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 - 1 0 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 - 1 0 increments. The out- standing reproducibility of + 0.2 % S.D. is combined with fast titrations of 1 - 4 rain.

1. Introduction

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 [1]. 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 [2]. With AMICA, this number is reduced to 4 - 1 0 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.

2. Instrumentation

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 [1]. 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 [3] 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 [1]. 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

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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 A M I C A 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 ( I • 1 7 7 R1) W ( l i A W ) + v ~

CF1

VsPF

MRmin 2, MRm~x2

= W('I -}- AW) V R2 (1 q- z]2) (1 -l- 3 AR2) -- L CF2

I

R1]

VsPF

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 [4], in limiting cases according to Hahn-Weiler [4].

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

M R i - 1 - - M R s _ 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" P F - V~) CF1 R 1 =

W

for the second endpoint:

(MR2 - M R O �9 Vs" PF. CF z R 2 =

W

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-ti trat ion 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.

4. Applications

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 easily be calculated from the m-value [5]. The m-value is obtained by a fixed endpoint titration to pH 4.3 with 0.1 N hydrochloric acid. The method parameters are listed in Table 1. At the beginning, the glass electrode is calibrated with the electrode calibration program incorpo- rated in the software package. Then, the configuration parameters of Table 2 are selected. Table 3 shows the results of five determinations of the same sample (drinking water at

Table 1. Method for the determination of the m-value

Method number Revision date Titrant Method type Sample weight Sample volume Expected result Minimum interval Max, electrode drift Method name Electrode Normality Predilution factor Blank Deviation of result Conversion factor Fixed pH

27 1-12-81 HC1 pH 0 mg 1 ml (default) 3 mMol/l 2.5% 2 mV/2 s m-Value Glass/Ag/AgC1 0.1 1 0.0005 ml + 50% lO0 4.3

Table 5.

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Method for the determination of the tin(II) concentration

Method number 16 Revision date 21-6-82 Titrant KI 3 Method type inflexion Sample weight 0 mg Expected result 20 g/1 Minimum interval 2 % Max. electrode drift 1 mV/1 s Method name Tin-(II) Electrode Platinum Normality 0. l Predilution factor 1 Blank 0 ml Deviation of result + 40 % Conversion factor 5.9345 Minimum mV-change 20 mV

Table 2. Configuration for the m-value titration

Left syringe Right syringe Total dispense volume Fill/dispense time Sample rinse volume

2.5ml 0.25 ml 2 ml 2s 2.5 ml

Table 6. Configuration for tin(II) titration

Left syringe 2.5 ml Right syringe 2.5 ml Total dispense volume 2 ml Fill/dispense time 2 s Sample rinse volume 2.5 ml

Table 3. Results for drinking water

Determination m-value (mMol/l)

Carbonate hardness (~

1 4.13 11.6 2 4.09 11.5 3 4.14 11s 4 4.11 11.5 5 4.11 11.5

Reproducibility 0.48 % 0.48 %

Table 4. Typical mixing ratios for m-value titration. Calibration line of the electrode mV = 434.09- 58.2173 pH

Mixing ratio pH-value

0.01381 (min.) 6.30 0.04836 (max.) 3.41 0.03774 5.21 a 0.04316 3.88 a 0.04141 4.39 a 0.04245 4.01 b 0.04141 4.47 b

Interpolated endpoint 0.04179 Result 4.13 mMol/1

a Coarse titration b Fine titration

Bonaduz ) . The m-va l ue c o r r e s p o n d s to the b i c a r b o n a t e c o n c e n t r a t i o n , as the p H of the sample was m e a s u r e d to be 7.82. Tab le 4 ind ica tes the d i f fe rent mix ing ra t ios of the f irst t i t r a t ion .

Table 7. Performance of the tin(II) titration

Mixing ratio mV-value

1.90545 (min) -3 .7 5.00752(max) 368.0 3.09744 47.1" 3.96273 349.9" 3.51412 331.9 ~ 3.29570 86.2" 3.23118 69.6 b 3.29570 76.4 b 3.36022 294.5 b 3.42473 324.5 b

Interpolated endpoint 3.32983 Result 19.8 g/L

Reproducibility < 0.2 % Accuracy of the method < 0.1%

a Coarse titration b Fine titration

The c a r b o n a t e h a r d n e s s is o b t a i n e d by mu l t i p l i c a t i on wi th the f ac to r 2.8. This of course is equ iva l en t to us ing the c o r r e s p o n d i n g c o n v e r s i o n fac to r di rect ly in the m e t h o d file. The to ta l h a r d n e s s was d e t e r m i n e d by a p h o t o m e t r i c t i t r a t i on wi th E D T A a n d Er io T as ind ica tor . The resul t for the same sample was 14~

In the s econd example the r e d o x - t i t r a t i o n of the s t a n n o u s ion in a s t rongly acid electropIating bath is d e m o n s t r a t e d . Tab le 5 c o n t a i n s the m e t h o d p a r a m e t e r s n e e d e d a n d Tab le 6 con t a in s the con f igu ra t ion . Tab le 7 gives the mix ing ra t ios of a typica l t i t r a t i o n a n d some qual i ty fac to rs of the m e t h o d . The same t i t r a t i o n is also poss ib le as a direct p h o t o t i t r a t i o n at a w a v e l e n g t h of 510 nm.

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Table 8. Method for non-aqueous titration of phenylbutazone

Method number 22 Revision date 23-6-82 Titrant TBAH Method type inflexion Sample weight 200 • 5 mg Sample volume 40 ml Expected result 100 % (weight) Minimum interval 1% Max. electrode drift 1 mV/1 s Method name PhButa Electrode Glass/Ag/AgC1 Normality 0.1 Predilution factor 0.9838 Blank 0.05 ml Deviation of result • 2 % Conversion factor 3083.8 Minimum mV-Change 10 mV

Table 9. Configuration for the titration of phenylbutazone

Left syringe 2.5 ml Right syringe 2.5 ml Total dispense volume 2 ml Fill/dispense time 4 s Sample rinse volume 2.5 ml

Table 10. Performance of the titration ofphenylbutazone, Sample weight 193.9 mg

Mixing ratio mV-value

0.15130 (min.) -206.8 0.18370 (max.) -602.9 0.16642 -528.9 a 0.15797 - 300.1" 0.16134 -446.2" 0.15652 -272.3 b 0.15797 -300.4 u 0.15942 -336.3 b 0.16087 -421.2 b 0.16232 -416.3 b

Interpolated endpoint 0.16022 Result 98.7 ~ (weight)

Reproducibility < 0.2 % Accuracy of the method < 0.1%

The last example illustrates the advantages of AMICA titration systems for non-aqueous titrations especially with air-sensitive samples or titrants. The purity ofphenylbutazone is checked by a potentiometric titration with TBAH accord- ing to [6]. Table 8 lists the method parameters and Table 9 the configuration. About 200rag of the dried substance are weighed into a sample tube and dissolved in exactly 40 ml of acetone. The blank volume is determined with acetone alone and the factor of the titrant is obtained from a titration of standard benzoic acid. The mixing ratios and the perfor- mance of the method are summarized in Table 10.

5. Discussion

The new titration principle has many advantages over the classical approach: To determine equivalence points less measuring points are needed, while the precision compares well with the one obtained by conventional algorithms.

Due to the stopped flow principle the instrument becomes very flexible as different indicating electrodes or even simple colorimetric devices with analog output (which normally is linked to the recorder) may be integrated at ease. The titration can be performed after many different algorithms to suit the specific needs of the chemist. Furthermore, by the stopped flow principle automation of sample changing becomes very simple and inexpensive. This is also true for process control as the needed aliquots are taken automatically anyway.

After titration the original sample is not lost, it may be inspected or reanalyzed by a different procedure.

The ease of automation and the high degree of precision make this titration principle especially suitable to obtain statistically significant figures for quality control.

References

1. Bartels HA, Walser P (1983) Fresenius Z Anal Chem, 315:6-11 2. Geil JV, Reger H, Richter W, Sch/ifer J (1982) Labor Praxis, Jan/

Feb : 24 3. Bartels HA, B6hmer M, Schatzmann HR (1982) Fresenius Z Anal

Chem 313 : 43 - 44 4. Ebel S, Kalb S (1976) Fresenius Z Anal Chem 278:109-114 5. Hfitter LA (1979) Wasser und Wasseruntersuchung. Diesterweg/

Salle, Frankfurt am Main Berlin Mt~nchen pp 155 - 160; pp 134-137 '6. US Pharmacopeia (1979) Vol XX, 15. ed. US Pharmacopeial

Convention Inc, Rockville, p 617

" Coarse titration b Fine titration Received December 1, 1982