gacycle T'itrimeter A 350-MC W. J. BLAEDEL
~
AND
H. V. MALM STADT, University of Wisconsin. Madison. Wis.
A stable a n d sensitive high-fre queney titrimeter u eonoentrie-line oscillators a n d cbperating a t 350 Mo. per seeona LS aescnma. AIL the basic types of t i t r a t i o n s 1h a v e heen performed with it, and it is possible to oarry o u t titrations with a eons.iderable q u a n t i t y of foreign electrolyte present. Precise and accurate titration DU rves are presented.
R
ECENTLY there have been described high-frequency titnmeters . . which measure frequency changes in the course of a titration (1, 7). The titration vessel is placed in the tuning cirouit of a high-frequency oscillator, and as the composition of the solution changes, the frequency of $heoscillakm changes. A plat of frequency against volume of standard solution gives B titration curve much like that for a conductometric titration. The value of such an instrument to the analytical chemist is obvious, for neither indicator nor electrodes nor physical contact of any sort with the solution are necersary to perceive the end point in a titration. A stable, sensitive titrimeter using the simple Clapp ( d ) oscillator, and operating a t 30 megacycles, has, been described in detail (1). Briefly, this titrimeter consists of two oscillators, one of which is loaded with the titration vessel, the other unxed y is
obtained on a conventional frequency meter. Because the frequency of the unloaded oscillator remains constant, the beat frequency is a measure of the change in frequency of the oscillator which is loaded with the titration vessel. Many different kinds of titrations may be precisely performed using the 30-Me. titrimeter, but the instrument possesses one serious fault which makes it difficult or impossible to perform many useful titrations: The sensitivity of the instrument drop4 off very rapidly when the electrolyte concentration in the titration vessel rises above a maximum value; For the 30-Mc. instrument, the maximum tolerable electrolyte concentration is rather low, and corresponds to about 0.06 M sodiuin chloride (1). Although .many kinds of titrations may be suecessfully performed helow this limit, others may not, and it is a definite disadvantage to be restricted to so low z t total electrolyte concentration. Considerations recently presented (1)show that the maximum tolerable electrolyte concentration is directly proportional to frequency. It follows, therefore, that the frequency of the titrimeter must be increased if the maximum tolerable electrolyte aoncent,ration is to he increased. From these considerations, a titrimeter operating a t about 350 Me. per second would have a maximum tolerable eledtrolyte concentration corresponding to 0.7 M sodium chloride or its equivalent. With such a titrimeter, it would he possible to carry out most titrations even with large amounts of foreign electrolyte present. In this paper, the construction, properties, and use of such a 350-Mc. titrimeter are dberihed, and typical titration curves are given. Quarter-wave-length concentric-line oscillators are used. The sensitivity and stability are sufficient to carry out most titrations, even when a considerable quantity of foreign rlectrnlyte is present. DESCRIPTION 0
believed necessary to maintain the same high stability at 350 Mc. per second aS found with the 30-Me. titrimeter, which possessed a stability of 5 eyoles per second-Le., B stability of 2 to 10'. A survey of the electronics literature for very stable and simple oscillators operating a t 300 to 500 Me. per second wm not encouraging. A quarter-wave-length concentric-line oscillator seemed the best of several kinds described (6),even though it was stated to poss?ss a frequency stability of only 1 to IO6. However, it appeared possible to improve this stability with lptter mechanieaI construction and certain other circuit changes. This proved to hi2 the case. The complete assemhlv of the oscillators and lines is shown ^. .... , ,,, ..' in Figure 1. Figure a IS s scnemauc oiagram 01 one 01 me osculators. The construction of the oscillators and lines is described in considerable detail in the following paragraphs for two reasons: (1) Extreme care in layout of parts and mechanical construction is .es&ntial. Reproduction of this equipment might be very difficult or unsuccessful without these details. (2) No dependence may be placed upon the literat- of electronics, for there is
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Figure 1. Assembled 350-Megacycle T i t r i m e t e r
1413
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ANALYTICAL CHEMISTRY
1414
no description available of a simple 300- to 500-Mc. oscillator with th? requisite stability. The quarter-wavelength line oscillator shown in Figure 2 consists of a brass cylinder, A , and a coaxial Invar rod, C. D and E are the input and output coupling loops, respectively. A w a made from brass tubing (0.125-inch wall, 3.5 inches in outside diameter, and 12 inchcs long).. The lower edge of the cylinder was machined with a No. 20 thread t.o screw into the square, brass plate'baae, B (6 X 6 X 0.5 inch), to a depth of 0.25 inch. The lower edge of the cylinder was beveled slighlly (see Figure 2), so that the inner edge dno tirrnlri i n t n t h o h.3.a R to make good high-irequeney electrical
this loop rc With the eqL., ...-..I .~l." -,y y v 111, ~'L'ar.u~r oscillations could not be oliminated by varying the length of loop from 3 to 4 inches. Use of t,he feed-back resist.or, Ri, eliminated parasitic oscillat,ions, but no st,udy was made to determine over what limits the loop length could be varied without rrintroduetion of the parasitics. E was the output coupling loop (also made from inch rod) which fed ~ o m eof the high-frequency energy to the mtxcr unit. The size of this loop was ohtsined by trial and error. A straight rod and small loops were first used, but these did not couple a sufficiently large signal int,o the mixer unit. A satisfactory loop n w of the shape shown in Figures 2 and 4. The height was 2.375 inches from B to the top of the loop. Because this loop proved successful, no further study was made to determine size limits or other possible configurat,ions. Loops D and E passed through porrelain insul;ktors, F, which were screwed into B. The insulators had ' / x ~ l 4threads, Forcelain was used rather than pal.vst~yrene.because polystyrene was susceptible to deformation by heat, when soldering leads. Horever, polystyrene would .probably have worked as well if excessive heat had not been applied. Brass fittings, G, held the loops firmly in plaoe and provided soldering points for leads to the oscillator circuit (see Figure 3 sku). J was a shielded aluminum chassis (3 X 3.5 X 2.5 inches deep) which was serewid to the bottom side of B. T h e output bo bhe mixer was taken through the coaxial junction, H (Amphenol WIR), which was connected with a very short lead to output loop E . The other parts of the oscillator are shown in the srhematic diagram, Figure 2, and their general lay-out in Figure 3. Figure 4 shows the resonant li?e with the cylinder removed. A 6-volt high-capacity storage battery wa used ior the filaments of both oscillators, and B batteries (225 volts) were used .for the plate supply. The cap ioor holding the titration vessel in the top of t,he quarter-wavelength line is shown in Figures 1 and 4. Dimensions were not critical, but good mechanical construction wits necessary to hold the titration vessel firmly in place and to allow no movement during titration. The titration vessel (a test tube, 8 inches X 1.5-inch diameter) slip-fitted into a split collar attached to the cap, and could be easily insert4 or removed by loosening or tightening a setscrew. The cap w a threaded to tit a. No. 32 thread on the top end of the b r a s cylinder ( A , Figure 2). This arrangement allowed precise positioning of the titration vessel in the high-frequency field $0 that any desired beat frequency or sensitiyity could lie oht;&d, "Y desrribcd lat,cr. Bot,h of t.he conceiitiic lines were equipped with such alps. ~
Figure 2.
SchernatioDiagmm of: Titrimeter
wrllp, ' h i btL wire diem
I.i.l.I.
KI. 150-oh Ilr.
T.
I2,WQ955 tu1
C w&san Invar rad (n/a*inch in diameter X 8.25 inches), threaded into B to a depth of 0.25 inch with a '/1-20 thread, so that. it was coaxial with A . The lower end of the rad u-as also heveled to give good eontact with the base. It. was the length of this rod which determined the frequency of oscillation, and for high-frequency stability it a a s necessmy t o keep the length invariunt. lnvsr was used hecausr of its law temperature eoeffieient. of expansion. In order to obtain high "Q' and high stahilit,y, the ratio of the inner diameter of A to the diamet,er C was chosen to be ahout :3.6; C, B , loops D sed E, a ~ theinner d surfsee .of .4 were all silver plnrad (6'). To'prevent radiation loss from t,he line, t.he cylinder was extended ahout one eighth of WI wave length ahove the Lop of the rod. The hairpin-shaped input coupling loop, D, as made from Invar rod (0.125 inch in diameter) and was */,G inch wide and 4 inches long. \Vilhout the feed-hack resistor, R,, the 1cngt.h ai
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Mixer. The mixer unit, that w&s first used w m b small crystal unit similar i n design to l.hc one described with the 30 M c . per second titximeter (1). Although this mix& gave beat frequencies and isolated the oscillators sufficiently, it powssed a nonlinear characteristic-that is, the k a t frequency output,irom the mixer,
V O L U M E 22, NO. 11, N O V E M B E R 1 9 5 0 as measured on a frequency meter, was not strictly proportional
to the actud difference in frequencies of the two oscillators. The cause of this was undetermined. It was actually possible to use
1415 500 cycles per second when titrating, so that "pulling" would
not occur.
It was common practice to N n through a titration rapidly with the meter set on mame range. It was possible to locate the end point roughly with this method by watching the meter and observing when the frequency change per unit volume of standard solution underwent an abrupt change. Another equal aliquot It was expedient t o use the duo-diode mixer contained in a war shrplus radio altimeter, APN-1 (4). The unit was removed of solution was then titrated carefully in the region of the end from the altimeter and kept intact, except that a coaxial junction point. The frequency meter was set on either fine or medium was used to re lace the coupling loop and lead which ordinarily sensitivity, and the frequency changes were precisely read and coupled into tEe transmitter of the altimeter. It was thereby recorded as a function of volume of standard solution added. possible to oouple both oscilhtors of the titrimeter into the mixer with the usus1 ooaxid leads. This unit worked very well. The For some titrations it was possible to use the differential isolation of oscillators was good, and "pulling" of the beat freprocedure described in connection with the 30-Me. titrimeter quency was noted only below 500 cycles. ( 1 ) : However, when a large quantity of foreign electrolyte was Frequency Meter. A simple, four-tube, direct-reading frepresent the frequency changes per drop of standard solution were quency meter was used. The frequency was read directly on a milliammeter (4 inches square, 0 to 1 mil full scale). Three usu$ly not large enough ta be precisely read. In order to be sensitivities were availilahle, corresponding to 2500, 5000, and consistent, one method of carrying out titrations with the 35050,000 cycles per second for full soale deflection, and meter Mc. titrimeter waa adopted. response was linear with frequency for these three ranges. This This method consisted of adding the standard solution in 0.5-ml. meter and its power supply were constructed with some modifications from a war surplus crystal duplicator (Majestic Radio increments over B range of several milliliters on both sides of and Television). the end p i n t , and recording the change in beat frequency after each addition on the medium sensitivity scale of the frequency The circuit diagram of this frequency meter is not given here. meter. (The fine sensitivity scale was used only for differential A more compact and versatile circuit is being built and will be titrations.) Commonly, the total frequency change in this region described iri a future publication. The circuit diagram of t.he was greater than 5000 cycles, correspocding ta full scale deflection mixer is not given; a t present a project is under way to construct on medium sensitivity. Jn such.cwes, the frequency meter was f~ simple and compact unit that will work well a t frequencies reset a the needle approached full scale by turning the holder even highpr than 350 Mc. per second. cap on the reference oscillator so as to bring the meter needle back to the fw left of the scale. Several such resettings were PROCEDURE FOR PERFORiMANCE O F TITR4TIONS sometimes required in the course of a titration. Titration curve8 The titration tube containing the solution to be titrated was :..---'",I ""A C."A C-".).. i" "n^:+:nn I -., +inhtanin" +I,- adarrau, similar in form to those for conductometric titrations were plotted by adding each successive heat frequency change to the total before i t and plotting total frequency change against volume of standard solution (see Figures.7 ta 9, inclusive). Curves from d a b t a k e n in this way were extremely smooth; errors due to occaDinnal and rare fluctuatinns, caused by jarring the instrument, were for the most part eliminated, as were errnrs ....., due to drifts occurring during temperature equilibration. Incentric line without introducing noticrahle Huctuntions in the spection of the curves in Figures 7 to 9 shows that the segments best frequency. .of the titration curves have little curvature. This indicates that the sensitivity of the instrument remained constant through the region over which the data was taken. The reason for this was twofold: (1) There was considerable foreign eleetmlyte present in most of the titrations. ( 2 ) The data were +ken only in the region about the end point. Both factors combined to maintain fairly constant ionic concentration (and therefore constant sensitivity).
this unit, but i t caused &me scattering of points used to determine the titration curves. Consequently, s. different mixer was used.
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CIIARACTERISTICS O F TITRIMETER
Figure 4. Concentric-Line Oscillator w i t h Outer Cylinder and \'esse1 EIolder Removed
The cap on the reference oscillator was lrdjusted for a heat frequency such that the frequenry meter needle fell a t the fa, left end of the scale, using minimum frequcuoy met,er sensitivity. Then, using the medium or fine sensitivity, the reference oscilletor was further adjusted to have 8 higher or lower frequency than the titration oscillator, depending on the titration performed, and so the meter needle slways traveled from left to right a t the start of a titration. The beat frequency was always kept, above
Stability. After 10 to 20 minutes were ,allowed for warming up, it. was found that the two oscillators beating together gave a beat frequeuey which had an average fluctuation of 50 cycles when operating a t 350 Me. per second. This represented a relative stability of about 1 to 10'. The time required for warming up was usually 15 to 20 minutes. After the solution had reached the equilibrium temperature of the titrimeter, the beat frequency drifted negligibly. This indicated that the dimensions of the frequency-determining resonant lines remained constant and that the amount of energy absorhed by the solution was so small thsd it did not heat appreeiahly. It was noted that, even after the instrument had warmed up, there welp very slow drifts of best frequency for B short time after insertion of B sample, probably due to temperature changes of the solution. These caused no difficulty in the titration procedure described above. Sensitivity. A quantitative study was made OP the dependence of sensitivity on concentration, To do this, the change in frequency was observed on adding standard hydrochloric acid into
1416
ANALYTICAL CHEMISTRY
hydrochloric acid solutions of known concentration. The same was done for sodium chloride. In Figures 5 and 6 beat frequency is plotted as a function of concentration of the electrolyte in the titration vessel. These plots show that the frequency changes with concentration only within certain concentration ranged, depending on the nature of the electrolyte. This is in accord with the theoretical considerations recently described (1, 3). As stated previously, the sensitivity could be varied simply by changing the distance between the bottom of the titration vessel and the top of the quarter-wave-length Invar rod. The adjustment of this distan,m WBS easy and provided an excellent means of selecting any desired sensitivity. The sensitivity curves for three different distances are given in Figures 5 and 6. It was noted that decreasing the distance from 1 to 0.75 inch tripled the sensitivity.
total electrolyte concentration consisting of 25 mole % silver nitrate and 75 mole yoof sodium nitrate at the beginning of the titration. In this case, the total electrolyte concentration at the end point was less than 0.1 M , and the addition of 0.1 M sodium chloride after the end point caused an increase in concentration and a reversal in the titration curve.
0
i k
g 0.2 1
I
0.01
Figure 6.
Figure 5.
Sensitivity Curves for Hydrochloric Acid Solutions
It was not possible to obtain a beat frequency a t a distance of 0.625 inch or less, even though the oscillators remained in
oscillation. Although the reason for this was not definitely established, it was believed due to setting in of a parasitic oscillation: It was considered likely that certain changes in design would have enabled a decrease in the distance between the titration tube and Invar rod with an attendant increase in sensitivity, These changes were not attempted for two reasons: (1) The attainable sensitivity was amply sufficient to carry out most titrations, even with a considerable quantity of foreign electrolyte present. (2) The changes required a completely different design and construction.
0.03
I
1
LO
Sensitivity Curves for Sodium Chloride S o h t ions
Figure 7, B, shows the titration of silver nitrate with 0.1 M sodium chloride when the total concentration of electrolyte consisted of 10 mole % of silver nitrate and 90 mole % of sodium nitrate a t the beginning of the titration. The total concentration a t the end point was about 0.2 M . The addition of 0.1 M sodium chloride after the end point thus caused a dilution and no reversal was observed. However, because of the preciseness of obtaining the beat frequency changes, a sharp and accurate end point was obtained. The presence of the precipitate did not affect the frequency stability. Standard sodium chloride and silver nitrate solutions were prepared from Acculute solutions, and were checked against each
0
\=L.
TITRATIONS PERFORMED
It was found that the 350-Mc. titrimeter could be used to determine end points in titrations based on acid-base, precipitation, soluble complex formation, and redox reactions. In all cases, observed end points agreed excellently with calculated equivalence points based on other accepted methods of titration. In the following paragraphs there are discussed only typical titration curves which illustrate certain characteristics or potentialities of the titrimeter. All titrations were carried out a t sensitivities between the 1-inch and 0.75-inch position (see Figures 5 and 6). Titration of Silver Nitrate with Standard Sodium Chloride. Figure 7, A , shows the titration of 25 ml. of 0.1 M silver nitrate with 0.1 M sodium chloride in an end-point volume of about 125 ml. Sodium nitrate was present as a foreign electrolyte, the
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0.I 03 MCI MOLARITY;
theor.z5oz 25.00 d. ml.
20
Figure 7.
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24 26 28 M L . 0.1 M. SODIUM CHLORIDE.
3
Titration of Silver Nitrate with Standard Sodium Chloride
A . 25 ml. of 0.1 Msilver nitrat etitrated with 0.1 M sodium chloride i n presence of 75 ml. of 0.1 M sodium nitrate E . 25 ml. of 0.1 M silver nitrate titrated with 0.1 M sodium chloride i n presence of 22.5 ml. of 1.0 M sodium nitrate
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V O L U M E 22: NO. 11, N O V E M B E R 1 9 5 0 other using the Mohr (chromate indicator) method. On the curves of Figure 7 are indicated the theoretical equivalence points calculated from the standard concentrations. Agreement of observed with calculated end points is excellent. These titrations show that a considerable quantity of foreign electrolyte is tolerable during a titration; this is not the case in conductometric titrations. Titration of Mercuric Nitrate with Potassium Thiocyanate. Figure 8 shows the titration of 26 ml. of 0.05430 Ai’ mercuric nitrate with standard 0.1 M potassium, thiocyanate in an endpoint volume of about 126 ml. This curve is plotted on an enlarged scale to illustrate the precision of the measurements, and to show how small are the deviations of the experimental points from the best straight lines through them. To prepare standard mercuric nitrate solution, reagent grade, red mercuric oxide was dissolved in an excess OT nitric acid. This solution was standardized against 0.1 M hcculute potassium thiocyanate solution, using ferric alum as an indicator. The theoretical end point on Figure 8 was calculated from these standard concentrations. Thew is excellent agreement of the observed and calculated end points. Titration of Oxalic Acid with Thorium Nitrate. In Figure 9 is given the curve for the titration of 25 ml. of 0.04972 A4 oxalic. acid with standard 0.02466 -11 thoriua hitrate in an end-point volume of 125 ml. The oxalic acid w&s weighed out as a primary standard and checked against Acculute potassium permanganate. The thorium nitrate was prepared from Baker’s reagent grade thorium nitrate and standardized gravimetrically ( 5 ) . The theoretical end point calculated from the standard concentrations is annotated on Figure 9 and agrees well with the observed end poiii t .
characteristics of the instrument supports the theory of highfrequency titrations advanced earlier by the authors. The existing titrimeter is considered an experimental model, for there appear to be many possibilities for improvement of this first instrument of the concentric-line type. An improved design is under construction in this laboratory, and a long-range study is planned to obtain maximum stability and sensitivity with this type of titrimeter. With increased stability and sensitivity, it might be possible to titrate small quantities of a soughtfor constituent in the presence of considerable quantities of foreign electrolvtes.
Ot
I 21
23
25
ML. STANDARD THORIUM I -
Figure 9. Titration of Oxalic Acid with Thorium Nitrate 25 ml. of 0.04972 M oxalic acid titrated with 0.02466 M thorium nitrate
d
6 \2 -
P
To date, the indications are that ‘stable and sensitive highfrequency titrimeters may be built and used in titrations to give an accuracy comparable to that of good gravimetric methodsi.e., 0.1%. These instruments are neither inexpensive nor simple to build. Once built, however, they are simple to use and very easy to maintain. If and when some of the potentialities of the high-frequency titrimeter are definitely proved and illustrated, it may become apparent that the time and expense of construction are more than compensated by the new methods of analysis made possible by this instrument.
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c, 23
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t
t-4
27 NITRATE.
End p t .
5 25
26
27
ob, 2713 ml. #?cor 27.15 m1.
28
29
M L . 0.1 M . K S C N .
Figure 8.
Titration of Mercuric Nifrate with Standard Potassium Thiocyanate
25 mi. of 0.05430 M mercuric nitrate titrated with 0.1 M potaasium thiocyanate
ACKNOWLEDGMENT
The authors thank V. C. Rideout and Han Chang of the Electrical Engineering Department for valuable advice and help with the electronic phases of this work. W.J. Larson provided the photographs of the equipment. This research was supported in part hy a grant from the Wisconsin Alumni Research Foundation. LITERATURE CITED
This titration illustrates how the 350-Mc. titrimeter may be used to devise new procedures in volumetric analysis. A simple arid relatively rapid method for the determination of thorium based upon the oxalate titration is being worked out. CONCLUSIONS
The 350-Mc. titrimeter is a stable and sensitive instrument, aiid may be used for most titrations, even when considerable quantities of foreign electrolytes are present. A study of the
(1)
Blaedel, W. J., and Malmstadt, H. V., AN*L. CHEM.,22,
734
(1 950).
(2) Clapp, J. K., Proc. Inst. Radio Engrs., 36, 356 (1948). (3)’Forman,J., and Crisp, D., Trans. Faraday SOC.,42A, 186 (1946). (4) R C A Rev., 9,352, 531 (1948). (5) Scott, W. W., “Standard Methods of Chemical Analysis,” p. 953, New York, D. Van Nostrand Co., 1939. (6) Solley, B. J., Wireless World, 51, 170 (1945). (7) West, P. W., Burkhalter, T. S.,and Broussard, L., ANAL.CHEM., 22, 469 (1950).
RECEIVEDMay 1. 1950.
