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A novel titration technique for the analysis of streamed samples—the triangle-programmed titration technique
Analytica Chimica Acta, 91 (1977) 87-96 QElsevier Scientific Publishing Company, Amsterdam
A NOVEL SAMPLES
and
Considerations
ZS. FEHKR
EG YT Pharmacochemical K. T&H Institute
in The Netherlands
TITRATION TECHNIQUE FOR THE ANALYSIS OF STREAMED - THE TRJANGLE-PROGR.AMMED TITR4TION TECHNIQUE
Part I. General
G. NAGY
-Printed
Works, Budapest
(Hungary)
and E. PUNGOR for General and Analyticd
(Received
Chemistry.
Technical
UniveEity.
Budapest
(Hungary)
17th January 1977)
SUMMARY The principle of a novel continuous titration technique with triangle-programmed reagent addition is described. The advantages of titration techniques, i.e. high precision, reliability, etc., are combined with the convenience and fast sample handling of mechanized analyzers of the flow-through type. The theoretical titration curves are discussed for detectors Mth logarithmic and linear signal conversion characteristics. The possibilities of different ty_pes of pro grammed reagent addition are summarized.
The use of instrumental end-point detection offers several advantages in the practical application of different analytical titrations. However, as far as time consumption is concerned, there is generally no improvement unless titration curves are recorded automatically. The first approach to the development of automatic chemical anaiyzers was the construction of the so-called mechanized titrators. Titrators belonging to this group can be used with different end-point detection techniques and are generally accepted as accurate tools. The various titrators may differ from each other in the manner of their operation (e.g. coulometric or volumetric reagent addition, the method of end-point location) and in the leve! of their automation, but common to all is a relatively low rate of anaiysis. As the continuous improvement of titrators has proceeded, new types of analyzer allowing high speeds of analysis and based on the direct signal transformation principle have appeared. Analyzers of this type employ the flow-through channel principle, the sample preparation, the detection, and the cleaning of the system being done continuously. By constructing an appropriate pattern of the flow system, a large number of samples can be analyzed for one or several components in a short period of time. Therefore, such analyzers have achieved an almost monopolistic position in analytical practice, es_peciaUy where many similar samples must be analyzed. Since analysis
68
in commercial flow-‘through channel analyzers is based on evaluation of a steady-state signal, the accuracy of the results is far less favourable than that of titration procedures. This is obvious, for the steady-state signal can be affected severely by many factors, such as temperature, sample composition (matrix effects), etc. The above summary indicates that further efforts to improve mechanized analytical systems will result in anaIyzers containing flow-through analysis channels, yet opera?ing on the basis of titrations. Apparatus of this kind should combine the advantages of both titrators and flow-through mechanized analyzers, i.e. high precision and high speed sample handling. The aim of this series of papers is to introduce and describe the new concept of carrying out titrations in flowing solutions. The principle of the technique is that discrete samples of small volume can he analyzed in a short time with high precision. Both theory and practice wiIl be described. This work can be related closely to two main fields of instrumental analytical research, i.e. mechanized titrators and flow-through analysis. These areas have been reviewed comprehensively [l, 23, so that a further survey is unnecessary here. Very few attempts have been made to develop analytical methods based on complete titrations in flowing solutions. The so-called continuous titrators which are capable of analyzing flowing solutions are considered to be outside this group, because they mainly involve balancing a preselected end-point by varying the speed of the sample or reagent addition [3, 4]_ Therefore, all the uncertainties of direct sensor signal transformation are generally incorporated in the results obtained. Moreover, it is difficult to imagine how a continuous titrator could be used to analyze rapidly discrete samples of small volume. In connection with continuous titrators, the remarkable pioneering work of Blaedel and Laessig [ 51 must be mentioned. Appropriately, the first report of an analytical method based on recording of a complete titration curve obtained in a flow-through system was made at a Technicon Symposium [ 61. Later, Fleet and Ho [ 71 worked out a titration method further developing Eichler’s principle, the gradient titration technique. In their method, constant fiow rates of both the reagent and sample are mixed; this operational mode is very favourable if the apparatus is to be assembled from modules of the Technicon type. The mixture passes through a homogenizer coil and enters a flow-through potentiometric detector section. The reagent solution of continuously increasing concentration is prepared by a gradient technique. The titration cume recorded is evaluated by plotting time intervals from the beginning of the titration to the end-point against concentration. However, thT%s highly original technique still has several drawbacks which must be overcome before the method can achieve widespread applicability. The inconvenience of gradient preparation, and the uncertainty in determining the starting point of the titration curve, seem to be the most serious. Some preliminary work on these problems, involving argentimetic titrations of chloride-containing samples in flowing solutions, has been reported [S] .
83
In this paper, the entire theory and some important factors governing the practice of the programmed titration technique are discussed. Further papers will show in detail its practical aspects according to the type of titration used. THEORETICAL CONSIDERATIONS If a continuous stream of a reagent (titrant) and a sample solution are mixed and homogenized in a certain section of a tube, the degree of titration in the outflow solution depends on the rate of input of the two masses. By changing this rate, the degree of titration can be altered. The degree of titration can be followed by an appropriate sensor placed in a flow-through detector; the reaction must be completed before the mixture of reagent and sample reaches the detector_ For a conventional titration curve, the signal provided by the detector is plotted against the whole amount of titrant added. However, if the noints of a titration curve are to be produced in flow-through conditions, then a constant mass flow of sample and a variable mass flow of titrant are essential. With a conventional titrator, the automatic recording of the titration curve is generally done with an X-Y recorder, which provides the possibility of a time-independent reagent addition. However, in some cases, special advantages can be gained by employing a constant rate of addition; a simple signal-time recording gives the titration curve itself. Looking at this problem in the case of flow-through titrations, it is clear that continuous automatic recording of the titration curve can be accomplished only by employing a strict time-dependent reagent addition program and a detector signal--t’Gne recording. Since the detector is always in delay to the reagent addition, it would be inconsistent to plot the instantaneous detector signal against the simultaneous addition rate of the titrant. If we assume (a) a constant mass flow (V,)of a sample of constant concentration (c,), (b) a linear increase in the reagent addition (from zero) with time (V, = tn, where V, is the mars flow of the reagent, t is time, n is a constant), and (c) an immediate titration reaction aS+- bR+ciP,+gP2
(1)
then a certain degree of titration will correspond to a given time period (t). This is true at the point where the reagent and sample flows come togetber, if their mixing at that point is instantaneous and complete. The reaction mixture flows continuously in the tube behind the point of confluence; thus, after a certain delay, the solution segment with a titration degree corresponding to the t period of reagent addition rate wi.lIpass through the system. The delay in detection will depend linearly on the flow-rate in the tube and on the distazxe between the point of detection and the point of confluence. At a certain point of time, t, the channel behind the mixing point contains a solution of continuously changing
9C!
t&ration degree. If Ming is not significant, i.e. the concentration in ul individual segment is constant during its passage through the tube, and if the reagent addition-time program v, = nt
(2)
is employed, then at a given instant each infmif&mal cross-section of the solution in the channel can be characterized by a V, reagent addition rate as well as by the corresponding degree of titration. Ln other words, each section of the tube belongs, or can be related, to a given point of a titration c1LIve.Accordingly, the titration curve itself can easily be recorded; and from this curve, the V, value corresponding to the equivalence point, and thus the sample concentration (for a known flow rate) can be determined. However, the determination of the reagent addition rate at the equivalence point from the recording is not free from uncertainties. The above-mentioned sources of errors, the delay in detection, the tailing, and the dilution caused by the increasing rate of addition ali cause difficulties in the accurate determination of the t = 0 point from the recording. Consequently, it is obvious that, for evaluation of V,,two distinct points are needed, one of which must be the equivalence point itself; the latter point is generally obvious on a titration curve. The accuracy of the determination can be improved gre+ly if two equivalence points serve as the basis of evaluation. A rec&ding with two equivalence points can be obtained by means of a reagent triangle addition program. The introduction of this novel concept greatly improves the capability and analytical value of the continuous titration technique in flowing sample solutions. The reagent addition program employing the triangle technique is shown in Fig. 1; the rate of reagent addition increases in the first part of the program according to eqn. (2). After t = 7, the rate of addition decreases at the same rate; in this range the rate of addition changes according to the equation v, = (27 -
t)n
(3)
where 27 is the duration of the whole program. Considering a constant flow of sample solution of a certain concentration and appropriate n and 7 values, the mass flow of the reagent and sample wil3 achieve chemical equivalence twice. Above VR values corresponding to the equivalence point, tbe stage of overtitration exists. For a defined reagent addition program, the time interval between the ap_pearanceof the two equivalence points is highly dependent on the mass flow of the sample solution (V,), which can be expressed by the equation t> = csu
(4)
where cs is the concentration and u the flow rate of the sample solution. According to this, if the flow rate is constant, the time klterval mentioned is Sfected by the concentration of ‘the flowing solution, as shown in Fig. 2,
91
Fig. 1. Triangular reagent addition program for continuous
titration in streamed samples.
Fig. 2. The time dependence of the reagent mass flow during a triangle-programmed continuous titration_ See text for explanation.
where the reagent mass flow ( VR) isplotted against time (t). The negative values of V, represent the excess of the sample mass flow with respect to the stoichiometry of the chemical reaction (eqn. 1). In Fig. 2, the difference of the reagent and sample flows is converted to the V, scaleaccording to the stoichiometry of the chemical reaction, which is represented by a solid continuous line. Three different cases are shown in Fig. 2; line A shows the case when V, = 0, whereas for line B the sample mass flow is smaller than it is in the case of C. It is obvious that V, = 0 corresponds to the chemical equivalence, and that the 27 time interval of the reagent addition program (case A) is delineated by two equivalence stages. Moreover, it can readily be concluded from Fig. 2 that the higher the sample mass flow, the shorter the section defined by the two equivalence points ctf&--
t&,
or t% -
t&).
This time period can be expressed quantitatively by introducing the following simplifying conditions: (1) the mixing of the sample and the reagent is complete and instantaneous at the point of confluence; (2) the confluence occurs in a section of infinitesima! thickness; (3) the chemical reaction (eqn. 1) is instantaneous and quantitative. At the equivalence point the reagent mass flow ( VRE) equals the constant sample flow, i.e. from ecps. (1) and (4) vRE =;
v, -2
c,v
(5)
However, during the total reagent addition program, there are two equivalence points appearing at times fEl and fE2. From eqns. (2) and (3), it follows that
(6)
9B
v,,
= n(2r -
tE2) =+lr
If@isdefmedas(t=two equivalence states,
(7) t~l), i.e. the time between the appearance of the
then eqns. (6) and (7) give
B = tEz -ttnl=27-2+v As can he seen, the Q value is related linearly to the concentration of the sample solution. Accordingly, if the detection of tEl and tE2 end-points is possible, then by measuring the & value and knowing all the other parameters 01 keeping them constant, the concentration of the flowing solution can easily be determine& It must be mentioned that *he slope of the Q vs. c, fimction, and therefore the sensitivity of the determination of c, is strongly dependent on the values of 7, n, u. On the basis of this priiciple of triangle-programmed reagent addition, analytical procedures can theoretically be developed for the titrimetric concentration measurement of flowing sample solutions. PRACTICAL
AS?ECTS
There are two important practical problems connected with this principle. First, an appropriate reagent addition program must be achieved; secondly, the best continuously operating technique for the detection must be selected. Tne programmed reagent mass flow is most easily obtained with a reagent solution. Either the volume or the concentration of the reagent solution can then be changed according to the triangle program. Some commercially available instruments are suitable either for direct use or after only minor alterations. The application of the concentration programmed method looks more favourable but requires more sophisticated instrumentation. Another convenient method of programmed reagent addition involves e%ctrolytic generation of the reagent, by a currentrprogrammed electrolysis of 100% current efficiency. We propose that if the triangle programmed titration is accomplished with an electrically generated reagent, then the method should be named triangle-programmed coulometric titration. The coulometric reagent addition - similarly to the classical coulometric titration - can be done by electrolysis in Cne sample flow (internal reagent generation) or separately in a generator cell (external reagent generation). As far as the continuous detection of different species in flov=ing solutions is concerned, many well known methods and instruments are available [9, lo]. However, depending on the concentrationsignal conversion equation for different detectors, the titration curves recorded will differ in shape. Specific differences may also arise depending on the individual cha.zzct&stics of the
93
detector and of the titration reaction employed. Accordingly, a great variety of recordings with different shapes can be expected with the contiiuous triangle titration technique, analogously to the great variety of titration curves obtained oscillometrically, potentiometrically, amperometrically, biamperometically, conductometrically, etc. The applicability and advantages of the continuous titration technique with programmed reagent addition can be explained by selecting two different types of titration curve. In potentiometric titrations, the concentration-signal conversion equation is logarithmic, whereas this equation is linear in amperometric titrations. Curves obtairted for logarithmic concentmtion-signal conversion If the detector gives a logarithmic signal, and is equally sensitive to the reagent and sample concentration, the appropriate titration curve (A) is given in Fig. 3. In the case shown, it is assumed that the flow rate of the solution in the fIow-through detector is constant. Fi,gure 3 also shows the equivalence level. From the theoretical titration curve, the expected recordings can easily be derived if the data of the reagent addition program and the sample flow am known. The expected recordings have been drawn for four different sample concentrations, a constant reagent addition program being assumed To explain these curves, it is obvious that during the reagent addition program as V, increases linearly in time, the detector signal (which is initiahy equal to the value corresponding to the c, concentration)
Fig. 3. ‘Ikeoreticai triangle-programmed detector.
logarithmic
titration curves OD a mass flow scale with a
94
changes continuously following the titration cmve. At instant ? = 7, however, Vrr reaches its maximum and starts to decrease. Consequently, ‘he detector signal also zch.ieves a maximum value (I’, . . . Pa), so that the V” vs. VR a/b recording would come down on the same track from point P if a signal vs. v, - V’ a/b function were recorded. However, since a signal vs. time curve is recorded, the part of the recording after t = c, or the appearance of point P, will appear as a mirror iniage of the first part. In Fig. 3, the Q values are also indicated. It must be noted that there is no Q value for the highest concentration of sample (cg4). The reason for this is obvious: the reagent mass flow with the program employed is not high enough to achieve equivalence even at the instant t = 7. The superiority of the triangle titration method over the direct measurement is obvious from Fig. 3. For example, if a logarithmic detector is used, detector drift, which is a serious source of error in direct measurements, is avoided. And, a small signal difference corresponding to a small concentration difference can be converted to a huge change in Q values by applying a suitable program. To give the theoretically expected recordings in their red form for the detector signal vs. time function, a few curves of this kind are shown in Fig. 4.
Fig. 4. Tkeoreticd detector.
triangle-prommed
tihrion
cm-x-es on a time scale with a logarithmic
95
Curves obtained with linear concen trationsignal conversion The theoretically expected recordings will also be discussed for a special case, where a linear signal-converting detector is used in connection with the triangle programmed technique. It is assumed that the excess of the titrant is related linearly to the detector signal, and that neither the product nor the sample affects the defection. Figure 5 shows such a titration curve (A); after the equivalence point the detector signal increases proportionally to the reagent concentration. c, . . . cs4 represent the concentrations of four different sample solutions and mark the starting point of the corresponding titration curves. When the same reagent addition program is used, the de&Am signal achieves i’s maximum (Pi . . . P4) at instant t = 7 and then starts to decrease. Since the recording is time-based, after point P the mirror image of the previous recording appears (shown by thin lines in Fig. 5). The ends of each reagent addition program in the mirror image are marked by L, . . . Lq. The Q values corresponding to the different sample concentrations arc also indicated. In Fig. 6 the theoretically expected curves of this nature are shown on a time-based scale. Curve A in this case is the recording expected in the absence of a sample (c, = 0). The sample concentration for curve c,: is higher than that for curve c,~, hence Q2 < QI, because a higher reagent mass flow is needed to over-titrate a solution of higher sample mass flow. Thus if the same triangle reagent addition prograa is employed, the higher the sample mass flow, then the shorter will be the part of the program falling under the region of over-titration.
&&--J : 4
=S-fjVFI
i
+k-=S
Fig. 5. Theoreticd tri&$e-prqpamxmd
detector of linear characteristics.
titrationcurveson a mzss flow scalewith a
Fig 6. Theoretical
triangieprogrammed
linear characteristics.
titration curves on a time scale with a detector of
CONCLUSIONS The programmed reagent addition titration technique has obvious advantages over the direct methods in analyzing flowing individual samples. Since the titration method is based on a chemical equivalence, neither a base-line drift nor a change in the slope of the linear signal-converting function of the detector will affect the value Q which serves as the bzsisfor evaluation. These factors are serious sources of error when methods based on direct evaluation of the detector signals are employed. In tiis first paper of the series, only the principles of the triangle-programmed r.eagent addition method have been described in detail, and the expected recordings have been shown and explained for two types of detector. The practice of the technique based on various acid-base, compleximetric,
iodimetric znd other titration methods, with different potentiometric, arnperometric and other detectors for applied analysis, will be reported in later
papers.
REFERENCES 1 J. P. Phiili_ps, Automatic Tittitors, Academic Press, New York, 1959; J. K Foreman and P. R Stockwell, Automatic Chemical Analysis. Ellis Horwood, Chichester, 1975. 2 W. J. Rlaedel and R. H. Lawig. Adv. AnaL Chem. Instrum.. 5 (1966) 69. 3 K. E. Hflikainen and D. J. Pompeo, Instruments, 25 (1952) 335. 1 &I_ M. Nicholson, Anal. Chem., 33 (1961) 1328. 5 W. J. Riaedel and I?_ I-L Laessig. Ana.l. Chem., 36 (1964) 1617; 37, (1965) 332.1255.1650. 6 D. L. Eicbler. Technicon Symposium, 1969. Vol. 1, Mediad. New York. 1970. p. 51. 7 B. Fleet and X Y. W. IIo, Anal. Chem., 46 (1974) 9. 8 G. Nagy, K. T&h and E. Pungor, Anal. Chem., 47 (1975) 1460. 9 Zs. Feher, G. Nagy, K. Thth and E. Pungor. Analyst (London), 99 (1974) 699. 10 E. Pungor. Zs. Feh& and G. Nagy. Pure Appl. Chem.. 44 (1975) 595.
A NOVEL SAMPLES
and
Considerations
ZS. FEHKR
EG YT Pharmacochemical K. T&H Institute
in The Netherlands
TITRATION TECHNIQUE FOR THE ANALYSIS OF STREAMED - THE TRJANGLE-PROGR.AMMED TITR4TION TECHNIQUE
Part I. General
G. NAGY
-Printed
Works, Budapest
(Hungary)
and E. PUNGOR for General and Analyticd
(Received
Chemistry.
Technical
UniveEity.
Budapest
(Hungary)
17th January 1977)
SUMMARY The principle of a novel continuous titration technique with triangle-programmed reagent addition is described. The advantages of titration techniques, i.e. high precision, reliability, etc., are combined with the convenience and fast sample handling of mechanized analyzers of the flow-through type. The theoretical titration curves are discussed for detectors Mth logarithmic and linear signal conversion characteristics. The possibilities of different ty_pes of pro grammed reagent addition are summarized.
The use of instrumental end-point detection offers several advantages in the practical application of different analytical titrations. However, as far as time consumption is concerned, there is generally no improvement unless titration curves are recorded automatically. The first approach to the development of automatic chemical anaiyzers was the construction of the so-called mechanized titrators. Titrators belonging to this group can be used with different end-point detection techniques and are generally accepted as accurate tools. The various titrators may differ from each other in the manner of their operation (e.g. coulometric or volumetric reagent addition, the method of end-point location) and in the leve! of their automation, but common to all is a relatively low rate of anaiysis. As the continuous improvement of titrators has proceeded, new types of analyzer allowing high speeds of analysis and based on the direct signal transformation principle have appeared. Analyzers of this type employ the flow-through channel principle, the sample preparation, the detection, and the cleaning of the system being done continuously. By constructing an appropriate pattern of the flow system, a large number of samples can be analyzed for one or several components in a short period of time. Therefore, such analyzers have achieved an almost monopolistic position in analytical practice, es_peciaUy where many similar samples must be analyzed. Since analysis
68
in commercial flow-‘through channel analyzers is based on evaluation of a steady-state signal, the accuracy of the results is far less favourable than that of titration procedures. This is obvious, for the steady-state signal can be affected severely by many factors, such as temperature, sample composition (matrix effects), etc. The above summary indicates that further efforts to improve mechanized analytical systems will result in anaIyzers containing flow-through analysis channels, yet opera?ing on the basis of titrations. Apparatus of this kind should combine the advantages of both titrators and flow-through mechanized analyzers, i.e. high precision and high speed sample handling. The aim of this series of papers is to introduce and describe the new concept of carrying out titrations in flowing solutions. The principle of the technique is that discrete samples of small volume can he analyzed in a short time with high precision. Both theory and practice wiIl be described. This work can be related closely to two main fields of instrumental analytical research, i.e. mechanized titrators and flow-through analysis. These areas have been reviewed comprehensively [l, 23, so that a further survey is unnecessary here. Very few attempts have been made to develop analytical methods based on complete titrations in flowing solutions. The so-called continuous titrators which are capable of analyzing flowing solutions are considered to be outside this group, because they mainly involve balancing a preselected end-point by varying the speed of the sample or reagent addition [3, 4]_ Therefore, all the uncertainties of direct sensor signal transformation are generally incorporated in the results obtained. Moreover, it is difficult to imagine how a continuous titrator could be used to analyze rapidly discrete samples of small volume. In connection with continuous titrators, the remarkable pioneering work of Blaedel and Laessig [ 51 must be mentioned. Appropriately, the first report of an analytical method based on recording of a complete titration curve obtained in a flow-through system was made at a Technicon Symposium [ 61. Later, Fleet and Ho [ 71 worked out a titration method further developing Eichler’s principle, the gradient titration technique. In their method, constant fiow rates of both the reagent and sample are mixed; this operational mode is very favourable if the apparatus is to be assembled from modules of the Technicon type. The mixture passes through a homogenizer coil and enters a flow-through potentiometric detector section. The reagent solution of continuously increasing concentration is prepared by a gradient technique. The titration cume recorded is evaluated by plotting time intervals from the beginning of the titration to the end-point against concentration. However, thT%s highly original technique still has several drawbacks which must be overcome before the method can achieve widespread applicability. The inconvenience of gradient preparation, and the uncertainty in determining the starting point of the titration curve, seem to be the most serious. Some preliminary work on these problems, involving argentimetic titrations of chloride-containing samples in flowing solutions, has been reported [S] .
83
In this paper, the entire theory and some important factors governing the practice of the programmed titration technique are discussed. Further papers will show in detail its practical aspects according to the type of titration used. THEORETICAL CONSIDERATIONS If a continuous stream of a reagent (titrant) and a sample solution are mixed and homogenized in a certain section of a tube, the degree of titration in the outflow solution depends on the rate of input of the two masses. By changing this rate, the degree of titration can be altered. The degree of titration can be followed by an appropriate sensor placed in a flow-through detector; the reaction must be completed before the mixture of reagent and sample reaches the detector_ For a conventional titration curve, the signal provided by the detector is plotted against the whole amount of titrant added. However, if the noints of a titration curve are to be produced in flow-through conditions, then a constant mass flow of sample and a variable mass flow of titrant are essential. With a conventional titrator, the automatic recording of the titration curve is generally done with an X-Y recorder, which provides the possibility of a time-independent reagent addition. However, in some cases, special advantages can be gained by employing a constant rate of addition; a simple signal-time recording gives the titration curve itself. Looking at this problem in the case of flow-through titrations, it is clear that continuous automatic recording of the titration curve can be accomplished only by employing a strict time-dependent reagent addition program and a detector signal--t’Gne recording. Since the detector is always in delay to the reagent addition, it would be inconsistent to plot the instantaneous detector signal against the simultaneous addition rate of the titrant. If we assume (a) a constant mass flow (V,)of a sample of constant concentration (c,), (b) a linear increase in the reagent addition (from zero) with time (V, = tn, where V, is the mars flow of the reagent, t is time, n is a constant), and (c) an immediate titration reaction aS+- bR+ciP,+gP2
(1)
then a certain degree of titration will correspond to a given time period (t). This is true at the point where the reagent and sample flows come togetber, if their mixing at that point is instantaneous and complete. The reaction mixture flows continuously in the tube behind the point of confluence; thus, after a certain delay, the solution segment with a titration degree corresponding to the t period of reagent addition rate wi.lIpass through the system. The delay in detection will depend linearly on the flow-rate in the tube and on the distazxe between the point of detection and the point of confluence. At a certain point of time, t, the channel behind the mixing point contains a solution of continuously changing
9C!
t&ration degree. If Ming is not significant, i.e. the concentration in ul individual segment is constant during its passage through the tube, and if the reagent addition-time program v, = nt
(2)
is employed, then at a given instant each infmif&mal cross-section of the solution in the channel can be characterized by a V, reagent addition rate as well as by the corresponding degree of titration. Ln other words, each section of the tube belongs, or can be related, to a given point of a titration c1LIve.Accordingly, the titration curve itself can easily be recorded; and from this curve, the V, value corresponding to the equivalence point, and thus the sample concentration (for a known flow rate) can be determined. However, the determination of the reagent addition rate at the equivalence point from the recording is not free from uncertainties. The above-mentioned sources of errors, the delay in detection, the tailing, and the dilution caused by the increasing rate of addition ali cause difficulties in the accurate determination of the t = 0 point from the recording. Consequently, it is obvious that, for evaluation of V,,two distinct points are needed, one of which must be the equivalence point itself; the latter point is generally obvious on a titration curve. The accuracy of the determination can be improved gre+ly if two equivalence points serve as the basis of evaluation. A rec&ding with two equivalence points can be obtained by means of a reagent triangle addition program. The introduction of this novel concept greatly improves the capability and analytical value of the continuous titration technique in flowing sample solutions. The reagent addition program employing the triangle technique is shown in Fig. 1; the rate of reagent addition increases in the first part of the program according to eqn. (2). After t = 7, the rate of addition decreases at the same rate; in this range the rate of addition changes according to the equation v, = (27 -
t)n
(3)
where 27 is the duration of the whole program. Considering a constant flow of sample solution of a certain concentration and appropriate n and 7 values, the mass flow of the reagent and sample wil3 achieve chemical equivalence twice. Above VR values corresponding to the equivalence point, tbe stage of overtitration exists. For a defined reagent addition program, the time interval between the ap_pearanceof the two equivalence points is highly dependent on the mass flow of the sample solution (V,), which can be expressed by the equation t> = csu
(4)
where cs is the concentration and u the flow rate of the sample solution. According to this, if the flow rate is constant, the time klterval mentioned is Sfected by the concentration of ‘the flowing solution, as shown in Fig. 2,
91
Fig. 1. Triangular reagent addition program for continuous
titration in streamed samples.
Fig. 2. The time dependence of the reagent mass flow during a triangle-programmed continuous titration_ See text for explanation.
where the reagent mass flow ( VR) isplotted against time (t). The negative values of V, represent the excess of the sample mass flow with respect to the stoichiometry of the chemical reaction (eqn. 1). In Fig. 2, the difference of the reagent and sample flows is converted to the V, scaleaccording to the stoichiometry of the chemical reaction, which is represented by a solid continuous line. Three different cases are shown in Fig. 2; line A shows the case when V, = 0, whereas for line B the sample mass flow is smaller than it is in the case of C. It is obvious that V, = 0 corresponds to the chemical equivalence, and that the 27 time interval of the reagent addition program (case A) is delineated by two equivalence stages. Moreover, it can readily be concluded from Fig. 2 that the higher the sample mass flow, the shorter the section defined by the two equivalence points ctf&--
t&,
or t% -
t&).
This time period can be expressed quantitatively by introducing the following simplifying conditions: (1) the mixing of the sample and the reagent is complete and instantaneous at the point of confluence; (2) the confluence occurs in a section of infinitesima! thickness; (3) the chemical reaction (eqn. 1) is instantaneous and quantitative. At the equivalence point the reagent mass flow ( VRE) equals the constant sample flow, i.e. from ecps. (1) and (4) vRE =;
v, -2
c,v
(5)
However, during the total reagent addition program, there are two equivalence points appearing at times fEl and fE2. From eqns. (2) and (3), it follows that
(6)
9B
v,,
= n(2r -
tE2) =+lr
If@isdefmedas(t=two equivalence states,
(7) t~l), i.e. the time between the appearance of the
then eqns. (6) and (7) give
B = tEz -ttnl=27-2+v As can he seen, the Q value is related linearly to the concentration of the sample solution. Accordingly, if the detection of tEl and tE2 end-points is possible, then by measuring the & value and knowing all the other parameters 01 keeping them constant, the concentration of the flowing solution can easily be determine& It must be mentioned that *he slope of the Q vs. c, fimction, and therefore the sensitivity of the determination of c, is strongly dependent on the values of 7, n, u. On the basis of this priiciple of triangle-programmed reagent addition, analytical procedures can theoretically be developed for the titrimetric concentration measurement of flowing sample solutions. PRACTICAL
AS?ECTS
There are two important practical problems connected with this principle. First, an appropriate reagent addition program must be achieved; secondly, the best continuously operating technique for the detection must be selected. Tne programmed reagent mass flow is most easily obtained with a reagent solution. Either the volume or the concentration of the reagent solution can then be changed according to the triangle program. Some commercially available instruments are suitable either for direct use or after only minor alterations. The application of the concentration programmed method looks more favourable but requires more sophisticated instrumentation. Another convenient method of programmed reagent addition involves e%ctrolytic generation of the reagent, by a currentrprogrammed electrolysis of 100% current efficiency. We propose that if the triangle programmed titration is accomplished with an electrically generated reagent, then the method should be named triangle-programmed coulometric titration. The coulometric reagent addition - similarly to the classical coulometric titration - can be done by electrolysis in Cne sample flow (internal reagent generation) or separately in a generator cell (external reagent generation). As far as the continuous detection of different species in flov=ing solutions is concerned, many well known methods and instruments are available [9, lo]. However, depending on the concentrationsignal conversion equation for different detectors, the titration curves recorded will differ in shape. Specific differences may also arise depending on the individual cha.zzct&stics of the
93
detector and of the titration reaction employed. Accordingly, a great variety of recordings with different shapes can be expected with the contiiuous triangle titration technique, analogously to the great variety of titration curves obtained oscillometrically, potentiometrically, amperometrically, biamperometically, conductometrically, etc. The applicability and advantages of the continuous titration technique with programmed reagent addition can be explained by selecting two different types of titration curve. In potentiometric titrations, the concentration-signal conversion equation is logarithmic, whereas this equation is linear in amperometric titrations. Curves obtairted for logarithmic concentmtion-signal conversion If the detector gives a logarithmic signal, and is equally sensitive to the reagent and sample concentration, the appropriate titration curve (A) is given in Fig. 3. In the case shown, it is assumed that the flow rate of the solution in the fIow-through detector is constant. Fi,gure 3 also shows the equivalence level. From the theoretical titration curve, the expected recordings can easily be derived if the data of the reagent addition program and the sample flow am known. The expected recordings have been drawn for four different sample concentrations, a constant reagent addition program being assumed To explain these curves, it is obvious that during the reagent addition program as V, increases linearly in time, the detector signal (which is initiahy equal to the value corresponding to the c, concentration)
Fig. 3. ‘Ikeoreticai triangle-programmed detector.
logarithmic
titration curves OD a mass flow scale with a
94
changes continuously following the titration cmve. At instant ? = 7, however, Vrr reaches its maximum and starts to decrease. Consequently, ‘he detector signal also zch.ieves a maximum value (I’, . . . Pa), so that the V” vs. VR a/b recording would come down on the same track from point P if a signal vs. v, - V’ a/b function were recorded. However, since a signal vs. time curve is recorded, the part of the recording after t = c, or the appearance of point P, will appear as a mirror iniage of the first part. In Fig. 3, the Q values are also indicated. It must be noted that there is no Q value for the highest concentration of sample (cg4). The reason for this is obvious: the reagent mass flow with the program employed is not high enough to achieve equivalence even at the instant t = 7. The superiority of the triangle titration method over the direct measurement is obvious from Fig. 3. For example, if a logarithmic detector is used, detector drift, which is a serious source of error in direct measurements, is avoided. And, a small signal difference corresponding to a small concentration difference can be converted to a huge change in Q values by applying a suitable program. To give the theoretically expected recordings in their red form for the detector signal vs. time function, a few curves of this kind are shown in Fig. 4.
Fig. 4. Tkeoreticd detector.
triangle-prommed
tihrion
cm-x-es on a time scale with a logarithmic
95
Curves obtained with linear concen trationsignal conversion The theoretically expected recordings will also be discussed for a special case, where a linear signal-converting detector is used in connection with the triangle programmed technique. It is assumed that the excess of the titrant is related linearly to the detector signal, and that neither the product nor the sample affects the defection. Figure 5 shows such a titration curve (A); after the equivalence point the detector signal increases proportionally to the reagent concentration. c, . . . cs4 represent the concentrations of four different sample solutions and mark the starting point of the corresponding titration curves. When the same reagent addition program is used, the de&Am signal achieves i’s maximum (Pi . . . P4) at instant t = 7 and then starts to decrease. Since the recording is time-based, after point P the mirror image of the previous recording appears (shown by thin lines in Fig. 5). The ends of each reagent addition program in the mirror image are marked by L, . . . Lq. The Q values corresponding to the different sample concentrations arc also indicated. In Fig. 6 the theoretically expected curves of this nature are shown on a time-based scale. Curve A in this case is the recording expected in the absence of a sample (c, = 0). The sample concentration for curve c,: is higher than that for curve c,~, hence Q2 < QI, because a higher reagent mass flow is needed to over-titrate a solution of higher sample mass flow. Thus if the same triangle reagent addition prograa is employed, the higher the sample mass flow, then the shorter will be the part of the program falling under the region of over-titration.
&&--J : 4
=S-fjVFI
i
+k-=S
Fig. 5. Theoreticd tri&$e-prqpamxmd
detector of linear characteristics.
titrationcurveson a mzss flow scalewith a
Fig 6. Theoretical
triangieprogrammed
linear characteristics.
titration curves on a time scale with a detector of
CONCLUSIONS The programmed reagent addition titration technique has obvious advantages over the direct methods in analyzing flowing individual samples. Since the titration method is based on a chemical equivalence, neither a base-line drift nor a change in the slope of the linear signal-converting function of the detector will affect the value Q which serves as the bzsisfor evaluation. These factors are serious sources of error when methods based on direct evaluation of the detector signals are employed. In tiis first paper of the series, only the principles of the triangle-programmed r.eagent addition method have been described in detail, and the expected recordings have been shown and explained for two types of detector. The practice of the technique based on various acid-base, compleximetric,
iodimetric znd other titration methods, with different potentiometric, arnperometric and other detectors for applied analysis, will be reported in later
papers.
REFERENCES 1 J. P. Phiili_ps, Automatic Tittitors, Academic Press, New York, 1959; J. K Foreman and P. R Stockwell, Automatic Chemical Analysis. Ellis Horwood, Chichester, 1975. 2 W. J. Rlaedel and R. H. Lawig. Adv. AnaL Chem. Instrum.. 5 (1966) 69. 3 K. E. Hflikainen and D. J. Pompeo, Instruments, 25 (1952) 335. 1 &I_ M. Nicholson, Anal. Chem., 33 (1961) 1328. 5 W. J. Riaedel and I?_ I-L Laessig. Ana.l. Chem., 36 (1964) 1617; 37, (1965) 332.1255.1650. 6 D. L. Eicbler. Technicon Symposium, 1969. Vol. 1, Mediad. New York. 1970. p. 51. 7 B. Fleet and X Y. W. IIo, Anal. Chem., 46 (1974) 9. 8 G. Nagy, K. T&h and E. Pungor, Anal. Chem., 47 (1975) 1460. 9 Zs. Feher, G. Nagy, K. Thth and E. Pungor. Analyst (London), 99 (1974) 699. 10 E. Pungor. Zs. Feh& and G. Nagy. Pure Appl. Chem.. 44 (1975) 595.