SUMMARY
New information was obtained as a result of this study. Both cis- and trans-stilbendiolate were demonstrated to be the product of the reversible, two-electron reduction of benzil in strongly alkaline media. They are both oxidized by processes having virtually identical values of E l l z . Al( O H ) c was found to stabilize cis-stilbendiolate and the experimental results were consistent with the conclusion that the presence of Al(OH)4- did not change the relative amounts of the two isomers produced by electrochemical reduction of benzil. In 1:1 methanol-0.1M NaOH, the
ketolization of cis-stilbendiolate to benzoin occurs with a rate constant of 0.6 f 0.2 sec-' and the rate constant for ketolization of trans-stilbendiolate is 4.7 0.8 sec-I.
*
ACKNOWLEDGMENT The authors thank John Gerlock for performing the ESR experiments.
Received for review December 18, 1972. Accepted February 22, 1973. The authors acknowledge the support of the National Science Foundation through Grant GP-18575.
Precise, Recording Amperometric Titrator Automatic Correction of the Titration Curve for Dilution of the Sample Solution with the Titrant P. M. J. Coenegracht Laboratory for Pharmaceutical and Analytical Chemistry, State University, Antonius Deusinglaan 2, Groningen, The Netherlands
An instrument for the automatic, precise recording of amperometric titration curves is described. Measurement precision has been improved by using a low-pass filter which reduces random current fluctuations due to variations of the thickness of the diffusion layer. The use of a low-pass filter required stepwise addition of titrant. The current is recorded at equal intervals after a waiting period, when equilibrium conditions are established. The accuracy of the determination of the end point has been improved by an analog computing circuit that corrects the measured current for the dilution of sample solution with the titrant. A larger part of the recorded titration curve could now be used for extrapolation. Construction of the instrument and observations on performance are described.
The majority of the instruments described in the literature for the automatic recording of amperometric titrations are continuously operating instruments (1-6). The titrant is added continuously from a motor-driven syringeburet. The speed of addition is synchronized with the chart speed of the recorder. Notwithstanding perfect synchronization, systematic errors result from time lag due to damping, to mixing, and to the reaction time of the chemical and electrochemical processes. These errors can be minimized by the stepwise addition of titrant. Application of this principle to potentiometric titrations has been described by several authors (7-11). The technique re(1) J. M . G. Barredo and J. K. Taylor, Trans. Electrochem. SOC., 92, 437 (1947). (2) M. Muryama. U.S. Patent 2834654 (1958). (3) A. Juliard, Anal. Chem., 30, 136 (1958). (4) S. Wolf. Chem. Rundsch., 13, 437 (1958). (5) A. Anton and P. W. Mullen, Talanfa. 8, 817 (1961). (6) S. A. Myers and W. B. Swan, Talanta. 12, 133 (1965). (7) S. Wolf. Chem.-Z.. Chem. App., 93, 676 (1969). (8) D. Jagner, Anal. Chim. Acta, 50, 15 (1970). (9) T. Anfalt and D. Jagner, Anal. Chim. Acta. 57, 177 (1971). (10) A. Johansson and L. Pehrsson, Analyst (London), 95, 652 (1970). (11) S. Wolf, Fresenius' Z. Anal. Chem., 250, 13 (1970).
quires the use of computers or nomograms for the determination of the end point. In amperometric titrations, the end point can be found by simple linear graphical extrapolation of the intermittently recorded current values (12, 13). In this paper, an automatic recording amperometric titrator based on the stepwise addition of titrant is presented, which is an improved modification of an apparatus described previously in a preliminary note (13).Although the earlier instrument allowed fairly high precision, some problems remained unresolved. They will be discussed and a solution will be presented. Measurement Problems. Recently Rosenthal and coworkers (14) discussed errors in linear extrapolation titration procedures. They showed that in the majority of the considered cases measurement errors were the most important cause of end-point error. Considered were 1:1 reactions that form a single soluble product. In amperometry the precision of the measurement of the current can be limited by random fluctuations of the indicator current (15). Turbulence of the solution causes random variations in the thickness of the diffusion boundary layer. These fluctuations can be reduced by improving the stirring conditions, but they can be removed more effectively by lowpass active filtering. However, the filter increases considerably the damping time of the system. Systematic errors can nevertheless be avoided by performing the titration in a stepwise mode. After each addition of titrant, a waiting period is observed. The current is recorded when equilibrium is established. Another source of measurement error can be the current amplifier. The relation between the measured current i, the input offset current is, the voltage offset Es, (12) E. D. Olsen and R. D. Walton. J. Chem. Educ., 43, 659 (1966). (13) P. M. J. Coenegracht. MPlAppl. Notes. 6, 1 (1971). (14) D. Rosenthal, G. L. Jones, and R. Megargle, Anal. Chim. Acta. 53, 141 (1971). (15) C. E. Champion. G. Marinenko, and J. K. Taylor, Anal. Chem., 42, 1210 (1970).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
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Figure
Schematic diagram c . .he recording, amperometric titrator
and the output voltage Eo of an operational amplifier is given by (16, 17)
-[iRi i- i,Rf i- E , R, f R F R,
Rf is the feedback impedance, Rs is the source impedance, A is the open loop voltage gain, and R I Nis the amplifier input impedance. Assuming that the E s [ ( R s R f ) / R s ]term is negligible and that the second factor is equal to 1, it can be seen that variation of is lowers the precision of the measurement and, hence, the determination of the end point is less precise. The variation of is is largely caused by temperature drift. The condition
+
is sufficient to obtain a measurement precision of 0.1% or better. Another argument for this condition will be advanced below (computing circuit). Electrolysis of the sample solution can cause a titration error. This is important only for titrations that have nonzero currents before the end point, due to electrode reactions of the constituent. If the error is to be less than 0.1% for the titration of V1. of c M constituent, and if an average current of i A flows for t sec before the end point, Faraday's laws predict that
i
VczF 10-~-
t
(3)
F is the Faraday constant and z the number of electrons in the indicator reaction. The practical consequence of Equation 3 is that the magnitude of the surface and the rotational speed of the electrode have to be chosen properly. Extrapolation Problems. It is often advantageous to use measurements far from the end point for the extrapolation when the titration reaction does not proceed quantitatively (18). If the correction for the dilution with the titrant is neglected, the possibility of using large extrapolation intervals after the end point is diminished. Slope uncertainty is increased as the recorded titration curve (16) R. Stata, Operational Amplifiers, Part IV, Reprint of Electromechanical Design, Analog Devices, Cambridge, Mass., 02142. (17) H. J. Vahldieck. "Operationsverstarker." Telekosmosverlag, Stuttgart, 1970, Chap. 6. (18) G. Charlot, "Les Methodes de la Chimie Analytique," Masson et Cie.. Paris, 1966, pp 257-265.
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shows increasing deviation from linearity. Even if the titrant is 10 to 20 times more concentrated than the sample solution (19, 20), the region of extrapolation has to be limited to the current values near the end point (12, 20) as the dilution error in the uncorrected current becomes too large a t greater distances after the end point. Very high concentrations of titrant can lead to experimental problems if small sample volumes are to be titrated; very small burets have to be used. A new solution to this problem is now presented. An analog computing circuit applies a correction to the current and compensates automatically for the dilution by the volume of added titrant. Larger extrapolation intervals a t a greater distance from the end point can now be used. INSTRUMENT DESCRIPTION A schematic diagram of the titrator is shown in Figure 1. The programming unit P activates the motor M1 of the buret B during the titrating period, t l , and the chart motor M2 of the recorder Rec. during the recording period, t 3 . It also determines the length of the waiting period, t z . The system is stopped manually or by the limit switch L.S. on the recorder (dashed lines) a t the end of a titration. The potential is applied to the rotating platinum electrode (RPE) by the millivolt source E, the current is converted 'to voltage by the chopper stabilized amplifier 1, random current fluctuations are removed by the active filter F, and the correction for the titrant added is applied by an analog computing circuit formed with follower 2 with controlled amplification. The amplification is controlled by mechanically linking the wiper of the ten turn potentiometer RE t o the motor of the buret (heavy dashed line). The programming unit consists of three electronic timers that function consecutively in a cycle. The first timer regulates the incremental addition of the titrant, AV, and can be adjusted from 0 to 13 sec. The second timer makes it possible to choose a waiting period up t o 210 sec. The third timer can be adjusted from 0 to 10 sec and activates the chart motor, so that a small length of chart paper, Al, is transported. The precision of the timers is better than 0.15%. Buret. A digital, microsyringe motorburet is used (Metrohm, Mikro-Dosimat E 412). The use of a macroburet is also possible. The buret was used in the stepwise mode ("Volumenschritt"). The delivery speed of the titrant for (19) J. T. Stock, ' Amperometrlc Titratlons," Intersclence. New York. N.Y., 1965, p 8. (20) I. M. Kolthoff and J. J. Lingane, "Polarography," Vol. I I , 2nd ed., Interscience, New York, N.Y., 1952, p 890.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
0,a 0
m
E
$
0.6
0 Q
2 0.4 0.2
L / l l l i l 0
4
8
12
16
sec.
I
Figure 2. Low-pass filter (step response)
a 1-ml buret is approximately 1 pl in 120 msec. For the automatic delivery of 10 pl, the buret has to be activated during 360 to 1200 msec. For the delivery of A V = N X 10 pl, the titrating period ti has to be ( N - 1) X 1200 360 < tl < N X 1200 msec. The precision of tl does not need to be better than about 2%. Hence the precision of A V depends only on the buret and is about 0.2% for A V = 100 p1 (relative standard deviation of 20 measurements). Measuring Circuit. This consists of the millivolt source, the current-to-voltage transducer, the computing amplifier, the low-pass filter, and the recorder. It is based on a commercially available modular system (MP-System 1000, McKee-Pedersen Instruments). The millivolt source provides rt0 to 4000 mV (MP-1008). The current-to-voltage transducer is constructed from the high impedance selector MP-1009, (R1 - Rb), a condenser C of 0.1 pF and the chopper stabilized amplifier MP-1031. The input offset current is smaller than A. The low-pass filter is constructed from an Analog Devices 702 L2B active filter. This is a two-pole Butterworth filter with a cutoff frequency of 0.1 Hz. The settling time of the filter is about 14 sec, as is illustrated in Figure 2, which gives the response to a step input u o . Preliminary investigations with active RC-filters with time constants ranging from 0.4 to 2.0 sec showed that the heavy damping provided by the 702 L2B is not fully required when a smoothly rotating electrode is used. However, when using this filter, adequate damping is provided when a stationary platinum electrode or a vibrating dropping mercury electrode is used in a magnetically stirred solution. Computing Circuit. This is based on an operational amplifier (MP-1006A) wired as a follower with gain. The output voltage, Eo, of the circuit is
B
+
(4)
480
610
+-
AEEO
PI REAGENT
Figure 3. Recorded titration curves of 10.0 ml of 3.9 X 10-5M iodate in M sulfuric acid with 5.0 X 10-3M iodide solution at a stationary platinum electrode with correction for the dilution (A) With low-pass filter; ( 0 ) without low-pass filter
tentiometer. When the buret is filled, the counter goes down through zero with the wiper being pressed against the lower end stop. To prevent damage and loss of calibration, the housing of the potentiometer is allowed to move freely between two adjustable cams. The distance between the cams corresponds with approximately 8 digits on the counter. When the buret is filled and the counter goes down through zero, the wiper contacts the lower end stop and the potentiometer turns slightly. It is stopped by one of the adjustable cams. When the counter goes back to zero, the potentiometer is returned to its original position by the friction between the wiper and the slidewire. This position is fixed in the deliver direction by the other adjustable cam. One digit on the counter corresponds with one ohm. An accuracy better than 2% is achieved easily without frequent recalibration. The measured current, ,i has to be corrected for dilution to give the corrected current, k , according to ,
Lc
Ei is the input voltage, R7 is a ten-turn 10 K helipotentiometer. Its value is selected in accordance with the titration to be performed. &, is a ten-turn l K helipotentiometer (linearity O . l % , tolerance 5%). The large piston drive gear in the house of the buret makes 10 revolutions to empty the buret. R6 is connected to this gear through an equal size gear attached to its shaft. Ten revolutions correspond with 1000 digits of the mechanical counter of the buret. The last revolution of the buret gear wheel has been limited somewhat to prevent the wiper from contacting the upper end stop of the po-
=
v, + vt v.
,
( 5)
Irn
V, is the initial volume of the sample solution, Vt is the volume of the added titrant. The proper correction will be applied if the ratio of and R? is:
The maximum relative error (21) in the corrected current (21) K . Eckschlager, "Errors. Measurement and Results in Chemical Analysis." Van Nostrand-Reinhold, London. 1969, p 12.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
9
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A
320
LEO
160
t u 1 REAGENT ADDED
1600
z o L REAGENT l ADDED
%
0
0
6
c Z30 1 LBO
320 c p I REAGENT ADDED
160
0
Figure 5. Recorded titration curves of 2.0 rnl of 9.7 X 10-6M iodate in M sulfuric acid with 4.0 X 10-4M iodide solution at the RPE ( A ) With correction for the dilution; ( B ) without correction for the dilution 1600
2400
0
c pI REAGENT ADDED
Figure 4. Recorded titration curves of 10.0 rnl of 1.6 X 10-4M iodate in M sulfuric acid with 5.0 X 10-3M iodide solution at the RPE (A) With correction for the dilution: (B) without correction for the dilution
be determined precisely. A second advantage is that the 23 chart speeds facilitate an adequate choice of Al, which has to be, chosen in accordance with A V in order to allow significant extrapolation to the end-point volume. The zero offset on the recorder can be used to compensate for the residual current.
EXPERIMENTAL Aic/ic, caused by small deviations ARg and ART, can be found from Equation 5 . Substitution of Re and R7 for Vt and Vsin Equation 5 and solution of
AiC _ . --6 In iCAR6 JR6
IC
In +-66R7
ic
AR7
gives
From Equation 6 , it follows that the maximum relative error in the corrected current is not constant during a titration. The value in ohms of ARg and ART is determined by the tolerance and the adjusted value of Rg and R7. For a given value of R7 and increasing values of Rg up to 1 K, Aic/icincreases with the volume of the added titrant. Therefore a small deviation of ic from linearity can interfere with the accurate extraoolation. In the following example, this deviation is calculated and is expressed as Aic/ic, when 2 ml of titrant have been added to 10 ml of sample solution. For ARg = 20 9 , AR7 = 100 $2, Rg = 1 K, and R7 = 5 K (tolerance of 2%), then Aic/& = 0.67%. If no correction is applied, the deviation from linearity is 20% of the measured current under the same experimental conditions. The computing circuit will introduce a curvature of the titration lines if the offset current, is, of the current amplifier is too large. It is reasonable to assume that the corVt)/V,, is about maximal when, a t the rection term (V, end of a titration, a volume of titrant equal to the volume of the sample solution has been added. If condition 2 has been fulfilled, then this error in the corrected current is equal to or less than 0.2%. The recorder is a stripchart recorder with a digital pulsemotor (steppermotor) for chart movement (Telsec 700). The use of a steppermotor virtually eliminates errors caused by inertia of the motor so that the length of A1 will
+
1678
The titration of iodate with iodide was selected to test the performance of the instrument. Potassium iodate and potassium iodide are primary standards in titrimetry of which very pure qualities are commercially available. Excellent results for the amperometric titration of iodide in different media have already been reported by Kolthoff and Jordan (22). In order to obtain a reserved L-type titration curve, the iodate was titrated with iodide. The titration was performed in 1M sulfuric acid and the potential of the platinum indicator electrode was chosen on the plateau of the anodic wave of the oxidation of I- to I2 (23). In 1M sulfuric acid is the titration reaction
51-
+ IOj- + 6Hf
-
312
+ 3H20
In 1M sulfuric acid plus 20% vjv Bcetone ( 2 4 ) , another medium used by KoIthoff and Jordan, the results tended to be too low, as was found in preliminary investigations. Reagents. Potassium iodate, Merck, (“Urtitersubstanz, Artikel 5053”), was dried a t 150 “C. Potassium iodide, Merck, (“Suprapur, Artikel 5044”), was dried over phosphorus pentoxide. Other chemicals were reagent grade, Merck, “pro analysi.” Demineralized water was distilled from a glass still. The specific conductivity was 1.1X 1 0 - 4 S m-I. Apparatus a n d Technique. Titrations were carried out a t room temperature in siliconized Metrohm titration vessels with a sample volume of 20 ml. The buret tip was a Teflon capillary with a very fine bore dipped into the sample solution. Calibrated burets, pipets, and measuring flasks were used. A microliter pipet (Eppendorf) was calibrated before use. Stock 0.025M potassium iodate solution was stored in borosilicate glass. Stock 0.1M potassium iodide solution was stored in black painted polyethylene bottles (25). Working solutions in the and lO-*M concentration range were prepared daily by dilution. The concentration of the solutions was calculated from the weighed amount of substance and the dilution factors (26). The indicator electrode was a (22) (23) (24) (25)
I . M. Kolthoff
and J. Jordan,AnaL Chem., 25, 1833 (1953).
G . Raspi, F. Pergola, and R. Guidelh, Anal. Chem., 44, 472 (1972). R. Berg, Fresenius’ Z.Anal. Chem., 69, 369 (1926). G . Tolg, “Ultramicro Elemental Analysis,” Interscience, New York, N.Y., 1970, p 37. (26) K. Doerffel.Fresentus’ 2. Anal. Chem., 157, 195 (1957).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, AUGUST 1973
Table I. Titration Results Av
Iodate added, PS
83.4* 330.9 165.5 83.4 41.7 20.8 4.2**
assay, YOfound
No. of analyses
Re1 std dev, O/O
A
B
A
B
A
B
99.7 100.3 99.7 99.6 99.8 100.6 99.7
...
0.14 0.11 0.13 0.22 0.24 0.53 0.61
...
5 5 5 5 4 5 5
...
98.8 98.7 99.1 99.2 100.1 97.0
0.16 0.30 0.28 0.12 0.45 0.74
5 5 5 4 5 4
t-test, = 0.05
Concn iodate c,,
01
+ + + + +
a c t = concentration of the titrant solution in mol: I . , c, = concentration of the sample soiution in rnol,'l. *stationary platinum electrode. 'V-rnl sample solution. rotated platinum electrode. The length of the platinum wire was approximately 2.5 mm and the diameter was 0.3 mm. The platinum wire was sealed in a mercury filled glass tube. The electrode was placed in a holder and was rotated at 1500 rpm with a synchronous motor (27). The electrode was pretreated by performing a test titration. A number of experiments were carried out using a stationary platinum wire electrode (Metrohm EA 202) in a magnetically stirred solution. The potential of the indicator electrode was 850 mV against the reference electrode. In all experiments, the reference electrode was a saturated silver electrode (SSE) placed in a electrolyte bridge with 2M potassium nitrate solution (27). The bridge solution was refreshed daily. Residual currents appeared negligible. Procedure. Potassium iodate working solution (100 pl) was added to a mixture of 3.0 ml of 6.67N sulfuric acid and 6.9 ml of water. The sample solution was titrated with potassium iodide solution, either with correction for the dilution of the sample solution with the titrant (mode A) or without that correction (mode B). Burets had capacities of 4, 2, and 1 ml, respectively, and were used under the following conditions: 4 ml, R7 = 2500 R and A V = 160 pl; 2 ml, R7 = 5000 12 and A V = 80 pl: 1 ml, R7 = 10000 R and A V = 40 kl. The smallest buret capable of holding the total volume of titrant VT (see Table I ) was selected for delivery. The waiting period t z was 15 to 30 sec; t 3 = 10 sec, and Al = 25 mm. Five to ten measurements after the end point were used to construct the titration curve. The titration value of the reagent blank was determined from a difference titration. A sample solution was titrated using mode A . Subsequently. a second volume of iodate working solution was added to the titrated solution. R7 was adjusted to a volume corresponding to the original volume of the sample solution plus the added volume of iodate working solution. Then the new amount of iodate was titrated without refilling the buret. The reagent blank was determined from the difference between the two titrations.
RESULTS AND DISCUSSION Low-Pass Filter. The effect of the low-pass filter on the measurement of the current is shown in Figures 3A and 3B, illustrating the recorded titration curves of the titration of 10.0 ml of 3.9 X lO-5M iodate solution with 5.0 x 10-3M iodide solution at the stationary platinum electrode according to mode A.
(27) P. M . J. Coenegracht, Pharrn. Weekbi., 108, 769 (1972)
mol/l.
3.9 x 1.6x 7.8 x 3.9 x 1.9x 9.7 x 9.7x
10-5 10--4 10-5 10-5 10-5 10-6 10-6
VT =
C,/CsQ
VTPlb
128 32 64 128 105 206 41
640 3040 1520 720 960 4a o 480
totai volume of the added titrant.
The results of the titration, as indicated in Table I by one asterisk, and Figure 3A, show clearly that the filter makes possible an accurate and precise titration a t a stationary platinum'electrode. Computing Circuit. Figures 4A and 4B show the recorded titration curves (bold line) of 10.0 ml of 1.6 X lO-4M iodate solution with 5.0 X lO-3M iodate solution a t the RPE according to mode A and B . In Figure 4A, the construction of the end point is shown (dashed line). In Figure 4B, the dashed line is drawn only t o show the deviation frqm linearity when no correction is applied. The quantitative effects of the correction of the titration curve were studied. Sample solutions containing 330 to 20 Fg of potassium iodate were titrated a t the RPE according to modes A and B, respectively. The table shows the titration results. The positive sign for the t-test indicates that the observed mean of mode A is significantly larger than the observed mean of mode B a t the 95% confidence level. The results show that the accurate and precise automatic titration of small amounts of iodate is possible if the correction is applied. They also show that the assay values are significantly lower when no correction is applied, even if the titrant is much more concentrated than the sample solution. Figures 5A and 5B show the recorded titration curves of a small ( 2 ml) volume of 9.7 x 10-6M iodate solution with 4.0 X lO-4M iodide solution. Although the titration curve shows no deviation from linearity when the correction is not applied (Figure 5B), the results of this titration, which are indicated in Table I by two asterisks, show clearly that the correction of the titration curve is necessary to obtain an accurate result. From the results, it can be concluded that the described apparatus allows accurate and precise automatic titration of microamounts of iodate and that the accuracy of the titration is increased by the correction of the titration curve for the dilution of the sample by the titrant. The described principle for the recording and correction of the amperometric titration curve can be applied to other linear titration curves. Received for review October 18, 1972. Accepted January 17, 1973.
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