An Automatic Differential Potentiometric Titrator H. V. MALMSTADT end
E. R. FETT 111.
Noyes Chemistry Laboratory, University of Illinois, Urbana,
A simple and inexpensive automatic differential potentiometric titrator is described which does not require any instrument adjustments prior to a titration. I t is not necessary to know and set the end-point potential, because the electronic circuit computes the second derivative voltage of the ordinary potentiometric curve, and this voltage is ideally suited to trigger a relay systern which turns the buret off at the inflection point (end point) of the titration. The instrument gives excellent precision and accuracy for the two oxidationreduction systems used in testing the titrator. The titrator is applicable for automatic potentiometric titrations where the end-point potential is not known o r changes with different titration conditions.
T
HE use of automatic titrators is becoming increasingly popular, chiefly because precise titrations can be performed more rapidly with good automatic instruments than by manual titrations. Many automatic potentiometric titrators are described in the literature and a comprehensive bibliography is given by Lingane (6). There are essentially two basic types of automatic titrators and both are commercially available. One type, originally presented by Lingane ( 5 ) , automatically anticipates and seeks the equivalence-point potential and turns the buret off when it is reached. There are commercial instruments available ( I , 6) which use this basic principle. Another type of automatic titrator records the potentiometric titration curve of potential against milliliters of titrant. The end point is read from the plot after the titration is completed. A recording instrument of this type is described by Robinson (8) and a commercia’ model is available ( 7 ) . Another type of automatic potentiometric titrator is now presented which is considerably different from those previously described. I t is known that the inflection point of a potentiometric curve is often equal to or sufficiently close to the equivalence point to cause negligible error in a titration (4). This new titrator automatically determines the inflection point and turns the buret off when it is reached. This is accomplished by electronically producing a voltage which is proportional to the second derivative of the ordinary electrode potential titration curve, and the second derivative voltage is ideally suited for triggering a relay system which turns the buret off a t the inflection point. I t is necessary to deliver the titrant a t a constant or uniform rate. A constant flow rate buret (e),a uniform flow rate buret (S), or coulometric generation of titrant a t constant current is suitable. Several advantages characterize the differential automatic titrator: The equipment is very simple, compact, and inexpensive; the end-point potential does not have to be known; various reference electrodes can be used and their potentials do not have to be known; and no instrument adjustments are required-it is only necessary to push the start button. The present model of the instrument also has certain disadvantages. I t is not suited for titrations where the solution or electrodes reach equilibria very slowly, because the system does not anticipate and slowly hunt for the equivalence point. The glass electrode cannot be used because of its high resistance. This can be remedied by redesigning the input amplifier stage. INSTRUMENTATION OF DIFFERENTIAL TITRATOR
The differential automatic titrator consists of two basic cir-
cuits. One is an amplifier-differentiator ciicuit which produces an output voltage proportional to the second derivative of the ordinary potentiometric titration voltage fed into the input. The other circuit is a relay system which uses the second derivative voltage to turn the buret off a t the inflection point (end point) of the potentiometric curve. Amplifier-Diff erentiator Circuit. The schematic diagram of the amplifier-differentiator circuit is given in Figure 1. The voltage between the electrode pair is fed directly to the control grid of a triode amplifier, which is one half of a 6SL7 twin-triode tube. The amplified voltage is differentiated by a simple resistancecapacitance differentiator, RICl, consisting of a 0.5-microfarad polystyrene condenser and a I-megohm resistor. The output voltage of the first resistance-capacitance differentiator is closely proportional to the first derivative of the electrode potential curve. The characteristics of a similar amplifier and resistancecapacitance diff erentiator are discussed by Blaedel and Malmstadt ( 3 ) . The output voltage of the first resistance-capacitance differentiator is fed directly to the grid of the second triode amplifier stage, which is the other half of the twin-triode tube. The amplified first derivative voltage is differentiated by a second resistance-capacitance diff erentiator, RVCy, also consisting of a 0.5-microfarad polystyrene condenser and a 1-megohm resistor. The output voltage from the second differentiator is closely proportional to the second derivative of the electrode potential curve.
Bt
t R4
i
+ Figure 1. Amplifier-DifferentiatorCircuit 1-megohm, 0.5-watt resistor 1-megohm resistor and a 2000-ohm resistor in series 2000-ohm, 0.5-watt resistors 1-megohm, wire-wound, 0.5-watt resistors e,,G . 0.5-microfarad, 300 WVDC, polystyrene condensers Ca, C4. 0.02-microfarad, 450-volt paper condensers A I , A2. 1.5-volt flashlight batteries 270-volt B batteries or electronic-regulated supply B, Vi. 6SL7 twin-triode tube
Ri. Rz. Ra, Rs. R I , Re.
.
The typical voltage curves which exist a t various points of the circuit when titrant is added a t a constant rate in the endpoint region of a potentiometric titration are illustrated in Figure 1. Resistance, R2, consists of a 1-megohm resistor and a 2000ohm resistor in series. This provides for a small fraction of the second differential output voltage to be observed on a recording potentiometer or millivoltmeter. 1348
1349
V O L U M E 26, NO. 8, A U G U S T 1 9 5 4 The amplifier-differentiator circuit is designed so that for relatively sharp end points the amplitude of the output voltage is 15 volts or more. The large output voltage is desirable for the type of relay system illustrated in Figure 2. Relay System. The relay system shown in Figure 2 is the most simple and reliable of several systems that were tested. The output voltage from the second differentiator is fed directly to the grid of a miniature 2D21 thyratron tube. The 110-volt alternating current line voltage is applied across the thyratron tube in series with the coil of a SPDT 110-volt alternating current relay. When no voltage is applied to the grid, the thyratron conducts on the positive cycles of the 60-cycle line voltage. If a rather large condenser, Cl, is put in parallel with the coil of the alternating current relay, it remains closed in the position shown when the grid voltage is zero. If the grid voltage of the thyratron goes about 1.5 volts negative, illustrated as point a on the second derivative input voltage, Figure 2 , the thyratron deionizes, stops conducting current, and relay 1 opens. \Vhen relay 1 opens, condenser C, is charged by battery B1 through resistance R1. The thyratron remains cut off until the grid becomes slightly more positive than minus 1.5 volts, illustrated by point b on the input voltage. At point b the thyratron again conducts and closes relav 1. This puts the charged condenser, C2,across the single-pole single-throw6-volt direct current relay 2 and momentarily opens the contacts of relay 2.
derivative voltage is usually negligible if the electrodes are p r o p erly positioned and there are suitable flow rates of titrant (Figure 3). However, if the stirring is inefficient or flow rate too fast, it is possible to have high local concentrations of titrant around the indicator electrode which can result in random voltage pulses in the region of the end point. If R1 were not in the charging circuit for Cz, it would be possible to charge Cp with a momentary sharp voltage pulse and cause relay 2 to open. Hoxever, if RI is of such a size that 1 or 2 seconds are required for Cz to be charged to sufficient voltage to operate relay 2, it is unlikely that any random and sharp voltage pulses a t the input of the thyratron can result in the operation of relay 2. The value for R1 depends on the usual time required to go from (I to b on the second derivative voltage curve, Figure 2. This time depends on several factors, including the titrant flow rate and the sharpness of the voltage change a t the end point. For most titrations the time from a to h is greater than 3 seconds.
In tJ 0
>
M I L L I L I T E R S OF T I T R A N T
Figure Figure 2. Relay System
3.
Recorded Second Derivative Titration Curve
Ri. 2000-ohm resistor
C , . 8-microfarad, 150-volt electrolytic condenser C2. 500-microfarad, 20 WVDC electrolytic condenser Push button (spring return) SPST switch SI. Relay 1. 110-volt alternate current, SPDT relay Relay 2. &volt direct current, SPST, normally closed relay Relay 3. 110-volt alternate current, SPST, normally open relay BI. 10-volt bias cell Lamp. 110-volt alternate current indicator lamp vz . 2D21 thyratron tube
The 110-volt line output to the buret motor or relay is normally dead because switch, S1, and the contacts of relay 3 are open. I n order to start delivery of titrant the 110-volt output to the buret motor or relay must be activated. This is done by depressing the push button (spring return) switch, SI, which puts the 110-volt alternating current across the coil of 110-volt alternating current relay 3, and the contact points of relay 3 immediately close. Consequently the 110-volt alternating current line voltage remains across the 110-volt outlet even though SI opens when released. Titrant is therefore continuously delivered from the time the start switch, SI, is depressed to the time that condenser, Cg, discharges through the coil of relay 2, and this corresponds to the inflection point of the titration. When the contacts of relay 2 open, the contacts of relay 3 open. Therefore, even though C2 discharges rapidly through the coil of relay 2 and the contacts are only briefly open, the 110-volt buret outlet remains dead because the contact points of relay 3 open. The buret outlet remains dead until SI is depressed for the next titration. There are several features about the relay system to consider. The condenser, Cz, is charged by battery B1 through resistance R1. Rt is not always essential in the circuit, but it acts as a safety device to prevent false end points when the noise level on the second derivative voltage is large. The noise level on the second
The relay circuit as shown in Figure 2 requires the input second derivative voltage initially to swing negative. Therefore the electrodes must be connected so t'he grid voltage at the input of the amplifier-differentiator circuit swings negative with respect to the cathode. This does not present any serious problem because the direction of voltage change of the indicator electrode is usually known. I n some cases it' might be convenient to leave the electrodes connected in one direction regardless of the direction of change of voltage a t t,he end point. This is possible by a somewhat more complicated relay system. The actual inflection point is shown as point c on the voltage input curve, Figure 2. This is slightly different than point b where the buret turns off, although the difference is negligible. If a case should arise where the difference between b and c is significant, a slightly modified relay sl-stem can be devised to turn the buret off a t exactly point c. Power Supplies. The amplifier-differentiator circuit requires a &volt filament supply and approximately a 250-volt B supply. The 6-volt filament voltage for the 6SL7 is best supplied by a storage battery. Six-volt alternating current introduces too much "noiseJ' into the circuit. The B supply can be readily obtained from either B batteries or a small regulated electronic supply. Current drain on the B supply is less than 1 ma. The relay system requires only the 110-volt alternate current line voltage. Delivery of Titrant. Motor-driven syringe burets (6) are very satisfact,ory for use with the differential titrator. The motor ia
ANALYTICAL CHEMISTRY
1350 plugged directly into the 110-volt alternate current outlet of the relay system. The uniform flow rate buret (3) is also readily adapted for use with the automatic titrator. The solution from the tip of the buret is run through a small-diameter gum rubber tubing which can be rapidly opened and closed by a pinch-clamp device operated by a 110-volt alternate current relay. The flow rate is readily changed by using different sintered-glass tubes through which the titrant passes. The system is simple, inexpensive, and the milliliters of titrant delivered are read directly from an ordinary-type buret. Coulometric generation of titrant a t constant current ( 6 ) is an excellent and accurate method of delivery.
I
1
I
’{
CURVE 0
EXPERIMENTAL RESULTS
The operation of the automatic differential potentiometric titrator is illustrated by the results obtained from titrations using two common redox systems-ferrous solutions against both dichromate and ceric solutions. After the delivery of titrant is automatically stopped, the titrated solution is allowed to equilibrate and the equilibrium potential is measured. The precision of the instrument is best illustrated by the reproducibility of the potential measurements for a given system. The accuracy of the instrument is shown by the comparison of the theoretical equilibrium potential a t the equivalence point to the measured potentials.
Table I. Precision of Automatic Titrator for Ferrous-Dichromate Titrations ( 1 O - m l . aliquots of 0.lN ferrous solution automatically titrated Xvitlt 0.1s dichromate solution) E n d - P t . Potential, Volt (Pt-Ca!. Electrode Pair) Determination
4 5
0.630 0.630 0.650 0.648 0.656
Av. Std. deviation
0.643 0.012
1 2 3
Preparation of Solutions. Solutions of dichromate, cerate, and ferrous iron were prepared by weighing out 4.9 grams of potassium dichromate, 56 grams of ammonium hexanitrato cerate, and 39 grams of ferrous ammonium sulfate; the dichromate and ferrous iron were dissolved and diluted with water to 1000 ml., while the cerate was dissolved in 56 ml. of concentrated sulfuric acid and then diluted to the mark in a 1-liter volumetric flask. Recording of Titration Curves. A typical recorded second derivative curve for the titration of ferrous iron with dichromate is shown in Figure 3. This curve is obtained by connecting the platinum-calomel electrode pair to the input of the titrator and by connecting a millivoltmeter recorder across the recorder leads a t the output of the amplifier-differentiator circuit (Figure 1). The relay system is disconnected to allow continuous delivery of titrant past the end point. The low noise level on the recorded curve indicates the stability of the titrator. Titrant is delivered from a syringe microburet a t the rate of 1.2 ml. per minute. A flow rate of 1.2 ml. per minute was also used for the titrations described in the following sections. Ferrous-Dichromate System. I n order to test the precision and accuracy of the automatic titrator without introducing buret errors the equilibrium end-point potentials are measured. The precision of the end-point potentials is converted to precision in terms of milliliters of standard titrant by using an expanded plot of potential against milliliters of titrant in the end-point region. The expanded plot is obtained by adding the titrant in the end-
MILLILITERS OF TITRANT
Figure 4. Expanded Potentiometric Titration Curves of End-Point Region A. Ferrous against dichromate B. Ferrous against ceric
point region from a Kirk ultramicroburet. The initial solution contains 10 ml. of 0.LV ferrous iron solution, 10 ml. of 6Ai sulfurio acid solution, and 5 ml. of 85’3” phosphoric acid, and is diluted in the titration vessel to about 50 ml. A calomel and a platinum, wire electrode are placed in the titration vessel and connected to a Leeds 8: Korthrup potentiometer, Model 7552. The standard dichromate solution is added from a 50-ml. buret to the ferrous solution to within 0.1 ml. of the equivalence point. T h e titration is then completed by adding the standard dichromate from the ultramicroburet. Care is taken to allow the solution tc, reach equilibrium before the potential is read. The expanded potentiometric curve in the region of the end point is shown in Figure 4, A. Five IO-ml. aliquots of 0.1S ferrous iron are titrated with standard 0.11i7dichromate, using the automatic titrator to determine the end point. After the buret automatically shuts off, the solution is given time to equilibrate and the potential of the solution is measured. The precision of the results are shown in Table I. The standard deviation of the electrode potential at the end point is 0.0120 volt, which is equivalent to 0.00086 ml. of 0.lK dichromate solution. The average end-point potential is 0.039 volt higher than the potential a t the end point determined by t h s classical method and represents a difference of 0.002 ml
Table 11.
Precision of Automatic Titrator for Ferrous-Ceric Titrations
(10-ml aliquots of 0 l A r ferrous solution are automatically titrated with 0 11‘ ceric solution; two different reference electrodes are used) Potential, Volt Pt-calomel Pt-Pt (lOYo Rh) Determination electrodes electrodes 0 0 0 0 0 0 0 0
Av. Std. deviation
818 817 821 820 824 826 825 823 0.822 0.0033
0.860
0.865 0.885 0.867 0.868
...
... 0.866 0.0034
Ferrous-Ceric System. An expanded plot of the end-point region of the ferrous-ceric system is made. Ten milliliters of 0.1N ferrous solution in the prePence of 5 ml. of concentrated sulfuric acid and diluted to about 50 ml. with distilled water are titrated with standard 0.1N ceric solution in the manner described foi the ferrous against dichromate system. Eight 10-ml. aliquots of ferrous iron are titrated with standard ceric solution using the automatic titrator and the calomelplatinum electrode pair. Upon completion of each titration the solution is allowed to equilibrate and the potential of the solution
V O L U M E 26, NO. 8, A U G U S T 1 9 5 4 is neasured. The precision of the results are shown in Table 11. Th:: standard deviation of the electrode potential a t the end point is 00033 volt, which is equivalent to 0.00018 ml. of 0.1N ceric solution. The average end-point potential is 0.068 volt higher than the theoretical end-point potential and represents an error of 0.0015 ml. Bimetallic Electrodes. It is easy to substitute various reference electrodes for the calomel electrode because the potential of the reference electrode does not have to be known for use with the automatic titrator. Five 10-ml. aliquots of 0.lN ferrous solution are titrated with standard ceric solution. The reproducibility of the end-point potential with a platinum indicator electrode and a platinum-lO% rhodium reference electrode connected to the input of the automatic titrator is given in Table I1 The end-point potential of the platinum electrode is measured with reference to a saturated calomel electrode. The standard deviation of the electrode potential a t the end point is 0.0034 volt, which is equivalent to 0.00019 ml. of 0.1,V ceric solution. The average end-point potential is 0.112 volt higher than the potential a t the end point determined by the classical method and represents a difference of 0.004 ml. Flow Rate Studies. In order to test the effect of the delivery rate of titrant on the precision and accuracy of the resultk, standard ceric solution was added to ferrous solutions a t five different flow rates varying from 0 4 to 2.8 ml. per minute. The reproducibility of the end-point potential a t all of the rates is about the same. There is, however, a rise in end-point potential with increase of flow rate. At the fastest flow rate studied, 2.8 ml. per minute, the end point is overshot by less than 0.02 ml. of 0.111’ ceric solution. These results indicate that for certain potentiometric titrations
1351 delivery rates of about 3 ml. per minute are possible without introducing significant error. Procedure for Performance of Titrations. The stirrer, a small, motor-driven glass propeller, is placed in a 150-ml. beaker, slightly offset from center and approximately one half inch from the bottom. The right-angled delivery tip of the buret is placed immediately above the ropeller and about 0.1 inch from the shaft of the stirrer, so t f a t the delivery flow is directed at the shaft. The reference and indicator electrodes are placed on the opposite side of the titration vessel about 0 . 2 5 inch from the bottom and close but not touching the sides of the titration vessel. The complete assembly is mounted so that the bottom of the titration vessel is above the table surface, thus allowing the vessel to be replaced without disturbing the electrode, buret, and stirrer assembly. The solution to be titrated is diluted with distilled water to approximately 50 ml., which allows sufficient volume to completely cover the electrodes, thus eliminating appreciable electrical noise during the titration. The stirrer is rotated as rapidly aa possible without introducing too much air into the solution. It is advisable to ground the stirrer and buret motor to prevent pickup of electrical noise a t the electrodes. The start button of the automatic titrator is pushed; completion of the titration is automatically determined. LITER4TURE CITED
(1) Beckman Instruments, Inc.. Pasadena, Calif., Bull. 239A (1951). (2) Blaedel, IT. J., and llalmstadt, H. 1‘ , ; ~ N Z L . CHEU..24, 450 (1 Q.52) (8) Ihid., p. 455. \ - - - - I
(4) Kolthoff, I. XI., and Furman, N. H., “Potentiometric Titrations.” 2nd ed., Yew York, John Wiley & Sons, 1931. ( 5 ) Lingane, J. J.. ANAL.CHEM..20, 285, 797 (1948). ( 6 ) Lingane, J. J., “Electroanalytical Chemistry,” New York, Interscience Publishers, 1953. (7) Precision Scientific Co., Chicago, Ill., Bull. 640A (1949). (8) Robinson, H. A., Trans. Electrochem. Soc., 92, 445 (1947). RECEIVED for review March 1, 1054. .4ccepted May 1.5, 1954
Automatic Recorder for Continuous Determination of Oxygen in Gases Using the Dropping Mercury Electrode TRESCOTT B. LARCHAR, SR., and MICHAEL CZUHA, JR. Government Laboratories, University o f Akron, Akron,
A constant control is needed to show the presence of oxygen in the head gas of reactors used for synthetic rubber production. By means of a continuous automatic analyzing system, the oxygen content of the exit gas from a nitrogen purification unit as well as in the hydrocarbon feed used in preparing synthetic rubber was placed’on a more reliable basis. This eliminates the error found in periodic sampling procedures and fulfills the need for more accurate and additional analyses of gases used in commercial systems where the presence of oxygen is detrimental.
0
S Y G E S plays an important role in the polymerization reac-
tions of olefins and diolefins. Small traces of this gas have been found to act as both polymerization inhibitors and activators, depending on the polymerization reactions involved. It is the general practice a t the Government Laboratories to reduce this variable to a minimum by purging polymerization e q u i p ment with butadiene or oxygen-free nitrogen prior to initiation. Because it is believed that a polarographic method is superior t o the classical manometric and Winkler methods for determining small quantities of oxygen, a potentiometric method ( 5 ) for the determination of oxygen in gases was developed a t the Government Laboratories and wed extensively in the analysis of gases
Ohio for purging polymerization units and laboratory assemblies (1). An automatic recording instrument was desirable in recording instantaneous changes in the oxygen content of the head gas in a 500-gallon reactor during purging and charging procedures. It was also desirable to record trawient phenomena in the stream from a nitrogen purification unit (6). Such recordings were not obtainable with the use of the manual apparatus. The design and operation of an electronic unit which automatically records the low concentration of oxygen in gases are described. THEORY
Molecular oxygen is irreversibly reduced a t the dropping mercury electrode a t applied potentials near zero (2, 3 ) . The diffusion current is reached a t approximately -0.3 volt us. the saturated calomel electrode. In neutral or alkaline solutions, the reaction proceeds according to the following equation: 02
+ 2H20 + 2e-
+
+ 20H-
H202
(1)
At potentials more negative than -0.5 volt, the second reduction step occurs:
HS02
+ 2e- +.20H-
(2)
The polarographic behavior of dissolved oxygen has been the basis of several methods for the determination of oxygen in gases
