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PROCESS FOR PH-CONTROL AND STOICHIOMETRIC PH-STAT MEANS

The present invention relates to a process for adjusting the pH to a given value, as well as a stoichiometric pH-stat means for completing the process.

In general, the chemical, biochemical and biological processes take place in a desired way, that is, e.g. at a proper rate and/or with a suitable result, only when a given pH exists. A change in pH occurring as a direct consequence of a certain process might induce a cease in the chemical reaction within the process or decrease the rate of reaction. Therefore, it is a general object that the actual and measurable pH of the reaction medium be as close as possible to a pH level that is optimal with respect to the course of reaction.

Maintaining pH at a given value is generally assured by making use of buffer solutions, or the change in pH is compensated through the titration type introduction of a strong acid or strong base. The use of buffers spread mainly in case of biological systems. Its drawback lies in the fact that the buffer capacity can not be calculated always precisely and hence, in general, a buffer of larger capacity than necessary is applied. Thus the occurring electrolyte effect might disturb the revelation of the course of reaction(s) taking place within the biological system under study. A further drawback of the use of buffers is that in certain cases, e.g. in systems of biocolloidal (protein, polysaccharide) solutions of poly- electrolytic nature, the presence of electrolytes leads to undesirable aggregation. Moreover, the ions of the buffer can come into specific interaction(s) with the molecules of the given system, and/or they can alter even the equilibrium process or reaction (e.g. an enzyme reaction) to be studied.

In general, the expression ,,pH-stat device/process/means" here refers to such a device/process/means by means of which the pH of a given chemical system can be maintained continuously at a pre-set fixed pH-value within a predetermined tolerance level, that is, the change of pH can be continuously compensated for.

All pH-stat devices known in literature control the pH of a reaction medium by means of PID (proportional, integral and differential), AAA (additive adaptive), ,,neural network" based algorithms or further mathematical algorithms of similar

concept through the estimation of so-called adaption parameters. The changes in the acidity or alkalinity of the reaction medium is to be compensated for as precisely as possible by means of measuring the kinetics (i.e. the rate of change) of the changes in pH; a strong acid or base (from now on, together a titrant) is fed into the reaction medium through a titration type procedure in an amount that corresponds to the adaption parameters estimated on the basis of the measured kinetics. For instance, EP Publication Pamphlet No. 0,457,989 A1 discloses a solution, wherein parameters determined from titration curves are used for a better/more precise estimation of the actual behaviour of the chemical processes taking place within the system.

A drawback of said estimation-based adaptive techniques is that the titrant dosing based on the kinetics of the change in pH is not accurate enough: the faster the pH changes, the less accurate the estimation and hence the determination of the amount of titrant to be introduced is, that is, the compensation of the change in pH itself after all. Thus, smaller or larger excesses of the optimum pH-value are always present in the system studied and after a repeated estimation one tries to compensate these according to needs through the introduction of a titrant inducing a change in pH just opposite to the one caused by the previously used titrant. Therefore, while in turn acid and base is added to the system, the actual pH-value is waggling, that is "oscillating", about the required optimum pH-value within a range depending on the values of the estimated adaption parameters. Hence, to soften the changes in pH, buffers are applied widespread in such cases, too.

In the system under study the reaction slows down mostly at a rate that corresponds to the reagent consumption, thus the rate of titrant introduction has to be adjusted continuously to the actual reaction rate. In lack of this, irreversible changes might arise in the system that are, in general, adverse to the final goal, which in certain cases, for instance when diagnostical assays of various samples are to be performed, is impermissible. The continuous adjustment of the rate of titrant introduction can be reliably reached merely by means of so-called self- adapting equipments that are extremely complex and expensive, such as e.g. the "neural network" based instruments. A possible example of said instruments is discussed in detail by J. Havel, P. Lubal and M. Farkova in the paper entitled

Evaluation of Chemical Equilibria with the Use of Artificial Neural Networks (Polyhedron, 21, 1375-1384, 2002).

The aim of the present invention is to provide a process and a special means for its completion which, for reactions with known course eliminate the above discussed problems related to pH-stat processes and equipments commonly used nowadays. In particular, the aim of the present invention is to provide a pH-stat process and means by the application of which the random and unexpected amount of oscillation of the actual pH-value, which is basically a consequence of the estimation of the parameters characteristic of the system itself, around the pH-value to be maintained can be avoided within the system under study. A further aim of the present invention is to provide such a process and means wherein no prediction for adaption parameters being crucial from the aspect of following up the change in pH is required. A yet further aim of the present invention is to provide such a process and means wherein the pH can be kept at a predetermined value or within a predetermined range around said value without the need for applying complicated self-adapting "neural network" based algorithms that are expensive to be implemented.

In our studies it was found that with having precise knowledge of the mechanism of the reaction(s) taking place in a system containing known compo- nents in known amounts, the pH of the system can be kept at a constant value within the required accuracy by means of introducing only one type of titrant (that is either an acid or a base) into the system in an amount calculated on the basis of the actual chemical equilibrium/equilibria that is/are characteristic of the system itself. In this manner the electrolyte effect decreases to a great extent within the system and the risk of an accidental damage of the system (e.g. of a diag- nostical assay) also reduces significantly. Moreover, there is a need neither to estimate adaption parameters nor to introduce titrants of opposite effect alternately in amounts determined on the basis of parameters being inaccurate in lot of cases. Finally, the pH-value required can be set precisely and be maintained continuously (within the measurement accuracy of the pH).

The object aiming at providing a process for adjusting the pH to a fixed value is accomplished by the process stipulated by Claim 1. Possible further preferred embodiments of the process according to the invention are defined by

Claims 2 to 6. The object aiming at providing a stoichiometric pH-stat means for maintaining the pH at a constant value is accomplished by providing the pH-stat means of Claim 7. Possible further preferred embodiments of the pH-stat means according to the invention are defined by Claims 8 to 12. The advantage of the pH-stat process according to the present invention and the stoichiometric pH-stat means for accomplishing thereof with respect to the automatic titrant apparatuses used frequently nowadays is that there is a need neither for adaptively estimating various parameters nor to include costly and lengthy learning periods when these are applied. Furthermore, for the inven- tive solution, the maintenance of pH at the pre-set level is assured by introducing only a single type of titrant (that is, either an acid or a base) in a precise amount which is calculated on the basis of the balance(s) that is/are actually characteristic of the system. In the process for adjusting the pH according to the present invention, the amounts of protons or hydroxide ions evolved in the process taking place spontaneously are neutralized in an equivalent amount by means of calculating the required amount of titrant to be introduced with knowledge of the chemical system. The variations about the required pH-value can be minimized by fixing the predefined tolerance level. In this manner the risk of excess of pH in an extent that can be harmful to the chemical system is fully eliminated or at least can be decreased to a minimal level. In addition, as it will be clear from the following detailed description, the elaborated pH-stat process and means can be easily tailored to any proton transfer process by adapting the equilibrium material balance equation(s) and the electroneutrality equation(s) to the system to be studied. Accordingly, in light of our studies performed earlier, the pH-stat process and means according to the present invention can be successfully applied also

(a) to keep the pH at a fixed level in a chemical system containing a strong acid/strong base;

(b) to set the pH to an arbitrary value within a chemical system containing a weak acid/weak base; (c) to keep the pH within a chemical system containing a weak acid/weak base when simultaneously an acid/base is consumed/produced in the system due to a given external reaction/process.

Hence, the pH-stat process and the stoichiometric pH-stat means for the completion of the process exhibit a wide-range and cost effective applicability, for instance in the field of chemical analytical assays.

In what follows, the invention is described in more detail with reference to the accompanying drawings, wherein

- Figure 1 illustrates a schematic diagram of the stoichiometric pH-stat means representing a possible embodiment of the invention;

- Figure 2 is a flowchart of the pH-control step that forms essential part of the pH-stat process according to the invention; - Figure 3 shows a block diagram of a preferred practical embodiment of the process for maintaining the pH at a fixed value;

- Figure 4A illustrates monitoring of the photocatalytic decomposition of di- chloroacetic acid (DCA) in the form of plotting a change in volume of the base added to DCA, as sole titrant, as a function of time, said monitoring is per- formed by the process and by the stoichiometric pH-stat means for completing the process as shown in Figures 2 and 3, respectively; and

- Figure 4B shows the change in pH taking place in relation with the photo- catalytic process of Figure 4A and its compensation as a function of time.

Figure 1 illustrates a schematic diagram of the stoichiometric pH-stat means 10 representing a possible embodiment of the invention. Basically, the pH-stat means 10 comprises two major parts, a measuring unit and an actuating unit, each of which is in data transfer connection with a processing unit 26. The measuring unit comprises a pH electrode 12, a signal converter 15 having at least one input electrically connected to the pH electrode 12 and a microcontrol- ler 18 having at least one input electrically connected to a suitable output of said signal converter 15. An output of the microcontroller 18, as an output of the measuring unit, is in data transfer connection with the processing unit 26. Said data transfer connections of the microcontroller 18 and of the processing unit 26 are preferably realized by means of a suitable interface (not shown in the draw- ing). The processing unit 26 comprises at least a memory 23, a processor 24 and a data storage means 25 that are electrically connected to one another. Preferably, the memory 23 and the data storage means 25 are physically separated from the processor 24, however, they can be realized as an internal memory of

the processor 24, too. In a preferred embodiment, the processing unit 26 is a (portable) personal computer.

The pH electrode 12 is provided in the form of an activated pH sensor with good reproduction capability (preferably at least of ±0.05 pH units) and of high precision (preferably at least of ±0.01 pH units) that generates the measured pH-value at its output in the form of an electrical signal, preferably as an electrical voltage signal. Depending on the actual chemical system under study, the pH electrode 12 can be substituted by other kind of sensors (e.g. by ion selective electrodes, redox electrodes, tenside selective electrodes and by similar further electrodes) that also generate an electrical signal, preferably an electrical voltage signal at their output.

The signal converter 15 converts the analogue signal appearing at its input into digital signals by means of an analogue-to-digital converter 16 which, preferably, forms part thereof. The analogue-to-digital converter 16 is preferably a 24-bit converter, however, a different kind of converter can also be used. Before being digitized, in case of need, the analogue signal appearing at the input of the signal converter 15 is subjected to amplification performed by a preamplifier 14. The simultaneous handling of a couple of incoming signals is aided by a built-in signal selector (multiplexer), not shown in the Figures, forming part of the signal converter 15. To ensure executability of the process to be discussed later in detail within the required accuracy, the sampling frequency of the analogue-to-digital converter 16 is chosen to be preferably 10 data/s, more preferably 15 data/s, and most preferably 20 data/s, however, a different sampling frequency can equally be made use of. The actuating unit comprises at least a dispensing means 20. The dispensing means 20 is preferably a programmable and automated dispensing means (e.g. a Dosimat [Metrohm] or any other kind of automated burette). The dispensing means 20 is in liquid transfer connection with a liquid reservoir 20a containing a titrant (that is either a strong base or a strong acid, as demanded, depending on the nature of the chemical reaction to be completed). Additionally, the dispensing means 20 is in data transfer connection with the processing unit 26. The dispensing means 26 has got a relatively small dispensing volume (about 2 μl) and a relatively high dispensing rate (about 1000 μl/s). When several

dispensing means 20 are applied, each of the individual dispensing means is connected to (a) liquid reservoir(s) each containing a titrant of the same nature (that is, either a base or an acid) or the feeding of titrant can be performed only by means of a single dispensing means 20 in the course of reaction. A possible further embodiment of the stoichiometric pH-stat means 10 may be equipped by various further supplementary elements besides the ones discussed above. Such a supplementary element is e.g. an electronically controlled magnetic valve 21 for regulating the feeding of an inert gas (e.g. nitrogen, N ₂ ) or the feeding of a reaction promoting gas (e.g. oxygen, O ₂ ) which are intro- duced in certain cases into the system to effect the measurement in a more precise manner, and an electronically controlled stirring means 22 for ensuring a homogeneous material distribution within the system during the reaction, and/or a temperature sensor 32 for measuring the temperature of the system under study (and thus of the reaction itself), as well as a thermostat 33 for setting the temperature within the system based on the signal of the temperature sensor 32 to a given/required value and maintaining it at that temperature. Generally, these supplementary elements are in direct electrical connection with the microcontroller 18, although their control/reception of their signals can be carried out by the processing unit 26, too. The solution of the aimed technical problem to be solved by the invention, that is, the pH-stat process which is effected by making use of the results of calculations performed for the chemical equilibrium state as control parameters generally takes place as follows.

As a start, with knowledge of the chemical reactions characteristic of the system, the material balance equations are established for the acid/base, as a component, to be titrated in the system (acid residue/base stoichiometry). In a like manner, the material balance equation for the proton, as a component, taking part in the equilibrium distribution is also established (proton stoichiometry). This reveals amongst what kinds of chemical moieties (speciation forms) the total proton amount distributes. The third equation required for completing the calculation defines the distribution equilibrium amongst the various speciation forms. Besides the relations obtained in this way, the condition of electroneutrality is also taken into account; according to this, the sum of anion concentrations in the

system is equal to the sum of cation concentrations in the system. The system of equations comprised of the thus obtained equations is reduced to a single equation characteristic of the system under study by performing simple algebraic operations (analytically or numerically). From this equation the proton concentra- tion, the amount of titrant to be added (preferably its volume) or the equilibrium dissociation constant can equally be expressed as a function of the two other quantities and that of further known quantities (concentration of the added titrant, initial volume of the system under study) or of equilibrium constants (such as the equilibrium dissociation constants for water or the reaction(s) taking place). To accomplish the pH-stat process according to the invention, the amount of titrant to be added is expressed from the equation at issue. It should be noted here that the proton concentration and the equilibrium dissociation constant can also be expressed from this equation which means that the obtained equation can serve as a starting point for the description of a titration curve or to characterize the quality and/or purity of the acid/base present in the system to be titrated. Said equations and the way of deriving them is given below in brief.

1. When an acid HA dissociates in accordance with the reaction [HA] <-> [A ^" ] + [H ⁺ ] and the relation for the equilibrium dissociation constant K _d of the process is also taken into account, the concentration of the dissociated acid residue can be calculated by the relation [A ^" ] = (K _d * CHA)/(K _C I + [H ⁺ ]), wherein [.] denotes the concentration of the ion considered and CHA is, in turn, the total acid concentration. Here, the relation C _H A = [A ^" ] + [HA] is also exploited.

2. When a titration of the acid HA by a base /W ⁺ OH ^" is carried out to set a given pH, the concept of electroneutrality, that is [M ⁺ ] + [H ⁺ ] = [A ^" ] + [OH ^' ], holds in every instant. Here, [M ⁺ ] can be expressed by the concentration c _ti t _r of the titrant (here of the base), the amount v _t jt _r of titrant added and the system's volume V ₀ measured before the titration step by the relation [M ⁺ ] = (c _ti tr * v _t jt _r )/(vo + v _t jt _r ), while [H ⁺ ] can be calculated e.g. on the basis of a calibration performed for the pH electrode 12, as it will be discussed later on. Exploiting the ion product of water, K _v = [H ⁺ ] * [OH ^" ], as well as the facts that the system volume increases if a titrant (e.g. a base) is added and due to the dilution, the total acid concentration decreases by a corresponding extent, the condition of electroneutrality can be written as

(Ctrtr * V _tltr )/(Vo + Vt.tr) + [H ⁺ ] = (K _d * (c _HA * V ₀ /(V ₀ + Vt.tr)) / (Kd + [H ⁺ ]) + (K _v / [H ⁺ ]). (1 )

From this latter equation the amount v _t ,t _r of titrant essential from the aspect of completing a pH-stat process can be unambiguously determined.

3. The yet required material balance equation pertaining to the protons, the distribution equilibria for the individual speciation forms, as well as the condition of electroneutrality characterizing the system as a whole can be established in the precise knowledge of the system being the subject of the pH-stat process. Without limiting the inventive solution to a particular process, a certain example thereof will be discussed later (for a given system and the reactions taking place within the system) in detail.

In light of the above, to realize the aimed pH-stat process the amount v _tltr of titrant to be added is expressed from the system of equations characterizing the chemical system. The pH-stat process itself is performed in subsequent steps. In the pH-control step of the process it is explored what the difference (δpH) of the pH-value (pH _m ) actually measured in the chemical system under study is relative to the fixed pH-value (pH _f , _x ) to be reached/maintained. If the difference δpH = |pH _m - pH _f i _X | exceeds a tolerance level defined through the relation δpH = IpH _f1x ± k pH _f ,χ| (wherein k«1 is an arbitrary small number), the amount of titrant to be added is calculated and then the calculated amount of the titrant is fed into the chemical system. Then, after performing a homogenization of the system (that is accelerated e.g. by stirring) the amount of titrant to be added is determined afresh by exploiting a system of equations established for the new equilibrium state, and then the pH measured in the new equilibrium state is compared with the fixed pH _f j _X -value. If the difference is larger than the prescribed tol- erance level δpH, the amount of the titrant to be added is determined again and then added into the chemical system. The present iterative process is continued until the course of the reaction concerned in the system under study is completed or the reaction itself is interrupted. It should be noted here that the possible minimum value of the tolerance level δpH is determined by the pH measure- ment accuracy and the smallest possible amount of the titrant that can be dispensed by the dispensing means, however, it depends on no further parameters. It should be also noted here that the change in pH of the chemical system can be

induced e.g. by adsorption processes, decomposition reactions, reactions leading to complex formation or chemical reactions that produce/consume acid/base. In what follows, the pH-control step based on a chemical equilibrium calculation and forming the essence of the invention is discussed in detail with ref- erence to Figure 2.

As shown in Figure 2, in the control step being the main subject-matter of the present invention, at first a pH measurement is performed in the chemical system by the pH electrode 12 (which has already been subjected to a calibration procedure to be discussed later in detail). The electrical signal obtained at the output of the pH electrode as a result of the measurement is fed into the signal converter 15, digitized and then the digital signal appearing at the output of the signal converter 15 is transmitted through the microcontroller 18 into the processing unit 26 which maps it to a pH-value on the basis of the calibration of the pH electrode 12. Then, in knowledge of the pH _m measured in this way, a de- cision is made on the issue whether or not the difference δpH = |pH _m - pH _f j _X | exceeds the pre-set tolerance level δpH. If the answer is not (see branch "No" of Figure 2), the chemical system requires no intervention, that is, there is no need for compensating the change in pH. If the answer is yes (see branch "Yes" of Figure 2), there is a need for compensating the change in pH. For this purpose, the system-specific equilibrium equations discussed above are solved (either numerically or analytically) using preferably the memory 23, the processor 24 and the data storage means 25, each being part of the processing unit 26. As a result of the calculation, the precise amount of titrant to be added into the chemical system is obtained which - as control parameter - is transmitted to the dis- pensing means 20. Having knowledge of the amount of titrant to be added an intervention is effected through the dispensing means 20: the calculated amount of the titrant (which is either a base or an acid) is introduced from the liquid reservoir 20a into the chemical system in order to compensate the change in pH due to the reaction. As a next step, to assure the higher accuracy (and thereby the more reliable pH-control), homogenization and/or temperature measurement and - depending on the temperature measured - temperature adjustment of the chemical system is performed optionally, provided that the pH-stat means used is equipped with suitable elements (that is, e.g. according to Figure 1 with a stir-

ring means 22, a temperature sensor 32 and a thermostat 33) for completing said operations. In the meantime, said chemical reaction is continuously taking place in the system, and hence the pH of the system is also changing. To decide whether or not a further intervention through the dispensing means 20 is re- quired, a new pH measurement is performed and depending on its result we proceed as discussed above. The decision option "exit?" shown in Figure 2 ensures the possibility, in case of need, for an interruption of the reaction (e.g. manually from the outside).

The pH of the system under study is converged towards the pre-set fixed value or is maintained in the vicinity thereof by feeding a single type of titrant into the system along with performing the pH measurement, as well as an intervention the extent of which depends on the result of the pH measurement, in such a manner that the difference δpH of the actually measured pH _m and the pre-set pH _f i _X remains within the tolerance level δpH all the time meanwhile. As is clear from Figure 2 showing the pH-control step, the amount of titrant to be added is preferentially derived by the processing unit 26 on the basis of the equilibrium equations only in that case if the difference between the actually measured pH of the system and the fixed pH _fix -value is larger than the prescribed tolerance level δpH. This allows the faster and more reliable completion of the pH-control step. In what follows, with reference to Figure 3, a pH-stat process put into practice preferably by means of the stoichiometric pH-stat means 10 sketched in Figure 1 is discussed in general, wherein said pH-stat process comprises the pH- control step forming the essence of the invention.

As is shown in Figure 3, before the commencement/start of the chemical reaction of known mechanism to be subjected to a pH-control, the pH electrode 12 is arranged within the chemical system to be studied containing no catalyst, the pH-stat means 10 is calibrated with respect to said chemical system (steps 100, 110), and then the initial value of the pH of the chemical system is measured (step 120). In what follows it will be discussed in detail how to perform an accurate calibration. After this, the initial concentration of the reagent of the chemical system to be brought into reaction is determined by means of the processing unit 26 by exploiting preferably the equations serving as basis for the chemical equilibrium calculations (step 130). Said initial concentration can be

(e.g. manually) altered according to needs. If the reaction requires the use of a catalyst, in the next step the catalyst facilitating the desired reaction is fed into the chemical system (step 140). After addition of the catalyst, to determine the pH which might change in certain cases, a new pH measurement is performed by the pH electrode 12 (step 150). Then, the required amount of titrant to be added so as to reach a fixed pHfj _X -value that is optimal from the aspect of the reaction to be effected in the chemical system is determined by a calculation performed by means of the processing unit 26 by exploiting preferably the system- specific material balance equations. The calculated amount of the titrant, as control parameter, is transmitted to the dispensing means 20 and the required amount of the titrant is fed from the liquid reservoir 20a by the dispensing means 20 into the chemical system (step 160). As a next step, the chemical reaction to be performed, which is preferentially a delayed-start reaction, e.g. photocatalysis, is commenced by a suitable action (by means of e.g. an external exposure) (step 170). After this, the further changes in pH are induced by the change in proton concentration due to the chemical reaction(s) taking place. During the course of reaction to be performed, the prescribed fixed pHfix-value is maintained all the time within the system through the pH-control (step 180).

In what follows, a possible preferred embodiment of the calibration proce- dure of the pH electrode 12 used in the pH-stat process is discussed in detail.

The basis for an accurate pH measurement and for the reliable proton- /hydroxide ion concentration calculation is the calibration of the electrode, of the titrant, as well as of the chemical system (that is, of an electrochemical cell composed of he components). The calibration, when integrated into the process of the pH-control, may form inherent part of the operation of the stoichiometric pH- stat means 10. The calibration procedure is carried out in two steps. As shown in Figure 3 (see step 100), in a first step the pH calibration of the pH electrode 12 to measure the pH is completed by means of different buffer solutions of known pH- values. For this purpose, electrochemical cells are assembled from the pH elec- trode 12 and the buffer solutions, cell voltage is measured on the individual cells, and when the cell voltage becomes constant said constant cell voltage, as well as the known pH of the buffer solution are recorded. For the pH calibration preferably at least three different buffer solutions are used; the accuracy of the pH

calibration can be enhanced by increasing the number of buffer solutions used. The pH calibration procedure aims at determining the cell voltage/pH relation. By fitting a linear function to the recorded data pairs, the cell voltage/pH relation (characterized by the parameters characteristic of the fitted lineal, that is, its slope and axial intercept) is obtained. The calibration of the pH electrode 12, that is, the cell voltage/pH relation, can be written in the form of an equation analogous to the Nernst equation; the slope is approximately equal to the Nernst factor. From now on, the thus obtained cell voltage/pH relation preferably stored in the processing unit 26 is used to determine the actual pH-value. After this, a concentration calibration of the pH electrode 12 is performed

(see step 110). For this purpose, a known amount of factored hydrochloric acid (HCI) is fed into an electrolyte solution of precise ionic strength. After stirring, the cell voltage is measured and then by exploiting the parameters (characteristic of a lineal) obtained during the pH calibration, the pH of the electrolyte solution is calculated. Then, a known amount (volume) of base titrant is added to the electrolyte solution and by means of a cell voltage measurement and of the pH determination as discussed above, data pairs of base volume/pH are derived. By fitting linear functions to the thus obtained data pairs in harmony with the relations 10 ^'pH = f(c _H +) and io ^~pOH = f(coH-). the base concentration, as well as further parameters (as slopes S ₃ = 10 ^"PH /CH+ and Sb = 10 ^'POH /COH-, wherein c _H + and C _O H- stand for the proton and hydroxide ion concentrations, respectively, of the system under study) characterizing the chemical system are obtained, which are preferentially stored in the processing unit 26 for the evaluations to be performed at later times. Finally, a strong acid of a known amount is titrated with a strong base; by evaluating the result, the relation between the analytical proton concentration and the measured pH is received which represents the calibration of the electrochemical cell used under the actual experimental conditions. Exploiting said relation, one can calculate the amount of the titrant (either an acid or a base) re- quired to be added in case of a process that aims at maintaining the desired pH. Said relation is preferably also stored in the processing unit 26. As the precision of the pH electrode 12 changes with time, the above discussed calibration procedure should be performed in every pH-stat process.

In what follows, the application of a stoichiometric pH-stat means 10 according to the invention, as well as the proton material balance equation and the condition of electroneutrality that are required for carrying out a pH-stat process according to the invention will be illustrated through a non-limiting example.

EXAMPLE

The above discussed pH-stat means 10 is illustrated on the one hand for the monitoring of photocatalytic decomposition of dichloroacetic acid (DCA) induced by ultraviolet (UV) exposure, and on the other hand for maintaining the reaction taking place at an optimum pH (that is, at pH _fix = 3,11). For the reaction, as catalyst, titanium dioxide (TiO ₂ ) is used, and the chemical system is subjected to heavy cooling. To enhance cooling, the photocatalytic decomposition is preferably performed along with circulating the chemical system in a closed circuit at a constant rate. The pH of the chemical system is measured in a certain zone of the circuit, preferentially along with stopping the circulation for the time period of the measurement. The temperature dependence of the measured pH is eliminated through the continuous thermostating of said measuring zone to a constant temperature.

Within said chemical system the concentration of DCA is continuously decreasing which is due to the titration (dilution) carried out (with a base) in order to maintain the pH at a constant value on the one hand and to the photocatalytic decomposition on the other hand.

Let's consider a decomposition step of finite length in time in which arbitrary number of decomposition events takes place. As a consequence of the decomposition of DCA molecules in this step due to a photocatalytic reaction, the concentration CDCA. _O I _C ! of the weakly dissociating dichloroacetic acid decreases with an amount of δC _D CA, which means that c _D cA,new = c _D cA,oid - δC _D CA holds; here the concentration CDCA. _O W is the diluted DCA concentration set before the decomposition according to the fixed pH _f j _X -value ([H ⁺ _Hx ]). Exploiting the relation that holds for the equilibrium dissociation constant K _d , the concentration of the DCA anions within the system after the decomposition process can be calculated by the equation [DCA ^" ] _new = ((cocA.oid - δC _D CA) * K _d ) / (K _d + [H ⁺ ]), wherein [H ⁺ ] is the

concentration of all the free protons (i.e. which are measurable by the pH electrode 12) present within the system.

As a result of the decomposition, every DCA molecule leads to two HCI molecules, which then dissociate and thus the concentration [Cl ^" ] of the chloride ions arising within the system will be equal to 2δC _D CA-

The condition of electroneutrality also holds in the new equilibrium state reached after the decomposition step, that is, the ion concentrations within the system satisfy the relation [H ⁺ ] + [Na ⁺ ] = [DCA ^" ] _ne w + [Cl ^" ] + [OH ^" ]. Employing the concentrations [DCA ^" ] _ne w and [Cl ^" ] obtained previously and the dilution of the system, the above relation can be rewritten as

[H ⁺ ] + (Ctitr * W(V ₀ + Vtitr) = (c _D cA,oid - δC _DC A) * K _d / (K _d + [H ⁺ ]) + 2δCDCA + MH ⁺ ].

From this latter equation, after simple algebraic operations, the relation

δCDCA = ([H ⁺ ] + Ctit _r *vtit _r /(vo+vtitr) - c _DCA ,oid * K _d /(K _d +[H ⁺ ]) - K _V /[H ⁺ ]} / (2 - K _d /(K _d +[H ⁺ ])) (2) can be obtained for the change in concentration of DCA. The process for main- taining the pH at a fixed value according to the invention is performed by exploiting a variant of the previously derived equation (1) that is adapted to the present chemical system (that is, C _H A = C _D CA), as well as equation (2) and the relation c _D cA,new = c _D cA,oid - δC _D CA within the framework of the previously discussed subsequent iterative steps in such a manner that when the amount vti _t r of titrant required in a given step is calculated on the basis of equation (1), the value of the total acid concentration CDCA reduced by the change in concentration. δC _D CA obtained from equation (2) in the previous decomposition step is used.

In the exemplified process, feeding of a base as titrant is required to maintain the pH at the fixed value. Figure 4A shows the change in base con- sumption as a function of the exposure time. Based on the previous considerations, the amount of the decomposed DCA can be accurately calculated from the amount of base required for maintaining the pH at the fixed value and/or the decomposition reaction's kinetics can be traced. Figure 4B illustrates the temporal variation of the measured pH of the chemical system. From Figure 4B it can be easily seen that the value of pH _fix = 3.11 , which is optimal as far as the photo- catalytic decomposition is concerned, can be kept by the stoichiometric pH-stat means 10 according to the invention within the accuracy of ±0.02 pH units (that

is, within the error of ±0.6%) in the TiO ₂ /DCA suspension all the time during the UV exposure. It should be noted that part of this error derives from the pH measurement's systematical error of ±0.01 pH units, which means that it can be decreased by enhancing the precision of the signal converter 15. For the present example the tolerance level, that is, the value of δpH = |pH _f j _X ± k-pH _f j _X | was fixed by the choice of k = 0.05.

Finally, it should be noted here that for (optionally catalytic) processes differing from the photocatalytic decomposition of DCA or for processes with changes in the weak acid concentration and/or proton concentration due to any other reason - provided that the equilibrium is governed by the dissociation equilibrium of a weak acid (buffer) present within said system - only equation (2) giving the change in concentration of the weak acid has to be remade by exploiting the material balance equations and the condition of electroneutrality of the reactions actually taking place within said system in order that the pH-stat process of the invention be accomplished.

Briefly summarized: the solutions according to the present invention provide a technique that is suitable for describing chemical reactions, wherein the exact analysis of the measurement data recorded by the pH-stat means takes place in accordance with a previously specified calculation scheme. The equations used pertain to proper chemical equilibrium/equilibria and contain neither approximations nor predictions. The elaborated stoichiometric pH-stat means uses neither adaptions to processes that took place and were measured earlier nor parameter predictions, function fits and/or kinetic equations. As a conse- quence, the solutions according to the invention are free of ambiguous approximations and exclusively based on the precise concepts of chemical equilibrium/equilibria and material balance equation(s).