1116
ANALYTICAL CHEMISTRY
titration of 0.01N ammonia with 13- acetic acid in methanol a t 18” C. If the four +values are taken as 0.5, 0.9, 1.5, and 1.123 and if the first end point lies a t E = 0.900, successive end points nil1 be 0.932, 0.953, 0.967, 0.975. . . On the other hand, if the four E-values are taken somewhat further from the equivalence point as 0.5, 0.8, 1.5, and 1.33, successive end points will br 0.900, 0.962, 0.985, 0.992, 0.998. For the titration of 0.01.V sodium acetate p i t h 1 Y hydrochloric acid in water a t 23‘ C., if the E-values are taken as 0.5, 0.8, 1.4, and 1.29, successive end points xi11 be 0.900, 0.986, 1.004, I n this case the convergence is very satisfactorv. These calculations point out the practical limits of the present method. As the change in slope a t the equivalence point be(xinips less sharp and the curved part of the titration curve \\.idens, the accuracy of the first end point estimate arid the convc’i’gence of successive estimates both become poor. The two effects work in concert, and in cases of very gradual change of slope the calculat,ion becomes prohibitively long. However, eveii i n these cases the convergence limit of successive end points is very close to the equivalence point. I n the titration of sodium acetate the first, estimate of the end [mint is not likely to be in error by more than 3y0 (Table I). A siiiyle calculation suffices t o find the final end point. Tliis ea, and €4 values. may then be verified with a second set of el, 111 the titration of ammonia with acetic acid in methanol, the first rstimate may be in error by IO$%; with practice this error c:in be made smaller. Even so, two or three successive calcula:we likely to be required. hen the convergence of successive end point estimates is poor, an alternative niethod of calculation may be used. In&:id of making a single first estima,te of the end point, several estimates are made in such a way as to bracket the equivalence point. For each of these estimates a single four-point calculation is made, and the calculated end point is plotted vs. the estimnted point. The correct end point is found on the plot as the point where the calculated and the estimated end points are equal. This method has the advant,age that the convergence limit’ is :ipproached from both directions. Practical Example. Figure 4 shows the conductometric titration curvc for 0.008N sodium azide with 0.lA‘ hydrochloric arid in water. The titration data were obtained on a Shedlovsky bridge (8) with earphone detector. The temperature of the tit,ration eel1 was constant t o within 0.2’ c. The cell constant was too large to obtain maximum accuracy in the resistance measurements ( 5 ) , but the experiniental points fell on a smooth curve with a mean deviation of 0.570. I n Figure 4, the ordinate Vo)/VoR,where V is the volume of titrant, Vo the initial is (1’ volume of sodium azide, and R the measured resistance. T h e factor (1’ VO)/VOcorrects for the dilution during the titration.
.
+
+
Table 1.. End Point Calculation for Titration of 0.0085 Sodium Azide with 0.LV Hydrochloric h i d in Water t
0 7 0 85 0 li 0 (i
€2
e3
€4
0.9 0.89 0.93 0.915
1.3 1.2 1.2 1.3
1.11 1.1 1.1 1.1
End Point, 111. 19.90 19.99 19.75 19.97 .I\-. 19.90 f 0 08
-4first estimate of 19.44 ml. for the end point was obtained by extrapolation of the nearly linear segments observed for 0 < T. < 10 and T 7 > 22. .A single calculation, using the four points 0.7, 0.9; 1.3, :tnd 1.11 multiplied by 19.44 ml., led to an end point voliinie of 19.89 ml. -4second calculation, using 19.89 ml. as the end point estimate, led to 19.90 ml. This end point vas chwked with three other sets of values of €1, E ? , €3, and €4. The results are shown in Table T’. T h e mean deviation of the four values \vas only 0.4%: all five calculations took less than 30 minutes. This titration is comparable to that of sodium acetate because the K A values of acetic and hydrazoic acids are nearly equal. The relatively large discrepancy between the first estimate and the final end point is not surprising. For similar +range selections, the tentative end point in the titration of sodium acetate occurred a t E = 0.974, as shown in Table I. This is in good agreement with the observed ratio, 19.44/19.90 = 0.977. By the potentiometric method this titration would have been very difficiilt. ACKNOWLEDGMENT
The author wishes to thank the Yad Chaiin Weizmann for t h e award of a Chaim Weizmann Fellowship, and Dan Golomb for supplying the titration data for Figure 4. LITERATURE CITED
(1) Bacarella, A. L., Grunwald, E., hlarshall, H. P., Purlee, E. L., J . Org. Chem. 20, 747 (1955). (2) Bjerrum, S . , Unmack, A., Zechmeister, L., KgZ, Dambe T’idenskab. Selskab., .Vat.-fus. M e d d . 5 , 11 (1921). (3) Goddu, R. F., Hume, D. S . , i l x a ~CHEM. . 26, 1679 (1954). (4) Ibid., p. 1740. (5) Golomb, D., Weizmann Institute of Science, Rehovoth, Israel, private communication. (6) Grunwald, E., AXAL.CHEM.26, 1696 (1954). (7) Harned, H. S., Owen, B. B., “Physical Chemistry of Electrolytic Solutions,” Reinhold, New York, 1943. (8) Shedlovsky, T., J . Am. Chem. SOC.52, 1793 (1930). R E C F I V Efor D review September 26, 1955. Accepted March 24, 1956
Automatic Photometric Titrations THOMAS L. MARPLE and DAVID N. HUME Department o f Chemistry and Laboratory for Nuclear Science, Massachusetts Institute o f Technology, Cambridge 39, Mass.
A simple logarithmic attenuator circuit which makes possible the direct recording of absorbance from the output of a Beckman RIodel spectrophoton,eter is described. When used in conjunction with a stripchart recording potentiometer and a constant-deliverY reagent the apparatus is to automatic Photometric titrations. The application to automatic iodometric and acidimetric procedures is described.
A
\TOKG several physicochemical methods available for lo-
cating titration end points automatically, measurement of light absorption has received surprisingly little attention. Several workers have suggested arrangements in which a large change in transmittance at the equivalence point could operate a trigger mechanism or be recorded as an indicator-instrument deflection ( 2 , 5, 7 , 14, 15). For many reactions, however, the equivalence point must be located by examination of an absorbance us. volume curve ( 4 ) . Heretofore, the only reported application of this technique to autornatic titration has been that of
V O L U M E 28, NO. 7, J U L Y 1 9 5 6
1117
Malnistadt and otherb (11, I?), who performed their titrations in a Cary recording spectrophotometer. There would be considerable advantage to being able t o use the more commonly available and much less expensive single-beam manual spectrophotometers, such as the Beckman Models B and DU, for automatic recording of titrations. This requires, however, some means of converting the output signal voltage of these instruments, which is linear with transmittance, to a logarithmic equivalent proportional to absorbance. The main portion of this paper is conrernetl with the description of a simple electronic converter wliiclli :iccomplishes this for the Beckman RIodel B spectrophotometer. THEORY
Several electronic circuits which are available for logarithmic atttaiiuation (1, 6, 1 3 ) might be modified to suit the requirements of the photometric titration. Of these, two appear to be partirii1ai.ly attractive: the circuit which 11Iuller ( I S ) employed in :in early linear absorbance-scale colorimeter, because of its simplirity; and that proposed by Howard, Savant, and Keiswander ( e ) ,Imause of its stability and accurary. The circuit of Howard, S:iv;tnt, and Seiex-snder was logarithmic as low as 0.3-volt input, sign:tI, but it n-as relatively complex. Although it was proposed tl years ago, Xiiller's circuit showed the greatest promise [ i f w s y adaptability t o the Model B spectrophotometer, and a nintiification of it was developed accordingly.
Sensit t v i I y Selector Per cent Transmittance
Rewriting this equation in the logarithmic form, one obtains the relationship
The actual absorbance relationship desired for photometric titrations follows the equation
A,
=
100 log 7 /o T
Thus, by the selection of operating conditions for the BSKT-GT where 2 is small, one would expert to obtain the desired logarithniic attenuation of the spectrophotometer output signal. It is noted that the response of the GSHi-GT comes to a finite value at E = 0 and one would expect some serious deviations from logarithmic attenuation a t low input voltages. If the absorbance scale is t o cover the range of 100 to 0% transmittance, the deviition would occur a t high absorbances. EXPERIMENTAL
Apparatus. The attenuator (Figure 1) was built into a metal cabinet 3 X 4 X 5 inches. The front cover of the Beckman RIodel B spectrophotometer was removed, the lead to the plub side of the transmittance meter was cut, and the necessar! soldered connections, A , B , and C, Figure 1, were made to the attenuator circuit. When the cover was replaced, the leads for the attenuator were most conveniently brought out of the hole provided by the manufacturer for convenience in adjusting wavelength calibration. When switch S , is in the off position, the attenuator and recorder do not respond and the instrument can be used in the normal manner. Recorder sensitivity is determined by the setting of As and zero adjustment made with R3.
To Reogenl Reservoir RI
Sw
Cornpensolor
OFF
Wl
1 Figure 1.
Rz
1y 1 -
1$(i
'
-E:;+
1
II
Cam
Logarithmic attenuator circuit
1, 2, 3. Leads entering spectrophotometer A , B , C . Connections made within spectrophotometer circuit R I . 0.1-megohm precision type resistor R I . 2500-ohm precision type resistor RI. 100-kilo-ohm W. W. variable resistor Rd. I-kilo-ohm resistor, 111 watt Rr. 0- t o 100-ohm preoision decade resistance box I'T. 6SK7-GT B I . 60-volt stabilized power supply B2. 1.5-volt Burgess 4FH battery S W . Switch
The vacuum tube selected for the critical logarithmic attenuation was the 6SK7-GT, the operational characteristics of which are described elsewhere (16). The important fact is that at plate operating potentials greater than 60 volts, the plate current does not follow the grid bias in a linear manner but more closely approximates the relationship e-klb
=
E
+Z
where e is the base of the Kaperian logarithms, Zb is the plate current, E is the grid potential, and k and Z are constants.
Figure 2.
Reagent delivery system
The compensation control of the logarithmic attenuator was mounted externally so that zero adjustments could be made easily. A precision decade resistance box was used as the dropping resistor (&) to facilitate the use of the attachment with recording potentiometers of different ranges. If a fixed resistance is desired, a 100-ohm resistor is suitable for use with a 5-mv. range recorder. The use of a variable dropping resistor gives the added advantage that the attenuator can be adjusted to several different absorbance ranges when used with a fixed-range recorder. The operating plate and screen grid voltages were supplied by a commercially available stabilized power supply (Kepco Laboratories, Flushing, S. Y.) which could, however, be replaced by conventional B batteries. It was found that a more constant potential than could ordinarily be obtained with the power supply was needed for the attenuator compensation control; hence, a 1.5-volt dry cell was used for this function. The actual recording of the absorbance during a photometric titration was made with a Weston recording potentiometer with a sensitivity of 5-mv. full-scale deflection. The chart speed wap 2 inches per minute.
1118
ANALYTICAL CHEMISTRY
A cam-driven syringe buret was used to provide a constant flow of titrant (8). The assembly was similar t o that used by Keily (8) for differential thermometric titrations and is shown schematically in Figure 2. T h e outside curvature of the cam at?, so that when was made to conform to the equation p = 12 the cam was made to rotate a t a constant speed, the volume displacement of the syringe would be linear mith time. The cam used in this work conformed t o the equation p = 2.000 inches
+
+
' 3 inch.
Thus, for each 0.360" angular displacement of the
T
cam, a linear displacement of 0.0015 inch should occur in order to preserve reasonable uniformity of flow. I n this work the steel cam was driven a t 0.1 r.p.m. by a Bodine Type K-2 synchronous motor operating through a 10 to 1 worm gear reduction. The head of the piston of the syringe was fitted with a glass prism to provide point contact on the cam surface. The contact surface was lubricated slightly with stopcock grease and a small spring was attached to the piston to hold it securely in contact with the cam.
Reagents. All the chemicals used in this work were of reagent grade and all solutions were prepared from deionized water of 1 to 2.5 X lo6 ohms specific resistance. The nitrogen used for deaeration of the solutions was Air Reduction Co., prepurified grade. Calibration of Logarithmic Attenuator. I n order t o ensure that the logarithmic attenuator produced an accurate signal conversion, a test was made over the 0 to 100% transmittance range. The results shown in Figure 3 indicated that serious deviations from logarithmic response occurred only Then the input signal voltage was less than that corresponding to about 15% transmittance on \vas the "1'' scale (about 3.2 volts). The sensitivity selector (RS) therefore adjusted so that only the region above 20% transmittance appeared on the recorder scale. Table I shows the response obtained with the logarithmic attenuator and the Weston recorder. The average deviation of the logarithmic attenuation from theoretical response (0.003 absorbance unit), while not suitable for precision photometric measurements, is satisfactory for photometric titrations. The attenuator alone gives a linear representation of absorbance over the range from zero to approximately 0.8 absorbance unit. When used in conjunction with the sensitivity range selector of the Model B spectrophotometer, the operating range becomes zero to 2.3 absorbance units in four steps. This range is adequate for most titrations; therefore, no attempt was made to extend the logarithmic response of the attenuator. RESULTS
T o test the response of the various components of the titration apparatus, several titration procedures n-ere examined. The first \vas a scaled-down version of the conventional titration of iodine, generated from potassium iodate and acid, with sodium thiosulfate. This titration seemed particularly important because iodometric determinations are so widely applicable.
20
1 0 8
6
4
l n o u l Signal -%Transmittance
I 16
I
I
S
4
I 2
1
I
I
VOLTS
Figure 3.
Test of attenuator response linearity
Abscissa represents input signal in vo!ts from spectrophotometer. equivalent per cent transmittance readings on sensitivi'ty "1" position also given
The volume delivery of the buret was calibrated by weighing aliquots; the maximum deviation from constant flow over 907' of the cam surface was 0.01 ml., indicating that the cam radius was accurate to 0.003 inch. When the buret was used in conjunction I\ ith the Weston recording potentiometer, the volume delivery was 0.20T6 ml. per inch of chart. The cam buret could, of course, be replaced by other means of constant reagent addition, such as the screw-activated syringe delivery unit of Lingane (10).
It was found necessary to have the buret delivery tip drawn into a fine capillary and positioned as far as possible from the light path in the titration beaker. If the buret was allowed to empty near the light path, small erratic variations were produced in the absorbance record during the titration. The photometric titrations were performed in the Beckman hIodel B spectrophotometer which had been equipped with the titration cell compartment previously described (3). T o facilitate reproducibility of the beaker position in the light path, two glass arms were fused to opposite sides of the titration beaker. The beaker was placed in the light path so that the arms fitted into slotted wooden blocks which were a part of the beaker stand. A 100-ml. beaker was used in all of the present work The volume of the solution in the beaker \vas adjusted t o 80 to 85 ml., so that air was not introduced into the light path when stirring the solution during a titration. When it was necessary t o perform the titration in an atmosphere of nitrogen, the cell was covered with a thin sheet of polyethylene in which a small slit was cut for the entrance of the buret tip. After an initial purging for 5 minutes with prepurified nitrogen, further passage of gas was found unnecessary, because entrance of air was prevented by the polyethylene film.
+ T
Figure 4.
Titrations with 0.01N thiosulfate
I . 0.0001M iodate solution in presence of acid and
excess iodide: h = 450 m p 11. 4.0-gram potassium iodide blank: X = 365 m p , maximum sensitivity
Solutions of iodate and thiosulfate were prepared as suggested by Kolthoff (9); the concentrations were such that they could be standardized on a macro scale t o better than 1 p.p.t. Aliquot8 of these reagents were taken to prepare the dilute solutions necessary for the photometric titrations. Table I1 shows the reproducibility of the titrations with
V O L U M E 2 8 , NO. 7, J U L Y 1 9 5 6
1119
sodium thiosulfate. The standard deviation of replicates titrated with 0.01N thiosulfate was approximately l%, which is consistent with the reliability of the automatic buret. The curves in Figure 4 indicate the type of curve obtained when titrating with 0.01S thiosulfate. The wave lengths were selected so that an absorbance change of about 0.5 unit occurred. For the blank estimation the wave length was selected so that a maximum change in absorbance resulted.
Table I.
Logarithmic Attenuator Response
Input Transmittance, Signal, Response, Absorbance Unit % Volts Recorder Theoretical Dev. 0.000 0.000 100 16.00 0.000 0.046 -0,007 90 14.40 0.039 80 12.80 0.092 0.097 -0,005 0.155 -0.003 70 11.20 0.152 0.223 0 222 +0.001 60 9.60 0.306 0 801 +0.005 50 8.00 40 6.40 0,401 0,398 +0.003 30 4.80 0.525 0.523 +0.002 20 3.20 0.699 0,699 0.000 Average deviation from theoretical response of logarithmic a t t e n u a t o r , 0.003 absorbance u n i t .
The incieased variability of the titrations made with 0,OOOSX thiosulfate can be attributed partially to the sloumess of the reaction a t these extreme dilutions. The titiation curves here did not show the usual abrupt changes in absorbance a t the start or end of the reaction.
Table 11. Automatic Photometric Titration of Microequivalent Quantities of Iodate Equivalents X 100 Taken Founds 8.72 8.70 4.36 4.2 4 grams KI 0.40 (blank) 10 grams K I 0.78 (blank) 0,872 0.8526 4gramsKI 0.30b (blank) a Corrected for blank unless b T i t r a t e d with 0.000809N 0,0101.“thiosulfate.
Std. Dev.,
Chart, Inches 4.33 2.23 0.19
Trials 5
0.37
6.8i 1.80
Error,
q0
% -0.34 -1.6
J
1 7 1.1 13.0
2
..
3
8.4 ..
5
2
..
..
need of a rapid reaction. Reaction velocity has been found t o be an important factor even in the conventional iodine-thiosulfate titration when the concentration of thiosulfate titrant was less than 1 X 10-3 N . The requisite of a fast reaction is not peculiar to photometric titration, but is a factor which must be considered in all automatic titration methods. A second factor m-hich may be a source of difficulty is the need for constant delivery rate of reagent. Malmstadt (fd) alleviated this problem by the use of coulometrically generated titrant. ~ particularly important when using The need for constant f l o is the Cary recording spectrophotometer, because absorbance is recorded as a direct function of time. I n the work described here the substitution of an X-T type recorder for the X-T type Weston instrument could be easily made. I n this case the volume delivery need not be constant if the delivery is directly coupled to one axis of the recording instrument. This type of system is used in the Precision-Dow Recordomatic Titrometer (17).
Table 111. Automatic Photometric Titration of Chromate Equivalents X 106 Chart, Taken Found Inchew Trials 50.20 50.8 4.69 5 25.1 24.9 2.30 4 5.02 4.80 4.42b 4 a C h a r t equivalent, 0.2076 ml. per inch. b T i t r a t e d with 0.005225 hydrochloric acid; hydrochloric acid.
Std. Dev.,
Error,
%
%
1 .o 1.0 3.2
+1.2
-0.7 -4.4
others with 0.05220N
I n all of the titrations reported in this work, the addition of titrant produced an immediate decrease in the absorbance of the solution. Thus, it was possible to determine both the start and the equivalence point of the titration from the recorded plot. I n titrations where the addition of titrant does not produce such a change, the start of the titration can be determined by always starting the buret a t a clearly identifiable chart marking. Preliminary investigations indicate that this is a suitable method for permanganate oxidations.
-2.3
..
a blank determination. sodium thiosulfate; others titrated with
ACKNOWLEDG,MENT
The authors are indebted to the Atomic Energy Commission for partial support of this work. LITER4TURE CITED
As an example of a neutralization procedure, the titration of chromate to dichromate with hydrochloric acid was studied. and Chromate is the anion of a weak acid ( K A = 3.2 X the conversion may be followed spectrophotometrically in the region from 400 to 430 mp. It was found desirable to remove carbon dioxide with nitrogen, but othem ise the performance of the titrations required no unusual arrangements. Titrations, particularly a t high dilution, showed rounding a t the equivalence point caused by partial dissociation of dichromate ion, but in every case extrapolation of the straight line portions of the titration plot could be made. -4s before, the solutions were standardized on a macro scale before dilution and titration. The reproducibility of the chromate titrations is shown in Table 111; the titration curves are similar to those of the iodine-thiosulfate system and are not shorn. DISCUSSION
The application of the automatic equipment for routine analytical determinations appears t o be limited principally by the
Ballantine, S., Electronics 2, 472 (1931). Barredo, J. 11. G., Taylor, S. K., Trans. Electrochem. SOC.92, 437 (1947). Goddu, R. F., Hume, D. S’., i l s . 4 ~ CHEM. . 22, 1314 (1950). Ibid., 26, 1679, 1740 (1954). Hickman, K., Sanford, C. R., IND.ENG.CHEM.,ANAL.ED. 5, 65 (1933). Howard, R. C., Savant, C. J., Neiswander, R. S., Electronics 26, 157 (1953). Juliard, A , , Cakenberghe, J. van, Heitner, C., Znd. chim. belge 17, 25 (1952). Keily, H. J., Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1955. Kolthoff, I. M., Sandell, E. R.,“Quantitative Inorganic Analysis,” Macmillan, Kew York, 1949. Lingane. J . J., ANAL.CHEM.20, 285 (1948). Malmstadt, H. V., Gohrbandt, E. C., Ibid., 26, 442 (1954). Malmstadt, H. V., Roberts, C. B., Ibid., 27, 741 (1955). Muller, R. H., J. O p t . SOC.Amer. 25, 342 (1935). Muller, R. H., Partridge, H. M., Znd. Eng. Chem. 20,434 (1928). Nichols, M. L., Kindt, H. H., ANAL.CHEM.22, 781,785 (1950). Radio Corp. of America, Harrison, N. J., “RCA Receiving Tube Manual,” (1954). Robinson, H. A., Trans. Electrochem. SOC.92, 445 (1947). RECEIVED for review November 14, 1955.
Accepted March 2, 1956.
