Analytica Chimica Acta 599 (2007) 256–263
Purity of potassium hydrogen phthalate, determination with precision
coulometric and volumetric titration–A comparison
Sebastian Recknagel ∗ , Martin Breitenbach, Joachim Pautz, Detlef Lück
Federal Institute for Materials Research and Testing (BAM), Division of Inorganic-Chemical Analysis, Reference Materials,
Richard-Willstaetter-Str. 11, D-12489 Berlin, Germany
Received 8 March 2007; received in revised form 5 July 2007; accepted 20 July 2007
Available online 2 August 2007
Abstract
The mass fraction of potassium hydrogen phthalate (KHP) from a specific batch was certified as an acidimetric standard. Two different analytical
methods on a metrological level were used to carry out certification analysis: precision constant current coulometric and volumetric titration with
NaOH. It could be shown that with a commercial automatic titration system in combination with a reliable software for the end-point detection
it is possible to produce equivalent results with the same accuracy in comparison to a definite method handled by a fundamental apparatus for
traceable precision coulometry. Prerequisite for titrations are that a high number of single measurement are applied which are calibrated with a
high precision certified reference material.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Potassium hydrogen phthalate; Precision constant current coulometry; Volumetric titration; Certified reference material
1. Introduction
Potassium hydrogen phthalate (KHP) is widely used both
as acidimetric standard for acid and base titration analysis and
as pH standard. Therefore, well characterised certified reference materials are necessary. Within a framework of BAM and
Sigma–Aldrich Production GmbH for certification of primary
substances for titration and standard anion solutions a batch
of 994 bottles of KHP was certified for its acidimetric purity
expressed as a mass fraction. It is intended to be used as an
acidimetric standard only.
For the certification of KHP as well as for all other substances
included in this certification program two independent analytical
methods are used for certification analysis. Traceability of these
measurements is ensured by using well characterised pure substances or certified reference materials for calibration in case
there is no absolute method like coulometry available. In the
case of KHP precision coulometry was used as primary direct
method [1–3] whose results are traceable to the SI-system.
∗
Corresponding author. Tel.: +49 30 8104 1111; fax: +49 30 8104 1117.
E-mail address: [email protected] (S. Recknagel).
0003-2670/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.aca.2007.07.062
KHP has been determined by precision coulometric acidimetric titration for about 50 years [4–7]. Since then the procedure was extensively automated [1,8–12]. The purity of KHP
was subject of CCQM-P36 and CCQM-K34/K34.1 where seven
metrology institutes compared their measurement capability to
determine the amount content of acid in solid weak acids. All
institutes used constant current coulometry. It was demonstrated
that the agreement of the results of all participants was good in
general [13]. On the other hand, this study showed again that
great care has to be taken during the sample preparation step
especially if some impurities remain undetected and the purity
of high purity materials is determined by the difference to 100%.
Although there has been a lot of work carried out on KHPdetermination using precision coulometry, it is still an extremely
extensive method not suitable for high sample throughput.
A fundamental apparatus for coulometry is commercially
not available. Therefore, individual experimental designs are
applied, which are only possible to build up if special know how
and knowledge of coulometry procedures and electrochemistry
techniques are available. Handling such a complex equipment
and performing precise measurements which are based on calibrated SI-quantities, e.g. mass, voltage, electrical resistance and
time, and knowledge to avoid chemical errors are only manageable by highly trained specialists.
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
To overcome these problems a special experimental design
should be developed to carry out certification analysis of a
large batch of a KHP-standard. Based on a commercially available automatic titration system in combination with a reliable
software for the end-point detection it should be possible to
produce equivalent results with the same accuracy in comparison to a definite method handled by a fundamental apparatus
for traceable precision coulometry. Felber et al. demonstrated
the capabilities of titrimetry under carefully controlled conditions for the complexometric determination of Cu2+ with
EDTA [14]. Brown et al. developed a high accuracy titrimetric
method for HCl-determination [15] and showed the equivalence
of the results of this method with coulometric acid–base titration
[16].
Prerequisite for high precision titrations are that a high number of single measurements are applied which are calibrated with
a high precision certified reference material.
In this paper the results of precision coulometric titration are
compared with those from precision volumetric titration used for
analysis and certification of a specific KHP reference material.
2. Experimental (I) precision coulometry
Coulometry is a primary direct method for measuring the
amount of substance. It is based on Faraday’s law of electrochemical equivalence. The amount content of substance in a
solution is proportional to electricity, which flows between the
generating electrodes. The basic requirement of a coulometric
257
titration [17,18] is practically 100% current efficiency of the
titrant generation.
The high precision of results is based on:
(a) a very precise weighing combined with high sample intake
(m);
(b) the possibility of very precise dosing of electricity;
(c) the exact determination of the electricity by precise measurement of the physical quantities: electrical resistance (R),
voltage (U) and time (t).
Therefore, traceability of results to quantities of SI (système
international d’unités) units is given.
2.1. Apparatus
The determinations performed in this study were carried out
using the apparatus given in Fig. 1. Measuring cell: Vertical
arrangement, cathodic compartment and anodic compartment
were separated by an intermediate compartment (all made of
boron glass), arranged between two glass frits. The glass frit
near the cathodic compartment was blocked with a pH-neutral
agar–agar gel plug. Generating cathode: Pt-wire (2 cm2 ); generating anode: Ag-rod (16 cm2 ); indicating electrode: pH-glass
electrode with fixed ground-joint diaphragm and Ag/AgCl reference system (6.0253.100, Metrohm, Herisau, Switzerland;
reference electrolyte: KCl gel (c(KCl) = 3 mol L−1 ); membrane
resistance: 80–200 M).
Fig. 1. Precision constant current coulometry system (principal sketch). Measuring cell for acid/base titrations, valve manifold and associated pneumatic connections:
) flow resistor, (IC) internal compartment. (1) Pt generating anode, (2) Pt generating cathode, (3) PTFE spray shield, (4)
(×) valves, (DT) deaeration tubes, (
indicating glass electrode, (5) agar diaphragma, (6) internal compartment.
258
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
The precision coulometer used was an electrochemical computerised system (for details of the titration software see [1]). The
assembly consisted of a constant current source model 8011A,
an indication unit 7011A, a valve unit 9018A (all Applied Precision Ltd., Bratislava, Slovakia), a piston burette type 765
Dosimat (Metrohm). For measurement we used four calibrated
devices: An analytical microbalance MC 5, resolution 1 ␮g with
an uncertainty uMC5 of the balance of uMC5 = 50 ppm (Sartorius
AG, Göttingen, Germany), a timer with an average relative frequency error and expanded uncertainty of measurement (k = 2)
of δf = (9.12 ± 0.08) × 10−7 (Applied Precision Ltd.) to control
the electrolysis time with a precision of 0.1 ppm (±1 ␮s). The
current was determined measuring the voltage drop on a resistor using a 6½-digit-multimeter DMM 2000 with 0.02 ppm per
90-day basis accuracy (Keithley Instruments, Inc., Cleveland,
Ohio, USA) and a certified 1 resistor type 742A (Fluke GmbH,
Kassel, Germany) with a minimum uncertainty of 2.5 ppm per 6
months (temperature coefficient: 0.1 ppm K−1 , calibrated value:
1.00000 ± 0.000017 , traceability chain: Fluke 742A – HP
3458A).
This system controlled the generator current, switched on/off
the titration time, registered the pH value versus time and rinsed
the intermediate compartment of the cell automatically.
solution using a small silica weighing cup. For the mass value
evaluation the air buoyancy correction of the weighing values
was performed, taking into account a model equation for the air
density which is based on measured values for the air temperature, air pressure and the relative air humidity assuming standard
air composition.
The coulometric titration consisted of three steps: the initial titration, the main titration and the final titration. Different
constant currents were used.
The purity p was calculated according to Faraday’s law from
the ratio of the experimental coulometric charge (Qtot ) and the
theoretically expected charge (zFm/M) using Eq. (1).
p=
MQtot
zFm
(1)
The amount content v in mol kg−1 was calculated applying
Eq. (2):
v(KHC8 H4 O4 ) =
U1 (t1∗ − t1∗∗ − tcorr ) + U2 t2 + U3 t3
zFmR
The mass fraction w in % was calculated using Eq. (3):
w(KHC8 H4 O4 ) =
2.2. Procedure
Potassium hydrogen phthalate reference material, KHP lot
no. 1291630 (Sigma–Aldrich product-no: 60357 [19]) was dried
at 110 ◦ C for 4 h and allowed to cool in a desiccator over
P4 O10 before analysis. After first drying the loss was <0.01%
and after the repeated drying the maximum mass difference
was ± 0.001%. As supporting electrolyte a 1 mol L−1 KCl solution was used. The initial titration (2 mA; 2 s pulses) was carried
out using potentiometric end-point detection at pH ∼ 6.9. After
the initial titration the sample was introduced into the cell using
a silica crucible. During the main titration 99.9% of the stoichiometric amount of hydroxyl ions were generated with a generator
current of 200 mA. The final titration (10 mA; 3.5 s pulses) was
performed using potentiometric end-point detection at pH ∼8.2.
The calculation of the purity of KHP was done using Eq. (1).
Biases resulting from impurities from the purging gas argon,
from the electrolyte and from the agar gel were minimised using
99.9999% argon, neutralisation of the agar gel prior to each
determination with an indicator, the use of water with a conductivity of κ < 2 ␮S cm−1 and KCl (≥99.5%, Merck, Darmstadt,
Germany).
To avoid losses by diffusion and (electro-) migration of
hydrogen phthalate ion (HC8 H4 O4 − ) into the intermediate compartment (IC) during the main titration, the IC was filled with
supporting electrolyte which was forced slowly into the working
compartment during the main titration.
Biases due to spraying, rinsing of the intermediate compartment with measuring solution and losses by sample introduction
were minimised using the following experimental conditions:
Application of a spray shield: This spray shield and the intermediate compartment were repeatedly rinsed with measuring
solution during titration. The sample was introduced into the
(2)
100M[U1 (t1∗ − t1∗∗ − tcorr ) + U2 t2 + U3 t3 ]
zFmR
(3)
with
Quantity
Unit
p
v
w
Qtot
mol kg−1
%
C
M
g mol−1
U1
t1 *
t1 **
tcorr
U2
t2
U3
t3
z
V
s
s
s
V
s
V
s
–
F
m
R
A s mol−1
kg
*
Description
Purity
Amount of substance content
Mass fraction
Amount of electricity between the end-point of
initial titration and the end-point of final titration
[Q = It], [I = U/R]
Molar mass of KHC8 H4 O4 = 204.2212 g mol−1
[20]
Average voltage during initial titration
Total time of the initial titration
Time of the initial titration, up to the end-point
Correction of the initial titration time
Average voltage during main titration
Time of the main titration
Average voltage during final titration
Time of the final titration, up to the end-point
Product of number of transferred electrons and
current efficiency
Faraday constant: 96485.3399 A s mol−1 [21]
KHP mass, corrected for air buoyancy*
Resistance of measuring resistor
Sample density used for buoyancy correction: 1636 kg m−3 [22].
Calculation of the measurement uncertainty was carried out
according to the BAM-Guideline for the evaluation of measurement uncertainties for quantitative measurements [23] based
on the ISO Guide for the Expression of Uncertainty in Measurement [24]. It was done by quadratic addition of type A
and type B uncertainty contributions. Type A is the statistical part (standard deviation of the mean), type B is the
non-statistical part based primarily on the apparatus. For calcu-
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
lation of the expanded uncertainty the coverage factor k = 2 was
used.
Uncertainty contributions of type B were calculated using the
individual uncertainties of the parameters used in Eq. (3) (see
Table 2).
The uncertainty contributions from the instruments used for
measuring the physical values were at most 0.005%, therefore
chemical factors like contributions for electrolyte and inert gas
impurities, diffusion, and phthalate reduction which were in the
same order of magnitude had to be considered.
259
dioxide from the air. Before starting a titration the sample solution was flushed carefully with argon (only 2 bubbles per second
to avoid any splashing) for 5 min to expel any CO2 from the
solution.
3.2. Procedure
The second analytical method used for the characterisation of
the potassium hydrogen phthalate and for homogeneity testing
of the whole batch was a volumetric method, acid–base titration with potentiometric end-point detection. Calibration was
done using certified reference material NIST SRM 84k acidimetric primary standard. This CRM was characterised by the US
National Institute for Standards and Technology using coulometric titration which is a primary method since it is directly
traceable to the SI. The certified mass fraction of potassium
hydrogen phthalate investigated via volumetric titration in this
study therefore is traceable to NIST SRM 84k and not directly
to the SI. For homogeneity testing traceability is not important
because the total mass fraction of the material investigated is not
needed. To check for inhomogeneities an analytical method as
precise as possible has to be used. Normally it is impossible to
differentiate between variations resulting from inhomogeneities
of the sample and variations coming from the analytical method.
In most cases it is the sum of both. The spread of the method
could only be determined if a sample of ideal homogeneity
would be available. Since this ideal sample normally does not
exist, the spread of results observed is always the sum of inhomogeneity contributions from the sample material and spread of
the method. The higher the spread of the method is, the higher
is the estimated inhomogeneity contribution to the uncertainty
of the certified mass fraction. Weber et al. showed that volumetric titration with a titration equipment similar to that used for
this investigation is precise enough to be used for homogeneity
testing [25].
Acid–base titration with 0.05 mol L−1 NaOH solution was
performed to determine the mass content of potassium hydrogen
phthalate. 175 ± 1 mg of sample were weighed after the material
had been dried for 3 h at 120 ◦ C and then cooled in a desiccator
over Mg(ClO4 )2 . A correction of the initial weight for buoyancy
was not necessary because sample and reference had the same
density. The volume of the NaOH solution used was approximately 17.4 mL. This solution was prepared using NaOH pellets
(p.a. Merck, Darmstadt, Germany) which were precleaned with
water to remove Na2 CO3 from the surface of the pellets. Dissolution was carried out using Milli-Q water (κ < 2 ␮S cm−1 )
degassed first with argon and second with ultrasound. The solution was stored under argon atmosphere in a glass bottle endued
with a CO2 -absorber (NaOH fixed on a substrate in an absorber
tube).
Standard reference material NIST SRM 84k potassium
hydrogen phthalate (99.9911%) was used for calibration of the
apparatus.
Sigma–Aldrich Production GmbH (Buchs, Switzerland)
filled a total number of 994 glass bottles each with 50 g of batch
material. The sampling of 35 randomly chosen bottles for certification analyses, taken out of the entire batch, was done by
Sigma–Aldrich Production GmbH. These bottles were sent to
BAM to carry out certification analyses. Analyses were carried out following the analysis scheme given in Fig. 2. Seven
subsamples out of each bottle were analysed to determine the
mass fraction of potassium hydrogen phthalate and to assess the
degree of heterogeneity of the whole batch of 994 bottles. In
total 301 determinations were performed which – regarding to
expenditure of time – is only possible with this special titration
equipment but not with the coulometric method.
Each of the seven titration runs consisted of 43 titrations,
i.e. 35 samples and eight portions of certified reference material
NIST SRM 84k.
3.1. Apparatus
4. Results and discussion
Titrations were carried out using a modular automatic
titration system (Metrohm, Herisau, Switzerland) consisting of a sample changer 730, a dispensing unit Dosino
700 with a GPTitrino 736 titroprocessor and titration software Metrodata “TiNet©2.4”. For potentiometric end-point
detection a combined pH-glass electrode with ceramic
pin diaphragm and Ag/AgCl reference system (6.0253.100,
Metrohm, Herisau, Switzerland; reference electrolyte: KCl gel
(c(KCl) = 3 mol L−1 ); membrane resistance: 150–400 M) was
used. End-point detection was an integral part of the titration
software used. Calculation was done using the second derivation
of the curve d (measurant)/d (volume). Titration was performed
under argon atmosphere to avoid any interference of carbon
4.1. Coulometric titration
3. Experimental (II) volumetric titration
Table 1a shows the results of the nine coulometric determinations of three different bottles of the investigated KHP batch
and the mean as well as the standard deviation of the mean.
As a check for a potential bias, eight additional measurements
with low (0.5 mg) sample intakes were carried out to establish
the recovery mass function. The purity was calculated as the
ratio of coulometrically determined amount of substance versus
theoretical amount of substance calculated from sample mass.
In Fig. 3 17 measurements are included, the results of the high
sample intake measurements are given in Table 1a, the results
of the measurements with very low sample intake are given in
260
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
Fig. 2. Analysis scheme of volumetric titration for certification.
Table 1b. The slope of this curve gave a bias corrected mass fraction of 99.990%. This value was used to calculate the certified
value of the material by combining it with the volumetric results.
The difference between the coulometrically determined mean
from Table 1a and the slope calculated from the mass-function
(n = 17), Tables 1a and 1b, was the bias of 0.004%.
Calculation of the uncertainty is shown in Tables 2 and 5.
The uncertainty contribution of type A for the KHP content
determined by coulometry could
√ either be calculated from the
standard deviation divided by m, if the mass fraction w was
obtained as mean value of n single results from m independent bottles or it could be taken from regression analysis of
the recovery function.
Fig. 3. Recovery plot of coulometrically determined amount of substance vs.
theoretical amount of substance from sample weight (n = 17).
Table 1a
Coulometric determination of purity of KHP lot no. 1291630, (Fluka product-no:
60357)
Bottle no.
Mass (m in g)
Acid amount content
(v in mol kg−1 )
Acid mass
fraction (w in %)*
1
1
1
0.723633
0.732635
0.748235
4.89671
4.89582
4.89649
100.001
99.983
99.997
2
2
2
0.817912
0.506147
0.682642
4.89593
4.89694
4.89561
99.985
100.006
99.979
3
3
3
0.752915
0.514089
0.713291
4.89681
4.89661
4.89634
100.003
99.999
99.994
4.89636
0.00047
99.994
0.010
Mean (n = 9)
Standard deviation S (n = 9)
w (%) = 100 × v (mol kg−1 ) × M (kg mol−1 ) with MKHP =
0.2042212 kg mol−1 .
*
4.2. Volumetric titration
The results of the volumetric determination are given in
Table 3. For each of the 35 bottles the means of seven single determinations are listed together with the corresponding
absolute and relative standard deviations. There was no hint
for any inhomogeneity of the material. The mass fraction of
Table 1b
Low masses measurements for recovery plot
Bottle no.
Mass (m in g)
Acid amount content
(v in mol kg−1 )
1
1
0.000553
0.000541
5.33124
4.69284
2
2
0.000503
0.000510
5.15955
4.98119
3
3
3
3
0.000543
0.000472
0.000466
0.000466
5.01092
4.94627
5.27164
5.05187
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
261
Table 2
Uncertainties, type B for coulometric determination of KHP
Effect
Distribution
Sensitivity
Uncertainty
Product
ci
Units
ui
Units
ci ui
Units
4.9E+02
1.0E+02
1.4E+02
6.0E−02
% V−1
4.0E−06
1.7E−05
3.5E−05
2.0E−04
V
g
s
2.0E−03
1.7E−03
5.0E−03
1.2E−05
%
%
%
%
5.6E−03
%
4.1E−04
2.0E−03
1.4E−03
1.0E−03
4.1E−04
1.0E−04
%
%
%
%
%
%
2.8E−03
%
4.2E−04
1.1E−03
%
%
Constants
1.2E−03
%
Total
6.4E−03
%
Voltage
Resistance
Mass
Time
Normal
Normal
Normal
Normal
% −1
% g−1
% s−1
Physical contributions
Phthalate reduction
Electrolyte impurities
Inertgas impurities
Diffusion
Incomplete rinsing
Current efficiency
Normal
Normal
Normal
Normal
Normal
Rectang.
8.2E+01
1.0E+02
1.4E+02
1.0E+02
1.0E+02
1.0E+02
–
–
–
–
–
–
1.1E−01
5.0E−01
% mol C−1
5.0E−06
2.0E−05
1.0E−05
1.0E−05
4.0E−06
1.0E−06
–
–
–
–
–
–
3.9E−03
2.2E−03
C mol−1
Chemical contributions
F(CODATA)
M(KHP)
Rectang.
Rectang.
% mol g−1
KHP was calculated using Eqs. (4) and (5). The certified value
of the material was calculated combining the mean value of
99.987% resulting from the volumetric determinations with the
coulometric results (see below).
f (titrant) =
m(RM) × w(RM)
V (titrant, RM)
w (sample) =
f (titrant) × V (titrant, sample) × 100%
m (sample)
(4)
(5)
with f (titrant): titration factor in mg mL−1 ; w (sample): mass
fraction of sample in %; m (RM): mass of reference material
used for titration in mg; w (RM): mass fraction of reference
material used for titration in %; V (titrant, RM): volume of titrant
used for titration of the reference material in mL; V (titrant,
sample): volume of titrant used for titration of the sample in
mL; m (sample): mass of sample in mg.
Table 4 shows potential contributions to the combined uncertainty of the results received from volumetric titration.
4.2.1. Type A uncertainty (uA )
Random deviations are expressed by the spread of the results
which is the repeatability of the determination. Since test samples and reference material were analysed alternately and the
volume of titrant was nearly the same for all titration solutions
any contribution from the uncertainty of the volume was also
included into the repeatability standard deviation.
Type A uncertainty consisted of repeatability of the factor and
the sample determination. These values were calculated using
the mean standard deviation of seven repeated titrations with
35 samples and eight determinations of the factor using NIST
SRM 84k with seven repeated single determinations.
The result√
ing standard deviation was divided by 7 for the number of
independent titrations.
g mol−1
The contribution of type A uncertainty decreased due to the
high number of repetitions performed
for the mass fraction deter√
mination (division by factor n).
4.2.2. Type B uncertainty (uB )
Variations of the concentration of the titrant by absorption of
carbon dioxide which would lead to increasing titrant volumes
and therefore give a bias were avoided by working under argon
atmosphere. A blank correction was not necessary because a
possible blank would influence reference material and sample
in the same way.
Beside uncertainty contributions which could be avoided by
careful handling there were some potential sources of uncertainty which had not to be considered because they were
compensated by using the same procedure for the calibration
substance and the test samples. This was true for a possible
influence of temperature on the volume which would affect reference material and test sample in the same way. This was also
the case for a possible bias of the end-point detection which
would also affect the determination of reference material and
test sample in the same way.
As mentioned above buoyancy correction was not carried out
because sample and reference had the same density. Therefore,
any uncertainty contribution based on buoyancy correction was
not taken into consideration for volumetric titrations.
Contributions to the type B uncertainty came from the weighing of samples and reference material – linearity of the balance
±0.125 mg which could be converted to a standard uncertainty
assuming a rectangular distribution – and the purity of the
reference material, given in the reference material certificate
[26].
As a result main contributions to the combined uncertainty
came from the weighing process of sample and reference material.
262
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
Table 3
Results of KHP-determination (volumetric titration)
Table 4
Potential uncertainty contributions of volumetric titration
Sample
u(Vtitr, sample ): volume of titrant
Mean values of all titration steps
1291630-050 (01)
1291630-094 (02)
1291630-095 (03)
1291630-190 (04)
1291630-248 (05)
1291630-262 (06)
1291630-282 (07)
1291630-291 (08)
1291630-315 (09)
1291630-323 (10)
1291630-376 (11)
1291630-392 (12)
1291630-474 (13)
1291630-481 (14)
1291630-485 (15)
1291630-496 (16)
1291630-516 (17)
1291630-517 (18)
1291630-537 (19)
1291630-563 (20)
1291630-587 (21)
1291630-589 (22)
1291630-616 (23)
1291630-626 (24)
1291630-647 (25)
1291630-667 (26)
1291630-669 (27)
1291630-680 (28)
1291630-683 (29)
1291630-733 (30)
1291630-776 (31)
1291630-812 (32)
1291630-840 (33)
1291630-888 (34)
1291630-960 (35)
Mean (%)
S.D. (%)
R.S.D. (%)
n
99.980
99.986
99.975
99.983
99.978
99.989
99.989
100.001
99.986
99.969
99.966
99.994
99.994
99.987
99.976
99.982
100.002
99.997
99.990
99.987
99.984
100.000
99.989
99.990
99.995
100.002
99.996
99.983
99.972
99.971
99.998
99.982
99.981
100.005
99.992
0.028
0.029
0.024
0.022
0.030
0.029
0.024
0.035
0.028
0.013
0.039
0.020
0.024
0.026
0.022
0.019
0.033
0.025
0.026
0.017
0.034
0.021
0.038
0.019
0.030
0.029
0.039
0.024
0.031
0.025
0.038
0.038
0.023
0.020
0.043
0.028
0.029
0.024
0.022
0.030
0.029
0.024
0.035
0.028
0.013
0.039
0.020
0.024
0.026
0.022
0.019
0.033
0.025
0.026
0.017
0.034
0.021
0.038
0.019
0.030
0.029
0.039
0.024
0.031
0.025
0.038
0.038
0.023
0.020
0.043
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
Mean of means
S.D. of means
R.S.D. of means
m
99.987%
0.010%
0.010%
35
4.3. Calculation of the certified value and its combined
uncertainty
The certified value of KHP, batch no. 1291630 which was
investigated in this study, was calculated as the mean value of
u(Vtitr, RM ): volume of titrant
u(Vend point, bias )
u(Vend point, )
u(MKHP )
u(Vtitr, T ): influence of temperature
on volume of titrant
u(msample )
u(mRM )
u(ksample ): buoyancy correction
u(kRM ): buoyancy correction
u(pRM ): purity of reference material
Not relevant because same volume
for reference material and sample
Not relevant because same volume
for reference material and sample
Same detection of end point for
reference material and sample
Part of result spread
Not relevant because same material
as reference material and sample
Part of result spread, compensated by
alternate determination of reference
material and sample
Linearity of balance, to be taken into
account
Linearity of balance, to be taken into
account
Not relevant because same mass for
reference material and sample
Not relevant because same mass for
reference material and sample
To be taken into account
the means of both methods (see Fig. 4):
(99.987 + 99.990)
= 99.989%
2
The combined uncertainty of the certified value resulted from
the combination of the uncertainty contributions of both methods
and the inhomogeneity contribution:
uc = u2Volumetry + u2Coulometry + u2Inhom
= 0.0212 + 0.0072 + 0.0102 = 0.024%
The inhomogeneity contribution to the uncertainty uInhom was
set to the experimentally determined between-bottle standard
deviation as the best estimate of the uncertainty due to betweenbottle heterogeneity [27]. Since homogeneity testing was carried
out using 175 mg of material, the minimum sample intake for
any user of the CRM must be above 175 mg.
The expanded uncertainty could then be calculated by multiplication of the combined uncertainty with the coverage factor
k = 2, i.e. U = 0.048%.
Fig. 4. Measurement results with uncertainties, uc = combined uncertainty, 2uc = expanded uncertainty.
S. Recknagel et al. / Analytica Chimica Acta 599 (2007) 256–263
263
Table 5
Comparison between volumetric titration and coulometry
Method
Volumetric titration
Coulometry
Coulometry
Traceability of results
Evaluation of determinations
Number of single determinations
Sample intake in mg
Number of bottles investigated (m)
Number of single determinations per bottle (n)
Result calculated as
Mass fraction in %
Standard deviation of mean in %; S (RM); S (sample)
SRM 84k (NIST)
Mean value
245
175
35
7 (no. of factor determination)
MMW mean of means
99.987
S (RM)
= 0.007;
S (sample) = 0.010; 0.012
Directly to SI
Mean value
9
514–818
3
3
MMW mean of means
99.994
S (sample)
0.005
Recovery plot ncoul = f (nweight )
17
0.5–817.9
3
≥5
Slope coul. vs. sample intake
99.990
Error of slope 0.004
Uncertainty type A in % (uA )
0.005
0.003
0.004
Uncertainty type B in % (uB )
Combined uncertainty in % (uc )
Expanded uncertainty in % (U; k = 2)
0.020
0.021
0.041
√S
n
5. Conclusions
The different results for both methods used for the determination of the mass fraction of KHP are summarised in Table 5.
Acidimetric purity of KHP is statistically not different from
100% purity. Very precise volumetric titration with regards to
bias and repeatability using optimised procedures shows within
uncertainties the same results as measurements with precision
coulometry. Whereby the volumetric method is calibrated with
a certified reference material and the coulometric determination
rely on traceable SI quantities. The purity of KHP is the same
with slightly different uncertainties while the throughput of the
volumetric titration is significantly higher than that of coulometric titration. This material is well characterised and can be
used as an acidimetric standard with low uncertainty. Thus, it
forms the basis for traceability of a high number of acid–base
titrations.
Acknowledgements
The authors want to thank J. Wüthrich from Sigma–Aldrich
Production GmbH for the successful cooperation and fruitful
discussions.
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