Fresenius Z Anal Chem ( 1983) 315 : 109 - 112 Fresenius Zeitschrift fiir
9 Springer-Verlag 1983
A New Approach to Titrimetry
H. Barrels 1 and P. Walser 2
! Central Analytical Department, CIBA-Geigy Ltd., CH-4002 Basel 2 Hamilton Bonaduz AG, CH-7402 Bonaduz, Switzerland
Anweudung eines neuen Titrierprinzips
Zusammenfassung. Es wird ein universelles Titriersystem beschrieben, welches sich ftir potentiometrische und photo- metrische Routinetitrationen eignet. Fltissige Proben k6nnen ohne Vorbereitung und Abmessen durch Wfigen oder Pipet- tieren direkt bestimmt werden, da die Titration im DurchfluB erfolgt. Fiir die Bestimmung des Endpunkts durch Interpola- tion werden nur 4 -10 Inkremente ben6tigt. Die Resultate werden nach Titrierzeiten yon 1 - 4 min mit einer Reprodu- zierbarkeit yon 0,2 % erhalten.
Summary. The universal titration system described is es- pecially designed for potentiometric and photometric routine titrations. The flow system implies the possibility to titrate liquid samples directly without pipetting. The interpolation of the endpoint is based on only 4 -10 increments. The out- standing reproducibility of + 0.2 % S.D. is combined with fast titrations of 1 - 4 rain.
In titrimetric analysis substances are determined by adding increments of a titrant with a known concentration to a sample of unknown concentration. The equivalence point is reached when all the substance in the sample has reacted stoichiometrically. This is indicated by the change of a suitable physical property of the titrated solution such as colour, electrochemical potential, conductivity, spectropho- tometric properties etc.
In a former paper we reported on a new highly flexible approach to the automation of photometric industrial control analysis with AMICA . With basically the same hardware the benefits reported for photometry may also be realized for titrimetric methods however in quite an unconventional manner: by the stopped-flow technique aliquots of the sample are mixed with aliquots of the titrant, measured and discar- ded. The degree of dilution is altered until the equiva- lence point is reached. As a new aliquot is taken for each measurement the problem of 'over-shooting' of the endpoint does not exist anymore.
Modern microprocessor controlled titrators need at least about 30 increments in order to find the endpoint . With AMICA, this number is reduced to 4 -10 increments or
Offprint requests to: H. Bartels
aliquots, respectively. Therefore, routine titrations can be run faster than before. Due to the flow-through principle, the sample change is extremely simple. The titration cell is cleaned automatically with aliquots of 2 ml of a sample titrant mixture. The principle is easy to automate : The autosampler dips the probe into the liquid, the corresponding aliquots are taken and mixed with titrant until the endpoint is found, the calculation is done and the probe is forwarded into the next sample. The probe may also be linked to a production stream.
The main instrument is the liquid processing unit (LPU), which contains two step-motor driven syringes, pumping aliqouts of sample and titrant through a static mixing chamber, A combined electrode is mounted at the outlet of this chamber and the potential of the electrode is digitized by the analog-digital converter of the LPU. A microcomputer with 64 kB memory, floppy drive and screen manages the LPU via interface of the type RS 232 C. All methods and all results can be edited on a matrix printer/plotter. Together with the autosampler - designed for up to 50 different samples - this gives a complete autotitrator system . For phototitration a spectrophotometer is added, which either may be interfaced to the microcomputer itself or connected to the analog-digital converter of the LPU. The liquid manifold is chemically inert and air-tight. The tubings are provided with threaded fittings made of Teflon FEP. The sample tubes  are covered with a silicon septum.
3. System Software
The software packages are subdivided into four sections: (I) Set-up-program for the establishment of methods and the configuration, (II) Run-program, (III) Result-summary- program and (IV) Auxiliary functions comprising mV/pH- measurement and plotting of titration curves. Thus, the operation of AMICA titration systems is thoroughly anal- ogous to that of the photometry system . This paper will deal more in detail with the algorithms related to the new approach in titrimetry with AMICA systems.
Algorithms for Endpoint Determination
As already pointed out AMICA approaches the endpoint from both sides by altering the mixing ratio of individually made and measured mixtures. To be clear: It does not add successive aliquots of titrant to a fixed sample volume. In practice the user has to define the expected result and the
percentage deviation in both directions. In control analysis this window will be small : e.g. 5 ~ to ___ 10 ~. In other cases it may be larger, up to + 85 ~. Together with the specification of the percentage deviation, the user has to give a minimum interval resolution, corresponding to the increment interval in ordinary titration.
With these data the instrument performs two titrations : a 'coarse titration', which locates the endpoint within the specified window to an accuracy of only 2 resolution interval, and a fine titration which locates the endpoint with high precision.
The search algorithm progresses in the following manner. The minimum and the maximum mixing ratios are calcu- lated:
varied with constant increments in upward or downward direction.
Another important feature of the AMICA titration systems is the way consecutive samples are treated, when the result of the first sample has been determined: As the contents of the samples normally is very similar in control analysis, the computer starts the titration directly with the fine titration. In this case, the endpoint can be determined definitively with a total of only four mixing ratios. The range of the fine titration may shift slightly during the run of a series of samples depending on the results. With variable sample weights, the starting-point of the fine titration is recalculated for each sample. If the contents vary considerably, each titration will start with the coarse titration.
MRmin 1, MRmax 1
aR1 ( I177 R1) W( l iAW) +v~ CF1
MRmin 2, MRm~x2
= W('I -}- AW) V R2 (1 q- z]2) (1 -l- 3 AR2) -- L CF2
R Expected result in the specified units, A Deviation of result in percent, AR Minimum incremental resolution in percent, W Weight of sample in rag, A W Deviation of weight input in percent.
Performing these mixtures and measuring the correspond- ing mV-values enables the instrument to decide whether the endpoint may be found in the specified window. If so, further mixing ratios are calculated by the program to encircle the endpoint.
With inflexion point titration, the interval of the mixing ratio is bisected geometrically on the primary interval with the largest mV-change of the electrode or the photometer. As soon as only four intervals with the minimum resolution are remaining, the shuttling behaviour of the 'coarse titration' is terminated and the remaining mixing ratios next to the endpoint are performed incrementally in the same direction as with conventional digital titrators.
The interpolation of the mixing ratio for the calculation of the equivalence point is made with four mixing ratios according to the method of Keller-Richter , in limiting cases according to Hahn-Weiler .
With fixed endpoint titration however, the bisection of the intervals is adjusted in relation to the fixed endpoint value given in mV, pH, absorbance or transmittance. The following mixing ratio MR~ is interpolated linearly from the preceding mixing ratios by the formula
MR - - MRi- 2 mVfl ~ - mVi _ 2 MRi - 1 - - MRs_ z mVi_ 1 - mV~_ z
Again, when the number of the remaining intervals with the minimum resolution is only four or less, the 'coarse titration' changes to 'fine titration', where the mixing ratio is
Algorithm for Final Calculation
From the equivalence point the final result is calculated in a conventional manner.
Several result units can be selected such as nil, Mol/1, mg per tablet, mg/ml, %-weight, %-weight from density and arbitrary units. The calculation formulas are for the first endp oint:
(MR1" Vs" PF - V~) CF1 R 1 =
for the second endpoint:
(MR2 - MRO 9 Vs" PF. CF z R 2 =
1, 2 Index for endpoint, R Final result in the specified units, MR Interpolated mixing ratio, Vs Sample volume in ml (default 1), PF Predilution or titrant correction factor (default 1), V~ Blank volume in ml (default 0), CF User defined conversion factor or further parameters like molec-
ular mass, normality, valence, W Sample weight in mg (default t), :~ For normal titration 1, for back titration -1.
The needed parameters are asked by the computer via dialogue and stored on the disk. For examples see Tables 1, 5 and 8. -
These few examples demonstrate the flexibility of the AMICA-titration principle. However in order to cope with the many specialities of practical samples even more sophisti- cated algorithms are included in the software package. They will be published in a forth coming paper.
To demonstrate the simplicity and reliability of the titrations some practical examples will be given. The first is an aqueous titration to a preselected endpoint. Drinking water usually has a pH in the range of 7 - 8.3. In these cases the hardness due to carbonates can