CONCLUSIONS
A coulometric titration has been defined as one in which a substance is made to undergo a quantitative, stoichiometric reaction with electrons (7). While generation of lanthanum ion by the constant current oxidation of lanthanum hexaboride does not meet either criterion, the process can be made quantitative by application of an empirical factor, the current efficiency, which calibrates the yield of lanthanum ion regardless of the stoichiometry of the starting material or of the stoichiometry of its electro-oxidation reaction. It should be mentioned that different samples of lanthanum hexaboride are likely to have different stoichiometry and, therefore, this calibration procedure must not only be employed but the calibration factor will be different for the different samples. In addition, experiments performed on a sample of lanthanum hexaboride having a density of 3.09 g/cma as opposed to the nearly theoretical density of the material used in this study, showed an irreproducible current efficiency of about 120z (a), indicating that for best results (7) D. D. DeFord and J. W. Miller, in “Treatise on Analytical Chemistry,” Part I, Vol. 4, I. M. Kolthoff, P. J. Elving, and E. B. Sandell, Eds., Interscience, New York, 1963, p 2476. (8) K. S. Fletcher 111, unpublished results, The Foxboro Co.,
Foxboro. Mass.
material having nearly theoretical density should be employed. The requirements of highest possible density should be explicitly stated when ordering the rod from sources of supply since some applications for the rod in other areas of study are better served by material of lesser density. As with most coulometric procedures, use of lanthanum hexaboride as an electrochemical source of lanthanum ion eliminated the need for preparation and storage of standard solutions. Once calibrated, the lanthanum hexaboride rod should be stable indefinitely in the absence of strong oxidants and will provide an extremely convenient source of lanthanum ion. In addition, the small size of the moles per coulomb ratio, l/nF, equal to approximately 5 X 10-7 moles/coul, shows that very small quantities of reagent (electrons) may be added and accurately measured. ACKNOWLEDGMENT
We thank J. W. Anderson for cutting the LaBB rod. RECEIVED for review June 10, 1968. Accepted July 10, 1968. Taken in part from the Ph.D. Thesis of K.S.F. 111. Work supported in part by University of Massachusetts Research Council.
An Automatic Digital Readout System for Reaction-Rate Methods E. M. Cordos,lS. R. Crouch, and H. V. Malmstadt Department of Chemistry and Chemical Engineering, UniGersity of Illinois, Urbana, Ill. 61801 A new integration technique for obtaining direct readout of rates is described that has high noise immunity. The measurement cycle can be varied from milliseconds to hundreds of seconds to provide optimum performance for very fast or slow reactions. Input signals ranging over a million-fold in mV/sec can be readily measured. Results for synthetic signals from a ramp generator show standard deviations and relative errors of about 0.2%. Test results with spectrophotometric reaction-rate methods for phosphate and glucose in the parts-per-million range are also presented.
IN RECENT YEARS several sensitive, selective, and accurate quantitative methods have been reported that are based on the measurement of initial reaction rates and these have been summarized in review articles (1,-.3), Various devices for obtaining a direct readout of the reaction rate data have also been developed to automate the procedures (4,5). Automatic measurements have been made usually by determining the concentration change in a preselected interval of time (fixed time method), or by measuring the time required for a change of concentration between two predetermined Present address, University “Babes-Bolyai,” CIuj, Romania (1) G. A. Rechnitz, ANAL.CHEM., 36,453R (1964). (2) Ibid., 38, 513R (1966). (3) Ibid., 40, 455R (1968). (4) G. E. James and H. L. Pardue, ibid., 40,796 (1968). ( 5 ) H. V. Malmstadt and S. R. Crouch, J . Chem. Educ., 43, 340 (1 966).
18 12
ANALYTICAL CHEMISTRY
levels (variable time method) (6). Both of these techniques involve measurements at two points along the reaction rate curve. With these two-point methods, the accuracy in the determination of Ac or At can be significantly affected by the noise. Because a high signal-noise ratio is necessary for high accuracy and general application of the readout device, it is important to develop new systems that are not greatly affected by noise and can be used for measurements of a wide range of reaction rates. The instrument described here is based on an integration procedure that is characterized by high noise immunity. Instead of making the measurement between two points, two portions of the curve are integrated, subtracted, and the difference automatically displayed on a digital readout. This digital readout is directly related to the reaction-rate and can be made equal to the concentration of the sought-for species. The integration averages the noise so that its contribution to the relative error is greatly reduced. The integrators used in the circuit have a “memory” so that the first portion of the integrated curve is taken as reference for the measurement. When a new measurement is to be made, the operation is repeated, and always the first of two successive integrated portions of the curve becomes the reference, regardless of its absolute value. Accordingly, the in(6) W. J. Blaedel and G. P. Hicks, “Advances in Analytical Chemistry and Instrumentation,” Vol. 3, Wiley, New York, 1964, pp 105-42.
a
W 0
3 c3 v)
z a a
I-
I 0 a LL
/
5 0 U LL
w
W 0
(3
5 0
d >
a
a
k
>
tl
t2
’3
t4
TIME
Figure 2. Expanded section of typical rate curve illustrating integration and subtraction of two areas A I and A2 separated by a measurement delay interval t r t 2
Figure 1. Expanded section of typical rate curve illustrating integration and subtraction of two sequential areas A1 and A2
strument can provide a digital readc’ut of the rate during any interval throughout the course of the reaction. The integration time can be varied from the order of milliseconds to minutes so the instrument can be used both for fast and slow reactions with optimum discrimination against noise, A variable delay time between the start of the reaction and the start of the measurement is provided so the slope of the desired part of the curve is measured. The instrument is easily calibrated to provide a direct digital readout of concentration, The precision and accuracy of the system is high with relative standard deviations and errors about 0.2 %. The circuit is readily constructed :kom commercially available digital and analog circuit cards and systems modules (7) that are rapidly interconnected to provide the direct readout of reaction rates. The results for the determination of phosphate and glucose in the parts-per-million range are presented. THEORY
For practical quantitative reaction-rate procedures, a transducer and input circuit are used to provide a voltage which is directly related to the concentratiori of some species in the reaction, By measuring the initial rate of the voltage signal, a readout is obtained that is directly related to the concentration of the sought-for species. The initial slope of the voltage-time curve is essentially constant over a finite time interval. An expanded section of th’e initial part of a typical rate curve of slope S is illustrated in Figure 1. If two equal time increments At (At = tz - tl = t 3 - tz) are taken, the difference A A between the areas AI and A Z is the parallelogram ABCD. The area of the parallelogram is AA
=
At
*
a
(1)
and because
S
=
tan a = --a At
(7) Heath lnstruction Manual 801A, “Modular Digital/Analog System,” (1968).
then substituting from Equation 1 into Equation 2, it follows that
(3) Because At is set as a constant, it follows that the slope is proportional to the measured difference in area AA. When the two time increments are not consecutive, as shown in Figure 2, but are separated by a time interval tt - tz, Equation 3 becomes AA S = (4) ( f 3 - tdAt (At)2
+
and as t3 - t2is also set as a constant, it follows again that the slope is directly rroportional to the measured area. The total time for the measurement is 2At ( t 3 - t2). Ideally for the best signal-noise ratio it is best to work as in Equation 3 where t 3 - fz = 0 and At is made as long as possible for the specific reaction. The integration of the two portions of the curve, subtraction, and digital readout can be automatically performed by the electronic systems described in the subsequent sections. Noise Averaging. The above considerations have been made assuming that the curve whose slope is to be measured is a straight line. Practically, because of working at high sensitivities and noise from different sources, the curve often is as shown in Figure 3. However, the presence of the noise does not change the principles of the measurement because the integration averages the noise as illustrated in Figure 4. Assuming that the noise is sinusoidal and referring to Figure 4 a simple calculation shows that the largest relative error, El(max), in the determination of A A for the two-point method with a constant At is AV B El (max) = - = ___ (5) V At sin a
+
where B is the amplitude of the noise. The maximum relative error, G(max), in the determination of the area by the integration technique over the same At is E2(max) =
2B area of half cycle total area ~ f ( A ttan ) ~a VOL. 40, NO. 12, OCTOBER 1968
(6) 1813
t
0
T I ME
TIME
Figure 3. Section of practical rate curve with associated noise
Figure 4. Expanded section of “noisy” rate curve with sinusoidal noise
wheref is the frequency of the noise. The ratio of the two maximum errors is Ezmax 2 Cos a - kT, TfAt At Elmax
(7)
where T, is the period of the noise. For a given phase angle k is a constant. Therefore, if the integration time interval At is much larger than the period of the noise T,, the error by the integration technique is much smaller than by the two-point method, as seen from Equation 7. Although the above analysis is based on sinusoidal noise, the same considerations could be made for specific types of random noise. INSTRUMENTATION
The block diagram of the system for measurement of reaction rates is shown in Figure 5. The sample is introduced in a reaction cell where the reaction is monitored by a suitable transducer. Then the signal is modified in order to obtain the proper input voltages for the integration and subtraction circuits. Here, by means of relays which direct the signal to different parts of the circuit, the operations of integration for two equal periods of time and subtraction are accomplished. The logic control system controls the operations in the integration and subtraction circuits by actuating the relay devices.
The logic control system can work continuously, making sequential measurements, or can be triggered to make one measurement. Triggering can be accomplished by the sample introduction system, or manually. After receiving a suitable trigger pulse, the logic system controls the start of the sequence of delay time, the length of the integration periods, the subtraction, and the readout. The same system can control the readout time and, when the readout is completed, the previous result is erased and the instrument is automatically reset for the next measurement. Integration and Subtraction Circuits. The slope measurement is based on Equations 3 and 4. The measurement can be accomplished by a circuit composed of two identical integrators and five relays as shown in Figure 6. The voltage form transducer T i s applied through relays R1 and Rzto integrator, O A l , for a preselected period of time At, that is controlled by the logic circuit. After a preselected delay ( t 3 - t 2 in Equation 4), the output is switched through Relays 1 and 3 to integrator OA2 for the same interval of time. The output voltage of each integrator corresponds to the areas AI and A2, respectively. The difference voltage is proportional to A A in Equations 3 and 4 which is directly proportional to the slope. This system requires a readout device with a floating input. The same operations can be accomplished by a circuit with one integrator and one inverter as shown in Figure 7 wherein RELAY 4
RELAY 2
RELAY DRIVERS
IDVM,PRINTER.J
I
READOUT
I I
CONTROL
I
5,
LOGIC CONTR
I
:M
FROM SIGNAL MODIFIER
INPUT
I
L------J
Figure 5. Block diagram of reaction-rate measurement system
18 14
ANALYTICAL CHEMISTRY
Figure 6. Integration and subtraction circuit with two integrators
R2
31l@o"T
RELAY 3
RELAY 4
RELAY I
RELAY 3
rn rn Elv
I
I
FROM SIGNAL MODIFIER
I
RELAY 2
Figure 7. Integration and subtraction circuit with one integrator and one inverter
"
r
VOLTMETER
w
I
CLOCK
I,
II
Figure 9. Diagram of ratemeter showing logic circuit
R1-15K RplSK
the output is referenced to ground. The signal is directed to integrator OA2 through Relays 1 and 3 during the first integration period. During the second integration period, the output is inverted and directed to the same integrator, OA2, via Relays 1 and 2. The integrating capacitor, C, of OA2, is charged in the first interval At and discharged in the second identical time interval. The input and output voltages of OA2 are shown in Figure 8 along with a simulated slope from a ramp generator. The two parts of the slope applied to the integrator are segments BC and DEin Figure 8a, and the areas to be determined by integration are A I and A z . During the measurement period, the output of OA2 rises during the first integration period (KL in Figure 8b) as capacitor C charges,
to 450K Pi-1K pot P2-100K pot cr-10 rf R D 1 to 4-relay drivers I, 11, 111, IV-J-K flip-flops G-Nand gate M-Monostable multivibrator Clock-signal generator of digital timing module
and falls during the second period ( M N ) as C discharges. At the end of the measurement period, the difference voltage AV is proportional to AA and thus proportional to the slope according to Equation 4. Range of Input Slopes. There are limits to the input slopes which can be measured with the circuit of Figure 7. However, by switching a few parameters input slopes which vary E D over a range of 106 can be measured. One of the important limitations is the output voltage of integrator OA2, which 0.2 cannot exceed the supply voltage (15 V in this case). Hence, OA2 does not parametersmust be adjusted to ensure that_ limit during the measurement. It is also necessary to place a lower limit on the output voltage of O A 2 ; namely the output voltage necessary to give a sufficient AV for readout pur-0.4 poses (10 mV is typical). The integrator time constant R3C -0.6 in Figure 7 can be adjusted to bring the output voltage of OA2 into the range 10 mV-15 V for practical input slopes. Another important consideration is the absolute value of the input voltage to OA2 at the start of the measurement period. This voltage often differs from zero depending on M the premeasurement delay, the nature of the transducer-signal i L+modifier system, etc. Although this voltage level will not affect the measured difference AV, it does contribute to the limits mentioned above. In many cases a simple suppression voltage can be added to bring the input of OA2 to nearly zero volts at the start of the measurement. Assuming that the input to OA2 is zero volts at the start of the measurement period, a simple calculation gives the range -0.2t of input slopes which can be measured for given values of RaC and the integration periods At, For example, with RS = 15K, I I C = 10 pf, and integration periods of 0.1 sec., input slopes ranging from 300 mV/sec to 4.5 X lo5 mV/sec can be mea-0.6 sured with output voltages in the proper range. A simple 0 0.2 0.4 0.6 0.8 I.o change of R Ballows measurement of much slower changing TIME (sec) voltages. For example, with RB= 450K, C = 10 pf and integration periods of 10 sec, slopes ranging from 0.45 mV/sec to Figure 8. Oscilloscopic traces of slope from ramp gen1.35 X loa mV/sec can be measured with the same limits on erator, and input and output voltages of operational amplifier the output voltage of OA2.
"'I
fl
::::I , , , , , , ; ,'
VOL. 40, NO. 12, OCTOBER 1968
0
1815
fllp-flop
mal I-K Ilip flop
card
card
Durl J+
Rta
Opcrrtionll W f m Wds
Wtiplr monostable connector mihubrater u d
CLOCK
Pi
urd
1
Mukiple
,
~
connedw
Nand gate
1 1
Relay urd
QM
~
1
7
U I
QI
QII
QIII
I I I I I
I
I
I
I I
I
1
I
I
I
I
I
1
I
i
1
QlV I
I II
ICL.-.
IDelay
__.___pLLI_
_ _ 4 42 .
BlN4RY INFORhUTIW MODULE
Dl6l7.41 TIMIN6 HDD’JE
Figure 10. Circuit card layout and connections Dual J-K flip-flop cards, Heath EU-800-CB Multiple connector cards, Heath EU-50-MD Nand gate card, Heath EU-800JC Relay card, Heath EU-800-JD A similar card using reed relays was made up for integration times of less than 1 second. Operational amplifier cards, Heath EU900-NA. Dual Monostable card, Heath EU-800-LA
Thus with only two different values of R3 and variable integration times, slopes ranging from 0.45 mV/sec to 4.5 X 106 mV/sec can be measured within the instrumental limits. Logic Circuit, The circuit for a ratemeter designed to make measurements after being triggered externally is shown in Figure 9. The ratemeter has been built on a “Heath Binary Information Module” EU801-12 combined with a “Heath Digital Timing Module” EU801-13 and power supply EU-801-11. The Heath circuit cards are listed under Figure 10. The integration circuit is of the type as shown in Figure 7. The 1K potentiometer P1 at the input of OAl is used to set the gain of the inverter to one. The logic circuit is composed of a divide-by-16 counter (built from J-K flip-flops), a “NAND” gate (G), a monostable multivibrator (M) and a signal generator (clock). The relays are activated (through relay drivers) by the different outputs of the divide-by-16 counter. The output wave forms are shown in Figure 11. The impulses from the “clock” are fed into the T inputs of the J-K flip-flops only for the interval of time when the measurement is to be made. This is accomplished by means of gate G which is open only when both QIV and QMare at logic level “1.” When the circuit is triggered, one impulse is sent to the input of M so QM changes from “1” to “0” and at the same time QIVchanges from “0” to “1.” The gate opens when QM goes back to “1,” after the delay time is complete. The gate closes after the eighth impulse from the clock changes the state of QIVfrom “1” to “0.” The time for measurement is equal to the length of eight cycles from the clock, It can be seen from Figure 11 that during this period QII goes to a “1” level twice and Q I I I only once during the total measurement period. The Q I 1 output is used 18 16
0
ANALYTICAL CHEMISTRY
-321
lintegr‘ period
liniegrl lpsri~di
II time
iMeasurernent
I
1
time
I
II I
Figure 11. Waveforms of sequencing signals for the logic circuit
to activate Relay 1 so that for two equal intervals of time the transducer signal is fed into the system. The Q I I I and &I,, outputs operate Relays 2 and 3 so that the signal goes directly to the integrator in the first part of the measurement period and through an inverter OAl to the integrator in the second part. For integration times greater than 1-second, the electromechanical relays on the Heath EU-800-JD circuit card are satisfactory. However, for the integration times less than 1second a relay card was prepared with Hamlin reed relays (actuating time 1 msec) on one of the EU-50 MD multiple connector/blank PC cards. The label on the top plastic cover is made identical to that for the EU-800-JD card so that the reed relay card can be substituted directly with similar patch connections. Readout. Any readout system that is sufficiently sensitive to detect the voltage difference AV can be used. For example, during the development stage of this instrument, a servo recorder was useful for recording values of AV. For the highest accuracy and reliability, an integrating digital voltmeter was used. With an integrating digital voltmeter as the readout, any additional noise at the output of OA2 is averaged which provides even better noise immunity. Even though the integration periods are made short by the logic control system, the readout can be held for any desirable duration. For routine use, the readout system would be blanked out during the charging and discharging of capacitor C by the addition of simple logic circuitry at the output of OA2. One simple way to blank out the readout system until the measurement time is over is to use the &IV output to operate a relay which connects the output of OA2 to the digital voltmeter at the end of the measurement time (see Figure 11). For the initial work described here, it was desirable to see both the charging and discharging of C as well as the difference voltage AV. Hence this additional circuitry was not used. However, the necessary connections to make the readout
system display only the difference voltage AV are shown on the circuit card layout in Figure 10. The readout can be made direct reading in concentration for those procedures whose working curves are linear and pass through the origin. The output of OA2 could be held after the measurement period and a portion of the output could be taken from a variable divider potentiometer across the output and fed to the readout. The circuit samples the difference voltage AV and holds it for the readout device until commanded to erase and read the next result. While the reading is being held the divider at the output of OA2 could be set to give a direct concentration readout.
Table I. Automatic Rate Measurements with Long Integration Time and Signals Typical of Slow Reactions Digital Input rate, readout," Proportionality Re1 std mv/sec mV constant dev, ?Z 2.50 111.8 0.0223 0.24 3.60 163.4 0.0220 0.24 5.30 239.7 0.0221 0.33 7.90 357.3 0.0221 0.15 10.80 485.6 0.0222 0.09 a Averages of 10 results; R8 = 450 K; integration time: 10 sec; premeasurement time: 30 sec.
PROCEDURES
Circuit Card Layout and Connections. The circuit cards were inserted in the modules and connected as shown in Figure 10. By following the numbering scheme on the diagram, the entire rate-measuring instrument can be wired in less than 30 minutes. Alternatively, a mother board could be prepared containing the various connections, and the entire system connected in a few minutes. Spectrophotometric Measurements. A Heath single beam spectrophotometer EU-701 was used for all spectrophotometric measurements. The photocurrent was recorded on a Heath EUW20-A Servo recorder equipped with a loglinear current module (Heath EUA20-28). The voltage output of the current-measuring recorder served as the input to the ratemeter (input to Relay 1, Figure 7). A thermostated cell, equipped with magnetic stirring, served as the reaction vessel. All measurements were made while circulating water at 25.0 "Cfrom a constant temperature bath. Reagents. For the determination of phosphate, all reagents were prepared as previously described (8). - For glucose determinations, reagents were prepared as described by Pardue er al. (9). Glucose standards of 5 , 10,15, and 20 ppm were prepared. Phosphate Determinations. For phosphate analysis a wavelength of 650 mp was used. The linear scale of the loglinear current module was adjusted to a sensitivity of 2 X 10-7 amp full scale. Because the reaction requires several seconds before steady initial rates are obtained, a delay time of 30-40 seconds is introduced before the measurements begin. All reagents were added as described (8), and the measurement timing sequence began as soon as the last reagent was injected. After the measurement time, the result appears automatically on the digital voltmeter or printer readout. Glucose Determinations. For the determination of glucose, the monochromator was adjusted to 365 mp. The sensitivity settings were the same as in the phosphate determinations. Again a short induction period necessitates a 30-second delay time. After 3.00 ml of composite reagent were added to the cell, the stirring was initiated. To start the reaction, 1.00 ml of glucose was injected into the cell with a hypodermic syringe, and the timing sequence begun. After the induction period, the result is automatically displayed on the digital voltmeter. For direct digital readout of concentration, the slit width of the monochromator was adjusted, while running a 10-ppm standard, to give the proper readout on the digital voltmeter. Alternatively, as described under Instrumentation, a slidewire potentiometer at the output of OA2 would be used to adjust the readout. (8) S. R. Crouch and H. V. Malmstadt, ANAL.CHEM.,39, 1090 (1967). (9) H. L. Pardue, M. F. Burke, and D. 0. Jones, J . Chem. Educ., 44,684 (1967).
Table 11. Automatic Rate Measurements with Short Integration Times and Signals Typical of Fast Reactions Input rate, Digital Proportionality Re1 std mV/sec readout,a mV constant dev, Z 180 81.8 2.20 0.24 385 175.3 2.19 0.20 590 268.8 2.19 0.14 795 362.8 2.19 0.11 Averages of 10 results; integration time: 50 msec; premeasurement time: 100 msec; Ra = 15K. 0
Table 111. Automatic Results for Phosphate Direct Phosphorus concentration, ppm digital Re1 error, Re1 std Z dev, 'Z readout0 Taken Found* 98 5.0 5.1 +2.6 3.8 153 8.0 8.0 0 2.0 191 10 ... ... 0.7 296 15 15.4 +2.7 1.6 4 Averages of 5 results. *Based on 10.0 pprn standard; integration time: premeasurement time: 30 sec.
10 sec;
Table IV. Automatic Results for Glucose Glucose concentration in ppm Re1 std Taken Re1 error, Z dev, 5.0 0.0 1.6 10.0 ... 1.o 15.0 +0.7 0.7 +O. 5 0.8 20.0
Direct concentration readouta 5.0 10.0 15.1 20.1
a Averages of 5 results; 10.0 ppm standard used to set readout; integration time: 10 sec; premeasurement time: 30 sec.
TEST RESULTS
To test the behavior of the automatic rate system, slopes of synthetic signals were first measured. In addition, the system was used in two quantitative reaction-rate procedures for the determination of glucose and phosphate in the parts-per-million range. In Table I, results of rate measurements on slowly changing synthetic signals are presented. These slopes correspond to output rates from typical reaction-monitor and signal-modifier systems (Figure 5) for slow reactions. Integration times were 10 seconds for these measurements. As can be seen from the proportionality constant, the output voltage is a linear function of the input slope with about 0.1 relative error, Relative standard deviations of about 0.2% were typical for these VOL. 40, NO. 12, OCTOBER 1968
1817
slowly changing signals. In Table I1 results are presented for rapidly changing synthetic signals. Resistor R I was changed to 15K and integrator times of 50 msec were used for measuring these slopes. Relative errors are again within 0.1 and relative standard deviations are about 0.2%. Results for the determinations of phosphate by the reaction rate procedure are shown in Table 111. These results were based on a single phosphate standard. In Table IV results of automatic determinations of glucose in the 5-20 ppm range are presented, In this case adjustments were made to obtain a direct digital readout of the glucose concentration. Rela-
tive errors and standard deviations of about 1% were obtained. Many of the rate curves recorded simultaneously indicated that inputs to the rate measuring system were often quite noisy. The results obtained here show the high noise immunity of the integration procedure. In addition, because of its versatility, it is possible to use the same readout system for reactions whose initial rates vary over a wide range, as described in the Instrumentation section. RECEIVED for review May 14,1968. Accepted July 3, 1968.
Reaction Rate Measurements with Fluoride Ion-Selective Membrane Electrode Formation Kinetics of Ferrous Fluoride and Aluminum Fluoride Complexes K. Srinivasan and G . A. Rechnitzl Department of Chemistry, State University of New York, Buffalo, N. Y. 1421 A study of the complex formation kinetics of FeF2+ and AIF2+ demonstrates the eminent suitability of the fluoride-selective membrane electrode for reaction rate measurements. Detailed experiments, carried out over a wide range of solution conditions, yielded the proposed mechanisms
Fe3+ Fea+
+ F-
F?
FeF2+
+ H F a FeF2+ + H+
and
+ H F a A1F2++ H+ AIOH~++ HF A I ( H ~ O ) ~++ FA10H2++ H F A1F2++ H20 Al3+
-P
for the formation of FeF2+ and AIF2+, respectively. Values for rate constants of steps previously identified have been obtained with the membrane electrode and are in excellent agreement with the available literature data. Additional new rate data have also been obta ined.
PREVIOUSLY, we reported ( I ) on the use of the fluoride ionselective membrane electrode in the study of solution equilibria between fluoride and hydrogen ions. The almost instantaneous response of the electrode (overall response rate limited by recorder response time of 0.5 sec.) and its Nernstian behavior with respect to free fluoride ions in acid solutions indicated that this electrode might be effectively employed in kinetic studies of reactions involving changes in fluoride ion concentration. The formation kinetics of monofluorocomplexes of metals were selected for detailed examination as representative dynamic systems, and the results of two such studies are presented here. The kinetics of the formation of FeF2+ were chosen for investigation because the relevant rate equation had been established by the spectrophotometric study of Pouli and Smith (2). Although different conditions 1
Alfred P. Sloan Fellow.
( 1 ) K. Srinivasan and G . A. Rechnitz, ANAL.CHEM., 40,509 (1968). (2) D.Pouli and W. MacF. Smith, Can. J . Chem., 38,567 (1960).
18 18
ANALYTICAL CHEMISTRY
were used, it was thought that a reasonable comparison could be made between the results of the present study at 25°C and those of the previous work. Once the reliability of the fluoride ion-selective electrode in monitoring a reasonably fast reaction such as the formation of FeF2+had been established, the electrode was employed with confidence to study the kinetics of the formation of AIF*+, a reaction known to be slow (3) but not previously studied from the mechanistic viewpoint, EXPERIMENTAL
Stock solutions of sodium fluoride were prepared by weight from the reagent grade salt after drying at 100 "C for 24 hours. Stock solutions of sodium perchlorate and perchloric acid were prepared by weighing anhydrous sodium perchlorate (supplied by the G . Frederick Smith Chemical Co.) and adding required amounts of perchloric acid to the solutions before final preparation. The concentration of the free perchloric acid in the sodium perchlorate solutions was determined by titration against standard sodium hydroxide. Stock solutions of ferric perchlorate were prepared from ferric perchlorate, Fe(ClO& * 6H20 (supplied by the G. Frederick Smith Chemical Co.), and calculated amounts of sodium perchlorate and perchloric acid were added to the solution to obtain the desired composition. The concentration of the ferric ion in the solution was estimated by titration with a standard solution of the sodium salt of EDTA using sulfosalicylic acid as the indicator. Stock solutions of aluminum nitrate were prepared by weighing reagent grade aluminum nitrate crystals, AI(NO&. 9Hz0, into solutions containing calculated amounts of sodium perchlorate and perchloric acid. The fluoride solution required for each kinetic run was prepared by mixing appropriate volumes of stock solutions of sodium fluoride and sodium perchlorate containing free perchloric acid, so as to obtain an ionic strength of 1.OM. In each experiment, 25 ml of the final solution was transferred to a dry polyethylene beaker thermostatted at 25 i 0.1 "C. The stock solution of ferric perchlorate or aluminum nitrate containing sufficient sodium perchlorate and perchloric acid to attain an ionic strength of 1.OM was also thermostatted at 25 & 0.1 "C. (3) C. Brosset and J. Orring, Suensk Kem. Tidskr., 55, 101 (1943).
