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A coulometric titrator using potentiometric end-point determination
Talanta,
1965. Vol.
12. PP. 111 to 118.
Pergamn
Press Ltd.
Printed
in NorthemIrtlmd
A COULOMETRIC TITRATOR USING POTENTIOMETRIC END-POINT DETERMINATION GILLIS JOHANSSON Department of Analytical Chemistry, University of Lund, Lund, Sweden (Received 9 September 1964. Accepted 29 September 1964) Summary_-A coulometric titrator using operational amplifiers has been built and tested A potentiometric titration can be made to a preset pH with a precision of fO.05 pH unit, using glass and calomel electrodes. The electrolysis current is reduced near the end-point to avoid over-titration. If the solution has been overtitrated the current is reversed. The number of coulombs required during a titration is determined by integration of the current. 0.2-O-4 mmole of perchloric acid was titrated with a standard deviation of about 0*1x, and O-20.8 mmole of benzoic acid with a standard deviation of 0.15 %.
WHEN the end-point of a coulometric titration is determined potentiometrically, two pairs of electrodes are immersed in the same solution. The potentials of the indicating electrodes are different from the potential of the working electrode. The simultaneous operation of a pH-meter and a coulometer at different potentials, connected through the solution, is subject to several possible sources of error. A current can flow between the chassis of the instruments. One path is through the solution, and the return path may be poor isolation to the line. This current will cause an erroneous reading of the pH-meter and it may also cause an error in the coulometric measurement. Another source of error is the capacitance between the indicating and generating instrument systems. A change in potential of the systems relative to each other will require a current to charge this apparent capacitor. The response of the indicating system will be slow. If two instruments are operated at different ground levels, only one of them can be connected to ground. The other instrument will pick up hum and noise. The disturbances will be most serious if the coulometric apparatus is grounded and the pHmeter has a floating ground. In spite of these difficulties, many coulometric analyses have been proposed using the technique criticised above. The technique has even been recommended by some manufacturers. Of course, the effects can be reduced by great care in mounting, but the danger of erroneous results will always exist. The difficulties will be greater for a current source of high accuracy, because the circuitry will be more complex. Especially in non-aqueous solvents this technique has been found to give very erroneous results. The easiest way to get rid of all these difficulties is to operate only one electrode system at one time. This method has been used by Smith and Taylor1 and by the present author.2 Both the generating and indicating electrodes were immersed in the solution, but a switch allowed only one of the electrode pairs to be connected to its instrument at any one time. The disadvantage of this method is that an analysis takes a very long time, and requires constant operator attendance. Several instruments have beendescribed which automatically perform a coulometric 9
111
112
GILLIS JOHANSSON
titration. A titration curve can be recorded when a constant current is passed through the solution, the end-point being determined graphically from the chart paper. Several titrators which shut off the current at the end-point have also been described in the literature. The number of coulombs is determined either by integration or by measuring the time of reagent generation. High impedance inputs are obtained by using a commercial pH-meter which actuates a relay,3*4 or a recorder with a slave potentiometer.s Most of the titrators described are useful only for low impedance electrodes.B-8 An interesting solution is presented by Burnett and Klavers The output of a pH-meter is fed into a magnetic amplifier which isolates the measuring circuit from the generating electrodes. Information about the accuracy of the end-point determination is usually lacking in the literature. The overall accuracy seems to be less than what could be obtained by manual titration. In this paper a titrator is described which measures the electrode signal directly, including the voltage to ground. The common mode voltage is cancelled in a dilferential amplifier, and the electrode potential minus a preset voltage is amplified and applied to the generating electrodes. When the electrode signal approaches the preset voltage the generating current will be reduced. If an overtitration has happened the current will reverse. EXPERIMENTAL Apparaius Titrafor. The input from the indicating electrode, e.g., a glass electrode, is connected to the follower,* Al, which consists of an operational amplifier with extremely high input resistance (G. A. Philbrick Res., Inc., model P2), as shown in Fig. 1. The reference electrode is connected to a less expensive follower, A2, with a moderate input resistance (model P65). The feed-back loop of A2 contains a lo-turn potentiometer over which 1.000 v is applied. The dial reads in mv. This voltage is obtained from a zener-stabilised supply floating with respect to ground; sign reversal is accomplished by a switch. The voltage set on this “set end-point”-potentiometer will cause a displacement of the output of A2 by the same amount. When the potential between the measuring electrodes equals the voltage set on the potentiometer, the output from the titrator will be zero; the titration will stop. The outputs from the two followers are connected to a differential amplifier A3. In this amplifier only the difference between the two follower outputs will be amplified. The common part will be cancelled. This common voltage includes the voltage between the measuring electrode system and the generating electrode, the voltage drop over the current measuring resistor and the hum and noise. The magnitude of the common voltage must, for amplifier P55, be less than f 10 v, and it is cancelled to better than 0.1%. By using the amplifier P2 throughout it should be possible to get a still better performance. The common mode rejection of this amplifier is better than 0.0001% and the common voltage may be as large as +200 v. However, the amplifier P55 was found to be sufficiently accurate for the present purpose. The common mode voltage is usually less than 2 v. The output from A3 is connected to an amplifier A4, because the total amplification required is too large to be made in one step. A4 is also provided with a damping control for the system. The response of a glass electrode will lag behind the actual pH in the solution. The time constant is of the order 10-25 sec. It can be reduced by etching the electrode in hydrofluoric acid. In the present investigation, however, unetched electrodes were used. If no damping is provided, the titrator will shut off the current when the electrode voltage equals the set end-point potential. The solution is then already overtitrated. When the glass electrode then moves towards the correct value a back-titration will start resulting in a pH-oscillation. The oscillations may be quenched by reducing the gain of A4. The gain had to be reduced so much, however, that the end-point became ill defined. The damping circuit R,, Ra and C, provides a damping against pH-oscillations by adding a * A follower has a very high input resistance. input voltage, i.e., the gain is unity.
The output is an accurate reproduction
of the
ChuIomeidc titrator
I / L_
114
GILLIS JOHANS~N
derivative function to the signal. When the output voltage from A3 decreases, the decrease will be enhanced in the output of A4 because the derivative function has been added. The titration may stop or reverse. When the charge on Ct leaks away through Rt the titration will proceed again. During this time the glass electrode will have had time to move closer to the actual potential. The amount of damping depends on the slope of the titration curve, on the time constant of the electrode and on the cell geometry. There will be a delay before the generated reagents will come to the electrode. This delay is an essential part of the damping system. It can be adjusted by moving the generating electrode to a new position and by varying the stirring rate. These parameters are adjusted, together with the potentiometer Ri, so that a titration of the solvent is critically or almost critically damped. This setting is then used for all types of titration. A damping system which is independent of electrode positions can be constructed, but it will make the apparatus more complicated. A current booster is incorporated within the feedback path of A4. The booster shown in Fig. 1 is a modification of a circuit described by Towers .I0 This booster has a small quescent current but can deliver large peak currents. The maximum output voltage is &12 v. The bias adjustment for the amplifiers P55 must be provided externally. The potentiometer for bias adjustment of A3 had a sufficiently great range for compensation of the asymmetry potential of most of the glass electrodes used. The adjustment is made in the following way. The glass electrode is immersed in a buffer solution and the end-point potentiometer is set to a value corresponding to the pH of the buffer, e.g., 0 mv for a buffer of pH 7.00. The auxiliary electrode is disconnected and a voltmeter is connected over the output terminals. The bias potentiometer is then adjusted until the voltmeter reads zero. A zener shunt-stabilised power supply provides power for the operational amplifiers. Two power transistors regulate the power to the current booster, the transistor bases being connected to the zener diodes. The titrator is contained in an enclosure 32 x 20 x 16 cm. Auxiliary equipment. Combined glass and calomel electrodes, Metrohm type EAlZlU or EA121X, were used. Type U is for genera1 use in the range pH O-14, the resistance being 400 Mfi. Type X is more resistant to physical shock, the pa-range is O-l 1 and the resistance is also 400 Ma. The reference electrode is in each case a saturated calomel electrode with a plugged tip. The titration vessel consisted of two Metrohm EA615 joined by a tube containing two sinteredglass discs, as described ear1ier.8 A silicic acid gel covered the glass filter disc in the auxiliary electrode compartment. The resistance of the cell was about 50 CI when filled with 120 ml of saturated Na,SOdsolution. The maximum current is then of the order of 200 mA. When the current had decreased to zero the liquid in the compartments between the glass filter discs was transferred into the titration vessel by applying pressure with a pipette filler. A small suction was applied to fill the compartments again. The procedure was repreated once or twice more. A vigorous stream of CO,-free air was blown over the liquid during the titration. The titration current was integrated by a chopper-stabilised integrator with a precision of 3 parts in 10,000. The integrator was calibrated against voltage and time. “Taken” in the tables means the value obtained when dividing the weight of the substance by the formula weight. “Found” means the actual readings which are founded on standardisation against current and time. The tables thus provide an intercomparison between these two independent methods of standardising. Reagents Zone melted benzoic acid with a stated purity of 100.00% was used (Hopkin and Williams, Ltd., Renzoic acid P.V.S.). Pro analysi sodium carbonate was dried at 150”. Other reagents were of pro analysi quality. Procedure After a warm-up period of 10-15 min the noise of the titrator with the glass electrode connected was found to correspond to less than 0.01 pH-unit, and the drift over 15 hr to be less than 0.05 pHunit. The measurement was taken with the glass electrode immersed in a phosphate buffer solution of pH 7.00. This solution had previously been used as a standard when the asymmetry potential of the electrode was compensated for. The drift of the operational amplifiers according to the manufacturer’s specifications is equivalent to &0.02 pH-unit in the worst case (per day and 5” in temperature change). In order to determine the linearity, the buffer adjustment was done as above. The end-point potentiometer was then set at + 15 mv (it had been set at 0 mv during the above adjustment). The titration started, and was allowed to go on until the current was less than 10 ,UA. The glass electrode was then connected to an expanded-scale pH-meter (Metrohm E-300) and the pH-value was noted. The pH-meter had previously been standardised against the same phosphate buffer solution.
Coulometric
115
titrator
RESULTS
Fig. 2 shows a plot of pH-values against the settings of the end-point potentiometer. First the values to the left of zero were measured in the direction from pH 7.00 towards higher pH-values. Then the titration was reversed and the points to the right of zero were taken in successive order. The points fall on two lines, depending on whether the titration is made upwards or downwards. This behaviour is partly caused by the hysteresis of the generating electrode. When base is generated, the platinum 6.00 -
a00 t -50
FIG. 2.-pH-values
f
1 0
I
1 +50
mV
of the end-point in a phosphate buffer solution plotted versus the dial settings on the coulometric titrator.
foil must be negative with respect to N.H.E., while it must be positive when acid is generated. The magnitude of the generating electrode hysteresis is thus the decomposition voltage of the solution divided by the loop gain, which was 1,000 times in the actual case. Another contribution to the measured hysteresis will be derived from incomplete cancellation of the common mode voltage in A3. Depending on how the followers are connected to the differential amplifier it will add or subtract to the hysteresis of the generating electrode. If the connection is made as in Fig. I, namely P2 to the “-” input of A3, it will be added, giving a higher total hysteresis. If the followers were connected for subtraction of the hysteresis effects an instability leading to oscillations would occur. The crossover distortion in the current booster might be another source of hysteresis. The two germanium diodes between the bases of the NPN and PNP transistors, together with the inclusion of the booster within the feed-back loop will reduce this contribution to a negligible value. The slope of the lines in Fig. 2 is 60.3 mv/pH-unit as compared to the calculated 59.4 mv/pH-unit. A pH-unit is taken to be equal to the reading of the Metrohm E-300 meter pH-meter. The agreement between slopes found and calculated proves that the input resistance of the titrator is sufficiently high for the present purpose; it is of the order of 30,000 megohms. Table I shows a set of coulometric titrations of perchloric acid to pH 7.00 in a medium of saturated Na,SO,. The anode was a silver foil, and sodium tetraphenylborate was added to the anode solution. The perchloric acid had previously been
GILLIS JOHAN~WN
116
TABLEL-TITRATION OF PERCHLORIC ACIDSOLUTION Taken, ,umole
Found, pmole
Taken, pmole
Found, pmole
2024
202,5 202.7 202.2 202.5 2024 202.3 202.4
404.9
405.2 404.4 4044
Mean
202.4
404.6
Standard deviation Deviation from taken
0.3 0%
O-5 -0.06%
standardised against sodium carbonate. The accuracy of the burette (Metrohm piston burette E 274) had been controlled by weighing. Table II shows the results obtained when benzoic acid was titrated to pH 8.10. The weighings were made on a microbalance and the weight was corrected for air buoyancy. The benzoic acid was dissolved in a few ml of ethanol and washed into the titration vessel through one of the ground joints at the top. The medium was as described above. A titration was completed in l&15 min. TABLEII.-TITRATION OF BENZOIC ACID Taken, ,umole
Found, pmole
Deviation, %
390.6 407.7 400.5 414.0 415.3 408.8 884.8 212.7
390.7 407.1 399.8 413.8 415.5 408.9 883.3 213.3
-to.01 -0.15 -0.22 -0.06 $0.03 +0*02 -0.16 +0.26
Mean Standard deviation
-0.03 0.15
In some cases the end-point setting may be calculated from tabulated pK-values. When this is impossible, a titration curve may be obtained from the titrator. The potential is set to a value on the early part of the titration curve, and the integral is noted when the current has ceased. The procedure is repeated for a number of points until the end-point is passed. The potential settings are then plotted aers~s the integrals. A titration curve of this type is shown in Fig. 3. This procedure is, of course, more timeconsuming than direct titration to a calculated end-point. However, it will be useful when the conditions for a coulometric titration are evaluated and when more elaborate calculation, e.g., derivation,ll is necessary for location of the end-point. DISCUSSION
The titrator itself can be reset with a reproducibility of the order of O-01 pH-unit (0.6 mv). The hysteresis limits the over-all precision to about f0.05 pH-unit (f3 mv). This precision was sufficient for the actual applications, especially because the electrodes in many cases limit the accuracy to a much lower value. The hysteresis can be
Coulometric
titrator
117
reduced somewhat by employing a higher gain in the feedback loops, but then pHoscillations are likely to occur in the titration of strong acids or bases. Substituting a P2 differential amplifier for the P55 will reduce the hysteresis to about f@02 pH-unit.* The present titrator reverses the current if a small overtitration occurs. This technique is useful only when the electrode reactions are reversible. For reversible systems, however, the possibility of current reversal will reduce the titration time
10
-
9-
PH 8 -
400
pcq
FIG, 3.-Titration of benzoic acid using the method described in the text. Ail points are corrected for the solvent base consumption.
significantly. The precision will also be increased as compared with titrations with pH-control in only one direction. In regions of small buffer capacity a precision of O-05 pH-unit will be difficult to attain without this positive control. The titrator has been tested only for acid and base titrations using glass and calomel electrodes. It can also be used in other types of titrations as well as with other electrodes. Acknowledgements-The author thanks K. J. Karrman for his advice and interest. He also thanks Miss Karin Norberg for obtaining the results. This work was supported by grants from the Swedish Technical Research Council. Zusammen~--Ein coulometrisches Titrationsgerat mit Servoverstarkung wurde gebaut und geprtift. Eine potentio~trische Titration kann bis zu einem vorher auf &O,OS Einheiten festgelegten pH-Wert gefuhrt werden, wobei zur Anzeige Glas- und Kalomelelektroden Gerwendet werden. Urn Ubertitrieren zu vermeiden, wird in der NBhe des Enduunktes der Elektrolvsestrom verrinpert. Bei Ubertitration wird de; Strom umgepolt. Die zur Titration verforderliche CoulombMenge wird durch Integration des Stromes ermittelt. 0,2 bis 0,4 mMo1 ~~r~hlo~~u~ wurden mit einer Stand~dab~ichung von etwa 91% und 0,2 bis 0,s mMo1 Benzoeslure mit einer Standardabweichung von OJ 5 % titriert. * An improved version of P2, called P2A, has just been made available by the manufacturer. still higher input impedance and a lower drift should be obtained if the P2A is used.
A
118
GILLIS JOIL~NS~~N R&na&-Gn a construit et experiment& un appareil de titrage coulometrique utilisant des amplificateurs opbrationnels. On peut effectuer un titrage potentiometrique, a un pH 8x6 au prealable avec une precision de &0,05 unite pH, en utilisant des electrodes de verre et calomel. Au voisinage du point final, on a reduit le courant d’electrolyse afin d’eviter un surtitrage. Au cas oh la solution est surtitrk, le courant s’inverse. Le nombre de coulombs rkcessaire au cours dun titrage a 6tt determine par integration du courant. On a dose 0,2-0,4 mmole d’acide perchlorique avec un &art type d’environ 0,1x. et 0,2&0,8 mmole d’acide benzolque avec un &cart type de 0,15 %. REFERENCES
1 S. W. Smith and J. K. Taylor, J. Res. Nat. Bur. Stand., 1959, 63C, No 1, 65. a G. Johansson, Talunta, 1964, 11, 789. * K. Jeffcoat and M. Akhtar, Analyst, 1962, 87,455. 4 P. G. W. Scott and T. A. Strivens, ibid., 1962, 87, 356. 6 D. W. Einsel, Jr., H. J. Trunt, S. D. Silver and E. C. Sterner, Analyt. Chem., 1956,28, 408 BC. B. Roberts and H. A. Brejcha, ibid., 1963, 35, 1104. ’ D. M. Coulson and L. A. Cavanagh, ibid., 1960,32, 1245. 8 E. Barendrecht and W. Martens, ibid., 1962, 34, 139. s R. L. Burnett and R. F. Klaver, ibid., 1963, 35, 1709. lo T. D. Towers, Wireless World, 1963, 69, 599. I1 G. Gran, Analyst, 1952, 77, 661.
1965. Vol.
12. PP. 111 to 118.
Pergamn
Press Ltd.
Printed
in NorthemIrtlmd
A COULOMETRIC TITRATOR USING POTENTIOMETRIC END-POINT DETERMINATION GILLIS JOHANSSON Department of Analytical Chemistry, University of Lund, Lund, Sweden (Received 9 September 1964. Accepted 29 September 1964) Summary_-A coulometric titrator using operational amplifiers has been built and tested A potentiometric titration can be made to a preset pH with a precision of fO.05 pH unit, using glass and calomel electrodes. The electrolysis current is reduced near the end-point to avoid over-titration. If the solution has been overtitrated the current is reversed. The number of coulombs required during a titration is determined by integration of the current. 0.2-O-4 mmole of perchloric acid was titrated with a standard deviation of about 0*1x, and O-20.8 mmole of benzoic acid with a standard deviation of 0.15 %.
WHEN the end-point of a coulometric titration is determined potentiometrically, two pairs of electrodes are immersed in the same solution. The potentials of the indicating electrodes are different from the potential of the working electrode. The simultaneous operation of a pH-meter and a coulometer at different potentials, connected through the solution, is subject to several possible sources of error. A current can flow between the chassis of the instruments. One path is through the solution, and the return path may be poor isolation to the line. This current will cause an erroneous reading of the pH-meter and it may also cause an error in the coulometric measurement. Another source of error is the capacitance between the indicating and generating instrument systems. A change in potential of the systems relative to each other will require a current to charge this apparent capacitor. The response of the indicating system will be slow. If two instruments are operated at different ground levels, only one of them can be connected to ground. The other instrument will pick up hum and noise. The disturbances will be most serious if the coulometric apparatus is grounded and the pHmeter has a floating ground. In spite of these difficulties, many coulometric analyses have been proposed using the technique criticised above. The technique has even been recommended by some manufacturers. Of course, the effects can be reduced by great care in mounting, but the danger of erroneous results will always exist. The difficulties will be greater for a current source of high accuracy, because the circuitry will be more complex. Especially in non-aqueous solvents this technique has been found to give very erroneous results. The easiest way to get rid of all these difficulties is to operate only one electrode system at one time. This method has been used by Smith and Taylor1 and by the present author.2 Both the generating and indicating electrodes were immersed in the solution, but a switch allowed only one of the electrode pairs to be connected to its instrument at any one time. The disadvantage of this method is that an analysis takes a very long time, and requires constant operator attendance. Several instruments have beendescribed which automatically perform a coulometric 9
111
112
GILLIS JOHANSSON
titration. A titration curve can be recorded when a constant current is passed through the solution, the end-point being determined graphically from the chart paper. Several titrators which shut off the current at the end-point have also been described in the literature. The number of coulombs is determined either by integration or by measuring the time of reagent generation. High impedance inputs are obtained by using a commercial pH-meter which actuates a relay,3*4 or a recorder with a slave potentiometer.s Most of the titrators described are useful only for low impedance electrodes.B-8 An interesting solution is presented by Burnett and Klavers The output of a pH-meter is fed into a magnetic amplifier which isolates the measuring circuit from the generating electrodes. Information about the accuracy of the end-point determination is usually lacking in the literature. The overall accuracy seems to be less than what could be obtained by manual titration. In this paper a titrator is described which measures the electrode signal directly, including the voltage to ground. The common mode voltage is cancelled in a dilferential amplifier, and the electrode potential minus a preset voltage is amplified and applied to the generating electrodes. When the electrode signal approaches the preset voltage the generating current will be reduced. If an overtitration has happened the current will reverse. EXPERIMENTAL Apparaius Titrafor. The input from the indicating electrode, e.g., a glass electrode, is connected to the follower,* Al, which consists of an operational amplifier with extremely high input resistance (G. A. Philbrick Res., Inc., model P2), as shown in Fig. 1. The reference electrode is connected to a less expensive follower, A2, with a moderate input resistance (model P65). The feed-back loop of A2 contains a lo-turn potentiometer over which 1.000 v is applied. The dial reads in mv. This voltage is obtained from a zener-stabilised supply floating with respect to ground; sign reversal is accomplished by a switch. The voltage set on this “set end-point”-potentiometer will cause a displacement of the output of A2 by the same amount. When the potential between the measuring electrodes equals the voltage set on the potentiometer, the output from the titrator will be zero; the titration will stop. The outputs from the two followers are connected to a differential amplifier A3. In this amplifier only the difference between the two follower outputs will be amplified. The common part will be cancelled. This common voltage includes the voltage between the measuring electrode system and the generating electrode, the voltage drop over the current measuring resistor and the hum and noise. The magnitude of the common voltage must, for amplifier P55, be less than f 10 v, and it is cancelled to better than 0.1%. By using the amplifier P2 throughout it should be possible to get a still better performance. The common mode rejection of this amplifier is better than 0.0001% and the common voltage may be as large as +200 v. However, the amplifier P55 was found to be sufficiently accurate for the present purpose. The common mode voltage is usually less than 2 v. The output from A3 is connected to an amplifier A4, because the total amplification required is too large to be made in one step. A4 is also provided with a damping control for the system. The response of a glass electrode will lag behind the actual pH in the solution. The time constant is of the order 10-25 sec. It can be reduced by etching the electrode in hydrofluoric acid. In the present investigation, however, unetched electrodes were used. If no damping is provided, the titrator will shut off the current when the electrode voltage equals the set end-point potential. The solution is then already overtitrated. When the glass electrode then moves towards the correct value a back-titration will start resulting in a pH-oscillation. The oscillations may be quenched by reducing the gain of A4. The gain had to be reduced so much, however, that the end-point became ill defined. The damping circuit R,, Ra and C, provides a damping against pH-oscillations by adding a * A follower has a very high input resistance. input voltage, i.e., the gain is unity.
The output is an accurate reproduction
of the
ChuIomeidc titrator
I / L_
114
GILLIS JOHANS~N
derivative function to the signal. When the output voltage from A3 decreases, the decrease will be enhanced in the output of A4 because the derivative function has been added. The titration may stop or reverse. When the charge on Ct leaks away through Rt the titration will proceed again. During this time the glass electrode will have had time to move closer to the actual potential. The amount of damping depends on the slope of the titration curve, on the time constant of the electrode and on the cell geometry. There will be a delay before the generated reagents will come to the electrode. This delay is an essential part of the damping system. It can be adjusted by moving the generating electrode to a new position and by varying the stirring rate. These parameters are adjusted, together with the potentiometer Ri, so that a titration of the solvent is critically or almost critically damped. This setting is then used for all types of titration. A damping system which is independent of electrode positions can be constructed, but it will make the apparatus more complicated. A current booster is incorporated within the feedback path of A4. The booster shown in Fig. 1 is a modification of a circuit described by Towers .I0 This booster has a small quescent current but can deliver large peak currents. The maximum output voltage is &12 v. The bias adjustment for the amplifiers P55 must be provided externally. The potentiometer for bias adjustment of A3 had a sufficiently great range for compensation of the asymmetry potential of most of the glass electrodes used. The adjustment is made in the following way. The glass electrode is immersed in a buffer solution and the end-point potentiometer is set to a value corresponding to the pH of the buffer, e.g., 0 mv for a buffer of pH 7.00. The auxiliary electrode is disconnected and a voltmeter is connected over the output terminals. The bias potentiometer is then adjusted until the voltmeter reads zero. A zener shunt-stabilised power supply provides power for the operational amplifiers. Two power transistors regulate the power to the current booster, the transistor bases being connected to the zener diodes. The titrator is contained in an enclosure 32 x 20 x 16 cm. Auxiliary equipment. Combined glass and calomel electrodes, Metrohm type EAlZlU or EA121X, were used. Type U is for genera1 use in the range pH O-14, the resistance being 400 Mfi. Type X is more resistant to physical shock, the pa-range is O-l 1 and the resistance is also 400 Ma. The reference electrode is in each case a saturated calomel electrode with a plugged tip. The titration vessel consisted of two Metrohm EA615 joined by a tube containing two sinteredglass discs, as described ear1ier.8 A silicic acid gel covered the glass filter disc in the auxiliary electrode compartment. The resistance of the cell was about 50 CI when filled with 120 ml of saturated Na,SOdsolution. The maximum current is then of the order of 200 mA. When the current had decreased to zero the liquid in the compartments between the glass filter discs was transferred into the titration vessel by applying pressure with a pipette filler. A small suction was applied to fill the compartments again. The procedure was repreated once or twice more. A vigorous stream of CO,-free air was blown over the liquid during the titration. The titration current was integrated by a chopper-stabilised integrator with a precision of 3 parts in 10,000. The integrator was calibrated against voltage and time. “Taken” in the tables means the value obtained when dividing the weight of the substance by the formula weight. “Found” means the actual readings which are founded on standardisation against current and time. The tables thus provide an intercomparison between these two independent methods of standardising. Reagents Zone melted benzoic acid with a stated purity of 100.00% was used (Hopkin and Williams, Ltd., Renzoic acid P.V.S.). Pro analysi sodium carbonate was dried at 150”. Other reagents were of pro analysi quality. Procedure After a warm-up period of 10-15 min the noise of the titrator with the glass electrode connected was found to correspond to less than 0.01 pH-unit, and the drift over 15 hr to be less than 0.05 pHunit. The measurement was taken with the glass electrode immersed in a phosphate buffer solution of pH 7.00. This solution had previously been used as a standard when the asymmetry potential of the electrode was compensated for. The drift of the operational amplifiers according to the manufacturer’s specifications is equivalent to &0.02 pH-unit in the worst case (per day and 5” in temperature change). In order to determine the linearity, the buffer adjustment was done as above. The end-point potentiometer was then set at + 15 mv (it had been set at 0 mv during the above adjustment). The titration started, and was allowed to go on until the current was less than 10 ,UA. The glass electrode was then connected to an expanded-scale pH-meter (Metrohm E-300) and the pH-value was noted. The pH-meter had previously been standardised against the same phosphate buffer solution.
Coulometric
115
titrator
RESULTS
Fig. 2 shows a plot of pH-values against the settings of the end-point potentiometer. First the values to the left of zero were measured in the direction from pH 7.00 towards higher pH-values. Then the titration was reversed and the points to the right of zero were taken in successive order. The points fall on two lines, depending on whether the titration is made upwards or downwards. This behaviour is partly caused by the hysteresis of the generating electrode. When base is generated, the platinum 6.00 -
a00 t -50
FIG. 2.-pH-values
f
1 0
I
1 +50
mV
of the end-point in a phosphate buffer solution plotted versus the dial settings on the coulometric titrator.
foil must be negative with respect to N.H.E., while it must be positive when acid is generated. The magnitude of the generating electrode hysteresis is thus the decomposition voltage of the solution divided by the loop gain, which was 1,000 times in the actual case. Another contribution to the measured hysteresis will be derived from incomplete cancellation of the common mode voltage in A3. Depending on how the followers are connected to the differential amplifier it will add or subtract to the hysteresis of the generating electrode. If the connection is made as in Fig. I, namely P2 to the “-” input of A3, it will be added, giving a higher total hysteresis. If the followers were connected for subtraction of the hysteresis effects an instability leading to oscillations would occur. The crossover distortion in the current booster might be another source of hysteresis. The two germanium diodes between the bases of the NPN and PNP transistors, together with the inclusion of the booster within the feed-back loop will reduce this contribution to a negligible value. The slope of the lines in Fig. 2 is 60.3 mv/pH-unit as compared to the calculated 59.4 mv/pH-unit. A pH-unit is taken to be equal to the reading of the Metrohm E-300 meter pH-meter. The agreement between slopes found and calculated proves that the input resistance of the titrator is sufficiently high for the present purpose; it is of the order of 30,000 megohms. Table I shows a set of coulometric titrations of perchloric acid to pH 7.00 in a medium of saturated Na,SO,. The anode was a silver foil, and sodium tetraphenylborate was added to the anode solution. The perchloric acid had previously been
GILLIS JOHAN~WN
116
TABLEL-TITRATION OF PERCHLORIC ACIDSOLUTION Taken, ,umole
Found, pmole
Taken, pmole
Found, pmole
2024
202,5 202.7 202.2 202.5 2024 202.3 202.4
404.9
405.2 404.4 4044
Mean
202.4
404.6
Standard deviation Deviation from taken
0.3 0%
O-5 -0.06%
standardised against sodium carbonate. The accuracy of the burette (Metrohm piston burette E 274) had been controlled by weighing. Table II shows the results obtained when benzoic acid was titrated to pH 8.10. The weighings were made on a microbalance and the weight was corrected for air buoyancy. The benzoic acid was dissolved in a few ml of ethanol and washed into the titration vessel through one of the ground joints at the top. The medium was as described above. A titration was completed in l&15 min. TABLEII.-TITRATION OF BENZOIC ACID Taken, ,umole
Found, pmole
Deviation, %
390.6 407.7 400.5 414.0 415.3 408.8 884.8 212.7
390.7 407.1 399.8 413.8 415.5 408.9 883.3 213.3
-to.01 -0.15 -0.22 -0.06 $0.03 +0*02 -0.16 +0.26
Mean Standard deviation
-0.03 0.15
In some cases the end-point setting may be calculated from tabulated pK-values. When this is impossible, a titration curve may be obtained from the titrator. The potential is set to a value on the early part of the titration curve, and the integral is noted when the current has ceased. The procedure is repeated for a number of points until the end-point is passed. The potential settings are then plotted aers~s the integrals. A titration curve of this type is shown in Fig. 3. This procedure is, of course, more timeconsuming than direct titration to a calculated end-point. However, it will be useful when the conditions for a coulometric titration are evaluated and when more elaborate calculation, e.g., derivation,ll is necessary for location of the end-point. DISCUSSION
The titrator itself can be reset with a reproducibility of the order of O-01 pH-unit (0.6 mv). The hysteresis limits the over-all precision to about f0.05 pH-unit (f3 mv). This precision was sufficient for the actual applications, especially because the electrodes in many cases limit the accuracy to a much lower value. The hysteresis can be
Coulometric
titrator
117
reduced somewhat by employing a higher gain in the feedback loops, but then pHoscillations are likely to occur in the titration of strong acids or bases. Substituting a P2 differential amplifier for the P55 will reduce the hysteresis to about f@02 pH-unit.* The present titrator reverses the current if a small overtitration occurs. This technique is useful only when the electrode reactions are reversible. For reversible systems, however, the possibility of current reversal will reduce the titration time
10
-
9-
PH 8 -
400
pcq
FIG, 3.-Titration of benzoic acid using the method described in the text. Ail points are corrected for the solvent base consumption.
significantly. The precision will also be increased as compared with titrations with pH-control in only one direction. In regions of small buffer capacity a precision of O-05 pH-unit will be difficult to attain without this positive control. The titrator has been tested only for acid and base titrations using glass and calomel electrodes. It can also be used in other types of titrations as well as with other electrodes. Acknowledgements-The author thanks K. J. Karrman for his advice and interest. He also thanks Miss Karin Norberg for obtaining the results. This work was supported by grants from the Swedish Technical Research Council. Zusammen~--Ein coulometrisches Titrationsgerat mit Servoverstarkung wurde gebaut und geprtift. Eine potentio~trische Titration kann bis zu einem vorher auf &O,OS Einheiten festgelegten pH-Wert gefuhrt werden, wobei zur Anzeige Glas- und Kalomelelektroden Gerwendet werden. Urn Ubertitrieren zu vermeiden, wird in der NBhe des Enduunktes der Elektrolvsestrom verrinpert. Bei Ubertitration wird de; Strom umgepolt. Die zur Titration verforderliche CoulombMenge wird durch Integration des Stromes ermittelt. 0,2 bis 0,4 mMo1 ~~r~hlo~~u~ wurden mit einer Stand~dab~ichung von etwa 91% und 0,2 bis 0,s mMo1 Benzoeslure mit einer Standardabweichung von OJ 5 % titriert. * An improved version of P2, called P2A, has just been made available by the manufacturer. still higher input impedance and a lower drift should be obtained if the P2A is used.
A
118
GILLIS JOIL~NS~~N R&na&-Gn a construit et experiment& un appareil de titrage coulometrique utilisant des amplificateurs opbrationnels. On peut effectuer un titrage potentiometrique, a un pH 8x6 au prealable avec une precision de &0,05 unite pH, en utilisant des electrodes de verre et calomel. Au voisinage du point final, on a reduit le courant d’electrolyse afin d’eviter un surtitrage. Au cas oh la solution est surtitrk, le courant s’inverse. Le nombre de coulombs rkcessaire au cours dun titrage a 6tt determine par integration du courant. On a dose 0,2-0,4 mmole d’acide perchlorique avec un &art type d’environ 0,1x. et 0,2&0,8 mmole d’acide benzolque avec un &cart type de 0,15 %. REFERENCES
1 S. W. Smith and J. K. Taylor, J. Res. Nat. Bur. Stand., 1959, 63C, No 1, 65. a G. Johansson, Talunta, 1964, 11, 789. * K. Jeffcoat and M. Akhtar, Analyst, 1962, 87,455. 4 P. G. W. Scott and T. A. Strivens, ibid., 1962, 87, 356. 6 D. W. Einsel, Jr., H. J. Trunt, S. D. Silver and E. C. Sterner, Analyt. Chem., 1956,28, 408 BC. B. Roberts and H. A. Brejcha, ibid., 1963, 35, 1104. ’ D. M. Coulson and L. A. Cavanagh, ibid., 1960,32, 1245. 8 E. Barendrecht and W. Martens, ibid., 1962, 34, 139. s R. L. Burnett and R. F. Klaver, ibid., 1963, 35, 1709. lo T. D. Towers, Wireless World, 1963, 69, 599. I1 G. Gran, Analyst, 1952, 77, 661.