High-Sensitivity, Direct-Reading, Linear, Recording Conductometric Titrator with Automatic Temperature Compensation or Proportional Temperature Control T. R. MUELLER, R. W. STELZNER, D. J. FISHER, and H. C. JONES Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.
b A high-sensitivity, direct-reading, linear, recording conductivity instrument designed around operational amplifiers has been developed for use in monitoring solution conductance or in conductometric titrations. The high-sensitivity feature makes it possible to titrate low concentrations of acid or other speciles in the presence of high concentrations of foreign electrolytes. The instrument has been used successfully in over 50 applications involving acid-base, complexometric, redox, precipitation, and metal ion titrations as well IYS for a number of absolute conductance measurements.
C
sented details of a complete recording conductometric titrator. ,ilthough each of these instruments possesses features which are desirable for conductometric titrimetry, each has characteristics which limit its versatility. It was the purpose of the present investigation to determine whether it was feasible to provide in a single instrument. t'he better aspects of these devices: more specifically, to apply a small- and constant-amplitude (1000 c.p.s.) sinusoidal signal to the electrodes; to measure the a x . current which flows through the cell under these conditions; to compensate the resulting voltage signal for temperature changes wit.hin the cell; to amplify and rectify this signal linearly; and to present the d.c. signal for cont'inuous, automatic recording on a linear, directreading conductance scale. Further, it was desired that a wide range of conductivities could be measured with a single cell geometry, that small changes in conductance could be measured accurately and precisely, and that the instrument could be duplicated without resort to circuit modifications. The high-sensitivity, direct-reading, linear, recording conductometric titrator that resulted from the present work was designed around operational amplifiers manufacturerd by G. A. Philbrick Researches, Inc. The principle of conductance measurement employed is
ONWUCTIVITY MEASURING IKSTRUMENTS which can be used for re-
cording titration curves automatically are available from the Leeds & Northrup Co., Industrial Instruments, Inc., and Radiometer Co. Anton and Mullen ( 2 ) have incorporated a Leeds & Northrup Xodel4958 conductivity monitor in their mu1til)urpose titrator. Circuits which provide for automatic recording of conductance (3, 10) or which could be so adapted ( 1 , 8,9) have been described. I3oardnian has published a conductance coircuit which, in conjunction with commercially available components. provides for autoniat'ic recording of conduct'onietric titrations (4).Colwin and I'ropst (5) have pre-
shown in Figure 1. Since inception of the present work, several publications have appeared which suggest the use of operational amplifiers for conductivity measurements (6, 7 , 14) ; however, sufficient data for an evaluation of the proposals are lacking. The operational amplifier is designed for stable d.c. operation. Consequently, its gain a t high frequencies has been attenuated. For example, the new K2-XA amplifier, which a t d.c. levels may have an open-loop gain of 30,000, has an open-loop gain of only 270 a t 1000 c.p.s. under the same conditions of feedback and load. The SK2-V amplifier has a d.c. open-loop gain of 100,000 but a 1000 c.p.s. gain of 1800. Thus, one is limited to circuit designs which demand only small closed-loop gains if excessive errors are to be avoided. Advantages accruing from the use of these amplifiers in the design of the titrator outweighed the disadvantage of low open-loop gain. THEORY
OF
OPERATION
If a voltage is applied to a pure resistance, the current which flows is given by Ohm's law. If the voltage is held constant, this equation may be written
Z
=
kG
(1)
where G is the reciprocal resistance or conductance. The conductance cell is not a pure resistance but may he approximated by an impedance represented by Figure 2. Here, C2R2 and CsR3 represent the electrical double layers a t each elec-
EO" T
R
= Conductance= G
'OUT
Figure 1 .
OC
Direct method for conductance measurement
-l
m Figure 2.
>
Equivalent circuit of conductance cell VOL. 37, NO. 1 , JANUARY 1965
13
Meosuring Resistor Tuned to 4000 cps
r\,
OmVp mq
+
I---+-
w
INITIAL CONDUCTANCE COMPENSATION N U L L DETECTION
SKP-V
SUETRACTOR KO-PA CONDUCTIVITY CELL
9
TEMPERATURE COMPENSATION
CONTROL AMPLIFIERS
1
.r'i4-. F i i Thermistor
AMPLIFIER
i
CONDUCTANCE COMPENSATION
SYNCHRONOU RECTIFIER
..... . -:ma
.. ... ........
Cell Voltage
* ,
?,e'
T Amplitude
SUBTRACTION VOLTAGE
Figure 3.
trode; R1 represents the bulk solution resistance; and C1. the interelectrode capacitance. I n aqueous solutions containing appreciable electrolyte and with a relatively low frequency of 1000 c.p.e. applied b e h e e n .I and B , CI is negligibly small-that is, its impedance is high in comparison with that of the alternate current path. K i t h 3.5 inv. r.m.s. (10 m v . peak 14
ANALYTICAL CHEMISTRY
I
1;
Phl'ase A d j .
A
I
Zcm offset
BUFFER AMPLIFIER
+
?T
Block diagram of conductometric titrator
to peak) a t 1000 c.p.s. applied to the cell, the faradaic impedances Rz and R3 are usually large in comparison with the reactances of Cz and C3. The equivalent circuit of the cell may thus be represented by a series circuit composed of C2, R1, and C3. For identical immersed electrodes, C2 = C3, and the effective capacitance, Celf, is 2 Cf. If Cefris large and R1 is also large, the
impedance of the cell is determined primarily by R1, and there is little phase shift with changes in R1. These conditions are approximated by using roughe.g., platinized platinum-widely spaced electrodes. For other cell designs, the current phase angle. $, is given by
Note 8
OSCILLATOR
I
I
Figure 4.
(frequency f in c.p.s., Ceff in farads). The direct-reading feature of the inst,rument about to be described is based on the assumption that p = 0. Equation 2 shows that p approaches zero for small G and large Cerr. At 1000 c.p.s. an error of lYc will result from phase shift for the conditions Ceff = 500 uf., R, = 2 ohms (0.5 mho). Figure 3 is a bl'ock diagram of the titrator. .1 t,ransistor-driven LC oscillator (Figure 4) supplies a constantamplitude, 1000 c . ~ ) , ssinusoidal .~ output of about 2.5 volts, peak to peak. Reference signals of the desired ainplitude are derived from a divider network on the output of the oscillator. The control amplifier (Figure 1 and 5 ) impresses a IO-mv. p - p voltage across the conductance cell. One elect'rode of the cell is physically grounded. The other electrode is controlled a t d.c. ground potential by the chopper-stabilized control amplifier. .1 current-measuring resistor, R,, of the appropriate value is placed in the feedback loop of this amplifier. The out'put of the control amplifier then bears the following relationship to the conductance, G, of the cell :
Equation 3 is onl? approximately correct, but it applieq within -O.1y0 a t full output in the present application.
VO LTA G E
D IV I D E R S
Oscillator and voltage dividers
K h e n G = 0, E,,, = E , , = 1 0 m v . This 10 mv. is subtracted from the signal in the second amplifier (Figure 6) to simplify subsequent circuitry. The outliut of the second aml)lifier feeds a temperat,ure-compensating network (Figure 6). The signal, attenuated by the divider action of the teniperaturecompensating network, is again amplified (K2-X-I, #1, Figure 7) and corrected for phase shift introduced by the amplifiers and coupling networks. The signal is nest rectified (Figure 7 ) by a transistor chopper (shunt type) driven synchronously with signal frequency. The d.c. output signal from the chopper is amplified by t'he USA-3 amplifier (Figure 8). A small capacitor in the feedback loop of the US.1-3 filters the output. The 30-volt (full scale) output of the tTS.1-3 feeds a voltage divider string that provides outputs of 5, 10, and 20 mv. (or ot'her voltages, if desired) for recording purposes. The basic instrument is suitable for static conductance measurements as well as for conventional titrations. If it is desired to perform titrat,ions or make other measurements where only small changes in conductance are expected (for example, titrations performed in the presence of high concentrations of indifferent electrolytes), the initial conductance compensation circuit may be used. The method of compensation is illustrated in Figure 9.
The circuit functions in the following manner. The control amplifier maintains the a.c. voltage of 10 mv. aci'oss the cell, but anj- fraction of the required current may be supplied by the compensator. When all of the current is supplied by t,he conipensation circuit, 10 niv. appears both across the cell (summing junction) and a t the output of the control amplifier, and no current flows in the measuring re value of t,he measuring resistor may then be increased to provide the required sensitivity without degradation of accuracy or linearity. The compensation circuit contains provisions for adjusting the niagnihde and phase angle of the current. Proper adjustment of phase and amplitude is indicated as minimum output on t,he recorder. Because rectification of the signal is normally accomplished synchronously, a diode (not phase sensitive) is used to rectify the signal while making the null adjustment (Figure 10). ;Ifter nulling, detection is switched back to the synchronous mode to record the conductance information. The complete circuit' of the compensat,or is given in Figure 11. The initial conductance compensation feature is useful for monitoring or t'itration applications. I t could also prove useful for cell-lead compensation in remote operations where high conductances are measured. VOL. 37, NO. 1 , JANUARY 1965
0
15
--_I
I
I
I I
I I I
,-i
I I I
=u
10
1z I
U
IF I I I
.- J
r-I
I
I I I I I
I I
I L---
I I I I
I I
I
16
ANALYTICAL CHEMISTRY
I
I N ITI AL CONDUCTANCE COMPENSATION NULL AMPLIFIER
O . O f p f / 200v
a Gil
I
“Manuol“
Note +I
“Out“
Helitrim tp.
TUNED SIGNAL AM PLI F1ER
Shield Thermistor
VECO 32A4
I I
Figure 6. Tuned signal amplifier, initial conductance compensation null detector amplifier, and temperature compensation circuits
CONSTRUCTION A N D CIRCUIT DETAILS
Power Distribution. Power connections and distribution are shown in Figures 12 and 13. The d.c. power supply used for the titrator is a n Embree Electronics, West Hartford, Conn., Model PS/200/3.5. T h e supply is well regulated and is capable of delivering 200 ma. a t zt300-volts d.c. I t also supplies 10 amperes a t 6.3-volts a.c. with a center t a p on the transformer biased a t - 170-volts a.c., and 6.3-volts a.c. with a center t a p a t ground. Filament power for the initial conductance compensator is derived from this same supply and also filament power and zt300-volts d.c. for the operation of a proportional temperature contyoller (15 ) . Current demand of the instrument is 160 ma. at -300-volts d.c. and 108 ma. at +300volts d.c., including that required for the proportional temperature controller. Maximum a x . power consumption is about 800 watts. All a x . filament power is carried to the amplifiers with #22 shielded, 2-conductor cable, the shields of which are common with the chassis. Tie points for =t300-volts d.c. circuit ground (G or GG), and chassis ground (SCG or SCG’) are provided on each chassis. All points indicated by
enclosure in a rectangular box on the circuit diagrams should be returned directly to the appropriate tie point. Some care should be exercised in the wiring layout to keep power leads away from signal leads. Oscillator. T h e oscillator circuit is similar to one described in “ A Handbook of Semiconductor Circuits” prepared for the Bureau of Ships, Department of the Navy (11). It was selected because of its reported frequency stability and low distortion. Operated from a well regulated supply into a fixed load, its output amplitude is also exceptionally stable. The oscillator circuit should be mounted remote from power transformers and from circuitry carrying the high level chopper-drive signal. Control Amplifier. T h e control amplifier is unusual and some comments on its design are in order. T o minimize polarization i t is necessary to hold the d.c. offset between the electrodes near zero. T h e a.c. signal must be superimposed on the “zero” d.c. level, and sufficient current must be available for high conductance solutions. T h e control amplifier is composed of SK2-V #1, a K2-PAA,and a class-h transistor current booster. The K2-PA was modified by placing a
0.01-pf. capacitor between pins 6 and 7 of the chopper. This modification may be accomplished without opening the amplifier case by inserting a test socket adapter between the amplifier and chopper. The capacitor is mounted with short leads, and the unused terminals on the adapter socket are clipped off. Without the modification described, the circuit shows considerable 60-c.p.s. noise as well as a low frequency (-6 c.p.s.) oscillation. Although the gain is reduced somewhat by the change, the low frequency oscillation is eliminated and the 60-c.p.s. noise reduced to about 30 pv.,-,, across the cell when the amplifier is biased to 0.0-mv. d.c. The d.c. drift is less than 0.1 mv. for extended periods. The method of a x . signal injection is similar to that employed by Walker, Adams, and Alden (18). 1o minimize summing point errors, 7
i.e., errors in the potential difference across the cell-the current-measuring resistor is chosen so that, it is always less than or equal t o the cell resistance. However, when the feedback (measuring) resistor is smaller than about 1000 ohms, the shunting effect on the cathode resist’or in the output stag? of the SK2-V causes the open-loop gain of the amplifier to be diminished ( 1 2 ) . For VOL. 37, NO. 1 , JANUARY 1965
17
the same reason booster amplifiers such as the Philbrick K2-Bl cannot be used. The two-stage current booster in the feedback loop permits the use of measuring resistors as small as 2 ohms without degradation in amplifier perform-
ance. The nature of the control amplifier circuit is such that prolonged shorting of the cell leads causes no damage, and recovery from severe overload is almost instantaneous. The measuring resistors are non-
>
0
R \
8 1c
i
18
ANALYTICAL CHEMISTRY
inductive, wirewound types for low noise and stability. Capacitive shunting of each resistor was necessary t o prevent oscillations. The total conductance range of 0.5 mho to 1 pmho for which the instrument is designed is
L 0,
3 0,
ii
divided into 13 ranges. Range 1 operates linearly from 0.5 to 0 mho (2 ohms to infinity); range 2, from 0.2 mho to 0 mho; etc. Thus, each range is direct-reading in conductance, and range switching ma,y be accomplished without zero shift. This feature is not found in most of the other recording conductometers described in the literature. I t would be particularly useful for monitoring applications where range
switching might be accomplished automatically. The 10-pmho range should have a lOOK ohm measuring resistor. The shunt capacitor, however, produces an impedance somewhat less than lOOK ohms. Consequently a 10-K ohm variable resistor is placed in series with a lOOK ohm fixed resistor and the combination shunted by a variable capacitor. After the instrument h m been adjusted for
operation on lower ranges, the 10-pmho range is trimmed to give full scalp reading with a lOOK ohm resistor huhstituted for the cell, and for 10% deflection with a 11i ohm resistor. For resistances greater than 111 ohm. some nonlinearity arises from phase shift. Measuring resistors other than those used in t h r construction of the instrument described may he used. ‘The product of mrasriring resistor and shunt
I
k
a
3
a
W
a
eg
n
z
W n
a)
a aJ O u,’o Y f f l z a
W
K
--m
.-c 3 .-
L U
U
D
C
0
5,
&I VOL. 37, N O . 1, JANUARY 1965
19
Current- Measuring Resistor
Phase Adjust Current Adjust
I
2
Figure 9.
Method of initial conductance compensation
capacitor should be about 0.2 psecond to produce maximum stability and minimum error. Temperature Compensation. For routine, automatic conductometric titrations, temperature compensation is of doubtful value. If the solution volume, sample concentration, and rate of titrant addition are about the same from sample to sample, the results of analyses performed with or without temperature compensation are within the limits of error associated with the method. I t is, however, necessary either to know the solution temperature or to relate automatically the measured conductance to the conductance a t some reference temperature if the measured conductance is to be correlated with concentration. Temperature compensation of conductance measurements with a thermistor has been extensively discussed (3,13, 16). Choice of a thermistor as the temperature-sensing element for the present work was based primarily
on two considerations: temperature coefficient and resistance. The VECO 32,11 thermistor has a temperature coefficient of -3.9% per degree C., a value from which the desired coefficient is easily derived. To reduce the effects of self-heating, it is desirable to operate the thermistor a t low signal level. X low resistance is preferred to minimize noise pick-up. The final form of the temperature compensation network is a voltage divider composed of a series-shunt circuit. The series resistor determines the temperature range over which linear compensation may be realized. Adjusting this resistor, a 10-turn Helipot with a calibrated dial permits linear compensation over approximately 10" intervals from 20" to 60" C. The calibrated dial allows the range to be reset once the setting for a given temperature has been determined. The dial could be calibrated directly in temperature. However, the present cost of thermistorb matched to the required tolerances for direct substitution pro-
hibits this refinement for most applications. Initial Conductance Compensation. I t was mentioned ureviouslv t h a t the function of the initial conductance compensation circuit is that of supplying current a t the proper phase angle. Phase shift is provided by using the two amplifiers to produce lead or lag. Amplitude-independent phase shifting is accomplished with the ganged Helipots, R,? and RI8. Constant amplitude of the variable phasing circuit is obtained by shunting RI8with sufficient resistance to maintain constant amplifier gain as the phase control is moved between limits. The control produces 26" phase shift from limit to limit. This control in conjunction with fixed phase shifts permits phase adjustment between +19.8" and -36". d maximum phase shift of 3.6" is observed when the load on T4is varied from 672K ohm to 910 ohms. The compensation unit is mounted on a separate chassis with its own control panel. Two advantages result from this arrangement. Shielding problems are reduced by having the high level signal frequency removed from the other circuitry, and the number of controls on the main instrument panel is reduced. Table I describes the procedure for compensating the initial conductance. A sensitivity increase of 100-fold is usually possible. If the initial conductance of the solution is low, however, noise may limit the useful sensitivity available. With an initial conductance in the order of 0.5 mho, no noise is visible on the recorded trace with 100fold increase in sensitivity if the temperature of the cell is held within 0.002" C. Recording Provisions. T h e output of the US.1-3 is about +30-volts d.c. for full-scale recorder deflection. The signal for the recorder input is derived from this 30 volts by a voltage divider on the output of the amplifier. The
Note
10
O c t a l Plug
>
--Figure 10.
20
(OK %3
R,J
Band-pass amplifier and rectifier for initial conductance compensation null detection
ANALYTICAL CHEMISTRY
recorder chosen for the instrument is a 10-mv. IJrowri Electronik which permits the inputs to “float.” alternate means of zero shifting is shown in Figure 13, should a recorder be chosen t h a t requires one input to be grounded. lllinneapolis-Honeywell
#9283-YR, 0-100, evenly graduated chart paper is recommended. This paper has 0.5 division beyond the 0 and 100 markings which allows the zero to be set accurately while providing a small amount of overranging. Zero offset of about 1.5 times full scale is provided.
Construction notes indicated on the circuit diagrams are listed in Table 11. Initial Adjustments and Checks. After wiring is complete and all plugin units, amplifiers, and interconnecting cables are in place, proceed as indicated in Table 111.
I-
o
VOL. 37, NO. 1 . JANUARY 1965
21
PERFORMANCE
Table I.
Procedure for compensating Initial Conductance
Turn S p a Off. Set Sgh to X1. 2. With the conductance cell attached, choose a range which gives maxim( ni on-scale recorder deflection. 3. If the initial conductance is between 5K and 5OIi pmhos, set S 3 c to position a ; between 50K and 200K mhos! set S a to position b ; bet'ween 200K and 5OOK pnihos, set S3 to ]losition c; and above 5OOK pmhos, set Sato position d . 4. Set Current potentiometers to niasiniuni CCTT- positions. Turn Sz On. 5 . Aidjust the highest resist,ance potentiomet,er to bring the recorder pen to within about 10% of full scale. 6. Switch 86 to position 5 . 7 . Xdjust potentiometers to give minimum deflection. 8 . hdjust Phase control to give minimum deflection. Kote that the recorder pen should novi be within 2% of full scale. If this is not the case, repeat steps 7 and 8. If t'he Phase control has been rotated to its C C W limit, deflection is not below 27, of full scale, and S3 is in position d , set Sa to position e , f . or g as required to bring the pen near zero deflection. Steps i and 8 should be carried out alternately and should be repeated until minimum deflection is obtained. 9. Set S6 to position 6. 10. Repeat steps 7 and 8 to obtain minimum deflection. Note that this is a inore sensitive position on s6 than is position 5. -1 0.3-mv. p - p , 1000-c.p.s. signal a t the output of SK2-V #2 will produce full-scale recorder deflection. 11. If increased sensitivity is desired, set S4d t,o the next lower conductance range. Repeat steps 7 through 11 until the desired sensitivity is obtained. 12. Keturn S6to position 1, 2, or 3 as desired. Switch 86 may be used as a multiplier to obtain sensit,ivities of 0.5, 1, or 2 times the conductance range selected. 13. If the conductance is expected to decrease with addit'ion of titrant', rotate Recorder Offset control so that Zero corresponds to 1 0 0 ~ oof full scale pen deflection. 14. I$-hen the cell is removed from the instrument the following sequence is preferred : (a) decrease sensitivity by setting Range selector to a higher conductance range. (b) Turn SBOff (e) Remove cell S2 is the compensation On-Off switch (Figure 11). b S. is the recorder inout selector switch (Figlire R). c S3is the current range selector switch 1.
(Figure 11). d S4 is the conductance range switch (Figure 5 ) .
22
ANALYTICAL CHEMISTRY
Accuracy. Current measuring resistors with &0.5yo tolerances were used in the construction of the range switch assembly. Shunt, capacitors across these resistors introduce a small negative error. The control amplifier may introduce a maximum error of -0.17, a t full scale. Phasing errors with respect to the chopper drive signal may also contribute a few tenths of 1% error. The recorder chosen for the titrator may cause a n error of 10.257, (guaranteed accuracy). The "worst case" combination of errors resulting from these sources should lie between +0.75% and -1%. Lead resistance, if uncompensated, may cause appreciable error for high-conductance measurements. Solutions of 0 . 1 s and 0 . 0 1 S HC1 were prepared by dilution from Fisher standard 1.OOOOiV HCl. The conductance of the 0.1.V solution was measured. From this measurement the cell constant of the conductance cell mas calculated to be 2.022 em.-' The conductance of the O . O l N solution was measured and found to be 0.002029 mho after correction for the water used for dilution. The conduct'ance calculated for a cell constant of 2.022 em.-' is 0.002037 mho-an error of less than 0.4%. A similar experiment wit,h a cell having a constant of -0.1 em.-' showed a negative error of 0.1%. In making these measurements, six conductance ranges were used. The measured conductances ranged between -0.39 mho and -6 pmho (2.6 to li0,OOOohms). The results are well within the limits of instrumental error, and it is inferred t,hat valid measurements of conductance were obtained. Specific conductances were calculated from the data of Stokes ( 1 7 ) . Measurements were made at 25' f 0.1' C. Conductance measurements were also made on KCI solutions of different concentrations. These measurements agreed with those obtained with an Industrial Instruments, Inc., Model RCM-15131 bridge within 11% for measurements between 12 kmho and 0.46 mho. The range of conductances over which the comparison was made was limited by the inability to obtain a balance on the bridge. A dip-cell with a constant of 0.1 em. -l was used in these measurements. Errors in measurement can be reduced to 1 0 . 1 to 0.2%. To obtain this level of accuracy, it is necessary to exercise considerable care in making the initial instrument calibration adjustments and to calibrate each range. The latter may be accomplished by substituting resistors of known values for the cell and using a potentiometer instead of the strip chart recorder. The procedure is described in the next section. Linearity. Linearity is more important than absolute accuracy for titration purposes, because end point location is generally determined by the intersection of extrapolated branches of the conductance us.
titrant-added curve. Usually the slope of the titration curve before the end point differs from that beyond the end point'. Thus, a n y error in the slope of either branch of t h e curve results in the location of a n incorrect end point. Linearity of instrument response was checked by substituting resistors in a General Radio Decade Resistance Box, Type 1432-X, for the cell. With this boy, resistance tolerances are *0.05yo for resistances of 10 ohms or greater, =t0.15yo between 1 and 10 ohms, and +0.5% from 0.1 to 1 ohm. The strip chart recorder was disconnected and the output signal at the recorder terminals was measured with a millivolt potentiometer. For conductance ranges below 0.1 mho, linearity was within +0.15% on all ranges from zero to full output. On the higher conductance ranges, where less accurate standards were used, measured linearity was within f0.28 yo. Linearity of response was also assessed by observing the results of titrations and dilutions. Solutions containing different amounts of HC1 in 300 ml. of solution were titrated with lLVXaOH. Over the linear portions of the titration curve, deviations from a straight line were consistently less than one pen width (+O.l%). Dilutions of KC1 solutions were carried out by constant rate addition of water. Linear response was also indicated for the dilutions. Actually, differences in linearity of response on the various ranges are expected only when the control amplifier is not able to supply the necessary a.c. current, because beyond the first stage (control amplifier) the signal level varies between the same limits on all conductance ranges. With a 2-ohm cell, the current demand is less than one third that available from the control amplifier system. From this fact and on the basis of the results of actual titrations, it is assumed that linearity of response is the same on all ranges. The above linearity checks were made with and without compensation for the initial conductance. The results were identical. There was no measurable drift over 24-hour periods at sensitivities of 100 times the measured resistance. a f t e r turning the instrument off over night and allowing a 2-hour warm-up, the output a t the recorder terminals is reproducible to within *O.l mv. at this sensitivity. The long-term stability of the instrument should make it well suited to monitoring applications. TITRIMETRY
Apparatus. The cell used for most of the titrations was a 400-ml. borosilicate glass beaker fitted with a Teflon cover. Holes through the cover permitted insertion of t h e electrodes, a thermometer or thermiqtor for temperature measurements, a contact thermometer, the cornliensating or control thermistor, a cold
N
I
LL
ez0
z
VOL. 37, N O . 1 , JANUARY 1965
e
23
finger, a gas inlet tube for blanketing the solution with a n inert gas, and the titrant delivery capillary. hpproximately 300 ml. of solution was titrated and the titrant concentration chosen so that dilution errors would be insignificant. Stirring was accomplished magnetically with a Tefloncovered stirring bar. For controlled temperature experiments, a 100-watt projection lamp (external to the cell) regulated by the contact thermometer or a thermistor-actuated proportional temperature controller (15) served to heat the cell. Heat was removed by circulating water approximately 2" C. cooler than the cell solution through the 13-mm. 0.d. cold finger. The temperature of the cooling water was regulated
with a Haake, Model F, circulating water bath. The rate of heating was adjusted by moving the projection lamp with respect to the cell. The cooling rate was adjusted by throttling the flow of water through the cold finger. Temperature regulation during a titration could be held within ~k0.005" C. with the contact thermometer or +0.002' C. with the proportional controller when operating the cell a t 25' C. with an ambient temperature between 21' and 27" C. The titrant delivery unit consisted of a 0.5, 1, or 5 p l . per division micrometric syringe fitted with a capillary delivery tip and driven a t constant (10.06%) speed by a Harvard infusion pump, Model 600-900, Harvard Ap-
paratus Co., Dover, Mass. T o obtain a constant speed output from the Harvard drive unit, it is necessary to power the unit from a constant voltage transformer. The delivery rate must be determined for each titrant usod because the pumI) speed is dependent upon load. For most of the titrations, delivery rates of 0.25 or 0.125 ml. per minute were used. h strip chart recorder with a 2-second full-scale response was used for recording titration curves. Chart speeds of 2, 4, and 8 inches per minute were available. For precision studies, chart speed and titrant delivery rate were chosen so that titrations required from 8 to 16 inches of chart travel before the end point.
1. C I 9is connected between pins 6 and 7 of the chopper. See text. 2. SK2-V amplifiers are mounted on the same block of brass, 4 X 25/8 X 3 j 4 inches thick. The block is attached to the chassis with four 1j2-poundshock mounts. Holes are drilled through the brass to accommodate two octal sockets. Numbers in circles refer to pin connections on octal base. 3. The 2x1279 should have a small heat sink. The heat sink may be common with the chassis. 4. Switch S1: 3 sections, 1-pol, 4-position, Steatite, 90" index, nonshorting. 5. Switch S4: 3 sections, 1-pol, 17-position, Steatite, shorting, Type J9008 (Centralab). 6. All resistors on S4 have *0.5% tolerances (Daven Type 1252) except R13 and RI4. RI3 should be DCF. RI4is high quality carbon or noninductive wire wound. Capacitors are mica. 7 . X Hughes HZ8377 diode was used. .1 6.8-volt 1N754 may be substituted. 8. Resistors R44-49,R52 and capacit'ors CZ5)c26, C30, transistors Q, and Q8, and diode Dg were mounted in an aluminum box, 23/4 X 2l/g X 1 5 / 8 inches (Bud, CU-3000-X), affixed to the underside of the chassis. CZ4 and Li were mounted directly above the box. 9. R53-56, c29, and C32were mounted in a 23i4- x 2lI8- x 15/g-in~haluminum box. Holes through box allow adjustment of Czg and R56. 10. Pin numbers refer t'o pins on octal socket and plug. Entire unit constructed on a l5Ig- X 31i2-inch circuit board and mounted in a Mallory KO. 74400 can with octal plug. Can common with pin 4. A11 resistors '14 watt. 11, S5; 1-pol, 4-positionj nonshorting, Steatite, 90" index. Stop set for 3-position operation. 12. Numbers in circles refer to pin connections on octal socket' and amplifier pins.
Table 11. Construction Notes 13. K2-XA No. 2 should be mounted somewhat remote from signal amplifiers. 14. A square-wave, lo00 c.P.s., -8volt p - p should appear a t Test Point 4. Symmetry may be adjusted with Ra. The amplitude of the signal will also change with adjustment of R63. Components and wiring between T.P. 4 and point K should be kept away from other signal leads and amplifiers. If other test points are brought to a common switch, this point should not be brought to the same switch. 15. Test Point 5. Adjust Casto give symmetrical, 1000-c.p.s., half-wave signal. Amplitude of peak half-wave signal is about 400 mv. for fullscale output. 16. The 2N270 may be replaced by any general purpose transistor-e.g., 2N1305 or 2N1307. 17. The numbers in circles refer to connections on Blue Ribbon Connector. 18. S6: 1-pol, &position, nonshorting, Steatite, 60" index (Centralab Ph-17). 19. If a recorder which requires one terminal grounded is used, break between A.4 and TC. Insert power supply shown in Figure 13. Connect TC+ terminal to circuit ground. 20. Test Point 6. Voltage a t this point should be between 25 and 35 volts, d.c. for full-scale output. 21. If the temperature compensation feature is not desired, the compensation circuit may be eliminated. I t should be replaced by a lOOK and a 1000-ohm resistor in series to ground. The signal is taken at the junction between the lOOK and 1000-ohm resistors to point F as shown in Figure 7 . 22. Rllo is 0.5 meg, carbon potentiometer. Rlll--114are 10-turn potentiometers. R110--114 are mounted on front panel and serve to adjust magnitude of compensation current. Rllbis '/?-watt carbon composition resistor. 23. Sa; 3-section, 1-pol, 11-position, 30" index, Steatite, section A , nonshorting; sections b and c, shorting.
Positions 5, 6, and 7 provide fixed phase shifts. 24. T o make phase adjustment amplitude independent move ganged potentiometers R Q and ~ RLo2to CW position. Measure a x . voltage a t pin 6 of K2-XA No. 4. Move potentiometers to full CCW position and adjust R I to~ give same voltage. R ~ and Q Rloz are ganged, 10-turn potentiometers with =tO.lyolinearity. 25. 811: Wired across Chart switch on recorder. 26. Ti, ORNL YO. Q880-61. Tz, ORNL NO. Q880-14; I.T.C. NO. UP8900. Other high quality transformers with current ratings given in Figure 13 may be substituted. Shielded transformers should be used if they are mounted on instrument chassis. 27. D.C. power supply is Embree Electronics, Inc., KO.PSj200/3.5. The +300-volts d.c. connections to terminal strip should be to those terminals controlled by the D.C. switch on the power supply. The connectors supplied with the PS/200/3.5 are unsuitable and should be replaced with Xmphenol MS or equivalent types. 28. The blower is a Bud, 250- to 500cu. ft. blower wired for 250 cu. ft. per min. The exit port is fitted with a deflector which directs the air to the underside of the main chasis. The power supply is mounted directly beneath the blower with a 13j4-inch panel spacer between the two units. 29. Q1-4 may be replaced by 2 h , 50PIV diodes (1x1341). Emitters on & I - 4 not connected. 30. Q5 and Q6 mounted on a Motorola Type LIS-10 heat sink. The heat sink is isolated from the chassis. R l s should be adjusted to give equal emitter currents through Q5and &e. 31. S8 permits positioning of syringe plunger prior to B titration. 32. Relay 3 acts as a reset control for the time-delay circuit, should the a x . power to the instrument be interrupted.
24
ANALYTICAL CHEMISTRY
T2
Note
Q5 39.Q
552
-6.5V
R128
Note 30
6.3 VAC
TFP 6.i VDC Regulated
(+I
!5V
Q, - Q6
- 2N458A
El
Note 2 9 6.3VAC ww
Ti Note 26
0.75 A
Figure 13.
Filament power supplies and alternate zero offset supply
, HNO) HCI H3P03
-, -
IO-)M 5 x 10m6M M 10'3 M
111
67 x H ~ B O- ~2 0 x
-
CondmIOmelriC Upper C u w e ktenriomrlric Lower Curve Titrant f N NoOH
Y
"
-
G
/ t DH
0
VOLJME OF TITRANT ADDED, arbitrary units
Figure 14. Conductometric curve fortitration of 4 X 1 O-3M H3P04with 1 N N a O H
1
2
3
4
1 . 1 1 5 6 7 8 9 1011 1 2 1 3 1 4 1 5 1 6 1 7 VOLUME OF T l T R 4 N l 4DDED. orbilrory units
Figure 1 5. Conductometric and potentiometric titration curves for a mixture of acids Branch A: " 0 3 , HCI, and one equivalent of tizP03; equivalent of H,iPOs; branch C: t i s 6 0 3
branch B :
VOL. 37, NO. 1 , JANUARY 1965
one
25
A titration is started in the following manner. The Titrator Advance and Chart Advance switches are Off. The Titrator hdvance switch is turned On and allowed to run until titrant emerges from the delivery tip. The Titrator advance switch is then turned Off. A reference line on the strip chart is
1. Turn Titrate, Chart Drive, and Compensation switches (&) Sz, and
S,,) off.
2 . Set Function selector to a x .
Off. 3. Turn On a x . and d.c. pouer supply switches. 4. Turn On main power switch. The main poner switch activates the blower, the recorder, the d.c. power supply, tube filaments, and the Monitor Iiilot light. After one minute, the d.c. pilot light should also light. If the Overload light glows a t this time, it may be ignored. 5. With an oscilloscope connected between T.P. 1 and ground, adjust inductor L1 (Figure 4) until the oscillator frequency is 1000 c.p.s. A signal of about 2.5 volts, p-p, should appear a t this point. 6. -4djust d.c. bias on SK2-V No. 2 and K2-XA KO. 1 so that pin 6 on each amplifier is a t approximately 0.0 volt, d.c. with respect to ground. 7 . Bias K2-XA No. 4 SO that its output is about +30 volts, d.c. 8. Set R63 (Figure 7) to C C W limit. 9. Set Function selector to Cal 1. 10. Connect oscilloscope between T.P. 2 (Figure 5) and ground, and adjust R50 to obtain approximately 10mv. p-p, 1000 c.p.s. 11. Connect oscilloscope between T.P. 3 and ground, and adjust LB (Figure 6) to obtain maximum amplitude 1000-c.p.s. signal. I n the event that no signal appears at this point, slight adjustment of R66 should provide adequate signal. Adjustment of L2 tunes this amplifier to 1000 c.p.s. 12. Adjust R56 and CZ9 (Figure 4) until the 1000-c.p.s. signal a t T.P. 3 is 0.0 mv. If the oscilloscope available is not sufficiently sensitive to detect about 0.1 mv., the recorder may be used for making this adjustment. Set Recorder Input selector to position 5 after reducing the signal to the limits of detectability with the scope. Adjust R66 and c29 until minimum deflection of the recorder pen is obtained. Switch to position 6 on this selector and repeat adjustments. 13. Set temperature compensation mode selector to Out. 14. ,idjust R39to about its midpoint (15 turns from either limit). 15. Move to Clf' limit (maximum resistance).
26
ANALYTICAL CHEMISTRY
selected and the chart advanced until the pen rests on this line. The titrator assembly is positioned to deliver titrant into the sample solution. After the desired conductance range has been selected, the titration is commenced by depressing momentarily the titrator Run button. The titration then pro-
ceeds automatically until the Stop button is depressed. End points are determined, except in some special cases to be discussed later, by conventional, linear extrapolation. Comparison of Conductometric and Potentiometric Titrations. A comparison of the precision of the conduc-
Table Ill. Initial Adjustments and Checks 16. Connect oscilloscope between T.P. 4 (Figure 7 ) and ground, and adjust Re3 to obtain a symmetrical square wave. The amplitude of this wave should be about 8 volts, p-p. 17. Zero recorder by adjusting the Offset control while Recorder Input selector is in the Zero (1) position. If the Overload light is not On, rotate the Function selector slowly off index. This operation opens the feedback loop in the control amplifier, and the resulting transient is usually sufficient to trigger the overload circuit. If this fails to cause the overload light to come on, move the Function selector to Operate, connect cell leads to cell terminals, and momentarily short the leads. Return Function selector to Call. 18. With the Overload light on, set Recorder Input selector to position 3. 19. Zero the recorder with the Recorder Zero control. 20. Depress and release the Reset button. Overload light should be extinguished. 21. Rotate R73 until the recorder pen returns to zero. 22. Connect oscilloscope between T.P. 5 (Figure 7) and ground. 23. Set Function switch to position Cal2. 24. Adjust C35 to obtain a symmetrical, half-wave rectified signal. 25. Adjust Recorder Span to bring recorder pen to 100%. 26. Allow the instrument to warm up for at least 2 hours. 27. Prepare a solution of KCI that is approximately 0.01N. Make provisions for varying the temperature of the solution between about 20' and 30" C., then set temperature a t 25' C. Place electrodes or dip-cell with a constant of 0.1 cm.-l into the solution. Connect the electrodes to the cell terminals on the titrator. Place the control thermistor into this solution and connect the thermistor leads to the Thermistor terminals. 28. Repeat steps 2 and 5 to 24, omitting steps 8 and 14. 29. Set RdOto about its midpoint (15 turns from either limit). 30. Set Function selector to Operate. 31. Select a range u-ith the Range Selector which gives maximum, on-
scale pen deflection. This is most easily accomplished by initially setting the range to the least sensitive position (0.5-mho range) and then moving it progressively to more sensitive positions. 32. Set Temperature Compensation Mode selector to Automatic. If pen deflection differs from the previous position by more than 10% of full scale, adjust to bring pen to about the same position obtained with the mode selector in the Out position. 33. Turn recorder Chart Drive switch to On to record conductance information. 34. Raise or lower the cell solution temperature through 5" intervals on either side of 25" C. while recording the conductance changes. Mark the recorded line with reference temperatures taken at about 1' intervals. 35. If the recorded line does not lie within *0.5Oj, of full scale from the original setting, vary RdOuntil this condition is obtained. Increase Rlo to obtain more compensation and decrease its resistance to obtain less. 36. If the recorded line is more linear below 25" C. than above (which is the more likely) decrease the resistance of Ra, (Range) until the maximum deviations are symmetrical about the 25' C. reading. 37. Return temperature of the cell solution to 25" C. 38. Record the conductance reading. 39. Set Temperature Compensation Mode selector to Out. 40. Adjust Rag to give reading obtained in step 37. 41. Set Functionselector to Cal2. 42. Adjust Recorder Span to give 1 0 0 ~pen o deflection. 43. Set Function selector to Operate. 44. Record conductance reading. 45. Set Temperature Compensation Mode selector to Auto and record reading. If this reading does not correspond to that obtained in step 43, set this selector to Out and adjust R39to produce the conductance reading obtained in the Auto positon. 46. Set Temperature Compensation Mode selector to Manual. 47. -idjust R38so that the conductance reading corresponds with that obtained in the Auto and Out positions. Record this setting of R38 for future reference.
~~~~~
Table IV. Cornparkon of Conductometric and Potentiornstric Titrations of HCI with N a O H
Standard deviation in chart divisions" ConductoPotentiometric metric
_ _ _ ~ .
Series 1
0.052
0 045
2 0.084 0.067 Average chart travel = 16.0 divisions; 14 titrations in each series. a
tometric method with t h a t of the potentiometric method was made. A saturated calomel glass electrode pair was used with a Leeds and Northup Model 7664 pH meter to measure the p H of the solutions during continuous titration of HC1 solutions with lAV NaOH. The p H meter was connected to a strip chart recorder with a I-second full-scale response and a chart speed of 2 inches per minute. T h e conductometric and potentiometric curves were recorded simultaneously on the same sample. Samples of 8.6 to 11.4 grams of 0.1,V HC1 were taken from a weight buret for each titration. T h e cell temperature 'was regulated a t 26.3' & 0.005O C. T w o series of 14 HC1 samples each were titrated a t a rate of approximately 0.125 meq. per minute with Fisher #So-S-266 1.OOOOY NaOH. Table IV summarizes the results. Linear regression techniques were used t,o determine the precision of the determinations because the samples were not all of the same size. For the number of observations availab'le, it is not possible to demonstrate a significant difference between the coiiductometric and potentiometric end poirit,s or between the precisions obtained by the two methods of end point detection (19). Other HCl-NaOH Titrations. Fourteen conductoimetric titrations of 1-ml. samples of l..OOOOS HC1 were made with 1.0000,V S a O H as titrant. Tit,rant delivery rate was approximately 0.25 ml. per minute. T h e mean end point was 8.002 divisions with a relative standard deviation of =t0.227'0. The branches of the conductomet'ric titration curve are quite linear before and after the end point, and little ambiguity exists as to how to perform the extrapolation to locate the end point. This system was, therefore, used as a control to spot check the performance of the titrator. Over a fivemonth period, eight single titrations were carried out on I-nieq. portions of HC1 in 250 to 350 nil. of solution. Titrations were I)erfonned with and without com1)ensation for the initial conductancc of the solutions, temperature compensation, and temperature control. Sam1)les were taken with the same microl)ii)et. The mean of the end points was 7.98 + C).5370. At this level of precision it is not possible to distinguish between this end point and that obtained in the pre\-ious titrations (19).
~~~
Table V.
~
Precision and Relative Accuracy for the Titration of H3Po4 with N a O H A. PRECISION
H3POa conc., molarity in cell 4 2 4
x 10-3" x 10-3" x
10-4b
Chart divisions and First end point 80.80 f 0,1470 40.16 f 0.337, 79.78 & 0.6170
rel. std. dev. Second end point 161.0 =t0.04% 81.20 f 0.30% 166.73 i 0.27%
No. of detns. 5 7
6
B . ACCURACY
Conductometric
Pot en tiometri c First E.P. 1 0025.IfC 0 9945M i 0 25V0d Second E.P. 1 0078Mc 1 000>Mi 0 % d a Titrant 1.1- NaOH. Titrant 0 . 1 s YaOH. c Sample diluted to approximately 4 X 10-3.1f before titration. d Precision on duplicate samples.
Other Titrations. I n addition to titrat,ions of HC1 and S a O H , a number of other acids and bases were tirated. Figure 14 shows the titration curve of 4 x 10-3.U with KaOH solution. The compensation circuit was used for this titration. The ascending branch of the titration curve past the second end point illustrates the linearify with which the instrument, responds in the vicinity of zero signal level. The precision of the titration and a comparison with potentiometric end point detection is given in Table V. The titration of a mixture of HN03, HC1, H3P03,and H3B03was performed with S a O H solut,ion. The conductometric and potentiometric curves were recorded simultaneously. The curve for each of these methods is shown in Figure 15. Section .-l corresponds to the titration of the H?u'Oa, HC1, and one equivalent of the H 3 1 3 0 3 ; section B , to one equivalent of H31'03; and section C, to the boric acid. I n addition to the above systems, 23 other acid-base titrations were gerformed successfully. Species t,itrated included strong and weak acids and bases, salts of weak acids and bases, and mixtures containing acids and uraniums (VI),nickel(II), or manganese(I1). Sulfate was titrated in SOYc (v./v.) aqueous methanol solution with 0 . 1 X Ba(CzH80&. The initial concentration of sulfate was approximately 0.lmM. Smooth platinum electrodes were used. The titration rate was chosen so that the rate of precipitation was not exceeded. h V-shaped curve with linear branches was obtained, and t'he end point corresponded to the equivalence point.
Considerable care must be exercised in the design of the cell and choice of electrodes if true conductances are t o be recorded. On the other hand, it will be shown t'hat it is not necessary, in some instances, to obtain true conductance measurements to derive analyticalljuseful information from the titration curves. Acid-Base Titrations. Three KC1HC1 mixtures titrated with S a O H solution are shown in Figure 16. T h e titrat'ions were carried out in a cell with a volume of 50 ml. The cell constant was 0.7 cm.-l, and the electrodes were heavily plat'inized. The KCl concentration was 0.32-11. The NaOH solution used as titrant was also 0.32M in KC1 to minimize dilution effects. The noisy appearance of curves =I and B results from the use of long, spiral electrodes which vibrated slightly as the solution was stirred.
Table VI. Titrations Performed Successfully in the Presence of Added Electrolyte
Ahximum molar
ratio of salt t o
Species titrated HC1
species
Added tielectrolyte trated" Titrant KC1 -10,000 SaOH KI 200 KBr 400 125 350 NaOH 1,300 YaOH 250 Ba-
TITRATIONS CARRIED OUT IN PRESENCE OF INDIFFERENT ELECTROLYTE
Titrations performed in the presence of excess indifferent electrolytes are listed in Table VI. Most of these titrations would have been exceedingly difficult, if not impossible, with conventional conductometric instruments. I n a number of these titrations, the change in conductance during the titration was less than 0.5% of the initial conductance of the solution titrated.
Na2S04
KC1 Fe +l
(OH), 200 Sa2C03 HCl H3POa 300 K2Cr20i 3,000 430 350
HC1 HClOa HaPo4 1,600 SaZEDTA KaOH 100 CaCL These ratios are riot necessarily the maximum possible.
VOL. 37, NO. 1 , JANUARY 1965
e
27
l
l
f
l
t
l
l
l
f
l
l
l
l
l
l
r
l
l
TITRANT A D D E D , arbitrary units
Figure 16. Conductometric titration curves obtained with heavily platinized electrodes for titration with 1 N N a O H of various concentrations of HCI in 0.32M KCI
4 . 0.033M KCI 2. 0 . 0 6 6 M K C I 3. 0.17M K C I 4. 0 . 3 3 M K C I 5. 0.67M KCI
[HCI
1=
3.3 x t o - 3 ~
A, 3.5 X 10-'M HCl; B, 2 X 10-3M HCI; C, 2 X 10-2M HCl V O L U M E OF T I T R A N T A D D E D , arbitrary units
Xine replicate titrat'ions of 3.5 X 10-411! HCl in 0.32M KC1 were preformed with a relative standard deviation of 2,8T0 in spite of the noisy appearance of the titration curve (curve A ) . The irregularities in the shape of the curve in the vicinity of the end point (conductance minimum) results from traces of carbonat'e in the KCl and water used in the preparation of the solutions, These irregularities are not noticed on the curves for higher concentrations of acid because, with the higher concentrations, faster titration rates were used without increasing the chart speed proportionately (curve C). Figure 17 illustrates the results obtained by using smooth or lightly platinized electrodes in highly conducting media. These titrations were performed in 300 ml. of solution. No electrolyte was added to the titrant because experiments carried out with electrolyte added to the titrant yielded curves with the same shape. Curves of the same shape were also obtained when the titrant was generated electrically within the cell. Curves similar to those shown in Figure 17 were obtained also for the titration of HCl with S a O H in LiI, KI, and KBr; for the titration of HC10, with Ra(OH)Q in Ba(ClO&; and for the titration of H2S04with S a O H in Na2S04. Some titration curves of this type, although not true conductometric curves, arp useful analytically. The concentration dependence of the minimum on the titration curve was checked for the HC1-KCI and H2SO4-Xa2SO4 solutions. For the HCI-KCl system, the HC1 conrentration was varied between 3.3 and 0.33m.V while the KC1 concentration \vas held constant a t 0.33N. For the H?SOn-r\'aQSOasystem, HzS04 28
e
ANALYTICAL CHEMISTRY
Figure 17. Curves obtained with smooth electrodes for titration with 1 N N a O H of 3.3 mM HCI in various concentrations of KCI
concentration was varied between 3.3 and 0.33mM, and the Xa2S04concentration held constant at 0 . 5 M . h strictly linear dependence on concentration of acid was obtained in both cases when the minimum was used a5 an indication of the end point. Moreover, the end point was constant within *0.22Q/, for nine determinations of 0.33mM HC1 when the concentration of KC1 was varied between 0 and 0.33144. I n 0.5M NasS04, the precision of end point detection for the titration of l.OmM H*SOl was =t0.5~o-the same precision obtained in the absence of Na2S04. Correlation of the minimum with the end point of the titration was possible only for strong acids and bases. With H3POl and the inflections in the titration curves in the presence and absence of added electrolyte do not agree. h sharply defined minimum is observed for the first end point in the titration of H3P04 with NaOH, but the inflection point for O.lmM H31303 in 0.3M KCl solution is barely detectable. I t appears, therefore, that curves of the type shown in Figure 17 (curves 1, 2,3, and 4) yield quantitative information for strong acid-strong base titrations only. Titrations performed on systems in which the pH of the solution remained nearly constant (Fe+*; EDTA in 1N NaOH) did not show this type of behavior. T o explain the abnormal appearance of the titration curves with sharp minima, several experiments were performed. The rate of titration was
varied from manual addition of titrant with a micrometer and screw-drive assembly to automatic delivery a t the rate of 0.5 meq. per minute. The end point was approached from the acid and from the basic side of the equivalence point. The potentials of the conductometric electrodes with respect to the solution were monitored with a saturated calomel electrode, and the d.c. potential difference between the electrodes was also monitored during titrations. The results of titrations performed with platinized and smooth platinum and with silver electrodes were compared. Electrical analogs of the conductance cell were constructed, and the resistive and capacitive elements varied to simulate a conductometric titration. The results of these experiments indicate that the effect results from a change in the electrode capacity during the titration. The cause of the change in capacity is less certain. Qualitatively, the shapes of titration curves obtained with silver and with smooth or lightly platinized platinum electrodes are the same; yet, the platinum electrode potential with respect to the solution changes by several tenths of a volt during a titration, but the silver electrode potential is well poised by the chloride ion concentration and does not change noticeably during the titration. If the capacity decreased and remained constant, a curve similar to that of Figure 17, curve 5, would be observed. To obtain curves similar to curves 1 to 4 of this figure, the capacity
would have to decrease, then increase immediately past the end point. I t appears, therefore, that the capacity change must be associated with the role of hydrogen and hydroxyl species in the double layer. This dependence is also consistent with the fact that the sharp minimum observed on some of the curves coincides with the equivalence point. Additional studies, beyond the scope of the present inrestigation, are necessary to elucidate further the specific cause of this behavior. With cells having sufficiently large electrode capacities, and with the electrodes spaced to include a relatively large bulk resistance, normal curves are obtained with the conductometric titrator. Titrations of Ferrous I r o n in H3P04. T h e titration of ii-on(I1) was performed in HCI, HCIOa, and in &Po4 solutions with 0.1S lKzCrzOias titrant. Thc shape of the titration curve is determined primarily by the change in hydrogen ion concen.tration. The most linear branches of the titration curves were obtained in H31’O4 solution. The t,itration was carried out on solutions containing initially 10-3 to lO-5Jf Fe+2 in 0.01631 &Pod. The teinperature was 25’ C., and the solution was sparged with nitrogen and blanketed during titration. The rate of titrant addition was 0.0125 nieq. per minute. Over the concentration range studied, linearity between concentration and end point inflection was within 1 2 7 0 .
The initial conductance compensator was used for all of the titrations. Other Measurements. The initial conductance compensation feature of the instrument was used for measuring specific conductance changes with temperature on solutions saturated with technical grade XHaC1 ( 512M). h dipcell with a constant approximately 2 em.-’ was used for these measurements. Specific conductance changes of about 0.006 mho-cm.-’ per degree C . were measuredwith a precision of io.Z17~ from 25‘ to 100” C . h 10-fold increase in instrument sensitivity was used. Compensation for initial conductance was also employed in studies on the conductometric determination of free acid in solutions containing high concentrations of iron and chromium. I n this determination the iron, chromium, and added complexing agent contribute significantly to the conductance of the solution to be titrated. The response time of the instrument was sufficiently railid to record conductance measurements in a polarographic cell employing a dropping mercury electrode with a drop-time of 0.5 second. LITERATURE CITED
(1) Anderson, L. J., Itevelle, R. R., ANAL. CHEM.19,264 (1947). ( 2 ) Anton, A , , Alullen, P. W., Talanta 8,817 (1961). (3) Ashman, L. E., Cohen, R . S., Glass, ,J. A , . Stillwell. H. R.. Jones. H. E.. i n s t r t h e n t s 24,710 (19;l).
(4) Boardman, W., Chem. Ind. 1963, April 6 ( Y o . 14), p. 565. (5) Colwin, L). W . j Propst, R. C., A N A L . CHEM.3 2 , 1858 (1960). (6) Ewing, G. I%., “Instrumerital Methods of Chemical Analysis,” 2nd ed., p. 390. AlcGraw-Hill. Yew York. 1960. ( 7 ) Eking, G. W.,’Brayden,’ T. H., A S A L . CHEM. 35, 1826 (1963). (8) Fischer, R . B., Fisher, 11. J., Ibid., 24, 1458 (1952). (9) Garman, I
