumstance limits the utility of the results of this KC to support claimed
uncertainties that are smaller than this value.


Table 10. Key Comparison Reference Valuea for CCQM-K73, xKCRV; its Standard
Uncertainty, uKCRV; Degrees of Equivalence, di; Standard Uncertainties of the di, u(di); and
Relative Values of these Quantities Referred to xKCRV.

Participant
(NMI)
Value,
xi/(mol·kg
-1)
di/(mol·kg
-1) u(di)/(mol·kg
-1)
Relative value,
xi/xKCRV
di/xKCRV u(di)/xKCRV
KCRV 0.100 930 --- 0.000 011 1.000 00 --- 0.000 11
IPQ 0.100 143 -0.000 786 0.000 054 0.992 21 -0.007 79 0.000 54
UMTS 0.100 424 -0.000 506 0.000 240 0.994 99 -0.005 01 0.002 38
INTI 0.100 871 -0.000 059 0.000 153 0.999 41 -0.000 59 0.001 52
CENAM 0.100 894 -0.000 035 0.000 025 0.999 65 -0.000 35 0.000 25
KRISS 0.100 906 -0.000 024 0.000 026 0.999 77 -0.000 23 0.000 26
NIM 0.100 917 -0.000 012 0.000 047 0.999 88 -0.000 12 0.000 46
NIST 0.100 922 -0.000 007 0.000 025 0.999 93 -0.000 07 0.000 24
SMÚ 0.100 937 0.000 007 0.000 025 1.000 07 0.000 07 0.000 25
NMIJ 0.100 942 0.000 012 0.000 025 1.000 12 0.000 12 0.000 24
INMETRO 0.100 974 0.000 044 0.000 025 1.000 44 0.000 44 0.000 24
GUM 0.101 039 0.000 109 0.000 131 1.001 08 0.001 08 0.001 30

a First line of table presents xKCRV, uKCRV, and uKCRV/xKCRV.


The above-tabulated relative values are presented in graphical form in Figure 2, with the
results sorted in order of increasing xi/xKCRV.

Page 15 of 22
Figure 2. Relative Degrees of Equivalence, di/xKCRV, for CCQM-K73. Error Bars Denote
Expanded Uncertainty of di, U(di)/xKCRV, with k = 2.




Determination of Impurities
CENAM and NIM determined impurities in the CCQM-K73 solution. The reported
determinations, in terms of mass fraction of the given element, are listed in Table 11.
Inductively coupled plasma – mass spectrometry (ICP-MS) was used in all determinations.

Page 16 of 22
Table 11. Reported Impurities in CCQM-K73 Solution.

NMI Impurity i
Mass Fraction
Comments
wi/(µg·kg
-1) Ui/(µg·kg
-1)
CENAM
Na 27.3, 27.5, 14.08 1.0, 2.2, 0.79 wi and Ui values listed for bottles
4, 44, 49, in that order K 16.9, 22.2, 10.6 1.5, 1.0. 1.5
NIM Br 336 17
Agilent 7500CE, standard
addition


How Far the Light Shines
Key Comparison CCQM-K73 directly covers the dissemination of the direct measurement of
νH+ at those NMIs that provide this service to customers. The value of νH+ typically measured
in such instances is on the order of 0.1 mol·kg-1. However, standardization of strong acids via
the determination of the anion of the strong acid (e.g., νCl− by argentimetry in HCl solutions)
is not covered by CCQM-K73. In addition, the measurement of significantly smaller νH+
values (e.g., acid rain samples) is not covered, unless the larger uncertainties for the
measurement in dilute solutions are taken into account.

In addition to the direct dissemination of the measurement of νH+, CCQM-K73 also provides
information on two other major uses of standard HCl solutions at NMIs.

The first use is in the certification of those base CRMs in which an HCl solution with νH+ on
the order of 0.1 mol·kg-1 is used as the titrant (or as the excess added substance in a
coulometric back-titration) for the acidimetric certification of the CRM. In such cases,
CCQM-K73 informs only regarding the attainable uncertainty for the standardization of the
titrant (or the excess added substance), not as to the overall certification of the base CRM
itself. In most such cases, the uncertainty of the CRM titration (or coulometric back-titration)
significantly exceeds that of the standardization of the HCl.

The second use of standard HCl solutions at NMIs is in the determination of the standard
electrode potential, E°, for Ag|AgCl electrodes used in the primary measurement of pH [3,9].
For this application, the value of νH+ is usually fixed at 0.01 mol·kg
-1. The relevant
uncertainty for the disseminated pH measurement is given by the pH KC for the
corresponding buffer [10-15]. However, CCQM-K73 can inform as to the expected
uncertainty for the standardization of the HCl solution itself. The claimed uncertainty must
take into account any increase in the uncertainty associated either with the titration of a
solution with νH+ = 0.01 mol·kg
-1 or with the gravimetric dilution of a solution with
νH+ ≈ 0.1 mol·kg
-1 to νH+ = 0.01 mol·kg
-1.


Conclusion
Eleven NMIs participated in Key Comparison CCQM-K73, Amount Content of H+ in
Hydrochloric Acid. The agreement among participants with the lowest uncertainties was not
as good as would be expected, although agreement among participants with large reported
uncertainties was acceptable. Candidate values for the KCRV and uKCRV were calculated
using several statistical estimators.

In an effort to resolve the observed discrepancy in the results, a Coulometric Workshop was
conducted in April 2010 at the joint meeting of the EAWG and IAWG. Although several

Page 17 of 22
NMIs reported detailed investigations of possible sources of bias at that Workshop and in
subsequent work, no specific cause for the dispersion of results was evident.

A part of the excess variation originates from the change in mass of the bottles during
shipment. However, this source of uncertainty was evaluated by a controlled protocol of mass
checks of the bottles on receipt. The results of these mass checks indicate that the change in
mass associated with shipment (see Table 3) only accounts for a small fraction of the
observed excess variation of the results among those participants with the lowest reported
uncertainties.

In the absence of a specific cause for the dispersion, the IAWG and EAWG decided to assign
a KCRV and uKCRV based on the DerSimonian-Laird statistical estimator. The uncertainty
uKCRV is dominated by the between-laboratory scatter of results in CCQM-K73. Owing to the
high between-laboratory scatter, the claims of the participants with the lowest reported
uncertainties cannot be supported by this comparison.

Acknowledgment
The coordinating laboratory gratefully acknowledges the contributions of all participants and
of the members of the CCQM Working Groups on Inorganic Analysis and Electrochemical
Analysis for their valuable suggestions concerning the measurement protocol and the
evaluation process. The contributions of David Duewer (NIST), Hugo Gasca-Aragón (NIST
and CENAM), and Steve Ellison (LGC) in the statistical evaluation are also gratefully
acknowledged.

References
1. Pratt K W 1994 Anal. Chim. Acta 289, 125-134 and 135-142.
2. Technical Protocol for CCQM-K73 and CCQM-P19.2, distributed 29 June 2009.
3. Máriássy M, Pratt K W and Spitzer P 2009 Metrologia 46 199-213.
4. BIPM (1998) Proceedings of the 4th meeting of CCQM, Bureau International des Poids et
Mesures (BIPM); see also Taylor P, Kipphardt H and de Bièvre P 2001 Accred. Qual.
Assur. 6 103-106; Milton M J T and Marschal A 2001 Accred. Qual. Assur. 6 270-271.
5. Máriássy M et al 2006 Metrologia 43 08008.
6. Certificate for NIM CRM GBW06101A, Document GB 10735–200X (updates GB10735-
1989). See also Taylor J K and Smith S W 1959 J. Res. Natl Bur. Stand. (US) A 63 153-
159.
7. Birge R T 1932 Phys Rev. 40 207-227.
8. Ellison S, personal communication (email) to Pratt K W and Duewer D L, 23 October
2009. Used with permission.
9. Buck R P et al. 2002 Pure Appl. Chem. 74 2169-2200.
10. Final Report for Key Comparison CCQM-K9, 12 December 2001, available at
http://kcdb.bipm.org/AppendixB/appbresults/ccqm-k9/ccqm-k9_final_report.pdf
11. Final Report for Key Comparison CCQM-K17, available at
http://kcdb.bipm.org/AppendixB/appbresults/ccqm-k17/ccqm-k17_final_report.pdf
12. Final Report for Key Comparison CCQM-K18, available at
http://kcdb.bipm.org/AppendixB/appbresults/ccqm-k18/ccqm-k18_final_report.pdf
13. Final Report for Key Comparison CCQM-K19, available at
http://www.bipm.org/utils/common/pdf/final_reports/QM/K19/CCQM-K19.pdf

Page 18 of 22

14. Final Report for Key Comparison CCQM-K9.2, available at
http://kcdb.bipm.org/AppendixB/appbresults/ccqm-k9/ccqm-k9.2_final_report.pdf
15. Final Report for Key Comparison CCQM-K20, available at
http://www.bipm.org/utils/common/pdf/final_reports/QM/K20/CCQM-K20.pdf

Page 19 of 22
Appendix
Technical Protocol

CCQM-K73/CCQM-P19.2 Amount Content of H+ in Hydrochloric Acid



Introduction

Key Comparison CCQM-K73 and the parallel Pilot Study CCQM-P19.2 are being performed
to evaluate the degree of equivalence of national measurement procedures for the assay of
hydrochloric acid. The measurand is amount content of hydrogen ion, νH+. The nominal
value of νH+ is 0.1 mol·kg
-1.

The measurement procedure is left to the participant. Any method or combination of methods
is acceptable. It is anticipated that the majority of participants will use coulometry or
titrimetry.

Information on impurities, particularly bromide, is also of interest. This information will be
provided as an annex to the Key Comparison and Pilot Study results.


Time schedule

Dispatch of the samples: 30 June 2009
Deadline for receipt of the Data Reporting Form 30 September 2009
Draft A report distributed 1 November 2009
Discussion of results and Draft A report EAWG/IAWG joint meeting, Nov. 2009
Draft B report 1 March 2010
Approval of Draft B report EAWG/IAWG joint meeting, April 2010


Description of the sample and details of shipment

The HCl comparison solution is prepared from deionized water and reagent-grade
hydrochloric acid. This solution is bottled in separately-numbered, 250 mL high-density
polyethylene (HDPE) bottles. The cap of each bottle is sealed with a transparent, heat-shrink
plastic seal that extends to the neck of the bottle. Each bottle is sealed inside two bags: a
transparent, interior polyethylene bag and an exterior aluminized polyethylene terephthalate
(PET) bag. Each bottle and its exterior PET bag are labeled with the number of the bottle and
a description of the contents.

Each participant will receive two (three, if requested) separately-numbered bottles filled with
the comparison solution. The bottles will be shipped in a cardboard box or other container by
air courier. The coordinating laboratory will send the tracking number by email to the contact
person of the corresponding receiving laboratory. The contents will be marked “aqueous
solution” with value 1 USD per bottle. Please be attentive to possible customs delays, etc.
Shipment to all participants will be performed at the same time.

The Coordinating Laboratory will verify the homogeneity of the material before shipment and
will perform a stability check in the course of the comparison.

Page 20 of 22
Two spreadsheets are being distributed simultaneously with this Technical Protocol. The file
K73_P19.2_bottle_masses.xls is for reporting the masses of the bottles and related
information, for verification of integrity of the shipment. The second file,
K73_P19.2_Data_Reporting_Form.xls, is used to report the results of the measurements of
νH+ and measurements of impurities.


Actions at receipt of samples

1. Inspect the bagged bottles for visible damage or leakage.
2. Confirm the sample receipt (by e-mail), report any damage, and send the weighing
data for the bagged bottles to the Coordinating Laboratory using the worksheet
“(1) Bagged Bottles”. Please send this information as soon as it is available, to permit
timely reshipment of a new bottle if necessary.
3. Store the bottles at room temperature in their original PET bags. Refrigeration of the
bottles is not necessary.


Instructions for participants

1. Weigh each bagged bottle with a resolution of 0.01 g or less to verify its integrity
during shipping. Allow the bagged bottle to equilibrate in the weighing laboratory
overnight before performing the weighing. Report both the weighing result (balance
reading) and the bottle mass (corrected for air buoyancy) on the worksheet
“(1) Bagged Bottles”. Use an assumed aggregate density of 1000 kg·m-3 for the
bagged bottle in correcting for air buoyancy. Also report on this worksheet the
ambient atmospheric pressure and temperature at the time the bottle was weighed.
2. Store the bottles in their original exterior bags until you are ready to perform the
measurements of νH+.
3. When you are ready to start the measurements of νH+, open the exterior bag by cutting
it between or above the red lines on the outside the bag. These red lines correspond
approximately to the upper edge of the interior polyethylene bag.
4. Remove the bottle with its transparent, interior bag from the exterior bag. Verify that
no drops of liquid are present on the inside surface of the interior bag. If drops are
noted, leakage has occurred. In this case, please contact the Coordinating Laboratory
immediately to obtain a replacement bottle.
5. Remove the bottle from the interior bag.
6. Weigh the bottle, removed from the interior bag, including its label and heat-shrink
plastic seal. Repeat the procedure in Step 1 of this section for the bottle removed from
both bags. Record these data on the worksheet “(2) bottles” and send the data to the
Coordinating Laboratory. Use an assumed aggregate density of 1000 kg·m-3 for the
unbagged bottle.
7. Remove the heat-shrink plastic seal before opening the bottle. Make a small cut
(1 mm to 2 mm) in the top portion of the seal with a scissors or knife. Then, peel the
remaining seal off the bottle.
8. Please send the file K73_P19.2_bottle_masses.xls to the Coordinating Laboratory a
second time with the masses of the unbagged bottles entered in the second worksheet.
9. Perform the assay measurements of νH+ using your selected procedure. To the extent
possible, your selected procedure should conform with that which you use to
disseminate this measurement capability at your institute.

Page 21 of 22
Reporting

The Data Reporting Form should be sent to the Coordinating Laboratory before 30 September
2009, preferentially by e-mail. The Coordinating Laboratory will confirm the receipt of each
Data Reporting Form. If the confirmation does not arrive within 1 week, please contact the
Coordinating Laboratory to identify the problem.

The Data Reporting Form has three worksheets, Summary, H+ results, and Method+Example.
The requested data should be entered into the corresponding boxes on each sheet. Certain
items are automatically copied from one sheet to another. These items only have to be
entered once. If you cannot enter your data into the cells as supplied, please change the
format as necessary or submit the data in another form. A separate text report in place of the
description “Analytical method - detailed description” is equally acceptable.

Please be sure to indicate in the Summary sheet the comparison in which you are
participating, by entering an “X” in the applicable box of the Summary worksheet. This X
will automatically cause the corresponding comparison to be entered into the worksheets and
graph titles.

The uncertainty calculations should conform to the ISO document Guide to the Expression of
Uncertainty in Measurement, 1st ed., ISO, Geneva, Switzerland, 1995. Both Type A and
Type B components of uncertainty and a summary of how they are calculated must be
included. Use the coverage factor, k = 2, to calculate the expanded uncertainty of your result.


Information requested:
1. Report the results as amount content of H+, accompanied by a full uncertainty budget,
on the worksheet “H+ results”.
2. Give a detailed description of the measurement procedure. For coulometry, this
should include the following: description of the coulometric cell, volume of electrolyte
in the working chamber, endpoint evaluation procedure, and the equipment used.
3. Give the complete measurement equation in the designated space in the worksheet
“Method+Example”. Include in the space below the values of the input quantities
(raw data) for a representative measurement. The data should enable the Coordinating
Laboratory to recalculate of the result of that measurement.
4. In the worksheet “H+ results”, report all the individual results, not only the final mean
value.
5. Provide a complete uncertainty budget for your measurement. This uncertainty budget
must include instrumental sources of uncertainty (mass, time, voltage, volume, ...) as
well as chemical ones (endpoint estimation, CO2 interference, side-reactions, purity of
calibration standards, ...)
6. In order to facilitate comparisons of your measured masses (for assay measurements),
please also provide either (1) the air density used for each buoyancy correction, or (2)
the air temperature, humidity and pressure in your laboratory at the time of each mass
measurement.
7. Report the details of the procedure used (a separate text file can be used).
8. Information on impurities is welcome, especially for Br−, owing to the influence of
trace Br− on the standard potential of the Ag|AgCl electrode in pH metrology.

Page 22 of 22
Reference value

The reference value will be agreed upon on the joint meeting of the EAWG and IAWG in
November 2009.


Participation

Participation in CCQM-K73 is open to all institutes eligible for a key comparison in this field.
Participation in CCQM-P19.2 is additionally open to other designated laboratories. National
Metrology Institutes that desire to use the results of the present comparison to support Claims
of Measurement Capability (CMCs) should participate in CCQM-K73, not in CCQM-P19.2.


Coordinating Laboratory and contact person:

Kenneth W. Pratt
NIST (National Institute of Standards and Technology)
100 Bureau Dr., Stop 8391
Gaithersburg, MD 20899-8391
USA

Tel.: +1 301 975 4131
Telefax: +1 301 869 0413
Email: kenneth.pratt@nist.gov