3801
DIFFERENTIAL ’THERMOMETRIC TECHNIQUE FOR RATEMEASUREMENT
A Simple Differential Thermometric Technique for Measuring the Rates of Chemical Reactions in Solutions bly Thelma Meites, Louis Meites, and Joginder N. Jaitly’ Department of Chemistry, Clarkson College of Technology, Potsdam, New York 18676
(Received April 1 , 1969)
This paper describes the construction and operation of a constant-temperature-environmentdifferential twin niicrocalorimetric apparatus for following the rate of a chemical reaction by monitoring the difference between the temperature of a reaction mixture, contained in one of two identical vessels, with that of a reference solution contained in the other. The temperatures are sensed by thermistors,whose resistancesare compared in a simple Wheatstone bridge. Data on the reaction between ethyl acetate and sodium hydroxideindicate that second-order rate constants can be evaluated with accuracies and precisions of a few per cent or better even if the overall change of temperature during a reaction is as small as 0.015”. Various tests for internal consistency indicate that the measured differential temperatures are reliable to i: 20 pdeg or better.
Introduction There have been many studies of the rates of chemical reactions in solutions by techniques like conductometry, absorption spectroscopy, and polarography, which reveal the time dependence of the concentration of some reactant, intermediate, or product while a reaction is in progress. None of these techniques is as versatile as one might wish: electrometric ones are useless in solvents having very low dielectric constants, spectrophotometry is inapplicable to reactions in which gaseous products or precipitates are formed, and so on. Difficulties are especially likely to arise in work with biochemical substances and biological fluids, where nonreactive substances may interfere by obscuring the response of the measuring technique to variations in the concentrations of reactive ones. Despite what would seem to be substantial advantages, thermometry has until very recently received very little attention from those engaged in kinetic work. Very many chemical reactions of interest involve enthalpy changes large enough to permit their extents to be followed, even at fairly high dilutions, with readily available temperature sensors and simple electrical circuitry. The technique should be applicable to reactions of any kind in any solvent, irrespective of the spectral, electrochemical, or other properties of the substances involved. Several workers in classical calorimetry2 have devised techniques for evaluating the overall temperature change resulting from a very slow reaction by extrapolating temperature-time data obtained while it is in progress, usually by assuming obedience to a first-order rate law. However, it was apparently DuclauxS who first explicitly calculated kinetic parameters from such data, and Barry4 who first obtained reaction rates and enthalpies from the data of a single experiment. More or less traditional calorimetric apparatus and techniques have since been used for these purposes by several other
authors,6p6two especially noteworthy approaches being those employed by Sturtevant. The first of these7!* involved measuring the time dependence of the emf of a 20-junction copper Advance thermocouple sensing the difference between the temperatures of the reaction calorimeter and a reference calorimeter, both of which were immersed in an oil bath adjusted to follow drifts in the temperature of the reference calorimeter. Heatexchange corrections were very small, the Newtonian heat-exchange constant for heat transfer between the bath and the reference calorimeter being only about 2 X 105 sec-l, and first-order rate constants with precisions of about *2% were obtained for reactions yielding total temperature rises of the order of 25 mdeg and having half-times of 10-30 min. The other approachg employed a pair of resistance thermometers, one in the reaction calorimeter and one in the reference calorimeter, connected to an ac bridge whose output, after amplification and conversion to dc by a phase-sensitive detector, was presented to an analog computer circuit serving two functions: it fed back a voltage proportional to the bridge output to a heater in the cooler calorimeter, and (1) This paper is based in part on a thesis t o be submitted by J. N. Jaitly to the Faculty of the Polytechnic Institute of Brooklyn, where this work was begun, in partial fulfillment of the requirements for the Ph.D. degree in Chemistry. (2) Cf. J. M. Sturtevant, “Calorimetry,” in “Physical Methods of Organic Chemistry,” 3rd ed, Vol. I of “Technique of Organic Chemistry,” by A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y., 1959, Chapter X, pp 639-648. (3) J. Duclaux, Compt. Rend., 146, 120 (1908). (4) F. Barry, J. Amer. Chem. Soc., 4 2 , 1296, 1911 (1920). (5) K. L. Wolf and K. Merkel, 2.Phys, Chem., A187,61 (1940). (6) A. K. Batalin and I. A. Shcherbatov, J . Gen. Chem. U.S.S.R., 10, 730 (1940). (7) J. M. Sturtevant, J . Amer. Chem. SOC.,59, 1628 (1937); J . Phys. Chem., 45, 127 (1941). (8) M. Bender and J. M.Sturtevant, J . Amer. Chem. SOC.,69, 607 (1947). (9) A. Buzzell and J.’ M. Sturtevant, ibid., 73, 2454 (1951). Volume 78, Number 11
Noamber 1960
3802
T.MEITES,L. MEITES,AND J. N. JAITLY
also provided a signal proportional to its square (and which the rate constant is easily deduced and on which hence to the rate of consumption or liberation of heat by deviations from first-order kinetics should be easily the reaction being studied) to an electromechanical perceptible. Pseudo-first-order rate constants having integrator. A record of the integrator output against average precisions of about .tl% were obtained for time was equivalent to a plot of the time dependence of reactions having half-times between 3.5 and 30 sec the extent of reaction. A reaction yielding a total and involving overall temperature changes between temperature change of 1.8 mdeg and having a half-time about 0.1 and 1 deg; in a few experiments where the of about 6 min could be followed with a precision coroverall temperature change was about 0.08 deg the responding to uncertainties of only about 5 pdeg in the precision of the rate constant was near &2%. A very instantaneous temperature. Sturtevant and his cosimilar arrangement, employing a single-junction therworkers employed this apparatus in studying the heat mocouple as the sensor and involving periodic measureand rate of inactivation of pepsin,l0 the hydrolyses of ments of its emf by means of a galvanometer driven by a various amide and peptide bonds,ll--la and other chemphotoelectric amplifier, had been used by W ~ a t t . ~ S ical and biochemical processes. I n work with reactions having half-times between 2 and Most other workers have attempted to study faster 120 sec and yielding maximum temperature changes of reactions with simpler apparatus. Roughton14 devised 0.2 deg or less, Wyatt obtained first-order rate constants a thermometric flow method for evaluating the rates of whose precisions were "often better than ==I 3%." acid-base and other very fast reactions, while Bell and This paper describes a constant-temperature-enc o w ~ r k e r s ~probably ~ - ~ ~ attained the acme of simplicity vironment differential twin calorimeter and its use for when they devised procedures based on measuring the evaluation of reaction rates. Heats of dilution and either the maximum change of temperature15or the time stirring, the effects of power dissipation in the temperaat which the maximum is attained.l6,l7 Others have ture sensor, and other phenomena that are troublesome employed this procedure since its in single-vessel techniques are compensated by the although, as was pointed out by Lueck, Beste, and Ha11,21 differential arrangement. Carefully aged and matched it suffers from several important disadvantages: it thermistors are used as temperature sensors. Secondyields only one rate datum per experiment, it propagates order rate constants with precisions of a few per cent onto the rate constant any error in the evaluation of the have been obtained for reactions having half-times beNewtonian first-order heat-exchange constant E, and its tween 18 and 300 sec and involving overall temperature changes as small as 15 mdeg. application to any but the simplest mechanisms would be frighteningly complex. This is because first-order Although many earlier workers have employed calorimeters for which heat exchange with the surroundings kinetics are assumed in computing a rate constant from is relatively rapid, and although this is indeed essential the experimental datum, so that deviations from firstto the success of the thermal maximum t e c h n i q ~ e , ' ~ - ' ~ order kinetics could be detected only through variations it is difficult to evaluate the time dependence of the of the computed rate constant with reactant concentraextent of reaction from the temperature-time curves obtions. Lueck, Beste, and Ha112l employed a pair of identical (10) A, Buizell and J. M. Sturtevant, J . Amer. Chem. Soc., 74, 1983 glass reaction vessels immersed in a thermostat. Each (1952). vessel contained a thermistor of relatively low resis(11) A. Dobry and J. M. Sturtevant, 6.Biol. Chem., 195, 141 (1952). (12) A. Dobry, J. Fruton, and J. M. Sturtevant, ibid., 195, 148 tance; by connecting the thermistors to a bridge whose (1952). output was amplified and recorded, temperature-time (13) J. M. Sturtevant, J . Amer. Chem. Soc., 75, 2016 (1953). plots were obtained. A similar arrangement was em(14) F. J. W. Roughton, Proc. Roy. Soc., A126,439,470 (1930) ; J. B. ployed by Eremenko, Kolesov, and Kustova.22 Lueck, Bateman and E'. J. W. Roughton, Biockem. J., 29,2622, 2630 (1935); F. J. W. Roughton, J Amer. Chem. Soc., 63,2930 (1941). Beste, and Hall computed first-order rate constants from their recorded curves by the method of S ~ i n b o u r n e , ~ ~(16) R. P. Bel1 and J. C. Clunie, Proc. Roy. Soc., AZIZ, 16 (1952). (16) R. P. Bell, V. Gold, J. Hilton, and M. H . Rand, Discussions which not only involves a great many tedious integraFaraday Soc., 17,151 (1954). tions of successive portions of the recorded curve but (17) R. P. Bell, M. H. Rand, and X. M. A. Wynne-Jones, Trans. Faradag Sac., 5 2 , 1093 (1956). also poses problems with reactions that are not strictly (18) P. Baumgartner and P. Duhaut, Bull. Sac. Chirn. France, 1187 first-order. (1960). Very recently Papoff and Zarnboninz4have described (19) N. H. Ray, J . Chem. Soc., 4023 (1960). a quasi-adiabatic arrangement : the reaction cell is (20) F. Beoker and F. Spslink, 2.Phhys. Chem. (Frankfurt am Main), immersed in a water bath whose temperature is main26, 1 (1960). (21) C. H. Lueck, L. F. Beste, and H. K. Hall, Jr., J . Phys. Chem., 67, tained within 0.01" of that in the cell, and the latter 972 (1963). temperature, which is sensed by a thermistor im(22) L. T. Eremenko, U. R. Kolesov, and L. V. Kustova, Zh. F i z . mersed in the reaction mixture, is recorded as a function Khim., 38, 1259 (1964). of time. Aft,er graphical correction for the heat of (23) E. S. Swinbourne, J . Chem. Xoc., 2371 (1960). mixing and for secular drifts of cell temperature, this (24) P. Papoff and P. G. Zambonin, Talanta, 14,581 (1967). (25) P. A. H. Wyatt,J.Chem. Soc., 2299 (1960). yields a plot of the extent of reaction against time, from The Journal of Physical Chemistry
DIFFERENTIAL THERMOMETRIC TECHNIQUE FOR RATEMEASUREMENT tained with such calorimeters. The extent of heat exchange is far too large t o neglect,21and corrections for it are large and uncertain. To obtain recorded curves minimally distorted by heat exchange ure have designed an apparatus for which the Newtonian heat-exchange constant is as low as is consistent with reasonable simplicity of construction and use.
Description of the Apparatus Two 5-oz PG-5 plastic cups (Sweetheart Plastics, Wilmington, Mass.) are used as the reaction and reference vessels. The normally convex bottom of such a cup is easily made concave by exerting gentle pressure on it, and it will then accommodate and stabilize the rotation of an egg-shaped Teflon-coated magnetic stirring bar. Each cup is supported in a hole, in the center of an 11-cm square platform made of 1/2-in.thick Lucite, whose diameter and taper are such that the CUP is snugly supported about 1.5 cm below its top. The platforms are attached to the floor of the inner enclosure of the calorimeter by l-in. diameter Lucite rods 6 cm long, so that the bottom of each cup is about 1cm above the floor of the enclosure. The platforms are isolated from each other by a l/d-in. air gap. Each cup is closed with a tapered cover made from '/Z-in. thick Lucite. Each cover is provided with a central hole to accommodate the barrel of a B and D hlultifit syringe used for reagent addition, a smaller hole to accommodate a Type 5lA75 thermistor (Victory Engineering Corp., Springfield, K.J.) held in place with a small neoprene stopper, and three small glass tubes that support and provide electrical connection to a resistance heater. The entire arrangement is rigorously symmetrical around the midline of the inner enclosure. Syringes of several different sizes were employed, and bushings of several thicknesses made from l-in. Lucite rod were made l,o support them at such a height that almost all of the liquid in the syringe was submerged beneath the level of the surrounding liquid in the cup during the initial thermal equilibration. An 18-gauge Teflon needle (The Chemical Rubber Co., Cleveland, Ohio, catalog number 0312/93) cut off 5 mm below the hub was affixed tio the tip of the syringe; this needle and the tip of the sgringe were filled with air before the syringe was placed in position, thereby guarding against leakage of reagent out of the syringe during the thermal equilibration. Two identical resistance heaters of about 20 ohms each were made by tightly coiling 80-cm lengths of 3-mil platinum wire on a mandrel having a diameter of 1 mm. Each end of each coil was welded to a short piece of 15mil diameter platinum wire sealed through the end of a short length of 3-mm i.d. Pyrex tubing firmly mounted in the stopper of a cup. A few mm of mercury in each of these tubes seived to make electrical connection to the source of current. A small hook of 16-mil platinum
3803
wire at the end of a third Pyrex tube was used to support the heater at about its midpoint. The value of the Xewtonian heat-exchange constant obtained with this apparatus was typically about 2 X sec-'. Most of the heat exchange occurs by conduction through the wires leading from the heaters to the external constant-current generator used to energize them ( E was about 3 X 10-5 sec-I when these wires were removed). Since this portion of the apparatus serves only to provide a value for the thermal capacity of the reaction vessel for use in calculating the enthalpy change involved in the reaction, quite slow reactions could be followed by removing these leads if the values of A H were uninteresting. The inner enclosure containing this apparatus is a rectangular box, 20 X 10 X 14 in. (w X d X h) made from 1/2-in.thick Lucite. Its front face has a rectangular cutout 10 X 8 in. providing access to its interior; during an experiment this is covered with a 12 X 10 X l/z-in. Lucite plate held in place by six cylindrical Lucite knobs drilled and tapped to accommodate nylon screws cemented into the front plate of the enclosure. One small hole on the midline of this enclosure serves to lead all of the wires out of it and is sealed with silicone putty. Two l/Z-in. Lucite rods, one directly above the plunger of each syringe, projecting through both the inner and outer enclosures and passing through tightly fitting oiled felt bearings attached to the outsides of both enclosures, are used to discharge the contents of both syringes simultaneously, and are withdrawn several cm immediately afterwards so as to isolate the plungers from the surroundings. The inner enclosure is supported on four l-in. diameter Lucite rods 4.75-in. long resting on, and cemented to, the floor of the outer enclosure. This is a doublewalled box, 32 x 22 X 26 in. (tu x d x h) outside, made of 1/2-in. thick Lucite sheets separated by a '/&~. space. Provision is made for circulating thermostated water through this space for measurements at various temperatures. In the work reported here, however, all of the measurements were made at 25" and the constancy of the laboratory temperature sufficed to permit using an air-jacketed enclosure. A l-in. diameter Lucite separator in the space directly beneath each cup was drilled to provide access for a l/z-in. diameter hardwood shaft having a bar magnet attached to its top and fixed in place by Teflon bearings. The shafts are so adjusted that the bar magnets are a few mm below the bottom of the inner enclosure, so that stirring is accomplished without thermal contact with the surroundings, and are driven by a single variable-speed motor through a train of belts and pulleys. These expedients so nearly equalize the energies liberated by stirring the two solutions that there is no perceptible drift of the difference between their temperatures. The front of the outer enclosure is provided with a double-walled porthole having a separate inlet and outlet for thermoVolume 73, Number 11
NoEember 1.969
3804 stated water; this provides access to the inner enclosure and is held in place by nylon screws and Lucite knobs similar to those used to retain the cover of the inner enclosure. The resistances of the thermistors were compared by means of a carefully shielded dc Wheatstone bridge employing matched 100,000-ohm standard resistances whose temperature coefficients were negligibly small. The bridge voltage was usually 2.68 V, obtained from a pair of mercury batteries; it was measured with a precision potentiometer at frequent intervals to permit computing differential temperatures from recorder deflections. Corrections for the nonlinearity of the relation between these are easily applied but were usually negligible in this work. The power dissipation in each thermistor was approximately 18 p W . In a few experiments intended to examine the effects of power dissipation a bridge voltage of 8.05 V was employed. Although the temperature of each thermistor must then have been well above that of the liquid surrounding it, no effect on the mean recorded differential temperature could be discerned. However, the noise level increased more than tenfold, evidently because of increased thermal convection. As Farm and BruckensteinZ6also encountered substantial convection with power levels exceeding about 18 p W although only a single drop of solution was in contact with each of the thermistors in their differential vapor-pressure apparatus, it appears that this convection may be confined to a very thin layer of liquid in the immediate vicinity of the thermistor rather than arising in the gas phase as they suggested. The unbalance voltage of the bridge was recorded on a Model SRLG Y-T recording potentiometer (E. H. Sargent & Co., Chicago, Ill.), which provided sensitivities up to 0.37 mV full-scale and had an input impedance large enough to obviate significant loading of the bridge. N o damping was ever employed beyond the minimum needed to suppress pen jitter at the sensitivity being employed with the input terminals of the recorder shorted. The temperature coefficients of resistance of the thermistors employed were evaluated from the resistances measured at a number of temperatures between 25 and 30" and were found to be (-4,660 deg-' at 25". With a bridge voltage of + 0.013) X 2.68 V this corresponds to a full-scale sensitivity of 11.57 mdeg, or 46.3 pdeg/mm, so that temperature differences as small as 5-10 pdeg should be observable. A precision of about +15 pdeg in measurements of differential temperatures was obtained in this work (cf. Table I) even though the maximum sensitivity of the recorder was not employed. Indeed, the precision of measurement seemed to be simply that of measuring the pen deflection on the recorded chart. Table I illustrates the precision and sensitivity attained in a dynamic system. The experimental data in the first two columns were obtained from the final cooling portion of the curve recorded for a reaction in which the overall temperature The Journal of Physial Chemistry
T.MEITEG,L. MEITES,AND J. N. JAITLY Table I : Precision of Differential Temperature Measurementsa
1946 ( = t * ) 2246 2396 2546 2696 2846 2996 3146 3296 3446 3596 3746
16.008 15.415 15,125
16.039 15.414 15.112
14.840
14.815
14.524 14.236 13.978 13.666 13,420 13.151 12.881 12.640
14.524 14.238 13.958 13.684 13.415 13.152 12.893 12,640
-31
+I +I3 +25
0 -2 +2o - 18
+5 -1
- 12 0
Std dev: =t15.5 pdeg a See text for experimental details. The values of ATcalodwere obtained from eq 1 with AT* = 16.039 mdeg and e = 1,323 X 10-4 sec-1.
change was just over 16 mdeg. These were fitted to the Newtonian equation In AT = In AT*
- e(t
- t*)
(1)
where AT is the measured differential temperature t sec after the addition of reagent, t* is an arbitrarily selected time at which the reaction is considered to be complete, and AT* represents the differential temperature at that instant. The values of AToalodin the third column of the Table were computed from the least-squares "best" values of AT* and the heat-exchange constant e; the differences in the last column represent the deviations from perfect internal consistency. As these data were obtained with a recorder sensitivity of 125.5 pdeglmm, their standard deviation corresponds to one of k0.12 mm in reading the pen deflection. Another test of internal consistency leading to the same conclusion is described in connection with the computation of AR,,,,,, below. To achieve such a result the noise level must be extremely low. Figure 1, a portion of the record obtained in a typical experiment, illustrates the noise level attained. This arose in part from the rotation of the magnetic stirrer, but by judicious choice of stirrer speed and rigorous dehumidification of the laboratory atmosphere the total recorded noise could be kept below f1 pV at worst and could generally be made invisible. From a curve given by Farm and BruckensteinzBit appears that the noise level in their differential vapor pressure apparatus was approximately A 0.5 pV, closely comparable with ours. These results lend further support to the slowly growing belief that properly stabilized thermistors are capable of far better precision than has been thought. One (26) R. J. Farm and S. Bruckenstein, Anal. Chem., 40, 1651 (1968).
DIFFERENTIAL ‘THERMOMETRIC TECHNIQUE
FOR
I 0
120
3805
RATEMEASUREMENT
I 240
360
480
I 600
720
Time, sec.
Figure 1. The unretouched initial portion of the curve obtained for the reaction between 0.0825 F sodium hydroxide and 4.72 mF ethyl acetate. The horizontal line preceding t = 0 represents the virtual attainment of thermal equilibrium before the addition of the reagent. The full-scale sensitivity and nominal pen speed of the recorder were 2 mV and 1 sec, respectively.
extreme view on 1-hissubject was expressed by BoucherJZ7 who wrote ‘(Underthe best conditions of operation. . . it should be possible to achieve long-term stability in temperature measurement, using a thermistor bridge, of =k0.01-0.02 deg.” However, we have recorded differential curve3 for many hours with two thermistors side by side in the same solution without observing any transient difference even as large as 20 pdeg. JordanlZswriting about the use of 2000-ohm thermistors at power levels of about 125 pLwl stated that “ZrTo useful purpose could be served by improving the accuracy of the recorder beyond 10 pVZ9.. . because random fluctuations on the order of 10 pV are invariably apparent on thermometric titration curves.” This is about the same as the noise level we obtained with a power of 160 pW and ascribed, as noted above, to thermal convection arising from excessive heating of the thermistors; in thermometric titrations there may also be momentary variations in the efficiency with which the incoming stream of reagent is distributed throughout the solution being titrated. At the other extreme, Tyrrell and Beezer30 felt that prior amplification of the unbalance voltage of the bridge should make “temperature changes of the order of deg detectable without difficulty. Boyd, et and Nancollas and Hardy32report having just attained such a sensitivity in work with an ac-energized thermistor bridge and phase-sensitive detector amplifier. Farm and BruckensteinZ6 originally claimed a precision of
about =t20pdeg and report 3 3 having further improved reported this to about =kt8 pdeg. illtiller and St01ten~~ sixteen years ago that they were able to detect temperature differences as small as 20 pdeg by using a vacuumtube voltmeter to observe the unbalance voltage of a dc bridge containing a single 100,000-ohm thermistor, and gave data corresponding to an average uncertainty of only about 60 pdeg in measurements made over periods of 50 min. Thermistors having nominal resistances of 100,000 ohms at 25” were chosen for this work to minimize the power dissipation resulting from the use of a convenient bridge voltage. Twenty-one thermistors were immersed in still water in a thermostat operating at 25 & 0.002” and a steady dc current of 10 p A was passed through them. Their resistances were measured (27) E. A. Boucher, J . Chem. Educ., 44, A935 (1967). (28) J. Jordan, “Thermometric Enthalpy Titrations,” in “Treatise on Analytical Chemistry,” I. M. Kolthoff and P. J. Elving, Ed., Interscience Publishers, New York, N . Y . , Part I, Vol. 8, 1968, p 5206. (29) This corresponds to 250 pdeg under the conditions being discussed. (30) H. J. V. Tyrrell and A. E. Beezer, “Thermometric Titrimetry,” Chapman and Hall Ltd., London, 1968, p 40. (31) S. Boyd, A. Bryson, G. H. Nancollas, and K. Torrance, J . Chem. SOC., 7353 (1965). (32) G. H. Nancollas and J. A. Hardy, Rev. Sci. Instrum., 44, 290 (1967). (33) S. Bruckenstein, personal communication, 1969. (34) R. H. Mtlller and H . J. Stolten, Anal. Chem., 2 5 , 1105 (1953).
Volume 75, Number 11 November 1969
3806 periodically over many months and corrected to 26.000” by employing the individual values of their temperature coefficients measured subsequently. The resistances generally fell during the first week, rose for 1-3 weeks thereafter, and then decreased to steady values (which were usually above, but occasionally below, the initial ones) reproducible within =k0.003%. With the aid of these data it was possible to select three matched pairs of thermistors. Each pair had resistances equal within 0.2 per cent at 26”, and one also had almost identical temperature coefficients of resistance. As thermistor mismatch would merely cause the two solutions to be unequally heated by the power dissipation in the thermistors, and as with the bridge voltage used here the power dissipation would change the temperature of 100 ml of solution only 14.6 pdeg/hr even if it were wholly uncompensated, the use of matched thermistors mas merely a minor convenience in that it made trimming the standard resistors in the bridge unnecessary. I n use each thermistor is subjected to a constant current of 13 pA which is never interrupted. The currents of 100-1000 pA recommended by JordanI6 for stabilizing 2000-ohm thermistors correspond to power dissipations ranging from 0.02 to 2 milliwatts, as against the 0.017 mW used here; Muller and StoltenZ1used a power of 1.26 mW to stabilize 100,000-ohm thermistors. It is possible that the very precise differential temperature data obtained in this work are due in part to this very low power level (which was of course chosen to eliminate deleterious effects arising from self-heating) or that thermistors having resistances of the order of 100,000 ohms are more stable than those having lower ones.
Technique of Operation An experiment is begun by pipetting equal volumes of solvent into two clean dry cups containing magnetic stirring bars, adding a known amount of one of the desired reactants to one, and adding an equal volume of solvent to the other. We chose to investigate the potentialities and limitations of the technique by studying the well-known alkaline hydrolysis of ethyl acetate, and always placed the ester in the reaction vessel to eliminate the danger of absorption of carbon dioxide by strongly alkaline solutions exposed to the atmosphere for prolonged periods. This is an obvious precaution but one that seems to have been ignored by several of those who have investigated this reaction. Reagentgrade ethyl acetate was used without purification; it was measured into the reaction vessel by means of a small glass syringe that was weighed before and after making the addition. The weights of ethyl acetate varied from about 10 to 70 mg in different experiments. Two identical syringes (1-, 2-, or 6-rn1, depending on the volume of reagent desired) were then charged with as nearly as possible identical volumes of 5.57 F sodium hydroxide. This solution had been prepared by diluting The Journal of Physical Chemistry
T.MEITES, L. MEITES,
AND
J. N. JAITLY
a 50% solution, from which the suspended sodium carbonate had been allowed to settle with water freed from dissolved carbon dioxide. It was standardized by weight against primary-standard grade potassium hydrogen phthalate and stored in a polyethylene bottle carefully protected from atmospheric carbon dioxide. An %gauge Teflon needle was permanently inserted through the stopper of this bottle and n7as closed with a small Teflon stopFer except when a syringe was being filled through it. The concentration of the stock sodium hydroxide solution was chosen with the aid of heat-of-dilution data tabulated by Parker, 36 which showed that this choice minimized the heats of dilution to the desired concentrations in the reaction mixture. The amounts of sodium hydroxide added to the two caIorimeter vessels were always equal within *5%) and the difference between the heats of dilution never corresponded to a differential temperature in excess of 100 pdeg. After weighing the filled syringes, they were inserted in their respective cups, the inner and outer enclosures were sealed, and the apparatus was allowed to come to thermal equilibrium with the stirrers on and the bridge connected to the recorder. When the differential temperature became constant, the Lucite rods above the plungers of the syringes were depressed rapidly and as nearly simultaneously as possible to begin the reaction, and the recording was allowed to proceed without further attention for something like 20 half-times. The mixing time was typically found to be 2-5 sec. This had no untoward effects in the experiments reported here, primarily because a somewhat unusual form of the second-order rate equation was employed in the computations. However, it would certainly be undesirably long if the half-time for the reaction mere only a fern sec13’and more efficient stirring would then be essential. This relatively long mixing time is believed to be due primarily to the fact that the density of the sodium hydroxide solution was over 20% above that of the solution to which it was added; on being ejected from the syringe, much of the reagent must have gone directly to the bottom of the cup, and it is not unreasonable that several sec should have been required to effect thorough mixing in the face of this difference of densities. The weight of sodium hydroxide solution remaining in the tip of the syringe and the Teflon needle after bottoming the plunger was determined separately and subtracted from the weight initially taken to find the weight actually added. Because the Newtonian cooling constant is finite, the (35) I. M . Kolthoff and E. B. Sandell, “Textbook of Quantitative Inorganic Analysis,” 3rd ed, The Macmillan Company, New York, N. Y . , 1952, pp 526-527. (36) V. B. Parker, “Thermal Properties of Aqueous Uni-univalent Electrolytes,” National Standard Reference Data Series, National Bureau of Standards 2, Washington, D . C., Apr 1, 1965. (37) M. Caselli, A. Cavaggioni, and P. Papoff, Talanta, 15, 1335 (1968).
DIFFERENTIAL THERMOMETRIC TECHNIQUE FOR RATE MEASUREMENT recorded diff ererttial temperature always passed through a m a ~ i m u m . ~ Shortly ~ - ~ ~ after it had done so, the recorder was set to its lowest chart speed (0.2 in./min) and the curve was recorded for 15-20 min more. Typical data obtained during this interval were shown in Table I; they were used t o evaluate E in eq 1. The recorder was then occasionally reset to a faster chart speed and an accurately known current between 6 and 60 mA, obtained from either a Metrohm E211 “Coulometer” or a Leeds and Northrup Type 7960 Coulometric Analyzer, was applied to the heater in the reaction vessel for a measured length of time. The recording was continued for some time after the constant-current generator had been turned off, thereby providing a second interval during which E could be evaluated. These data could be used t o obtain a value of the thermal capacity of the reaction vessel and its contents and thus to calculate the enthalpy change involved in the reaction. In the present work. this was rarely done because the value of AH was of little interest; the few values that were secured were in rough agreement with, but always distinctly below, that expected. This is attributable to the less of a little of the ester by volatilization during the protracted initial approach to thermal equilibrium.
Calculations Second-order irate constants were computed with the aid of a Hewlett-Packard Model 9100A programmable calculator. Copies of the programs and directions for their use may be obtained from the authors. Values of the recorder deflections AR (in arbitrary chart divisions and in increments of 2-5 per cent of the maximum deflection obtained) and the corresponding times t were read from the recorded chart. If the unbalance voltage of the bridge becomes appreciable the values of AR should be corrected for deviations from linear dependence on differential temperature. Beginning at a time t* when the reaction is judged to be complete, the values of t and AR are fitted to eq 1 by a leastsquares calculation to evaluate the heat-exchange constant E. Corrections for heat exchange during the reaction interval are then applied by numerical integration, using the equation ARn,corr =
ARn
E
-t2
n 2=1
(ARi
+ ARi-J(ti
- &-I)
(2)
in which AR, and ti are the observed deflection (corrected if necessary for bridge non-linearity) and time, respectively, at the ith measured point, ARo and to are both zero, and AR,,,,,, is the deflection that would have been observed a t the nth point in the absence of heat exchange. As long as E is less than about a tenth of the pseudo-first-order rate constant, the integrated heatexchange correction will be less than about 5y0until the reaction is about 99% complete. The values of ARC,,, approach constancy as the reaction approaches completion. In a typical experiment,
3807
25 successive values of ARC,,, computed in the interval 508 I t I 1234sechad amean (denoted below as AR,,,,,,) of 63.950 and a standard deviation of 0.056 division. The latter figure corresponds to an uncertainty of 0.14 mm in the measured deflection and to one of 17.8 pdeg in the differential temperature; the first of these uncertainties was essentially the same in all of our experiments, while the second naturally varied with the recorder sensitivity employed. Values of the ratio ARcorr/AROorrlm are taken to be proportional to the fraction of the reaction that has taken place. Since the finite mixing time leads to an uncertainty in the instant at which the reaction is initiated, which might be appreciable if the reaction is fast, it is convenient to begin the calculations at an arbitrarily chosen time t’ where the irregularities accompanying mixing have subsided. When the reaction was fast enough to require the use of the highest chart speed of the recorder, t’ was usually between 3 and 6 sec; for slower reactions it was taken for convenience at the first vertical division of the chart crossed by the pen after the start of the reaction. Assuming that the value of AR’corr at the instant t = t‘ is proportional t o the amount of the ester ( = A) that has reacted at that instant, which implies that the difference between the heats of dilution in the two vessels is negligibly small but does not require that the value of t’ be known, then integrated rate equation for a second-order reaction may be written in the form
The equivalent form for a first-order reaction would of course be
In ( A R c o r r , , -
ARcorr)
-kCo(t - t ‘ ) In
(ARcorrjm
+
-
AR’corr)
(4)
+
Equation 3 is of the form y = az b with a = k(CBO - CAO). Values of a were computed from a leastsquares program, employing all of the data obtained between t‘ and the instant at which the reaction was 90% complete. The choice of termination times was arbitrary but clearly reflected a deviation from straightforward second-order kinetics: the computed rate constant invariably drifted upward during the last 10% of the reaction. It is by now well known24s38 that the alkaline hydrolysis of ethyl acetate does not exactly follow the simple second-order rate law: in fact, data obtained in the presence of excess base yield second(38) H. Tsujikawa and H. Inoue, Bull. Chem. SOC.Jup., 39, 1837 (1966).
Volume 73, Number 11
November 1969
T. MEITES,L. MEITES, AND J. N. JAITLY
3808
20
0.135
40
97.5
60
c
'0
e:
.:
7-
0.130
0.125
0
I
I
I
I
50
100 Time, sec
150
200
Figure 2. Plot of the second-order rate constant k , computed as described in the text, against the elapsed time (on the lower abscissa scale) and the percentage of the ethyl acetate reacted (on the upper abscissa scale) for the reaction between 0.1498 F sodium hydroxide and 6.40 mF ethyl acetate.
order rate constants about 20% larger than those obtained with excess ester or with equivalent concentratioris of the two reactants.
Results Figure 2 is a typical plot of the computed second-order rate constant against both the time (on the lower abscissa scale) and thc fraction of the ester that has reacted, Le., the ratio AR,o,,/AR,o,,,, (on the upper abscissa scale). After a short initial period during which the value of k fluctuates widely because it is based on measurements of small temperature differences on a chart obtained at a recorder sensitivity chosen for convenience in measuring the larger ones obtained later in the reaction, a value stable within a few tenths of a per cent is obtained. Using the value ( k = 0.1309 1. mol-' sec-l) finally selected to compute the values of ARC,,, that would have been obtained if the data had been perfectly consistent internally, it was found that the standard deviation of the 29 experimental points measured in the range 6 5 t _< 130 sec was 0.21 mm of chart deflection or 53 pdeg in the differential temperature. Much of the difference between the latter figure and the one shown in Table I is due merely to the difference of recorder sensitivity. The upward drift of k as the reaction nears completion is consistent with results obtained by Tsujikawa and Inoue38 and by Papoff and Z a m b ~ n i n . ~ The ~ former authors observed a downward drift of k as the reaction progressed in the presence of excess ester; the latter observed an increase of k on increasing the concentration of sodium hydroxide when this was in excess. Superimposed on this variation of k with the ratio of the concentration of base to that of ester is the expected variation of k with ionic strength. I n work with solutions containing 0.50 F sodium hydroxide, Papoff and Z a m b ~ n i nfound ~ ~ that k decreased uniformly with increasing concentration of sodium chloride between 0 and 1.5 F , and asserted that their data agreed with those of
*
The Journal
of
Physical Chemistry
S ~ h a d e . Extrapolation ~~ to p = 0 gives k = 0.145 1. mol-' sec-I, and our values are in approximate agreement with this at the lowest concentrations (0.0170.035 F ) of sodium hydroxide. It is interesting to note that the values of k at the lowest concentrations of base parallel those of Arrhenius140who found that k decreased slightly when the concentration of sodium hydroxide was increased from 0.003 to 0.025 F , and then rose on increasing the concentration of sodium hydroxide further to 0.05 F . However, Arrhenius' values of k are uniformly lower than ours because he obtained them with equal concentrations of base and ester. Our values are in good agreement, with that deduced from the results of Amis and Siege14' by extrapolating a plot of In L us. 1/D to D (the dielectric constant) = 78.5 and correcting to a temperature of 25". Table I1 summarizes the values we have obtained, and also includes for comparison those obtained by Papoff and Zambonin under comparable conditions. It may conservatively be concluded that the technique
Table I1 : Second-Order Rate Constants for the Alkaline Hydrolysis of Ethyl Acetate at 25' Overall temperature
Initial conoentretions EtOAc,
NaOH, F
0.01718 0.0348 0.0337 0.0697 0.0709 0.0728 0.0743 0.0825 0.1079 0.1498 G . 1595 0.2208 0.267 0.2744 0.502 0.505 1.01 a
mF
2.35 6.75 6.73 4.11 10.09 2.60 6.58 4.72 6.31 6.40 1.49 6.57 10
6.26 12.1 16 16
rise ___ ( sA T o o ~ n m ) ,
mdeg
19.6 56.1 68.3 39.5 94.0 21.8 66.5 41.0 64.8 64.2 15.6 68.4 ... 65.0
... ... ...
t'/zl
sec
285 153 158 78 81 74 74 64 51 36 32 24 20.3 18.3
... 10.2 4.9
k , 1. mol-' aec-1
0.152 0.144 0.136 0.131 0.130
0.1305 0.1315 0.135 0.131 0,131 0.138 0.132 0 . 131a 0.140 0 . 137a 0.137" 0,141"
Value reported by Papoff and Zambonin.lz
is capable of yielding rate constants having accuracies and precisions of a few per cent or better over the ranges of half-times and overall temperature rises shown jn Table 11. Further work now in progress with other systems is aimed at revealing the smallest values of both of these parameters that can be handled. (39) E. Bchade, Thesis, Gniversitat des Saarlandes, Saarbrucken, 1965. (40) S. Arrhenius, 2. Phys. Chem., 1 , 110 (1887). (41) E.S. Amis and €3. Siegel, J. Amer. Chem. Soc., 72,647 (1950).
3809
DIFFERENTIAL HEATOF ADSORPTIONAND ENTROPY OF WATER Acknowledgment. This investigation was supported by PHS Research Grant No. GM 16561 from the National Institute of General Medical Sciences. It is a
pleasure to acknowledge the help and advice given us by Professor Kenneth R. Jolls during the early stages of this work.
Differential. Heat of Adsorption and Entropy of Water Adsorbed
am
Zinc Oxide Surface
Iby Mahiko Nagao and Tetsuo Morimoto Department of Chemistry, Faculty of Science, Okayama University, Tsushima, Okayama, Japan (Received April 1, 1969)
The adsorption isotherm and the heat of immersion isotherm of water were measured on two ZnO samples pre1,reateda t 250 and 450°, respectively. B y combining these two kinds of data, we obtained the differential heat of adsorption, the free energy of adsorption, the entropy of adsorption, and the site-energy distribution for the system ZnO-HzO. A clear hump appeared a t a region of moderate relative pressure of water adsorption isotherm, but we could not find any corresponding anomaly in other properties examined here. Only in the curve of the differential entropy of adsorption could a slight abnormal change be discovered, which seemed to have some connection with the hump of adsorption isotherm. The site-energy distribution curves derived by differentiating the plot of the differential heat of adsorption V S . the amount of adsorption showed two kinds of peaks; one corresponds to a group of physisorption sites with energies less than 5 kcal/mol HzO, and the other to that of chemisorption sites with energies of 20-25 kcal/mol HzO.
Introduction By combining the data of the heat ol immersion and of the adsorption isotherm on a given adsorbentadsorbate system, we can get useful information about the interaction between the solid surface and molecules. One of the most important ways to study the adsorption state is to obtain the entropy of adsorption. I n 1952, Jura and Hill' introduced the equation which enables us to calculate the entropy of adsorption from the measurements of the heat of immersion and the adsorption isotherm. Since then, several studies on the entropy of adsorbate molecules have been published on such adsorbents as graphon,2 a ~ b e s t o s Fe203,4 ,~ A1~03,~ and Ti02.6 This method is distinguished by the point where the data obtained refer to the net heat of adsorption. The present authors have investigated the interaction between the surfaces of ZnO and water molecules through the measurements of the heat of immersion' and of the desorbability of chemisorbed water.8 As a result, the characteristic feature has been found that the adsorption isotherm of water on ZnO shows a hump at a region of moderate relative pressure of water, which has not been discovered on any polar adsorbent-polar adsorbate systems. The mechanism of this phenomenon is the problem to be worked out hereafter. The pur-
pose of the present work is to examine whether, in the case of ZnO-HzO system in which a hump occurs in a moderate pressure region of the adsorption isotherm, a noticeable change appears in the heat of immersion isotherm and related properties. When the surfaces of metal oxides are exposed to water vapor, the chemisorption usually occurs in addition to the physisorption, each of both adsorption amounts being uncertain unless special precaution is paid. In the past investigations cited above, the energetics has been developed without analyzing in detail the role of chemisorption. In the present work, however, the contribution of chemisorp(1) G. Jura and T. L.Hill, J . Amer. Chem. SOC.,74, 1598 (1952). (2) G. J. Young, J. J. Chessick, F. H. Healey, and A. C. Zettlemoyer, J . Phvs. Chew, 58,313 (1954). (3) J. J. Chessick, A. C. Zettlemoyer, F. H. Healey, and G. J. Young, Can. J . Chem., 33,251 (1954). (4) F. H. Healey, J. J. Chessick, and A. V. Fraioli, J. Phys. Chem., 60, 1001 (1956).
(6) R. L. Venable, W. I€. Wade, and N. Hackerman, ibid., 69, 317 (1965). (6) M. Miura, H. Naono, T. Iwaki, T . Kato, and M. Hayashi, Kogyo Kagaku Zasshi, (J. Chem. SOC.Jap., Ind. Chem. Sect.), 69, 1623 (1966). (7) T. Morimoto, M. Nagao, and AM.Hirata, Kolloid-2. Z . Polym., 225, 29 (1968). (8) T. Morimoto, M. Nagao, and F. Tokuda, Bull. Chem. SOC.Jap., 41, 1533 (1968).
Volume 73, Number 11 November 1969
