planations are equally likely. Additional work is required to settle this point. The irreversible reduction of copper (11) ion in the pyrophosphate medium in the presence of approximately 1 0 - 3 x Triton X-100 gives a well-defined wave with a half-wave potential of about -1.57 V. The limiting current is proportional to the concentration of copper ions. However, in the presence of an equal concentration of ferrous ion, the limiting current is decreased by about 20z. The reason for this decrease is not understood. The presence of ferric ion causes an increase in the copper limiting current, perhaps because of incomplete separation of the ferric ion wave. An equimolar amount of Fe3+ion gives about a 10% increase in the copper ion limiting current. Thus, ferric ion interferes with the copper ion reduction wave, and copper ion interferes with the ferric ion reduction wave in the pyrophosphate medium. The quantitative determination of both ions in an unknown mixture, therefore, appeared only to be possible with a rather complex iterative procedure, if at all. To avoid this problem, at a minimum ncrease in sampling requirements, the copper first is deter-
mined in an acid sulfate supporting electrolyte, after which a suitable pyrophosphate aliquot is added and the ferric and ferrous ions are determined. The pH of the buffer increment added was adjusted to give a final pH value of 8 for the mixed solution. In a 0 . 1 M potassium sulfate solution of pH -2 (to prevent hydrolysis of ferric ion), copper ion gives a well-defined reversible reduction wave with an El/2 of -0.028 volt. The presence of iron has no effect on this wave. Moreover, the presence of the final sulfate concentration was shown not to effect the determination of ferric and ferrous ions. Calibration curves for ferric, ferrous, and copper ions are all linear. By determining the concentration of copper ion independently, its contribution to the ferric reduction wave can be determined and a correction made. The reproducibility of the measurement of all three ions in the 10-'M concentration range was found to be * 5 % . Investigation of other potential interferents was not made.
RECEIVED for review August 2, 1972. Accepted November 27, 1972.
Bipolar Current Method for Determination of Solution Resistance P. H. Daum and D. F. Nelson Northern Illinois University, DeKalb, Ill. 60115
A bipolar method for measurement of solution resistance has been developed which involves the successive application of constant current pulses of equal magnitude, but of opposite sign, to a conductance cell, and integration of the resultant cell voltage to determine the area of the voltage-time curve. I t is shown that this area is directly proportional to the solution resistance, independent of the magnitude of the series cell capacitance C,, and essentially independent of the parallel capacitance C, over a wide range of values. The design and construction of the instrument, which features a solid state MOS-LSI memory for the rapid accumulation of data points, is detailed. Application of the instrument is illustrated with studies of low resistance KCI solutions and with kinetic studies of the acetyl chloride ethanolysis reaction. THERE HAS BEEN a good deal of interest generated recently in extending the available range of conductance instrumentation to include measurements in experimental situations which are usually avoided. These include the rapid precise measurement of solutions with high resistances, as in the study of solvolysis reactions in nonaqueous solvents and the measurement of solutions with extremely low resistances as those encountered in the study of the characteristics of fused salt systems. Classically, the approach to the measurement of conductance in systems such as these has been to experimentally adjust the parameters of the system such as the cell constant so that the measured conductance falls within the linear operating region of normal conductance instrumentation. However, this has proved not to be a practical approach for many applications because of stringent design considerations of size, electrode placement, and so forth, which must be placed on conductivity detectors for other reasons. This has prevented the use of conductivity detectors
in a number of systems for which conductance measurement is uniquely applicable. A good example of this is the potential usefulness of conductivity detectors in i,on-exchange chromatography. The requirements of such a detector necessitate close placement of the electrodes to limit the dead volume of the detector so that the sensitivities are high. This requirement means that the cell constants in such systems are going to be rather large and, consequently, the measured resistances very low in many circumstances, and changes representing elution of solute even smaller. Using conventional instrumentation, the dependency of measured conductivity with concentration will be nonlinear for many situations, because normal apparatus is not designed to measure systems which have resistances which are less than 1 Kohm. Thus, what is potentially a sensitive and generally applicable detector has not enjoyed wide use for quantitative work. There are a good number of problems associated with making measurements on solutions which have either extremely high or low resistances. The problems arise from the unfortunate fact that conductance cells cannot be modeled as a simple resistance; associated with that resistance are series and parallel capacitances, contact and lead resistance, and a faradaic impedance. These factors cause the observed solution resistance to be frequency dependent and the errors caused by the existence of these extraneous factors become increasingly important when the solution resistance is either very high or very low. The origin of these undesirable effects is due to the complicated nature of electrochemical systems in general, and can best be understood with reference to Figure l a . This figure depicts a reasonably complete model of conductance cell, ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
463
important. For low resistance solutions, the contribution of the series capacitance to the measured cell resistance becomes important, and this contribution is not compensated for by the existence of the adjustable capacitance in the variable bridge arm. It has been pointed out recently by Robbins (1-3), that the condition for bridge balance (neglecting C,, because it is unimportant in low resistance solutions) is that Rb = R, l/R22C,2w2where Rb is the resistance read from the bridge and o is equal to 2rf. It can be seen from this equation that for low resistance solutions the error due to C, can become significant. For example if R, = loa, C, = 10 pF, and the measurements are made at a frequency of 1000 Hz, the resistance read from the bridge will be in error by 25%:. In addition to the impedance problem at low resistances, such factors as contact and lead resistance become important. One must also contend with the possibility of the occurrence of a faradaic process, since relatively large currents will flow through the system and the double layer capacitance may be charged significantly. For resistances on the high end of the scale, the contribution of the impedance of C, is generally negligible, and at any rate can be minimized by the use of a relatively high frequency. However, in this case, the impedance of C, becomes an important factor in determination of the error. For as R, increases and/or if high frequencies are used, C, may conduct a significant amount of the current that flows through the cell. This causes a negative error in the determination of the solution resistance. A variety of instrumentation and experimental techniques have been developed to overcome the limitations of normal conductance instrumentation. The most common and obvious method is to platinize the electrodes to obtain a large C, and to adjust the cell constant to keep R, within the linear range of the instrument. However, such techniques often do not suffice. Mathematical methods have been developed to correct for residual errors in which conductances are measured a t several frequencies, and from the frequency dependence correction factors can be calculated for the effects of C, and C, ( 4 ) . Other approaches have involved modification of the basic bridge circuit to overcome these problems electronically. Robbins ( 3 ) developed a conductance bridge for low resistance solutions which was accurate to 0.5% in the 100-ohm region by inserting a series rather than a parallel capacitance in the bridge arm. Phase angle voltmeters have been used as null detectors with some degree of success ( 5 ) . These respond only to the signal which is in phase with ac voltage and greatly simplify the tedious balancing problems of normal bridge measurements. It can also be shown that such instruments, if operated at the proper frequency, cafl measure with essentially zero error ( 4 ) . Other approaches using capacitances in two arms of the bridge have also been tried and have been shown to be quite accurate (6). While all of the above approaches have a good deal of merit in that they can ultimately determine conductance very accurately over a wide range, they have a common fault in that they are extremely cumbersome to use. They generally in-
+
b
Figure la. Equivalent circuit of a conductance cell R, = solution resistance Cd = double layer capacitance Z f = faradaic impedance Re = contact and lead resistance C, = contact and lead capacitance C, = interelectrode capacitance Figure lb. Simplified equivalent circuit C,. = combined series capacitance C, = combined parallel capacitance R, = solution resistance
where R, represents lead and contact resistance, C,, lead capacitance, C, is the double layer capacitance, C,, the interelectrode capacitance, and where Z , is a frequency dependent impedance arising from a faradaic process. If it is assumed that lead and contact resistances and their associated capacitances are unimportant and that experimental conditions are adjusted so that the polarization which causes faradaic processes is eliminated, then the above model can be simplified to a series combination of R, and C, in parallel with C, (Figure lb). A discussion of the problems in normal methods of determining conductivity can be readily understood with reference to this simplified model. Generally measurements are accomplished using some variant of an ac Wheatstone bridge, in which a small amplitude ac voltage is applied to the cell and the conductivity is determined by adjusting the resistance in one arm of the bridge until a null reading is attained on a detector. Generally, a variable capacitor is included in parallel with the variable bridge arm in order that balance be attained, since the voltage across and the current through the cell are out of phase. Alternating-current bridge measurements work very well for resistances between 1 Kohm and 10 Kohm and with some modification can be extended to make meaningful measurements to 60 Kohms, provided several experimental conditions are met. These are that C, must be fairly large so that its impedance is small with respect to R, and the impedance of C, must be large with respect to the series combination of C, and R,. It can be easily seen that the first condition is true if C, and R, are large (but R, not so large as to make the impedance comparable to that of C,) and/or if the frequency of the applied signal is relatively high. These conditions are usually met by platinizing the conductance electrodes to obtain a large C, by using a source frequency of at least 1 KHz, and by adjusting the cell constant so that the measured resistances are in the proper range. For resistances which are outside of the general range of 1 Kohm to 60 Kohm, several sources of error can become 464
0
(1) J. Braunstein and G. D. Robbins, J . Chem. Educ., 48,52 (1971). ( 2 ) G. D . Robbins and J. Braunstein, J . Electrochem. SOC.,116, 1218 (1969). (3) G. D. Robbins and J. Braunstein, in "Molten Salts: Characterization and Analysis," G. Mamantov, Ed., Marcel Dekker, New York, N.Y., 1969, p 443. (4) D. E. Johnson and C. G. Enke, ANAL.CHEM., 42,329 (1970). (5) K. Schmidt, Reu. Sci. Insfrum., 47,671 (1966). (6) R. Wershaw and M. Goldberg, ANAL.CHEM., 37, 1180 (1965).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
volve tedious balancing procedures which limit their usefulness to systems which are essentially steady state, and hence a number of potential applications of conductivity in rapidly changing systems have not been exploited. Recently, however, a method has been developed by Johnson and Enke ( 4 ) which eliminates many of the classical experimental problems encountered with other methods and has the advantage of being capable of measuring very rapid changes in conductivity. The method involves the application of two successive constant voltage pulses of equal magnitude but of opposite sign sequentially to a conductance cell. The resulting current is sampled at the end of the second pulse and it was found that the conductance measured in this fashion was essentially independent of either the parallel or series capacitance normally associated with conductance cells over an extremely large range of capacitance and resistance values. Furthermore, the design of the system allows extremely rapid measurement of the conductance, and thus the system is uniquely applicable to the determination of conductance in reacting systems for kinetic studies. Though the system works extremely well for resistances from 1 Kohm to 1 Mohm, some difficulties are encountered when applying the technique to systems in which the resistances are low. The difficulty arises from the requirement that the pulse time T be much less than R,C,. Obviously, as R, decreases, one must apply ever shorter pulses to the system in order that the error in the determination remain within acceptable limits, and the resultant requirements on the timing and measuring circuits become extremely stringent. Phenomenologically, if T E RJ,, appreciable charging of C, occurs during the first pulse, and when the second pulse comes along, the current through the system is enhanced because of the polarization of C,, and C, discharges more than it should during the second pulse, thus causing a negative error in the conductance. In this communication we would like to report the development of a bipolar method for determining the conductance of solutions which circumvents the difficulties of the JohnsonEnke method at low resistance levels, but retains its essential advantage, in that the resistance measurements are essentially independent of any reasonable values of the series or parallel capacitance. The principle of the method is that the current through the cell is controlled rather than the voltage so successive constant current pulses of equal duration and magnitude but of opposite sign are applied sequentially to the cell, and the voltage is observed as a function of time. The resistance can be determined in either of two ways. The cell voltage can be sampled at the end of the second pulse, in which case the resistance is directly proportional to the voltage, or alternatively, the cell voltage can be electronically rectified and integrated to determine the area under the curve. In this case the resislance is directly proportional to the area for given pulse magnitude and duration. In either case the measurement of the unknown resistance is completely independent of the series capacitance C,, no matter what its value, and is essentially independent of the parallel capacitance C,, provided the pulse time is of the proper length.
B
A
TlME
Figure 2. Theoretical rectified voltage time curves for cell response
R, = lOOK ohms, C, = 0, C, = 0 B. R, = lOOK ohms, C , = 0.1 pF, C , = 0 C. R, = lOOKohms, C , = 0.1pF C, = 0.001
A.
PF
creased by eel,, due to the charge remaining on C,, and C, will discharge linearly to e, = 0. If the cell voltage is measured at the end of the second pulse it can be seen that E2 = -iR, and all effects due to C, disappear. If the cell voltage is rectified, and the area determined, as shown in Figure 2 , it can be seen that the excess area in the first pulse due to the charging of C, is exactly equal to the decrease in area in the second pulse due to the discharging of C,. The integrated area can be shown to be A = 2iR,~,which is completely independent of C, as long as the pulse magnitudes and durations are the same. With the inclusion of Cp in the model, the response of the cell becomes a little more complicated though just as easily understood. It can be shown that the voltage response to the first pulse is
and correspondingly for the second pulse
where i is the magnitude of the current pulses, T~ and T~ are the durations of the first and second pulses, respectively, and 1 1 C, is defined as ljC, = -. If the assumptions are
c,
+ CP
made that T~ = 7 2 = T , and that T >> R,C, then it can be shown that the voltage at the end of the second pulse reduces to
THEORY
(3)
To illustrate how the method operates, consider the application of a bipolar current pulse to the simplified cell model depicted in Figure l h , assuming initially that C, = 0. Durit/C,, and the ing the first pulse, the potential El will be ZR, capacitor C, will charge linearly to some voltage eci,. When the current switches, the iR, for the second pulse will be de-
+
This in turn reduces to iR, if the further assumption is made that Cp > R,Cs
+ C,)*
+
2i R,2C,2 C, 2 (7) (C, CpI3
+
If the further assumption is made that Cp > R,C, can be determined by appropriate simplification and reduction of Equations 3 and 7 to produce for the relative error in the determination of the voltage at the end of the second pulse
then Equation 6 reduces
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
and for the relative error in the determination of the rectified area,
Obviously, on the basis of these equations, the error in both approaches is determined by the ratio (Cp/C,) and in the
DAC
Front
panel
S W1R M
memory register
F
G
BC D counter
Figure 4. Master control circuit -
limiting case where T >> R&, the relative error in either method is the same. This error is primarily determined by the amount of current required by C, to increase its voltage as C, charges. This causes both the IR, drop and the amount of charging of C, to diminish, and EI?will be somewhat less than it should be. There will be a corresponding fractional decrease in the area, for the amount of current diverted to charge Cp will be a constant provided C, charges linearly. The limiting error can theoretically be attained for any system by ensuring that the pulse width is long enough. However, there are some practical limitations to the length and magnitude of pulse which can be applied to a system, since the application of a constant current will linearly charge C,, and if the voltage across C, becomes large enough, a faradaic process will occur causing drastic errors in the determination of the solution resistance. Obviously then, pulse characteristics must be carefully chosen so that the pulse is long enough to minimize capacitive errors, and yet not so long as to cause appreciable errors due to polarization. EXPERIMENTAL
Apparatus. It was decided to construct the instrument to measure the area beneath the rectified voltage time curves because it was felt that this approach, since it was integrative, would result in greater noise immunity, and because the nature of the integrator circuit would result in a direct digital output without the use of a separate A-D converter. This approach requires some sacrifice in measurement speed because of technological limitations on switching times and so forth, but proved to be fast enough for the intended purposes. The instrument was constructed using a modified Heath A D D chassis and power supply and preconstructed Heath cards wherever possible. All components were solid state, with the exception of the Nixie tube display, and all timing functions were based on a 1 MHz crystal oscillator (Heath EU-800-KC). The pulse times and measurement repetition rate were independently variable over a wide range of values to accommodate a variety of experimental conditions. A solid state memory was included t o record the results of rapid changes in conductance as encountered in kinetic studies. Data readout was cia a three digit Nixie tube display with a n over-range capability. The display could read either from the memory, or from the output of the counter as data were
memor y register
BC D counter C
R
Figure 5. Memory and readout circuit
taken. Provision was made to offset the integrator so that scale expansion could be accomplished, and provision was also made for D-A conversion so that data stored in the memory could be read out and recorded in analog form a t a slow time scale. Operation of the Instrument. The operation of the instrument can be understood with reference to the circuit diagram in Figure 3 and its associated signal diagram. Current is supplied to the cell by placing it in the feedback loop of an OA (operational amplifier) (Analog. Devices 455) whose inputs are connected to positive and negative constant voltage sources. When, a command for a measurement is given to the master control circuit, Figure 4, it sends out pulses which sequentially turn these sources on and off, giving signal A , Figure 3. This causes an IR drop to occur in the cell which is followed by the output of the OA, since the O A maintains its virtual ground. This is shown as signal B. B is then sent to OA-2, which functions as a half-wave rectifier and operates when the cell voltage is positive. OA-3 sums the currents coming from R t and Rq, thus completing the full wave rectification (signal C) and integrates the signal, ultimately producing a train of digital pulses which are proportional to the area beneath the curve signal D. The function of integration is performed by sensing when the output of OA-3 deviates from zero with a comparator, which opens a clock gate and allows pulses from the crystal oscillator to switch a precise constant voltage source in the feedback loop of the OA on and off. The voltage source is connected through R 5to the inverting input of the integrator, and thus extracts discrete amounts of charge Q = ( V / R 5 ) t from C , with each clock pulse, where t is the pulse duration. When Cfis discharged to zero volts, the comparator changes state and turns the clock gate off. The resolution of the integrator can be controlled by variation of R5,thereby determining the amount of charge extracted by each pulse. Scale expansion can be accomplished by feeding a current pulse to the integrator input for the duration of the input signal. Thus the count output of the integrator will represent only a desired fraction of the input signal. The pulse train from the output of the integrator is counted by three decade counters which feed into the readout memory circuit, Figure 5 . The memory was constructed from two MOS-LSI shift registers (TMS 3112 J. C.) connected in parallel. Each LSI ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
467
Figure 6. Readout sequencing and control circuit
40i 30
' O I 0
/
/ 20
40-
60
80
100
~rncasurcd
Figure 7. Experimental us. theoretical resistance of KCl solutions
contains 6, 32-bit shift registers with recirculating logic, thus the memory was capable of storing 32, 12-bit BCD numbers. The readout storage circuit was designed so that the Nixie tube readout could be used to observe either the output of the counter or the memory. The recirculating logic on the memory makes it possible to nondestructively read the contents of the memory a t a specified rate. The timing pulses for the operation of the digital readout and memory circuit are generated by the control circuit shown in Figure 6. This circuit is timed by the output of Flip-Flop-2 (FF-2) signal F of the master control circuit which a t the end of a measurement cycle, undergoes a 1 to 0 transition. This transition triggers monostable-I (MS-1) into its stable state and momentarily, T goes t o 1 causing a data transfer into the data latches. When T returns to 0, MS-2 is triggered, which resets the BCD counters. The data are then shifted from the data latches into the memory and the decoder drives for the Nixie tubes. The remainder of the control circuit provides the pulses necessary to shift the data in and out of the memory. It is designed to shift the recirculating memory 32 times when a set command is received from a front panel control button. A two input to one output multiplexer allows the operator to time the shifting pulses automatically from the output of MS-2 or manually by a n external push button switch. A cycle works in the following manner. Initially, the modulo-32 counter is zero, the FF is cleared, and the input gate to MS-3 is closed. When the FF is set, the input gate to MS-3 is opened and the next 1 to 0 transition from the multiplexer triggers MS-3. S makes a 1 to 0 transition which shifts the memory and advances the modulo-32 counter. After 32 468
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
such transitions a t S, the counter resets, which toggles the FF back to its cleared state, and the circuit is in a stable state until another set pulse is received. Provision is made to recirculate the memory at a slow time scale so that the stored data can be copied or so it can be fed to a D A converter and recorded on a strip chart recorder at a slow speed. Master Control Circuit. The main timing and control circuit in the instrument is shown in Figure 4. Its function is to provide the necessary pulses for control of the constant current sources, the shorting switches around the cell and integrator, as well as storage and readout sequencing. The circuit consists of three Flip-Flops (SN 7476N) and four nand gates (SN 7400N) labelled G, H. I, and J connected to the appropriately labelled switches in Figure 3. The circuit operates in the following manner: a constant frequency signal (frequency controlled by front panel switches) is fed continuously into toggle input of FF-1 which divides the frequency of A by two to give G. This normally has no effect on the outputs of the logic gates since the Flip-Flop array is initially in a stable state with the Q output of FF-2 a t a 1 logic level. A measurement is initiated by a 1 to 0 transition of signal C (from crystal oscillator scaler) which is differentiated by a n RC network and sent to the set input of FF-3. This causes the Q output of FF-3 to go to 1 (signal E ) , and since this is connected to the clear of, FF-2 will then toggle on the next 1 to 0 transition of signal B , thereby making signal F a 1. This releases control of the logic gates and their outputs will now be determined by the logic levels at their other inputs. The following sequence of events will occur as soon as signal F undergoes its 0 to 1 transition. Gate J will undergo a 1 to 0 transition, opening the shorting switches around the cell and integrator and releasing the system for a measurement. At the same time, gates H and I will undergo 1 to 0 transitions, gate H thus turning on the negative current source and applying a constant current pulse to the cell and gate I causing the offset current control on the integrator to go on. The next time A goes to 1, gate H will be turned off thus terminating the negative current pulse, and gate G will be turned on, thus applying the positive constant current to the system. Gates I and J are unaffected by this transition. On the next 1 to 0 transition of signal A , gates G , H, and I will return to their original states and on the next complete cycle FF's 2 and 3 will return to their original stable states where signals E and F are both 0, gate J will return to its original state, and the measurement cycle is complete. RESULTS AND DISCUSSION Instrument Tests. The operation of the instrument was checked with a series of measurements using dummy cells in the configuration shown in Figure 2 for the simplified model. The measurements were accomplished by first calibrating the
instrument in a given range using a standard resistor (0.1 %) with no series or parallel capacitance. Then a number of resistances in the range were measured using various values of C, and C, to determine the instruments ability to discriminate against capacitive effects. Resistances between 100 ohms and 100 Kohms were measured in this fashion using a pulse time of 4 msec for all measurements. Capacitances were varied from C, of 1.0 pF to 100 pF and C, from 0 to 10-10 F. The results of these measurements were in essential concordance with the determinate errors predicted by the theoretical analysis in the previous section. In the worst possible case, where R, = 100 Kohm, C, = 1.0 pF, and C, = 100 pF, the error in the measurement of the resistance was only 2 ppt. With smaller values of C,, the error was reduced to that of the readout device of 1 1 ppt. It is assumed that the observed errors could be made smaller if more significant figures were available in the readout, and if the pulse time were adjusted so that the minimum error condition was attained for all resistance measurements. Tests with KCl Solutions. To test the operation of the instrument under real conditions, and under conditions in which it is extremely difficult to obtain measurements using normal conductivity bridges. a series of measurements was made using concentrated KCl solutions in an experimental situation such that the measured resistances were on the order of 10 to 100 ohms. The measurements were made in a thermostated bath at 25.0 =t 0.1 "C, using a conductance cell with a nominal cell constant of 2.5, and whose electrodes were platinized and of about 1 cm* in area. The determinations were made by first calibrating with 100 ohm standard resistor, and then measuring the solution resistance. Calibration was checked before each measurement to ensure the greatest possible accuracy and reproducibility. Results were plotted as shown in Figure 7 where measured resistance is plotted as a function of lOOOjXC, where X is the equivalent conductance and C is the concentration. lO0OjXC represents the resistance which would be measured in a cell with a cell constant of unity. The plot should be a straight line with the slope being equivalent to the experimental cell constant. The data were plotted in this fashion to eliminate the effects of lead and contact resistance and calibration error, and to illustrate the linearity of the instrument. The experimental curve was analyzed by least squares analysis and the slope and intercept were calculated to be 2.692 and 0.220, respectively. The slope was taken as the experimental cell constant and the intercept was assumed to be equivalent to the lead and contact resistance of the experimental apparatus which was not accounted for in the standardization of the instrument. This is a reasonable assumption and would account for the offset of the curve in the fashion which was observed. The constants were combined to give an empirical equation for data of R, = 2.692 R , - 0.220, where R, is the measured resistance and R,is the resistance which would be measured in a cell with a cell constant of 1. This empirical equation was used to correct the measured resistance values and these values in combination with the experimentally determined cell constant were used to calculate values of the equivalent conductance. The results agreed with the values reported in (7) to within the resolution limits of the readout (7) "Handbook of Chemistry and Physics," R. C. Weast and S. M. Solby, Ed., The Chemical Rubber Co., Cleveland, Ohio, 1967, p D93.
18-
h
0 1'
80 v
0
9
Figure 8. Experimental kinetic data for acetyl chloride ethanolysis a. T = 30.1 "C, k = 0.241 b. T = 14.9 "C, k = 0.0718 C. T = 5.2 "C, k = 0.0309
device. It is felt that these parameters could be measured even more accurately with modification of the instrument to increase the number of digits in the readout so that multiple period accumulation of area counts could be accomplished. Kinetic Measurements. The specific design of the instrument was directed toward a conductance measuring device which would be applicable to the study of the kinetics of relatively fast reactions in which the progress could be followed by the change in conductivity of the solution. Consequently, the instrument was designed with a solid state memory so that data points could be taken rapidly and stored in a digital form to be later retrieved and analyzed. To test the applicability of the system to the measurement of the conductance of reacting systems, it was decided to repeat the experiments of Johnson and Enke ( 4 ) involving the solvolysis of acetyl chloride in ethanol. The experiments were carried out using unplatinized platinum electrodes of about 1 cm2 in area, separated by a distance of a few mm, C, for the system was approximately 1 p F , and the measured resistances were in the range 100 Kohms to 10 Kohms. The experiments were accomplished by injecting small quantities (1-2 pl) of freshly distilled acetyl chloride into about 100 ml of thermostated ( 1 0 . 2 ") ethanol [purified by the method of Lund and Bjerrum (S)] with a microsyringe. The solution was rapidly stirred with a high speed Teflon (Du Pont) stirrer, and measurements were initiated as soon as the solution was sufficiently homogeneous to give meaningful kinetic data. Measurements were initiated by pushing a front panel suitch which set the memory timing FF and started the memory cycle which resulted in measuring and storing 32 data points at evenly spaced time intervals. The measurement repetition rate was controlled so that most of the measurements were recorded during the time when the conductance was changing most rapidly, to ensure that data were taken in the most significant manner possible. Care was taken to ensure that the reaction was complete before a measurement of the resistance at infinite time was made. After completion of the measurement cycle, the memory was -
(8) H. Lund and J. Bjerrum, Ber., B64, 210 (1931). ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
469
Table 1. Rate Constants for Ethanolysis of Acetyl Chloride at Various Temperatures Temperature, No. of "C k (sec-l) expts s 5.2 0.0309 6 0.0007 11.2 0.0530 2 0 0002 14.9 0.0711 7 0.0009 20.1 0.1118 7 0.0022 30.1 0.2355 4 0.0060 I
reported by the authors of as much as 11 of the measured rate constant. The standard deviation generally increases as the temperature and the reaction rate increase, as might be expected. We feel that the results of the present investigation are much more reliable than those previously reported. We also feel that had Johnson and Enke measured the reaction rate over a wider temperature range, they probably would have obtained essentially the same results as we have obtained. The activation energy calculated from our data is 13.95 kcal/mole in comparison to 13.23 kcal/mole by Euranto and Leimu and 12.93 kcal/mole reported by Johnson and Enke. 10YT
Figure 9. Temperature dependence on reaction rate 0 This investigation A Johnson and Enke E
Euranto and Leimu
recirculated and the data aere analyzed by a least squares procedure. Measurements were made at 5 different temperatures and the average values of the rate constants are reported in Table I along with the standard deviation. Typical experimental curves, plotted as log(Gm/Gm- G) cs. time, where G is the conductance, are shown in Figure 8 for three different temperatures illustrating both the linearity of the data and the range of rate constants which could be measured using the instrument, though the limitation at the fast end of the scale is due to mixing, rather than instrumental limitations, and we estimate that with faster mixing techniques, rates of at least an order of magnitude greater could be measured. The reported results agree quite well with results published by Johnson and Enke (4, who studied the reaction using a fast conductometric procedure, and with the low temperature results of Euranto and Leimu (9), all shown in Figure 9. The present results, however, deviate considerably from those obtained by Euranto and Leimu at high temperatures, as can be seen, and in general, the rates which are presently reported are larger. We feel that the observed deviations are not unexpected because of the procedure which these authors used to determine their kinetic parameters. This involved the use of a fast quenching method in which water was rapidly mixed with the ethanol acetyl chloride solution to stop the reaction. In reality, though, ethanol continues to react with the acetyl chloride after addition of the water, and ultimately what is determined through a complicated titrimetric procedure is the amount of ethyl acetate produced before the water was added. This type of experiment is fraught with difficulties and corrections, not the least of which are mixing time and determination of the relative rates of hydrolysis and ethanolysis. The experimental difficulties are reflected in the standard deviation
CONCLUSIONS A fast conductance method has been developed which can be used to advantage in a variety of experimental situations. The method is particularly adapted to the measurement of small (less than 100 ohms) solution resistances, where it completely eliminates the problems associated with the series capacitance C,. The accuracy of the method has been shown to be dependent on C,jC, and since this ratio is usually quite small (
