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Validation of Titration Methods
Application brochure 16
Editorial
Dear Reader
this Application Brochure provided by METTLER TOLEDO shows you how to
validate a titration method. The recommendations and remarks have been put together by Chris Walter, Application Chemist of the Market Support AnaChem. He
also measured all the results and evaluated them.
A validation of a method brings indeed some work, but thoughtful planning and
careful preparation limit the efforts. And you win a reliable method which you daily
apply with certainty.
We got the preface by courtesy of a user in the pacific region, who is a long time
expert in “method making”.
We wish you many successful titrations
G. Reutemann
Manager Market Support
North East Asia
Page 2/28 METTLER TOLEDO
H. Huber
Regional Market Manager
Validation of Titration Methods
Contents
Preface .................................................................................................................. 4
1
Summary .............................................................................................................. 5
2
Principle of Validation ......................................................................................... 5
3
3.1
3.2
3.3
3.3.1
3.3.2
3.4
3.5
Steps of Validation and Recommended Limits ................................................. 6
Definition of Accuracy .......................................................................................... 6
Definition of Precision .......................................................................................... 6
Systematic Errors and Linearity ............................................................................ 7
Definition of Systematic Errors ............................................................................. 7
Definition of Linearity ........................................................................................... 7
Definition of Robustness and Ruggedness ............................................................ 8
Definition of Determination Limit ........................................................................ 9
4
4.1
4.2
4.3
4.4
Practical Hints ................................................................................................... 10
Preparations and Precautions ............................................................................... 10
Titration Control Parameters ............................................................................... 10
Titration Evaluation Parameters .......................................................................... 10
Titration ............................................................................................................... 11
5
Possible Sources of Error .................................................................................. 11
6
Recommendations for Troubleshooting ........................................................... 12
7
Results not Conforming to Specifications ....................................................... 13
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Examples ............................................................................................................ 14
Determination of Sulphuric Acid ........................................................................ 14
Titer Determination ............................................................................................. 15
Precision and Accuracy ....................................................................................... 16
Systematic Errors, Linearity ................................................................................ 17
Robustness and Ruggedness ................................................................................ 18
Determination Limit ............................................................................................ 20
Closing Remarks ................................................................................................. 21
9
Appendix 1 ......................................................................................................... 22
10
10.1
10.2
Appendix 2 ......................................................................................................... 24
Assessment of Results ......................................................................................... 24
Precision versus Accuracy ................................................................................... 24
11
Glossary .............................................................................................................. 25
12
Literature ........................................................................................................... 26
Validation of Titration Methods
METTLER TOLEDO Page 3/28
Preface
In this increasingly competitive world of business, the challenge of delivering highest-quality products to consumers is a must. Behind any quality product are robust analytical methods that ensure accurate addition of ingredients needed to deliver what is promised.
The method must be simple yet accurate. Serious consideration must be given to the possibility of the method being automated. This strategy eliminates human errors, increases productivity and reduces the time needed to release the product to consumers without compromising
method accuracy and reproducibility hence, product quality. Of course along with all the
methods simplification comes analysis cost-saving. In addition, the method must be environment-friendly via reduction, if not elimination, of the conventional use of organic solvents,
especially non-biodegradable and toxic chemical reagents.
Accepted protocols/SOP's followed during method validation work are generally universal,
irrespective of country, industry, company or product category. The only thing that is different between them is the accuracy required, with the strictest limits applied to those products
prepared for human consumption, e.g., food and medicine.
In this brochure, METTLER TOLEDO summarizes the general method development protocols.
These include accuracy, reproducibility, linearity, ruggedness and limit of determination. Each
method must pass all these tests, just like the consumer products for which the method will be
used.
Page 4/28 METTLER TOLEDO
Validation of Titration Methods
1
Summary
The goal of all measurements and determinations is to generate correct results. Correct results are accurate compared to the true value and precise in their statistical deviation [1].
A detailed method is applied to obtain correct results. This method describes all the different
steps from the sampling to the result. Whether correct results can be obtained or not with a
certain method has to be validated. Validation of a method comprises tests for accuracy,
precision, linearity, systematic errors, robustness/ruggedness and detection limit/determination limit. So the validation of a method proves, whether or not the instruments used for this
purpose fulfill the specific requirements.
In the context of validation a variety of expressions is used. Please refer to the glossary
(chapter 11) for a short definition of the expressions used in this brochure.
2
Principle of Validation
Accuracy, Precision, Linearity, Systematic Errors, Robustness/Ruggedness and Determination limit are checked, considering the complete analytical procedure from taking the sample
to result calculation and documentation.
• Use of a standard substance (Primary standard) allows the assessment of accuracy.
• Statistical evaluation of multiple sample series shows precision/reproducibility.
• Varying the analyte concentration indicates the linearity and systematic errors.
• If the results show no deviations due to different analysts, time or day of analysis, instruments and electrodes, temperature or matrix effects, the method can be considered as
robust/rugged.
• The smallest amount of substance giving a detectable potential change with a quantifiable
titrant consumption is the detection limit. The smallest amount of sample that can be titrated with a good precision is the determination limit. So for the validation only the
determination limit is needed, since it includes the detection limit.
The following application serves as a guideline, showing how a titration method can be validated. As an example, the method for the determination of sulphuric acid was validated.
Recommended limits for accuracy, reproducibility and linearity are subject to the tested method.
Other methods e.g. analysis of foods and drugs may require much stricter limits.
Validation of Titration Methods
METTLER TOLEDO Page 5/28
3
Steps of Validation and Recommended Limits
The titrant to be used in this validation has to be standardised first against a primary standard.
Primary standards are commercially available substances with the following characteristics
[1], [2], [3]:
•
Clearly defined composition and high degree of purity.
•
Large equivalent mass (minimizing weighing errors).
•
Accurately weighable (not hygroscopic, insensitive to oxygen and/or CO2).
•
Stable in solutions and easily soluble in adequate solvents.
•
Rapid and stoichiometric reaction with the titrant.
See appendix 1 for typical combinations of titrant and primary standard.
3.1
Definition of Accuracy
Multiple series of standard samples or of samples with exactly known concentration are titrated. The analyte concentration therein should cover the complete determination range. The
sample size should be varied randomly and result in a consumption of titrant of ca. 30 to 90%
of the burette volume. A refilling of the burette should be avoided.
The mean value x of each series represents the result of the titration. The difference between
this mean value and the true value (i.e. the known concentration) allows the determination of
accuracy.
Recommendation:
Results obtained should not deviate from the true value by more than 0.3%.
3.2
Definition of Precision
Multiple series of a sample are titrated. Thereby the analyte concentration in the titration
beaker should cover the complete determination range. This is done by varying the sample
size randomly so that a titrant consumption of ca. 30 to 90% of the burette volume results. A
refilling of the burette should be avoided.
An outlier test according to Grubbs [1] is performed on the results of these sample series in
order to eliminate distinct outliers. Then a statistical evaluation is performed on each sample
series to get the mean value and the relative standard deviation RSD. The RSD expresses the
precision of the method.
Recommendation:
The relative standard deviation obtained from individual samples series should not be greater
than 0.3%.
Page 6/28 METTLER TOLEDO
Validation of Titration Methods
3.3
Systematic Errors and Linearity
To discover systematic errors and the linearity of the method, the titrant consumption obtained in Chapter 3.2 is plotted against the respective sample size which determines the analyte
concentration per single analysis.
A linear regression is performed on these data. The regression line is described by the formula y = a + bx , where a represents the intercept on the y-axis and b is the slope of the
regression line.
3.3.1 Definition of Systematic Errors
Systematic errors of a titration are for example disturbing influences due to the method itself
or to solvent blank values.
In the linear regression according to chapter 3.3 systematic errors show up as a significant
deviation of the y-axis intercept a of the regression line from the zero point coordinates (see
graph 1), i.e. asys is clearly different from zero.
asys
volume
graph 1:
sample size
Recommendation:
The systematic error asys should be smaller than 15 µL. If it can not be eliminated by optimizing
the method or the reagents, it has to be corrected for in the results calculation of the titration
method.
3.3.2 Definition of Linearity
Linearity expresses whether a certain method produces correct results over the interesting
concentration range [4]. In titration the analyte concentration depends on the sample concentration, on the sample size and on the solvent volume added for the analysis. By varying the
sample size and thereby the analyte concentration, the linearity of a titration method may be
detected in the range of interest.
Validation of Titration Methods
METTLER TOLEDO Page 7/28
There are two practical ways to check a titration method for linearity:
A)
The regression coefficient (R2) of the linear regression described in graph 1 must be
better than a given limit, depending on the demanded accuracy for the specific determination:
i.e.
B)
R2 > 0.995
A significant positive or negative slope b (resp ∆R/∆V) of the regression line in graph
2 (results of the titration versus sample size) indicates a non-linearity of the titration
method, meaning that the result depends on the sample size.
result
result
graph 2:
non linear
linear
sample size
sample size
Recommendation:
If ∆R/∆V is greater than 0.1%, a systematic non-linearity has to be assumed.
3.4
Definition of Robustness and Ruggedness
The ROBUSTNESS describes whether a titration method is sensitive to "hardware effects",
such as different instruments (electrodes, titrators etc.), time and day of analysis, different
operators or varying ambiental conditions in different laboratories. To check the robustness,
the validation steps should be repeated with the same sample by different persons on different days and on different titrators.
This kind of check also is recommended, if unsatisfactory results are subsequently obtained:
(a) during certain steps of the validation procedure and/or
(b) during the routine application of the method.
The RUGGEDNESS describes the correctness of the results obtained under disturbed experimental (analytical) conditions such as different matrices (e.g. solutions, reagents etc.), other
temperatures of the analyte solution or elsewise deviating conditions. To determine ruggedness, the same sample is titrated with and without exposure to relevant disturbances. If the
results are the same, the method is considered to be rugged against this specific influence.
Page 8/28 METTLER TOLEDO
Validation of Titration Methods
The method is checked against influences likely to occur e.g. temperature deviations in a
specific laboratory or CO2 uptake of a titrant etc.
Multiple series of samples are titrated under the condition to be evaluated. The sample size
should be varied in random order and result in a consumption of titrant of ca. 30 to 90% of the
burette volume. Refilling of the burette should be avoided.
An outlier test according to Grubbs is performed on the results of the sample series in order to
eliminate distinct outliers. Then a statistical evaluation is performed on these experimental
data. The results obtained are compared with the results obtained in the precision evaluation.
If the method is rugged, there should not be any difference.
Recommendation:
In normal routine titration the deviation should not be greater than 0.3%.
3.5
Definition of Determination Limit
Since the detection limit for a specific titration method is of rather academic interest only, it
is not determined in a regular validation. Though in very special cases this could change.
graph 3:
rel. stand. dev. [RSD]
The determination limit is determined by titrating sample series, each with a continuously
reduced amount of sample. The determination limit is the smallest amount of substance (mmol)
or sample, which can be titrated with a good precision (RSD) of ≤ 0.3%. It can be evaluated
by intrapolation of the graph “amount of substance versus relative standard deviation”.
determination limit
0.3%
amount of substance [mmol]
In normal routine titration the determination limit is not a problem, since one can simply
enlarge the sample size to get a better response from the electrode. However, this can be
different, if the analyte has a very low concentration in the sample.
Validation of Titration Methods
METTLER TOLEDO Page 9/28
4
Practical Hints
4.1
Preparations and Precautions
In order to obtain good results it is essential to observe the following points:
• The primary standard must be dried in a drying oven (e.g. 2 h at 105 °C, depending on the
type of primary standard) and cooled to ambient temperature in a desiccator for at least 1
hour. It should always be stored in a desiccator.
• For acid/base endpoint titrations, it is necessary to calibrate the pH electrode. Certified
buffers from METTLER TOLEDO may be used for this purpose.
• The experimental setup must be protected from direct sunlight and should be in thermal
equilibrium with the environment.
• The analytical balance must have a vibration free standing and should be calibrated regularly. METTLER TOLEDO balances of the MT, AT and PR series offer FACT (Fully
Automatic Calibration Technology), which automatically executes a calibration whenever
needed. All steps to ensure proper weighing must be observed [5].
4.2
Titration Control Parameters
The control parameters are subject to the titration performed. Titrations with primary standards should be executed with the same or very similar parameters as the titrations of the
sample. This is especially important for the basic settings such as [1]:
4.3
Titration mode:
Endpoint
Equivalence point
Titrant addition:
Dynamic
Continuous
Measure mode:
Equilibrium
Fixed time interval
Incremental
Titration Evaluation Parameters
The evaluation procedure is subject to the type of the titration reaction and the indication. For
acid/base titrations and by default, the standard evaluation procedure is applied.
Evaluation procedure:
Page 10/28 METTLER TOLEDO
Standard
Maximum
Segmented
Asymmetric
Minimum
Validation of Titration Methods
4.4
Titration
• Samples should be titrated immediately after weighing and dissolution. Enough solvent
must be added to cover the sensor.
• When performing a series of titrations, the interval time between samples should be kept
to a minimum.
• In sample series, the electrode as well as stirrer and temperature sensor should be rinsed
between two measurements.
• Temperature compensation is essential for pH endpoint titrations.
5
Possible Sources of Error
• Primary standard
unsuitable, impure, moist, inhomogeneous, no guaranteed primary
standard quality, contaminated (e.g. by CO2, O2).
• Sample size/Balance
balance not accurate, air humidity too high or too low, contaminated balance, temperature changes or gradient from titration vessel to balance, careless weighing, sample weight, concentration or
volume too low or too high, sample inhomogeneous, improper
sampling.
• Titration vessel
contaminated, unsuitable.
• Dispensing unit
tube connections not tight, contaminated burette cylinder (visible
corrosion marks), leaky piston (liquid film or crystals below the
piston), leaking burette tip, air in tubing system, three-way stopcock leaking.
• Sample
matrix effects from other species.
• Reaction kinetics
too slow.
• Solvent
impure (blank value), poor solubilising power, not stable, contaminated (e.g. by CO2, O2), wrong pH value or ionic strength.
• Titrant
impure, decomposed, contaminated (e.g. by CO2), light sensitive,
wrong pH value or ionic strength, very high or low concentration.
• Measurement
unsuitable sensor type, contaminated electrode, blocked diaphragm,
loose contact at connector, faulty cable, poor mixing of sample
solution, unfavourable arrangement of burette tip and electrode,
excessive response time of electrode, insufficient rinsing of electrode and stirrer before the next titration.
• Titration parameters
unsuitable titration mode, wrong measure mode parameters, titration rate too fast or too slow, unsuitable evaluation procedure.
Validation of Titration Methods
METTLER TOLEDO Page 11/28
6
• Temperature
temperature fluctuations, especially perceptible with titrants in
organic solvents, highly endothermal or exothermal reaction.
• Environmental
changing, fluctuating, adverse conditions (humidity, temperature,
lighting).
Recommendations for Troubleshooting
a)
Relative Standard Deviation too high
(poor reproducibility)
• Ensure complete dissolution of the weighed sample in the solvent.
• Optimise the arrangement of burette tip, electrode and stirrer.
• Regenerate or replace the electrode.
• Optimise titration parameters (see METTLER TOLEDO Application Brochures).
• Remove the burette, clean and possibly change tubing as well as piston and/or cylinder.
• Weigh the sample only after establishing a temperature equilibrium between balance, titration vessel and sample.
• Increase the sample concentration if possible.
• Select bigger or smaller burette size.
• Check temperature of sample solution (e.g. use water bath).
• Optimise pH value of sample solution (e.g. add buffer).
b)
Relative Systematic Deviation too high
(accuracy unsatisfactory)
• Use pure solvent (without blank value), degass the water if necessary.
• Dry the primary standard substance.
• Ensure complete dissolution of the weighed sample in the solvent before titration starts.
• Visual inspection of the burette and its replacement if need be.
• Check electrode. Eventually regenerate or replace.
• Check titration parameters.
• Increase the sample concentration if possible.
• Check the balance.
• Optimise solution temperature using a water bath, and pH value adding a buffer.
• Increase concentration of sample solution if possible.
• Reduce, if not eliminate possible influences, e.g. filtration, centrifugation, extraction etc.
Page 12/28 METTLER TOLEDO
Validation of Titration Methods
7
Results not Conforming to Specifications
If inaccurate or imprecise results, systematic errors, non-linearity or problems with the robustness/ruggedness are found, an attempt must be made to optimise the titration method in
order to meet the required limits.
In some cases it may be necessary to use an unchanged method. However, systematic errors
and non-linearity can then be compensated for in the calculations.
All non-conforming values must be reported and commented on in the validation record and
the subsequent procedure noted and explained.
If relevant deviations are found, the sections “Possible Sources of Error” and “Recommendations for Troubleshooting” must be checked carefully and the disturbing influences eliminated. It is essential to repeat the validation afterwards.
The titrators of METTLER TOLEDO have undergone various tests during development and
manufacturing. Furthermore, they have been time tested by numerous users in different applications all over the world and considered to be okay. If irregular results are obtained,
primary consideration should be given to the working technique of the operator or to wrong
or accidentally altered titration parameters.
Validation of Titration Methods
METTLER TOLEDO Page 13/28
8
Examples
8.1
Determination of Sulphuric Acid
METTLER TOLEDO DL70
Sample:
Sulphuric acid solution
Substance:
H2SO4 0.05 mol/L
Preparation:
40 mL deion. water
Titrant:
Sodium hydroxide
c(NaOH) = 1.0 mol/L
Instruments:
METTLER DL77
Option RS232
Option Temperature
Sample changer ST20A
Printer HP Deskjet
Accessories:
DT120 T-sensor
Indication:
DG111-SC
Page 14/28 METTLER TOLEDO
Method
Val1
Version
Titrator V1.0
Jim 4
Mettler Toledo AG
Market Support Laboratory
Determination of H2SO4
22-Dec-1995 20:33
Title
Method ID . . . . . . . . .
Title . . . . . . . . . . .
Date/time . . . . . . . . .
Sample
Number samples . . . . . . .
Titration stand . . . . . .
Entry type . . . . . . . . .
Volume [mL] . . . . . . .
ID1 . . . . . . . . . . . .
Molar mass M . . . . . . . .
Equivalent number z . . . .
Temperature sensor . . . . .
Pump
Auxiliary reagent . . . . .
Volume [mL] . . . . . . . .
Stir
Speed [%] . . . . . . . . .
Time [s] . . . . . . . . . .
Titration
Titrant . . . . . . . . . .
Concentration [mol/L] . . .
Sensor . . . . . . . . . . .
Unit of meas. . . . . . . .
Titration mode . . . . . . .
Predispensing 1 . . . . .
Volume [mL] . . . . .
Titrant addition . . . .
∆E(set) [mV] . . . . .
Limits ∆V . . . . . .
∆V(min) [mL] . . .
∆V(max) [mL] . . .
Measure mode . . . . . .
∆E [mV] . . . . . . .
∆t [s] . . . . . . . .
t(min) [s] . . . . . .
t(max) [s] . . . . . .
Threshold . . . . . . . .
Maximum volume [mL] . . .
Termination after n EQPs
n = . . . . . . . . .
Evaluation procedure . .
Rinse
Auxiliary reagent . . . . .
Volume [mL] . . . . . . . .
Calculation
Result name . . . . . . . .
Formula . . . . . . . . . .
Constant . . . . . . . . . .
Result unit . . . . . . . .
Decimal places . . . . . . .
Record
Output unit . . . . . . . .
Raw results last sample . .
Table of values . . . . . .
E - V curve . . . . . . . .
Conditioning
Interval . . . . . . . . . .
Time [s] . . . . . . . . . .
Rinse . . . . . . . . . . .
Auxiliary reagent . . . .
Volume [mL] . . . . . . .
Statistics
Ri (i=index) . . . . . . . .
Standard deviation s . . . .
Rel. standard deviation srel
Outlier test . . . . . . . .
Record
Output unit . . . . . . . .
All results . . . . . . . .
. . . Val1
. . . Determination of H2SO4
. . . 22-Dec-1995 20:33
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6
ST20 1
Fixed volume U
30.0
H2SO4
98.08
2
TEMP A
. . . H2O
. . . 30.0
. . . 50
. . . 10
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NaOH
1.0
DG111-SC
As installed
EQP
mL
2
DYN
8.0
Absolute
0.05
0.3
EQU
1.0
1.0
3.0
15.0
3.0
10.0
Yes
1
Standard
. . . H2O
. . . 10.0
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H2SO4 Conc.
R=Q*C/U
C=M/z
g/L
5
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Printer
Yes
Yes
Yes
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1
10
Yes
H2O
10.0
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R1
Yes
Yes
Yes
. . . Printer
. . . Yes
Validation of Titration Methods
8.2
Titer Determination
The titer of this NaOH (1.0 mol/L) was determined against the primary standard potassium
hydrogen phthalate (dried for 2 h at 150 °C). The following results were obtained:
Results:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Size
[g]
Result
[—]
0.94376
0.69729
1.44905
0.76393
1.28186
0.91697
1.09282
0.61858
1.73847
1.32274
1.63289
1.17670
0.64051
1.52071
1.30135
0.72725
1.04305
0.62867
1.79993
1.68623
1.77458
1.38162
1.0011
1.0014
1.0015
1.0003
1.0012
1.0002
1.0015
1.0044
1.0024
1.0011
1.0008
1.0011
1.0018
1.0017
1.0004
1.0012
1.0010
1.0024
1.0009
1.0017
1.0010
1.0024
Number of samples:
Mean value x:
Standard deviation:
Relative Standard Deviation:
Titer vs. Sample Size
1.050
1.045
y = 1.0019 - 4.160e-4x
1.040
1.035
1.030
1.025
1.020
Titer
Number
1.015
1.010
1.005
1.000
0.995
0.990
0.985
0.980
0.0
0.3
0.6
0.9
1.2
1.5
1.8
Sample Size [g]
22
1.0012
9.06 • 10-4
0.0905 %
Comment:
The standardization is highly reproducible and linear. Results do not depend on the sample
weight.
Validation of Titration Methods
METTLER TOLEDO Page 15/28
8.3
Precision and Accuracy
To assess precision and accuracy of the method, a commercially available H2SO4 solution,
c(H2SO4) = 0.05 mol/L, was titrated with the titrant standardized in the previous chapter,
c(NaOH) = 1 mol/L.
The results were compared with the true value (compensated for a temperature of 21°C) to
determine the ACCURACY, and the PRECISION was evaluated with the standard deviation
obtained from the measurements.
Result H2SO4 vs. Sample Size [g/L]
Results:
950
Number
Size
[mL]
Result
[g/L]
75
34
44
60
35
44
77
32
52
91
31
42
4.90143
4.90828
4.89803
4.90046
4.90870
4.90672
4.89912
4.90273
4.90995
4.90584
4.91109
4.91117
945
Temperature:
y = 4.9106 - 1.030e-4x R =21
0.43 °C
Theoretical Content: 4.9030 g/L
No. of Samples:
12
Mean Value:
4.90529 g/L
Stand. Dev.:
0.004752 g/L
Rel. Stand. Dev.:
0.0968%
940
935
930
925
920
H2SO4 [g/L]
1
2
3
4
5
6
7
8
9
10
11
12
1234567890123456789012345678
1234567890123456789012345678
1234567890123456789012345678
905 1234567890123456789012345678
1234567890123456789012345678
1234567890123456789012345678
915
910
900
895
890
885
880
Theoretical content
Mean value
± 0.3% from theor.
content
1234
1234± S from mean
1234
value
875
870
865
860
855
850
20
40
60
80
100
Sample Size [mL]
Number of samples:
Theoretical value:
Mean value found:
Deviation to theoretical:
Relative deviation to theoretical:
12
4.9030 g/L
4.90529 g/l
0.00229 g/L
0.0467%
Standard deviation:
Relative standard deviation:
0.04752 g/L
0.0968%
Comment:
Precision as well as accuracy are excellent. The requirements are easily met.
Page 16/28 METTLER TOLEDO
Validation of Titration Methods
8.4
Systematic Errors, Linearity
The equivalence volumes (VEQ) were plotted versus the sample size. A linear regression was
performed on these data to determine systematic errors. In case, systematic errors manifest
themselves in a significant deviation of the y axis intercept of the regression line from the
zero point coordinates (see diagram below).
Equivalence Volume vs. Sample Size
10
75
34
44
60
35
43
77
32
52
91
31
42
VEQ
[mL]
7.4871
3.3989
4.3894
5.9885
3.4492
4.3972
7.6831
3.1953
5.2001
9.0925
3.1008
4.2011
Result
[g/L]
4.90143
4.90828
4.89803
4.90046
4.90870
4.90672
4.89912
4.90273
4.90995
4.90584
4.91109
4.91117
y = -0.00839 + 0.09997 x
R2 = 0.9999
9
Equivalence Volume [mL]
Size
[mL]
8
7
6
5
4
3
2
1
0
0
20
40
60
80
100
Sample Size [mL]
Result vs. Sample Size
To determine the linearity there are two practical
ways, as we said in chapter 3.3.2.
4.95
The second way to determine the linearity is to
plot the results of the titration (H2SO4 in g/L)
against the sample size, as one can see in the graph
nearby. Then a linear regression is performed on
these data. A significant positive or negative slope
b of the regression line y = a + bx indicates nonlinearity of the titration method, i.e. that the result depends on the sample size.
H2SO4 [g/L]
4.94
The first one is to check the regression coefficient
(R2) of the linear regression above, which has to
be better than 0.995 to prove linearity. The
achieved R2 of 0.9999 proves an excellent linearity of the method.
y = 4.9106 - 0.000103 x
4.93
4.92
4.91
4.90
4.89
4.88
4.87
4.86
4.85
20
40
60
80
100
Sample Size [mL]
Validation of Titration Methods
METTLER TOLEDO Page 17/28
Comment:
The results show a systematic error (SE) and non-linearity (NL). Presumable causes are
pipetting errors when preparing the samples.
µL
Systematic error:
8.4
Correl. coefficient R2 :
0.9999
Non linearity:
1 • 10-4 (g/L)/mL
SE as well as NL are very small and well below the recommended limits.
8.5
Robustness and Ruggedness
In this example the ruggedness of the method was tested against the carbon dioxide uptake of
the titrant only.
The uptake of carbon dioxide CO2 from ambient air is the major threat of alkaline titrants.
CO2 reacts to CO32-. Carbonate precipitation and reduction of the strength of the titrant are
the consequences.
Other analytical influences as well as the robustness (see chap. 3.4) can be checked in a
similar way.
CO32--Content
Air exposure
[day]
1
2
3
4
6
7
Result CO32[mg/L]
2526
5026
8793
14422
20684
24568
Result CO32- [mg/L]
The ruggedness of the sulphuric acid method was evaluated by exposing the titrant to air and
thereby also to CO2. Batches of NaOH titrants were exposed to air for 1, 2, 3, 4, 5, 6, 7 days.
The CO32- content of each sample was determined by titration with sulphuric acid.
30000
20000
10000
0
0
Page 18/28 METTLER TOLEDO
2
4
6
8
Air exposure
[days]
Validation of Titration Methods
The uptake of carbon dioxide is almost linear and very fast! After 2 days already 5 g/L CO32are present in the NaOH titrant. The NaOH concentration (as to OH-) thereby is reduced from
the initial 40 g/L to ca. 37 g/L in these two days.
Each NaOH batch was then standardised against potassium hydrogen phthalate. Then it was
used as the titrant to determine the H2SO4 concentration. The following table shows the corresponding results.
Air exposure
[day]
Result
[g/L]
Theoretical
content
Systematic
Deviation [%]
Reproducibility
(RSD) [%]
1
2
3
4
6
4.837
4.586
4.308
4.152
3.906
4.9017
4.9017
4.9020
4.9017
4.9040
1.31
6.44
12.11
15.20
20.35
0.051
0.139
0.178
0.108
0.162
Comment:
The method was found not to be rugged at all against exposure to air. Even the NaOH sample
exposed to air for only one day did not allow correct determinations any more.
Reason:
When titrating strong acids with NaOH that contains CO32-, a typical double
jump of the titration curve is found, caused by the following reactions:
1. EQP:
2. EQP:
NaOH
Na2CO3
+
+
H3O+
H3O+
-->
-->
Na+
NaHCO3
+
+
2 H2O
H2O
+
Na+
NaHCO3
+
H3O+
-->
Na+
+
2 H2O +
CO2
However, this double jump does not occur when titrating weak acids such as potassium hydrogen phthalate, which is mainly used for the titer determination. Therefore, the carbonate
error cannot be compensated for by frequent standardization of the titrant. It is advisable to
periodically check the carbonate content by a specific titration and dispose of the titrant if a
significant amount of carbonate is found.
Validation of Titration Methods
METTLER TOLEDO Page 19/28
8.6
Determination Limit
The determination limit was examined using 0.005 mol/L NaOH. Series of 5 to 6 samples
were run, in order to check the reproducibility (RSD) with a low amount of sample.
No. of
Samples
3
5
5
6
6
5
Mean Value
[mmol]
Standard
Deviation [mmol]
Relative Standard
Deviation [%]
0.000012
0.000022
0.000038
0.000037
0.000048
0.000031
0.092
0.408
0.944
1.369
3.581
3.945
0.013135
0.005380
0.004065
0.002735
0.001335
0.000785
The results show, that in the sample with less than 0.01 mmol sulphuric acid the Relative
Standard Deviation RSD increases drastically and continuously, while the absolute standard
deviation s remains more or less constant. The uptake of CO2 from the air is very severe in
this concentration range. Therefore the titrant has to be protected from air intake with an
absorption tube filled with NaOH on a carrier. Even then, it remains usable only for one day.
Comment:
The determination limit was
obtained with a titrant of very
low concentration, c(H2SO4) =
0.005 mol/L. When using the
standard NaOH solution of 1
mol/L, which was employed in
the other titrations in this brochure, the determination limit is
defined by the resolution of the
burette and not by the chemistry.
Page 20/28 METTLER TOLEDO
4
RSD [%]
The smallest amount of substance, which can be titrated with
a good reproducibility of ≤ 0.3
% RSD, was determined by
intrapolation. As the following
graph shows, that is about 0.01
mmol H2SO4 per sample.
3
2
1
0
0.000
0.005
0.010
0.015
mmol H2SO4
Validation of Titration Methods
8.7
Closing Remarks
It has been shown with this example how a titration method can be validated. The chosen
acid/base titration gave excellent results in all areas.
The limits for different parameters or the set up of priorities in the validation process have to
be adapted by the user depending on the method and the specifications for a given task (e.g.
other tests for the determination of ruggedness).
Anyway the basic course of a method validation remains the same. Thus, this example may
well serve as a guideline for further validations.
Validation of Titration Methods
METTLER TOLEDO Page 21/28
9
Appendix 1:
Standardisation of Titrants
Titrant
Standard Substance
Merck
Order
No.
Solvent and
Auxiliary
Reagents
Intervall
Protection of
Titrant / General
Remarks
Alkalimetry
Sodium hydroxide
c(NaOH) = 1.0 mol/L
Potassium hydrogen
phthalate
C 8H 5KO 4; M = 204.23
Dry at: 150 °C
104876 Deion. H2 O
weekly
Protect from CO2
(tube filled with
NaOH on carrier).
Sodium hydroxide
c(NaOH) = 0.1 mol/L
Potassium hydrogen
phthalate
C 8H 5KO 4; M = 204.23
Dry at: 150 °C
104876 Deion. H2 O
weekly
Protect from CO2
(tube filled with
NaOH on carrier).
Tetrabutyl ammonium
hydroxide
c(TBAH) = 0.1 mol/L
Benzoic acid
C 7H 6O 2; M = 122.12
Dry at: 105 °C
100135 Isopropanol
weekly
Protect from CO2
(tube filled with
NaOH on carrier).
Sodium methylate
c(NaOCH3) = 0.1 mol/L
Benzoic acid
C 7H 6O 2; M = 122.12
Dry at: 105 °C
100135 Methanol
daily
Protect from CO2
(tube filled with
NaOH on carrier).
Potassium hydroxide
c(KOH) = 0.1 mol/L
Benzoic acid
C 7H 6O 2; M = 122.12
Dry at: 105 °C
100135 Ethanol
weekly
Protect from CO2
(tube filled with
NaOH on carrier).
Sulfuric acid
c(1 /2 H2SO4) = 0.1 mol/L
Tris(hydroxymethyl)aminomethane [THAM]
C4H 11NO 3; M = 121.14
Dry at: 105 °C
108365 Deion. H2 O
Every 2
weeks
Hydrochloric acid
c(HCl) = 0.1 mol/L
Tris(hydroxymethyl)aminomethane [THAM]
C4H 11NO 3; M = 121.14
Dry at: 105 °C
108365 Deion. H2 O
Every 2
weeks
Perchloric acid
c(HClO4) = 0.1 mol/L
Tris(hydroxymethyl)aminomethane [THAM]
C4H 11NO 3; M = 121.14
Dry at: 105 °C
108365 Acetic acid
weekly
Silver nitrate
c(AgNO3) = 0.1 mol/L
Sodium chloride
NaCl; M = 58.44
Dry at: 105 °C
106405 Deion. H2 O
acidify to pH
3.5
Every 2
weeks
Barium chloride
c(BaCl2) = 0.1 mol/L
Sodium sulfate
Na 2SO 4; M = 142.05
Dry at: 105 °C
106649 Deion. H2 O
* 1)
Buffer pH 4
Thorin
weekly
Complexone III
c(EDTA) = 0.1 mol/L
Calcium carbonate
CaCO 3; M = 100.09
Dry at: 105 °C
102060 Deion. H2 O
Indicatorbuffer-tablet
Every 2
weeks
Use PE bottles.
Complexone VI
c(EGTA) = 0.1 mol/L
Calcium carbonate
CaCO 3; M = 100.09
Dry at: 105 °C
102060 Deion. H2 O
Indicatorbuffer-tablet
Every 2
weeks
Use PE bottles.
Acidimetry
Precipitation
Keep bottle in dark.
Complexometry
Page 22/28 METTLER TOLEDO
Validation of Titration Methods
Titrant
Standard Substance
Redox - Titration
Merck
Order
No.
Solvent and
Auxiliary
Reagents
Intervall
Protection of
Titrant / General
Remarks
(Reducing titrants)
Sodium thiosulfate
c(Na2S2O3) = 0.1 mol/L
Potassium iodate
KIO3 M = 214.00
105053 Hydrochloric
acid 0.1 M
biweekly
Hydroquinone
c(C6H6O2) = 0.1 mol/L
Potassium dichromate
K 2Cr2O 7 M = 294.19
104868 Sulfuric acid
5%
weekly
Keep bottle in dark.
Ammonium ferrous (II)
sulfate
c(FAS) = 0.1 mol/L
Potassium dichromate
K 2Cr2O 7 M = 294.19
104868 Sulfuric acid
5%
daily
Protect from
Oxygen.
Redox - Titration
(Oxidizing titrants)
Iron(III) chloride
c(FeCl3) = 0.1 mol/L
Ascorbic acid
C 6H 8O 6; M = 176.13
100127 Deion. water
* 1)
biweekly
Potassium dichromate
c(1 /6 K2Cr2O7) = 0.1 mol/L
(CH2NH3)2SO4 • FeSO4
•4H 2O; M = 382.15
103914 Sulfuric acid
5%
biweekly
Iodine
c(1 /2 I2) = 0.1 mol/L
di-Arsenic trioxide
As 2O 3; M = 197.84
100120 Deion. water
NaHCO3
daily
Cerium sulfate
c(Ce(SO4)2) = 0.1 mol/L
di-Sodium oxalate
C2Na2O 4; M=134.00
106556 Deion. water
Sulfuric acid
5%
biweekly
Potassium permanganate
c(1 /5 KMnO4) = 0.1 mol/L
di-Sodium oxalate
C2Na2O 4; M=134.00
106556 Sulfuric acid
5%; 70 °C
biweekly
Sodium nitrite
c(NaNO2) = 0.1 mol/L
Sulfanilic acid
C 6H 7NO 3S; M = 173.19
100686 HBr
* 1)
0.5 mol/L
weekly
Fehling solution
Glucose 1% in water
C6H 12O 6; M = 180.16
108337 Deion. water
* 1)
weekly
Prepare Glucose
solution daily.
2,6-Dichlorophenol-indophenol sodium salt
c(DPI) = 0.01 mol/L
Ascorbic acid
C 6H 8O 6; M = 176.13
100127 Deion. water
* 1)
daily
Keep bottle in dark.
Keep in PE bottles.
Keep cool.
Keep bottle in dark.
Keep in PE bottles.
Keep cool.
Keep bottle in dark.
Turbidimetric Titrations
.
Sodium dodecylsulfate
c(SDS) = 0.01 mol/L
N-Cetylpyridinium chlo102340 Deion. water
ride [CPC] monohydrate;
* 1)
M = 358.01
biweekly
Rinse bottle and
beakers with deion.
water before use.
Hyamine
c(Hyamine) = 0.01 mol/L
Sodium dodecylsulfate
[SDS]; M = 288.4
112012 Deion. water
* 1)
biweekly
Rinse bottle and
beakers with deion.
water before use.
N-Cetylpyridinium chloride
c(CPC) = 0.01 mol/L
Sodium dodecylsulfate
[SDS]; M = 288.4
112012 Deion. water
* 1)
biweekly
Rinse bottle and
beakers with deion.
water before use.
* 1)
These substances can not be acchieved as guaranteed primary standard substances from MERCK.
So the highest aviable quality is indicated.
Validation of Titration Methods
METTLER TOLEDO Page 23/28
10
Appendix 2
10.1 Assessment of Results
Errors
Deviations from the correct or expected value
Gross errors
Avoid
Systematic errors
Random errors
Accuracy
Precision
The measurement
result is wrong
The measurement
result is unreliable
Correctness
10.2 Precision versus Accuracy
high precision
(small RSD)
low precision
(big RSD)
high accuracy
(found = true)
Page 24/28 METTLER TOLEDO
low accuracy
(found ≠ true)
Validation of Titration Methods
11
Glossary
Validation:
A check whether or not correct results can be obtained with a given
method under all circumstances.
Correctness:
The sum of accuracy and precision.
Accuracy:
Deviation of the found value from the true (theoretical) value.
Precision:
Also called repeatability. The results of a multiple determination
of a sample (e.g. 10 times in a row) do not diverge to much from
the found mean value (small relative standard deviation).
Systematic Errors:
Result offsets due to method inherent parameters. Shows itself in
the linear regression “titrant consumption versus sample size” by
a y axis intercept, which is clearly different from zero.
Linearity:
There has to be a linear correlation between the amount of sample
present and the titrant volume consumed. Therefore the correlation coefficient of this regression has to exceed a certain value
(i.e. R2 ≥ 0.995).
Or in the plot “result of titration versus sample size” of a single
sample the slope of the regression line should be zero. This shows
that the results do not depend on the sample size (i.e. dilution volume).
Robustness:
Also called reproducibility. Closeness of the agreement between
the results of measurement of the same sample carried out under
changed conditions of measurement, such as different days, instruments, operators, laboratories, methods. Expressed as the relative standard deviation of the different results obtained.
Ruggedness:
Inertness against chemical/physical influences likely to occur (solvents, reagents, temperature, etc.).
Detection Limit:
The smallest amount of substance giving a detectable potential
change and a quantifiable titrant consumption.
Determination Limit:
The smallest amount of substance that can be titrated with a good
precision.
Sample:
Sample to be analysed (liquid or solid).
Sample size:
Exact volume or weight (of sample) used for the titration.
Analyte concentration:
Concentration of the substance to be analysed in the titration beaker.
Validation of Titration Methods
METTLER TOLEDO Page 25/28
12
Literature
[1]
METTLER TOLEDO: Fundamentals of Titration, ME-704153A (1993).
[2]
METTLER TOLEDO: Standardization of Titrants, Applications Brochures No. 8 and
9, ME-51724650 resp. ME- 51724652 (1994).
[3]
MERCK: Primary Volumetric Standards; E. Merck AG, Darmstadt, D.
[4]
Analytical Methods Committee: Uses (Proper and Improper) of Correlation Coefficients; Analyst, Vol. 113, pp 1469 - 71 (1988).
[5]
METTLER TOLEDO: Encyclopedia of Weighing; ME-720113.
[6]
G. Mücke: How Little is “Nothing”?, Fresenius Z Anal Chem, Vol. 320, pp 639 - 641
(1985).
This application bulletin represents selected, possible application examples. These have been tested with all possible
care in our lab with the analytical instrument mentioned in the bulletin. The experiments were conducted and the
resulting data evaluated based on our current state of knowledge.
However, the application bulletin does not absolve you from personally testing its suitability for your intended methods,
instruments and purposes. As the use and transfer of an application example are beyond our control, we cannot accept
responsibility therefore.
When chemicals and solvents are used, the general safety rules and the directions of the producer must be
observed.
Page 26/28 METTLER TOLEDO
Validation of Titration Methods
Validation of Titration Methods
METTLER TOLEDO Page 27/28
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