Calorimetric Investigations of Organic Reactions. II. A New Calorimeter

C.4LORIMETRIC ISVESTIGATIONS OF ORGANIC REACTIONS

127

obtained. Approximate agreement is obtained also on comparison of differential entropy change values. 8. I t is found that the heating treatment not only stabilizes each paper insofar as the effect of previous drying history upon moisture adsorption is concerned, but also decreases to almost indetectable amounts the differences in moisture adsorption characteristics between the two papers, one example being the shift of the curves of log A and l / n (the constants of the equations for the isotherms) against temperature toward common values for the two papers. REFERES'CES (1) HOTJTZ . ~ N DMCLEAN: J. Phys. Chem. 43, 309 (1939). (2) KATZ:Proc. . h a d . Sci. Amsterdam 13, 958 (1910). (3) ~ ~ U R P HA AY D K O H M A N : Paper presented a t the annual meeting of the Conference on Electrical Insulation of the National Research Council, Pittsburgh, 1938. (4) S A L L E Y : Textile Research 6, KO.11, 493-508 (1935). (5) S P E A K M A S A N D STOTT: J. Textile Inst. 27, T183 (1936). (6) S T A i m A X D LOUGIIBOROUGA: J. Phys. Chem. 39, 121 (1935). (7) URQUHART A N D W I L L I I M S : J. Textile Inst. 16, T138 (1924). (8) U R Q C H A R T A N D W m L I A a r s : J. Textile Inst. 20, T125 (1929). (9) VOLBEHR: Thesis, University of Kiel, Germany, 1896.

CALORIMETRIC ISVESTIGATIONS O F ORGASIC REACTIOSS. I1

A

S E W CALORIMETER.

THE hfUTAROTATION

O F CY-

AND P-d-GLVCOSE'

JCLI..IN AI. STURTEVAXT Department of Chemistry, Y a l e Cnwersaty, ,Vew Hacen, Connecticut Receaved A\rocember 89, 19.30

In the first paper (13) of this series there was described a calorimeter for determining the velocities and heats of liquid-phase reactions having half-times of several minutes to several hours. This calorimeter was unstirred, so that it was impossible to initiate the reactions within the calorimeter. Because of this limitation the measurement of heats of solution was impossible, and direct comparison of the heats of reaction obtained with those calculated from combustion data could not be made. In the present paper a new apparatus is described which remores this limitation. Since considerable elaboration of the apparatus was necessary P a r t of the material i n this paper was presented a t the Ninety-seventh Meeting of the American Chemical Society, held in Baltimore, Maryland, .4pril, 1939.

128

JULIAN M. STURTEVANT

to provide a means for starting reactions within the calorimeter, it was decided to increase the sensitivity so that measurements could be extended to more dilute solutions and to reactions giving smaller heat effects. The general method employed in the earlier work has been continued here. The rate of heat evolution or absorption is measured by observing the temperature changes in an adiabatic calorimeter. From these observations the rate of the reaction is calculated; the rate is used to extrapolate the temperature readings back to the instant of mixing the reactants and forward to the completion of the reaction. The heat capacity of the system is determined electrically a t the end of the reaction; this gives all the data necessary for calculating the heat of the reaction. The heat of mixing is given simply from the difference between the observed temperature immediately before the start of the reaction and the (extrapolated) temperature a t the start. The new apparatus has been tried out with measurements on the heat of solution, and the rate and heat of mutarotation of a-and 0-glucose. These mutarotatlon reactions serve as a critical test of the apparatus because of their small heat values. At 25°C. a-glucose evolves 0.97 cal. per gram and @-glucoseabsorbs 0.57 cal. per gram. These reactions have been measured a t concentrations of about 5 per cent. DESCRIPTION OF APPARATUS

In the design of a calorimeter to be used for measuring such slow heat effects that extrapolation to the completion of the effect is necessary, two important considerations arise: In the first place, the calorimeter should be as nearly adiabatic as possible. The t w o main sources of heat loss from calorimeters are usually direct heat exchange with the surroundings and evaporation of the contents of the calorimeter. In the present design, an adiabatic jacket of aluminum, the temperature of which is automatically kept the same as that of the calorimeter, is used to keep direct heat losses very low. The calorimeter itself is tightly sealed by a rubber gasket SO that evaporation losses are completely eliminated. In the second place, the time lags betneen the temperature of the rcacting liquid and that of the temperature-measuring device should be small. To achieve this end, all non-metallic materials have been reduced to a minimum and include only three small rubber gaskets, a small rubber tube, and a small amount of paper and varnish insulation.

Calorimeter assembly The calorimeter (D, figure l ) , having a capacity of about 150 cc., is constructed of tantalum. It is closed by a tantalum cover carrying a dilution cup (B) also made of tantalum. A rubber gasket and twelve small screws are used to seal the cover tightly, and the dilution cup is held onto

CALORIMETRIC INVESTIGATIONS OF ORGANIC REACTIONS

129

the cover by eight tantalum screws through two rubber gaskets. Brass nuts (on the outside of the cover) are used with the tantalum screws so that they may be dissolved off with nitric acid if they show a tendency to “freeze” to the screws. Between the two rubber gaskets is a bellows (A) mounted on a disc and carrying a cylindrical cutter; the entire bellows assembly2 is made of platinum-iridium, all soldering being done with pure gold. The capacity of the dilution cup with the bellows in place is about 10 cc. The dilution cup is closed at the bottom by gold foil or other suitable material3 held in place by a snap ring (C), an appropriate gasket or sealing material being used if necessary. The dilution cup is opened a t the desired instant by about 10 pounds per square inch pressure, applied through a tube (E) which is connected by small rubber tubing, wrapped once around the outside of the adiabatic jacket (G), to the tube (H), the

i FIG.1. Calorimeter assembly

latter being connected by heavy-walled Neoprene tubing to a tank of nitrogen. The cutter on the bellows removes practically the entire bottom of the dilution cup. The small heat effect of this operation (about 0.007 cal.) is corrected for. The calorimeter is supported within an aluminum adiabatic jacket (G) by means of four fine steel wires, the two a t the bottom being in a plane perpendicular to the plane of the upper two. The wires are anchored in screws to permit adjustment of the tensions. A paper cylinder (F) protects the heater and thermel wires in the space between the calorimeter and the jacket.

* I n some of the experiments reported herein a brass bellows assembly was used. A t the low acid concentrations encountered, corrosion was prevented by a thin coat of glyptal varnish 3 Thin waxed paper has been found satisfactory in the absence of organir solvents. A very thin tissue similar t o Kleenex is paraffined a t about 160°C

130

*


The jacket is supported in a cast aluminum submarine (L) by means of Bakelite spacers. The submarine has two side arms, one of which carries a manifold (X) through which the various lead wires, eighteen in number, are brought out, tight seals being effected by filling the manifold with Picefn cement. The leads are of very flexible stranded cotton-covered copper wire and are coiled in two spirals of several turns each, one spiral containing thermocouple leads and the other heater leads. These spirals lead to binding posts above the level of the oil in the thermostat (see below), and effectively prevent breakage of the leads as a result of the oscillation of the submarine described below. From the binding posts the leads are carried in two shielded cables to the electrical instruments for measurement and control. The other side arm of the submarine contains a chromium-plated copper cylinder (J) within a silvered Dewar flask. The temperature of the copper cylinder serves as the reference temperature. The submarine is made vacuum-tight by hpiezon putty in all joints except at the top where a Neoprene gasket is used. It was hoped that the thermal isolation of the calorimeter could be improved by evacuating the system through a side arm (M); however, this proved to be impossible because of the very large heat effects produced by removal of the gases adsorbed and pocketed by the electrical insulating materials on the outside of the calorimeter. I t is helpful to evacuate the apparatus occasionally between runs in order to dry it out thoroughly to prevent surface electrical leakages. The submarine is supported on two bearings and is connected by a chain and sprocket drive to an oscillating mechanism, driven by a synchronous motor, which rocks it through 360 degrees with a frequency of 44 cycles per minute. This method of stirring the contents of the calorimeter has proven to be very effective, as mentioned in a later section. With water in the calorimeter the heat of stirring amounts to about 0.007 cal. per minute. An unexpected difficulty was encountered with this method of stirring. Sufficient E.5i.F. (as high as 0.4 microvolt) is generated by the motion of the thermocouple wires in the earth’s magnetic field to render it impossible to make accurate temperature readings during stirring. This trouble has been nearly but not completely eliminated by using an appropriate compensating coil centered around the axis of rotation of the submarine in series with each thermocouple. Even after this compensation was accomplished it was found to be preferable to stir only during the mixing of the reactants and the introduction of electrical energy into the calorimeter, except in the reactions a t 35°C.; the higher velocities encountered in these runs necessitated a brief stirring period preceding each reading. This procedure has the added advantage that the correction for the heat of stirring is kept smaller. The submarine is submerged in a 40-gallon bath of transformer oil, the

CALORIMETRIC INVESTIGATIOXS O F ORGANIC REACTIONS

131

temperature of which is controlled by a resistance thermometer-thyratron circuit4 (14),together with occasional manual adjustment during each run. A t intervals the E.M.F. of a five-junction thermocouple between the “cold calorimeter” (copper cylinder (J)) and the tube I is observed, and the setting of a low-resistance slide wire in series with one of the thermometers is changed to correct for any drift in the temperature of the oil bath. In this way the temperature of the bath can be held constant to about =k0.0005°C. with only infrequent attention. It is to be noted that this additional manual control is possible only with a regulator giving continous rather than off-and-on control. The oil bath is heated by two 36-in. Chromalox strip heaters. The half-time of the heat exchange between the oil bath and the cold calorimeter is about 5 hr. Since the difference between the temperature of the oil bath and that of the cold calorinieter will average very closely to zero, it is safe to assume that the cold calorimeter furnishes a sufficiently constant reference temperature.

Temperature measurements The temperature of the oil thermostat is measured by Beckmann thermometers which have been calibrated by means of a Bureau of Standards certified resistance thermometer, using an Eppley-Mueller bridge. These temperature measurements are thus accurate to 10.02OC. The temperature of the calorimeter relative to the cold calorimeter, and the temperature difference between the calorimeter and adiabatic jacket, are measured by twenty-junction copper-Advance thermels. The forty calorimeter junctions are made of t in. of 0.0008 by & in. Advance ribbon soldered to 1 in. of 0.002 by +g in. copper ribbon. The junctions lie flat on the outside surface of the calorimeter, being evenly distributed over it and insulated from it by a thin layer of vaiLiished paper. The twenty jacket junctions are also composed of Advance and copper ribbon, and are mounted on the outside of a thin chromium-plated copper cylinder which is pressed tightly against the inside of the adiabatic jacket. The coldcalorimeter junctions are made by soldering together the lead wires, S o . 32 Advance and S o . 36 copper, both double silk covered; they are reinsulated by fine cotton thread and are bound into a tight bundle and inserted into the larger of the holes in the copper cylinder (J),all excess space being filled with paraffin. The “main” thermel (calorimeter to cold calorimeter) and the “jacket” thermel (calorimeter to jacket) are both made in two halves, which may be opposed to each other to test for the presence of stray E . R ~ . F . ’ and s of The sensitivity of this circuit was doubled by using two resistance thermometers (made of nickel wire wound on wooden strips and exposed directly to the transformer oil) in opposite arms of the A.C. Wheatstone bridge.

132


temperature irregularities over the surface of the calorimeter and jacket. The E.M.F.’S of the thermels are observed with a Leeds and Northrup “HS”narrow-coil galvanometer by means of a telescope and scale, the latter being located 3 meters from the galvanometer. The main thermel is connected in series with a special thermal E.M.F.free potentiometer (Leeds and Northrup), having a range of 550 microvolts in steps of 5 microvolts. ‘ In the galvanometer circuit there are also suitable ballast resistors to secure proper damping of the galvanometer, series reof full sistors and shunts to enable using the galvanometer at p6 and sensitivity, and switches for selecting the desired thermel and sensitivity. The resistors are bifillar windings of Manganin, and the switches are solid copper 60-degree knife switches; all resistors and switches are immersed in transformer oil in a draft-free, dehumidified box, the switches being manipulated by means of arms extending outside the box. The potentiometer is also enclosed in this box. The zero point of the galvanometer is observed by connecting it to a Manganin resistor in the oil bath, the leads from which are carried in the same shielded cable as the thermel leads. All the usual precautions in regard to shielding the low-voltage circuits against leakage currents have been taken, though there is evidence that small leakage currents are still present, probably arising mainly within the calorimeter assembly where proper shielding from the heater circuits is impossible. It is important to note that no accurate calibration of the thermels or the potentiometer is needed, unless one wishes to determine heat capacities. In connection with the reaction rate and heat determinations,.all temperature measurements are left in terms of microvolts, and the heat capacity of the calorimeter plus the reacting system is measured in terms of joules per microvolt. I t is, however, essential that the E.M.F. of the main thermel be a linear function of the temperature difference over a range of a few tenths of a degree, and that the potentiometer coils have the proper resistance ratios, An approximate thermel calibration is needed in connection with small correction terms described in the first paper (13) of this series; such a calibration is easily made by determining the heat capacity in joules per microvolt of the empty calorimeter, and of the calorimeter filled with a liquid of known heat capacity. Obviously this calibration also allows the determination of relative heat capacities, but with inferior accuracy, since the value of the heat capacity of the empty calorimeter cannot be accurately measured. Heater circuits The calorimeter heater is a bifillar winding of 0.0008 by & in. Advance ribbon, wound over the thermocouple junctions on the outside of the calorimeter and insulated from them by thin varnished paper. The heater

CALORIMETRIC INVESTIGATIONS O F ORGANIC REACTIONS

133

is supplied with copper potential and current-carrying leads in such a manner as to eliminate any significant error due to liberation of heat in the leads. The heater is connected in series xith a 50-ohm resistor (calibrated on an Eppley-Mueller bridge) and a variable resistor. The voltage drops across the heater and the 50-ohm resistor are measured by means of a “Queen” potentiometrr (Gray Instrument Company) and an Eppley standard cell calibrated on an Eppley potentiometer against the laboratory standard set of six cells. Provision is made for discharging the &volt battery used as heater supply through a dummy resistor until the heater is turned on. The adiabatic jacket is heated by two independent bifillar windings of Advance ribbon, the heaters being distributed over the outside surface of the various parts of the jacket in proportion to the weights of these parts. The heaters are each connected to the secondary of a 6-volt transformer, the primary voltage of each transformer being independently adjustable from 0 to 130 volts by means of an autotransformer. One heater circuit is opened or closed manually, while the other is automatically controlled as described bel0~7.5

Adiabatic control A switch is included in the thermel circuits which allows the jacket thermel to be connected in series with a second Leeds and Korthrup “HS” narrow-coil galvanometer. Light is reflected from the mirror of this galvanometer, falls on a spherical mirror 2 meters away, and is reflected onto a photocell placed a t the focus of the spherical mirror. The edge of a movable shutter in front of the mirror determines the position of the galvanometer mirror a t which the photocell is actuated. This arrangement eliminates any trouble due to overshooting, since the reflected light is always on the photocell unless blocked off by the shutter; the intensity rather than the position of the light on the photocell is changed by movement of the galvanometer mirror. The galvanometer, mirror, and photocell are placed in a light-tight box. The photocell and amplifiers first tried in this arrangement mere much too insensitive for the present purpose. This difficulty was eliminated by placing a small gas-filled triode’ between the amplifier and the sensitive mechanical relay furnished with the amplifier, thereby increasing the sensitivity some thirtyfold. The motion (about 1 mm.) of the image of the 6 It was originally planned to have the voltage on the first heater, the continuous heater, automatically regulated to increase when the on-off heater was on, and uzce versa, as described by Kistiakowsky (J. Am. Chem. SOC.67, 65 (1935)). However, the temperature rises encountered are so small and the adiabatic control so sensitive that this elaboration proved to be unnecessary. Purchased from G-Ivf Laboratories. 7 The circuit is describt,d by Sturtevant (Rev. Sci. Instruments B, 331 (1938)).

134

JULIAX M. STURTEVANT

lamp filament on the spherical mirror necessary to actuate the relay corresponds to less than 0.1 microvolt impressed on the galvanometer. With a twenty-junction thermel this corresponds to 0.00013"C. The lag between the jacket heater and the jacket thermel is very small, so that the reading of the jacket thermel under normal conditions remains zero within about &0.0003"C. The sensitive relay actuates another relay which controls the primary of the intermittent heater transformer. The rate of heat exchange between the jacket and the calorimeter containing the usual quantity of water (about 120 cc.) is less than 0.01" per minute per degree temperature difference. Bearing in mind that the fluctuations of the calorimeter-jacket temperature difference should largely cancel out, it would appear that the adiabatic control would be quite satisfactory, even for prolonged experiments. However, this expectation was not fulfilled, probably owing mainly to conduction along thermocouple wires not completely controlled by the temperature of the jacket and to the presence of stray E.M.F.'S in the jacket thermel. I t was thus necessary to observe the departure from strict adiabaticity a t the completion of the reaction and to apply the appropriate corrections.

Timing of the experiments As pointed out in a previous paper (12), it is desirable to make the microvolt readings a t equal time intervals, even with reactions following more complicated rate laws than the first-order law. I t is thus necessary to observe the moving galvanometer a t definite instants, if one wishes to avoid the cumbersome procedure of reading microvolt values from a large-scale plot of the experimental data. If attention must simultaneously be given to a moving clock hand, considerable psychological error may be introduced in the case of fast reactions. The experiments a t 25°C. reported here are open to this objection, since the timing was done with a watch supported near the galvanometer where it could be more or less readily observed without shifting the eye much from the telescope. The experiments a t 35°C. were timed by means of audible signals given by the apparatus described below.. In this way the operator can give full attention to the motion of the galvanometer for some time before the reading is t o be made, and after some practice can train himself to respond very rapidly t o the audible signal. The timing apparatuss consists of a precision, electrically driven tuning fork, the output of which is amplified and drives a synchronous clock. The fork and clock were purchased from the General Radio Company; the amplifier was assembled according t o the circuit diagram shown in figure 2. The fork has a frequency of 100.0002 cycles h0.002 per cent 8 The author wishes to express his appreciation of a grant from the George Sheffield Fund with which the timing apparatus was purchased.


135

a t 25OC.; its frequency decreases 0.002 per cent per degree temperature rise, and increases 0.001 per cent per volt increase in driving voltage. Since it is driven by a 4-volt storage battery, the latter change is entirely negligible. Thus the frequency is correct to within 0.01 per cent for any temperature between 20" and 30°C.; since this precision is more than ample for the present purpovs. it was unnecessary to thermostat the fork: The synchronous clock runs with about 30 milliamperes of D.C. polarization in order to prevent slipping, so that its accuracy is exactly that of the fork.

FIG.2. Circuit diagram of amplifier for precision tuning fork. TI = microphone to single grid audio transformer, ratio about 2 0 : l ; Tz = single plate to500-ohm line audio output transformer; TI = power transformer; secondaries: 600 volts (center t a p ) , 50 milliamperes; 5 volts, 2 amperes; 2.5 volts (center tap), 2.5 amperes. Ci, CZ= lGmicrofarads, 50 volts, electrolytic; C3, Ca = 16microfarads,450 volts, electrolytic. R,, Rp = 100,000-ohm potentiometer, 1 watt; R3 = approximately 1200 ohms, 10 matts (adjust for 35 milliamperes D.C. in 45 tube); Ra = approximately 2500 ohms, 10 watts (adjust for 8 milliamperes D.C. in 56 tube); Rs = 50 ohms, 10 watts, center t a p ; Re = 50,000 ohms, 25 n-atts. LI, Lp = filter choke, 12 henries at 75 milliamperes. The negative leads of the electrolytic condensers go t o ground.

A special contact on the main shaft of the clock is supplied for closing a circuit four times each minute? on the minute and a t 25, 30, and 55 sec. after the minute. Part of the output of the fork is amplified and fed into a small speaker, the speaker circuit including the clock contact. In this way a signal is obtained erery 30 sec. n-ith a warning signal 5 sec. before it, so that readings may be taken every half-minute or multiple thereof. The watch used in the experiments a t 25°C. was checked against the synchronous clock and found to run 0.03 per cent slow.

136

JVLIAN M. STURTEVANT INVESTIGATION O F ERRORS

In view of the relatively complicated expressions connecting the final results with the experimental data, and the number of experimental quantities which have to be measured, it is important that due attention be given to the magnitude of the errors produced in the heat and velocity data by the uncertainties in the observed quantities. We shall concern ourselves here with reactions which follow the first-order law. It is probable that similar conclusions would be reached for reactions of other types.

Errors in temperature measurements Ordinarily the velocity of a reaction approximately doubles for a 10' rise in temperature. The absolute temperature of the experiments is known to f0.02"C., so that the error in the velocity from this source will not usually exceed f 0 . 2 per cent. Since the heat of a reaction is usually relatively insensitive to temperature changes, errors arising from errors in the absolute temperature are entirely negligible. The velocity constants are calculated by means of Roseveare's (9) equation

+

+

where kl, pZ,and w3 are the microvolt readings a t ti, ti Atl and tl 2At, respectively. If chemical errors and errors in the absolute temperature are left out of consideration, and thus all error in k is attributed to errors in the w's, it is.easily shown that AP !!= f 10.8 k P i - I-

if At is taken approximately equal to the half-time of the reaction. Ap, the random error in the kJs1is of the order of f 0 . 0 2 microvolt, so that in most of the present experiments A k l k is about f 2 per cent. The heat of reaction A H is proportional to po - M - , where POis the hypothetical reading a t the instant of initiating the reaction. Keglecting the small correction necessitated by the fact that t,he reaction is not strictly isothermal, po - p- is given by

+

where = tl At, Analysis of this expression in the usual way leads to the result that the error in AH due to random errors in the P'S is a minimum


137

when b/At = 1.68. In the present work &/At has averaged about 1.5; for this value

less than a quarter as large as the error in k caused by random variation in the w’s. This point is rather important to the calorimetric accuracy of the method described in this paper for obtaining the heats of slow processes. As might be expected, since the only use made of the velocity constant in calculating the heat data is in two relatively short extrapolations, the heat data are insensitive to the value of the constant. By using velocity data in this way it is unnecessary to observe the reaction until it is finished, so that the time of each experiment is greatly reduced, and calorimetric errors are thus cut down. Another important advantage of the present method is that the extrapolated value of pa gives directly the heat of solution or mixing when subtracted from the reading obtained just before the reaction is started. The value of po is obtained from equation 2 and the expression

I t is easily shown that = &5.7Ac(, or approximately k 0 . 1 2 microvolt. Since the temperature changes accompanying solution in the present work all exceed 150 microvolts, this error is small.

Errors in timing Errors in timing, in so far as they affect At and the p’s, have been included in the preceding discussion. I t remains to consider the effect of error in tz on the value of AH. The chief source of error in f2 is the fact that the mixing of the reactants is not instantaneous; a reliable estimate of the error from this source is difficult. In the present experiments with glucose, finely powdered material was used, and as nearly as could be told by observation of the temperature of the calorimeter the solution of the glucose was essentially complete in about 15 sec. This would cause t2 to be too large by a maximum of about 8 sec. I t is easily shown that A(AH)/AH = +kat,, where At, is the error in t,. For a half-time of 30 min., k = 0.023, so that A(AH)/AH = +2.3 per cent per minute error in t z . Therefore the error in tz introduces an error in AH of a t most +0.3 per cent in the experiments a t 25’C. and +0.6 per cent in the experiments a t 35°C. I t should be noted that the sum of the heats of reaction and solution is independent of b, since the extrapolation of the p’s according to equation 3 does not involve t 2 .

138


Lag errors The outside surface of the calorimeter, on which are mounted the thermel junctions, lags in temperature somewhat behind the solution. It is important to ascertain that errors caused by this lag are not serious. It has been shown (11)that the magnitude of the lag, considered as a time lag, is approximately independent of the rate at which the temperature of the calorimeter is changing. Therefore, if Ap is the lag error in p3, the lag errors in p2 and pl are, respectively, 2Ap and 4Ap. We have, therefore, that 2Ar ~z - 113 (kwm+- k)At = In pi - 12 =o

+

PZ - p3

- PZ

pi

4-Ap

Thus any lag will have a negligible effect on k . In a similar way we find (PO

- p=Jwrr. 1 - P-

PO

4AP

~

(pi

- P-1

Thus a given Ap arising from the lag of the calorimeter will cause nearly twice as large an error in AH as the same Ap occurring as a random errbr in pll p2, p3. No evidence as to the presence or absence of such a lag error can be obtained from the presence or absence of a drift in the AH values during a single experiment. However, good evidence that any lag errors are very small is given by the fact that the AH obtained from a run having a half-time of 15 min. a t 25OC. agreed very well with the AH for runs having half-times of 30 min. The Ap in the former case should be twice as large, so that any serious error would shorn up clearly.

Other errors The determination of AH involves the evaluation of the heat capacity of the calorimeter and contents. The measurement of the electrical energy input in the heat capacity determinations is readily carried out with a precision greatly exceeding the precision of the determination of the temperature rise, so that errors from the latter source only need be considered. A temperature rise of 15 to 20 microvolts is used; assuming Ap to be about 0.02 microvolt, the precision of this measurement is about 0.1 to 0.2 per cent. In all work of this sort systematic errorssmay be very important. I t is probable that determinations of reaction velocity are particularly susceptible to chemical errors, though it should be pointed out that even considerable errors in the velocity constants due to small amounts of catalytic impurities would have very little effect on the values of AH. I n the present measurements the chief systematic error in AH probably arises in the estimation o f t h e purity of the a- and @-glucoseby means of their optical


139

rotations. The assumption has been made in this estimation that the values for the rotations and mutarotational velocities of the pure sugars are correct as given by Isbell and Pigman (7), and that the rotation of mixtures of the two sugars is a linear function of the composition. Aside from the validity of this assumption, the experimental error in the estimation of the purity of the samples used may be as high as 1 0 . 5 per cent. This would cause a smaller percentage error in the heats of solution, since both a- and 8-glucose absorb heat on dissolving, but a somewhat larger percentage error in the heats of mutarotation. Consideration of all these sources of error makes it seem that a conservative estimate of the probable error of the heat values reported here is 1 0 . 5 per cent in the heats of mutarotation and h 0 . 3 per cent in the heats of solution. It will be seen, however, that the reproducibility of the measurements is better than twice this good, mainly because any chemical errors which are present are constant. I t should be emphasized that in the mutarotation experiments the total temperature change, of which about 60 per cent was actually observed, averaged 0.025OC. in the case of aglucose and 0.02OC. in the case of @-glucose. EXPERIMENTAL PART

Preparation of materials a- and 8-d-glucose were prepared by recrystallization of Baker's analyzed d-glucose by the methods of Hudson and Dale ( 5 ) . The purity of the samples was estimated by determining their specific rotations a t OOC. and comparing with the data of Isbell and Pigman ( 7 ) . The sugar was dissolved in water a t 0°C. and several readings of the rotation, using sodium light, were made over a period of 20 to 30 min. The individual values were calculated back to the time of mixing, using the rate equation given by Isbell and Pigman. Since the rate of mutarotation a t 0°C. is slow and the rotations are not sensitive to temperature, no great care was given to the control of the temperature in these measurements. I t probably varied between 0" and 0.5"C. The results are given in table 1. The errors given are average deviations from the mean. The purities were calculated on the basis of the values given by Isbell and Pigman for the pure sugars, assuming that only CY- and @-glucoseare present and that the rotation of mixtures of the two sugars is a linear function of the composition. All the heat data have been corrected appropriately, using these percentage purities. The hydrochloric acid was a Baker's analyzed product; the stock solution was standardized gravimetrically. Distilled water, boiled and then cooled in a stream of carbon dioxide-free air, was used throughout. All weighings were corrected by the appropriate buoyancy factor.

140

JULlAN M. STURTEVANT

Description of a typical experiment.

The mutarotation of 8-glucose at R6'C.

The &glucose was placed in the dilution cup and its weight determined by difference. The dilution cup was closed by a piece of waxed paper, a tight seal being obtained by a thin film of vaseline and the snap ring. The water and hydrochloric acid were run into the calorimeter from weight burets, and the calorimeter cover was immediately put in place and tightly closed. The jacket and submarine were closed and the apparatus lowered into place on the bearings. During the filling operations the submarine was supported on a removable brass table, with the cold calorimeter just below the surface of the oil thermostat so that its temperature would not depart from the proper value. An estimate was made of the magnitude of the heat effect to be expected on solution of the glucose. Since both this process and the mutarotation TABLE 1 Estimation of purity oj a- and 8-d-glucose

degrees

3 977

a-Glucose a-Glucose

I

Mean

..I

@-Glucose. . . . . . . . . . . . . . . @-Glucose.. . . . . . . . . . . . Mean

1103kO6 1104*02

1 2

1 ::::; I 1

110 35

I

1

per cent

1

,

1

18.9 0.3 19.2 & 0 . 3

j

19.05

1

98 75

99 30

absorb heat, it was necessary to heat the calorimeter to a temperature exceeding that of the jacket by an amount larger than the fall in temperature produced by dissolving the glucose, and to insure that during the mutarotation the jacket would be sufficiently hotter than the oil bath so that its natural rate of cooling would exceed that required by the mutarotation. The calorimeter was accordingly heated to about 310 microvolts, about 255 microvolts above the jacket. While the calorimeter was being oscillated, its temperatureg and the difference between its temperature and that of the jacket were observed each minute for 4 min. At 41 min., 12 pounds pressure was put into the dilution cup bellows and immediately released ; the jacket, was then heated as rapidly as possible to 9 A correction t o the readings of the main thermel under these conditions is neressitated by the fact that the thermel junctions do not obtain the true calorimeter temperature when the jacket is a t a considerably different temperature.


141

bring it to the temperature of the calorimeter. This was accomplished within 2 min. Stirring was continued for a n additional 6 min. During this time the adiabatic control was adjusted, and readings of the temperature of the calorimeter were started at 15 min., a reading being made every minute; the first two readings were discarded because, for some reason, they were out of line with the others. Readings were made a t minutes 17 to 26, 50 to 59, and 83 to 92. The following day the heat of stirring, the heat capacity, and the deviation from adiabaticity were determined. The deviation from adiabaticity was found to be -0.00523 microvolt per minute a t 70 microvolts, the approximate mean temperature of the calorimeter during the mutarotation. The heat of stirring caused a temperature change of fO.045 microvolt per minute. The heat capacity was determined over two heating periods, one of 7.5 min. and one of 8 min., the calorimeter being rocked in each case for 2 or 3 min. after the completion of the heating period. The data for these periods are given in table 2. TABLE 2 Determination of the heat capacity oj the calorimeter and of the &glucose solution ___

~ mrnutca

1 2

Mean

7 50 8 00

_

_

I

mirrorolia

1

13 43 18 71

_ mlcrovdk

'

-0 52 -0 50

I

1

I

1 2793 1 4713

~

1 1

0 01591 0 01830 I I I

i o d e a per

muraolt

0 7092 0 7087 0 7089

In table 3 the data for the determination of the heat of solution and the heat and velocity of mutarotation are given. In the first column are listed the times of the second reading in each set of three, in the next three columns the three readings, after correction for non-adiabaticity, and in the fifth column the values of the velocity constant. The temperature change during these readings is so small (0.015"C.) that it is unnecessary to apply the temperature correction previously described (13); the velocity constant can be corrected to 25OC. on the assumption that the reaction was isothermal a t 70 microvolts. The sixth column in table 3 gives the total temperature change caused by the mutarotation, uncorrected for the temperature coefficient of the reaction, calculated according to equation 2. As shown previously (13), this is readily corrected as indi1 dk cated in table 3. y is the product of - - ( T = temperature) and the temk dT perature sensitivity of the thermocouple. In the present experiments at

142


25'C., y = 0.00012, calculated from the data on the glucose mutarotation given by Hamill and LaMer (2) and the sensitivity of the main thermel. The seventh column lists the values of the extrapolated infinity reading (uncorrected). Obviously, addition of this to the total temperature change gives the extrapolated temperature at the start of the reaction; the difference between the observed temperature at the start and this extrapolated TBBLE 3 Mutarotation of 8-glucose at 86.09"C. 5.7852 g. of 8-glucose; 117.67 g. of carbon dioxide-free water; 0.980 g. of HC1 (0.00962 molal); temperature a t start of reaction (corr.) = 300.3 microvolts; At = 33 min. fa FROM

START OF

TEYPERATUREII, I N OCROVOLTB (CORRIDCTED PO1 NON-ADUBATICITY)

:UNCORRECTEDFOR TEXPEBATURI COEFFlCIIiNT OF VELOCITY)

REACTION

PI minutes

45.50 46.50 47.50 48.50 49.50 50.50 51.50 52.50 53.50 54.50

78.90 78.57 78.20 77.86 77.52 77.23 76.95 76.71 76.37 76.18

-

71.15 70.99 70.87 70.70 70.58 70.44 70.26 70.15 70.02 69.91

67.57 67.52 67.43 67.38 67.33 67.25 67.16 67.10 67.02 66.98

Mean.. . . , . . . . . . . . . , . . . . . . . . . Average deviation.. . . , . . . . . . . AH

ma 7;; = (M:

- M:)

[l

+

y (M:

0.01017 0.01028 0.00996 0.01012 0. 00998 0.00994 0.01012 0.01008 0.00987 0,01001 0.01005 f l . O per ceni

- 9:)l

19.31 19.24 19.27 19.16 19.06 19.12 19.18 19.28 19.18 19.31 19.21 f 0 . 4 per cent

64.50 64.59 64.39 64.51 64.47 64.42 64.48 64.45 64.33 64.41 64.46 * O . l per cent

= 19.25 microvolts

AH = 424.9 joules per mole = 433.0 joules per mole (corrected for a-glucose)

+

64.46 19.25 = 83.71 microvolts mo AHaoln.- = (300.3 - 83.7) = 216.6 microvolts C AH,.I.. = 4780 joules per mole = 4738 joules per mole (corrected for or-glucose) * Since this reaction is reversible, k = kl k2, the sum of the velocities of the forward and reverse reactions. NO =

+

temperature gives the temperature change due to the dissolution of the glucose. Since the heat capacity used is that of the products, the heat of mutarotation is to be assigned to the temperature a t the start of the mutarotation. The heat capacity change during the mutarotation is assumed to be negligible, so that the heat of solution is to be assigned to the temperature just before the dilution cup was opened.

TABLE 4 Mutarotation of a- and @-d-glucose

Mutarotation of a-glucose a t 25°C. joules per mole

0.1566 0.1727 0.1792 0.1872 0.2278

1

- 768.9t -728.3 -727.3 -728.9 -730.7

1.011 0.992 1.004 1.022 1.037

7.20 7.57 8.99 8.63

joulca per mole

10,803 a

10,691 10,710 10,743 10,716 f O . l per cent

Mean Average deviation 0 2365

1

9.58 6.85 8.12 7.94

0.2283 0.2477 0.2588 0.2707

1

I

: 11 1

3,143

0.967 1.016 1.005 0.997

429.1 437.1 431.0 432.6

0 996 1 f.1 5 per cent1 1921

I

I

Mean.. ................................... Average deviation, . . . . . . . . . . . . . . . . . . . . . . . I

0.1924 0.1957 0.2133

1

4,693 4,662 4,687

438 2

I

I

433.6 kO.7 per cent,

4,678 4,680 1 0 . 2 per cent

Mutarotation of a-glucose a t 35°C.

1

1

11.03 11.03 11.03

.I

Mean. . . . . . . . . . . . . . . . Average deviation.. . . . ./

2.639 2.549 2.592

-770.9 -769.8 -768.3

2.593 f 1 . 2 per cent1 ~

12,193 12,251

*

i

-769.6 d ~ 0 . per 1 cent/

12,222 1 0 . 2 per cent

Mutarotation of @-glucosea t 35°C. 0.2450 0.2518 0.2745

j

1

11.03 11.03 11.03

1 I

Mean. . . . . . . . . . . . . . . . . . Average deviation.. .....

2.570 2.510 2.553

1 ,

'

1

f 02.554 . 9 per cent;

479.0 481.6 486.9 482.5 1 ~ t 0 . 6per cent!

6,004 6,025 6,015 1 0 . 2 per cent

Sensitivity of main thermel: 0.001259" per microvolt a t 25°C.; 0.001225" per microvolt a t 35°C. Value not obtained because of necessity of heating calorimeter rapidly immediately after mixing to neutralize cooling due to mixing, i.e., the calorimeter-jacket temperature difference was improperly adjusted before mixing. t Value excluded from mean. There was evidence that the glucose dissolved Slowly in this experiment. 143

144


Summary of results Several runs of the mutarotation of or- and 8-d-glucose were made at 25°C. and 35°C. These are summarized in table 4. A total of five runs for which the derived values deviated excessively from the mean of the others have been omitted from this summary. In all but one of these cases there was a known reason for this deviation. The velocity values and heat data have been corrected to 25OC. and 35"C., respectively; the heat data have been corrected for the purity of the a- and 8-glucose. Examination of the data in table 4 fails to reveal any significant variation of the heat values with glucose concentration. This being the case, we can summarize the heat data in the following equations: a-Glucose (solid) = a-glucose (as.); AHze8 = 10,716 joules per mole AH308 = 12,222 joules per mole a-Glucose (aq.) = ,%glucose (as.);

AH208

= -1,162 joules per mole

AHso8 =

8-Glucose (aq.) = 8-glucose (solid);

AH298 AH808

- 1,252 joules per mole

= -4,680 joules per mole = -6,015 joules per mole

Summation of these equations gives or-Glucose (solid) = 8-glucose (solid) ; AHZ9a = 4,874 joules per mole AH808 = 4,955 joules per mole The difference (1.6 per cent) between the value at 25OC. and that at 35°C. seems definitely to exceed the experimental error. The validity of the assumption that the heat capacity of the calorimeter and its contents remains constant during the mutarotation is demonstrated as follows. By the relation ( b A H / b T ) , = ACpl we find that AC, w - 5 joules per degree per mole. Since approximately 0.03 mole of glucose was used, the actual change in heat capacity is seen to be about -0.15 joule per degree. This amount is negligible, since the total heat capacity is about 500 joules per degree. If one assumes that no additional forms of glucose are involved in the equilibrium, one can calculate the equilibrium constants at 25°C. and 35°C. from the observed heats of reaction. This leads to the values K B = 1.677 and K s = 1.595, giving the ratio Kss/Kzs= 0.949. A value for this ratio may also be obtained from the value of AH for the reaction, using the van't Hoff equation and assuming AH independent of concentration but linearly dependent on temperature. This calculation gives the result Kss/Km = 0.984, 3.7 per cent higher than the experimental value. This discrepancy seems to be much larger than the experimental error; moreover, the ratio

CALORIMETRIC INVESTIGATIONS

OF ORGANIC REACTIONS

145

Kas/Kp~is only slightly affected by the omission of any correction for the purity of the a- and 8-glucose. It therefore seems necessary to conclude that the equilibrium constants cannot be calculated from the ratio of the heats of reaction of a- and 8-glucose. The only reasonable explanation of this which can be advanced is that one or more additional forms of glucose are involved in the equilibrium. It would be perfectly possible for additional forms to be involved to an extent sufficient to account for the above discrepancy without making their presence known by trends in the velocity constants or AH values during a run. Such would be the case, for example, if we had the following scheme involving two additional forms: (rapid) 7 + 1 --f

(slow) at 2

(rapid)

8t 3

y2

I t has been well established (8, 10, 15, 7) in the case of certain reducing sugars that the mutarotational equilibrium involves more than two forms. Worley and Andrews (15) claimed to have obtained evidence that such is the case with d-glucose, though Riiber and Minsaas (8) were unable to find any such evidence on the basis of dilatometric, refractometric, or polarimetric observations. More recently Isbell and Pigman ( 7 ) reported that they could not verify the conclusions of Worley and Andrew, so that it has seemed that d-glucose remained one of the few sugars showing simple mutarotation. In an effort to obtain further evidence on this point an experiment was performed in which a- and @-glucose,in quantities corresponding to the apparent equilibrium mixture, were dissolved a t 25'C. The observed heat of solution agreed satisfactorily with that expected on the basis of the amounts of the two sugars used, and the mutarotational heat was zero within the sensitivity of the apparatus. This experiment is, of course, not conclusive, since additional equilibria would not show up if they involved relatively small heat effects or were so rapid as to be included in the solution heats. Previous determinations of the heats of solution of a- and @-&glucose have been made. Hendricks (3, 4) and his collaborators obtained results a t 21.6' and 21.7'C., which, calculated to 25OC. using the temperature coefficient obtained in the present work, are a-Glucose (solid) = a-glucose (0.022 molal) : AH298

= 10,950 joules per mole

@-Glucose(solid) = ,%glucose (0.017 molal) ; AH2s* = 4,690 joules per mole

Considering the doubt in the correction of these figures to 25OC. and the fact that these authors assumed the mutarotation of a- and @-glucoseto be accompanied by no heat effect and therefore included a certain amount

146


of mutarotational heat in the solution heats, it must be concluded that the good agreement between their results and the present ones is somewhat fortuitous. Barry (1) also determined the heat of solution of a-d-glucose, ignoring the mutarotational heat, a t 19.6"C. to a concentration of 0.22 molal, obtaining AHma = 11,320 joules per mole. This result seems definitely too high. It is perhaps significant that Barry concluded that he got essentially the same heat of solution in 1.6 molal hydrochloric acid as in water, though in the former case the whole of the mutarotational heat, amounting in magnitude to 7 per cent of the solution heat, would presumably be included. Huffman and Fox (6) have determined the heats of combustion of aand 8-d-glucose; they state that they have not as much confidence in the value for the 8-form as for the a-form. From the heats of formation that they give for these substances one can calculate that a-Glucose (solid) = 0-glucose (solid); AH298= 6,280 joules per mole The discrepancy between this value and the value reported here amounts to about 0.1 per cent of the heat of formation of either isomer. A determination of the heat of mutarotation of a-glucose was made by the present author (13) with a less precise calorimeter. The value obtained, AH = -676 joules per mole, is 7 per cent below the present value, the discrepancy probably being due to the fact that Baker's analyzed glucose was used without further purification, so that there was probably considerable &glucose present. This point cannot be tested because the sample of glucose is no longer available. The velocity constants (kl k2) listed in table 4 agree satisfactorily with those obtained by Hamill and LaMer (2). Their values, corrected to 25°C. and 35"C., are 0.01043 and 0.02592, respectively, in solutions of such low hydrogen-ion concentration that acid catalysis is negligible. In the present research the mean values obtained are 0.01006 a t 25°C. and 0.02558 a t 35"C., the latter figure being corrected for the catalysis of 1.1 X molal hydrochloric acid. These values are 3.5 and 1.3 per cent lower than those of Hamill and LaJIer. One experiment a t 25°C. with 0.03143 molal hydrochloric acid (0.03051 normal, using the I. C. T. value for the density of the glucose solution) gave 0.300 for the catalytic coefficient, while Hamill and LaMer report 0.311 for this quantity.

+

SUMMARY

An adiabatic calorimeter of novel design is described. With this calorimeter it is possible to determine, for homogeneous reactions in the liquid phase having half-times greater than about 10 min., the heat and velocity of reaction and the heat of mixing the reactants. Heat measurements may also be made on very rapid processes. The apparatus has been

CALORIMETRIC INVESTIGATIONS O F ORGANIC REACTIONS

147

tested by observations of the mutarotation of a- and P-d-glucose a t 25OC. and 35OC., the results obtained agreeing satisfactorily with previous values where such exist. Evidence is presented that the mutarotational equilibrium of d-glucose involves more than two forms of the substance. However, if one neglects any additional forms, the heat data may be summarized as follows: a-Glucose (solid)

=

a-glucose (as.); AHzs8= 10,716 joules mole-' AH308 = 12,222 joules mole-'

a-Glucose (as.) = @-glucose (as.); AH2:&= -1,162 joules mole-' AH308 = - 1,252 joules mole-' P-Glucose (solid) = @-glucose(as.) ; AHzs8= AH308=

4,680 joules mole-' 6,015 joules mole-'

The deviations of the individual determinations of these quantities from the means averaged 0.3 per cent. REFERESCES

(1) BARRY:J. Am. Chem SOC.42, 1927 (1920). A N D LAMER:J. Chem. Phys. 4, 395 (1936). (2) HAMILL (3) HESDRICKS,DORSEY,LEROY,ASD MOSELEY:J. Phys. Chem. 34, 418 (1930). (4) HEXDRICKS, STEIKBACH, LEROY,A X D MOSELEY:J. Am. Chem. SOC. 66, 99 (1934). (5) HUDSOK AND DALE:J. Am. Chem. SOC.39, 320 (1917). (6) HUFFMAN A N D Fox: J. Am. Chem. Soc. 60, 1400 (1938). ASD PIGMAN: J. Research Natl. Bur. Standards 18, 141 (1937). (7) ISBELL (8) RIIBERAND MINSAAS:Ber. 69, 2266 (1926) J. Am. Chem. SOC. 63, 1651 (1931). (9) ROSEXEARE: (10) SMITHA N D LOWRY:J. Chem. SOC. 1929, 666. (11) STURTEVANT: Physics 7, 232 (1936). (12) STURTEVANT: J. Am. Chem. SOC. 69, 699 (1937). (13) STCRTEVAST: J. Am. Chem. SOC.69, 1528 (1937). Rev. Sci. Instruments 9, 276 (1938). (14) STCRTEVANT: AND ANDREWS: J. Phys. Chem. 32, 307 (1928). (15) WORLEY

Calorimetric Investigations of Organic Reactions. II. A New Calorimeter

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