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ANALYTICAL CHEMISTRY, VOL. 50, NO. 14, DECEMBER 1978
Microprocessor-Controlled Differential Titrator Norbert Busch, Peter Freyer," and Hubert Szameit Abteilung Physiologische Chemie der Technischen Hochschule Aachen, 5 1 Aachen, West Germany
One of the most accurate methods for potentiometric titration of acids (or bases) is the direct registration of differential titration curves using two identical glass electrodes ( I , 2). T h e essential advantage of this measuring technique compared with other methods of titration is t h a t errors in measurement caused by zero-point-drift of the glass electrodes can be completely compensated for and that errors due to drift of the slope of the glass electrodes can be extensively adjusted. On the other hand, the handling of the apparatus used in direct registration of differential titration curves is relatively complicated and high demands are made upon the measuring-amplifier with regard to input impedance and the screening of input stages. T h e present work describes a further development of the a / m measuring apparatus with higher resolution and a higher degree of stability for fully-automatic registration of differential titration curves.
INSTRUMENTATION AND METHOD Figure 1 shows a general view of the whole apparatus. The mechanical components comply essentially with the arrangement already described, consisting of the measuring cell in which the measuring electrode and the reference capillary electrode, which is filled by a pneumatic pumping mechanism, immerse and a dispenser (Hamilton, Model 77002) which permits stepwise addition of equal amounts of titrant ( > 2 WL). Calibration is simplified by the use of a calomel electrode which is removed from the solution during the actual titration. The electronic component of the measuring apparatus (Figure 2) was designed on rather new lines. The electrometer stages ( A l , A2) were extended by a further one (A31 for the calomel electrode, removed from the actual differential electrometer to increase stability, directly attached to the electrodes, and thermostated. With the relays S1 to S4, the potential of either of the glass electrodes against the calomel electrode (calibration) and the potential difference between the two glass electrodes (measurement), can be determined (differential amplifier: A7). By
:ALOMEL-ELECIRODE GLASS-ELECTRODE IRi GLASS-ELECTRODE IMJ I DIFFERENTIAL ELECIROMEIER
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Figure 1. Schematic representation of the measuring setup
using potentiometers P1 and P2, the amplification of amplifier combinations ( A l , A4) and (A2, A5) can be adjusted to the same, defined value, e.g., to 100 mV/pH. The apparatus is controlled via a corresponding interface by a microcomputer (Intel MCS-SO) with a 2k Byte PROM and a l k Byte RAM so that the run of titration and recording of data is carried out fully-automatically. Figure 3 shows the program for the recording of differential titration curves as a flow-chart. The program is available from the authors. At the beginning of each measurement the parameters, M = maximum number of additions from dispenser, J = maximum number of measuring cycles for determination of final value, and D = stability of value, are entered at the teletype. Titration is then started and first the voltage E,, which is found when both electrodes are in the same solution, is measured and stored. Then an aliquot of titrant (base or acid), adjusted at the dispenser, is added N times to titration solution (CALL DISPENSER), till the voltage E measured after 5 s is just greater than 0.01 V corresponding to I p H = 0.1, but not more than five times. Afterwards the final value of E is determined and N and IE = E - E , are printed or punched at the teletype. Finally the electrodes are rinsed 5 times (CALL ELECTRODE) so that the solutions in the measuring cell and in the capillary electrode are completely mixed and the value E , re-determined after a further
f Figure 2. Block diagram of the differential amplifier. R,-R, = lKQ, R,-R, = 20 KR, R,,-R,3 and R16-Rl, = 10 KR, Rl,-R,5 = 7 KR. CI-C, = 470 pF, C&, = 1 nF. A,, A, = Operational amplifier (Analog Devices, model 311 J); A3 = Operational amplifier (Analog Devices, model 42 K); A4-A, = Operational Amplifier (Analog Devices, model 184 K). S,-S, = Herkon relays. Pi, P, = 5 K (Beckman Helipot) 0003-2700/78/0350-2166$01.00/0 C 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 14, DECEMBER 1978
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5 s. This cycle is repeated as often as necessary till the initially given number of additions from the dispenser (hfl is attained or just exceeded. On determining E , or the final value of E , the measurement as an average value from 10 single measurements is repeated until two consecutive values are stable within the given value D (e.g., D = 0.0003 V), repeated at the most, however. J times.
RESULTS AND DISCUSSION In order to check the apparatus regarding resolution and reproducibility, we have carried out titrations on diluted aqueous solutions of citric acid and compared the results with theoretical values which were calculated on the basis of an iterative method using mean activity coefficients and under consideration of the dilution during titration. As a tri-basic acid, citric acid has a differential titration curve with three peaks where t h e first two peaks are only detectable on high resolution of the titrator because of the small difference in p K values. In Figure 4 two titration curves recorded under identical experimental conditions (citric acid from Merck. Stock no. 244 p.A., concentration: 0.01 mol/L acid + 0.1 mol/L KC1, temperature T = 25 "C) are compared with the calculated curve (pK1 = 3.128. pK2 = 4.761, pK3 = 6.396 (pK values from Bates ( 3 ) ) )plotting , the log(ApH/Aq) against the titrant equivalent q . T h e precision of t h e apparatus with which the two quantities ApH/Aq and q can be determined, depends on volumetric errors of t h e dispenser on the one hand, and titrimetric errors of small p H differences on the other. By the use of standard buffers ( 4 ) pH differences with a relative error
Figure 4. Differential titration curve of citric acid. 0.01 M acid 0.1 (x) measured values, drawn line was calculated M KCI at 25 OC. ((-I-), using the following pKvalues: pK, = 3.128, pK, = 4.761, pK, = 6.396)
of 0.2% can be determined. Accordingly, small p H differences (ApH
