AN ISOTHERMAL CALORIMETER FOR SLOW REACTIONS‘ E. D. COON
AND
FARRINGTON DANIELS
Laboratory of Physical Chemistry, University of Wisconsin, Madison, Wisconsin Received October 15, 1932
This calorimeter has been designed for the study of phenomena involving the slow evolution of heat, particularly in the study of chemical kinetics and biological processes, It can be used at different temperatures. The heahing effect is exactly counterbalanced by a cooiing effect produced by evaporating carbon tetrachloride or other liquid in a regulated air stream. The amount of carbon tetrachloride evaporated is determined by adsorption in silica gel. The increase in weight is converted into calories by calibration with electrical heating. In its present form the calorimeter is limited to a precision of about one per cent, and it is not recommended for rapid reactions with plenty of material where standard calorimeters are now satisfactory. Endothermic reactions can be measured accurately and easily by balancing with measured electrical heating. Exothermic reactions have been balanced by melting ice at OOC. as in the Bunsen ice calorimeter, by vaporization of a liquid at its boiling point as in the ether calorimeter (l),by addition of cold water (2), cold mercury (3) or a salt which absorbs heat on solution (4). The Peltier effect existing between two dissimilar metals, when a current of electricity flows, has been used also ( 5 , 6). DESCRIPTlON O F T H E CALORIMETER
The calorimeter is shown in figure 1. It consists of two vacuumwalled vessels, I and N, mounted with various accessories on a frame, immersed in a large thermostat 20 cm. below the water level. The vessels are connected by a multiple junction thermel. The “reference” unit I, which stays at constant temperature, contains fine oil of low vapor pressure, an electric heater, and a stirrer. A second thermel (not shown) indicates equality of temperature between the oil and the water of the thermostat. The “variable” unit N of 400 cc. capacity contains kerosene. The cover of nickel-plated iron sets into a mercury seal shown at F. A ring of sheet iron, held in place with rubber, contains the mercury and the whole seal is protected on the outside with large rubber tubing. Various acFurther details of this investigation me contained in part of a Ph.D. thesis filed in the Library of the University of Wisconsin by E. D. Coon in January, 1932. 1 TEE JOURNAL OF PHYSICAL CHEMISTRY, VOL. X X X V I I , NO. 1
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E. D . COON AND FARRINGTON DANIELS
cessories, passing through small tubes in the cover, are attached with litharge-glycerine cement, In the first models the whole calorimeter was filled with carbon tetrachloride and short sections of rubber tubing were exposed to the vapor, but it was found that the variable vessel was always a little colder than the thermostat even after standing twenty-four hours. This cooling effect, which persisted no matter whether the room was colder or warmer than the thermostat, was finally traced to solution of the carbon tetrachloride vapor in the rubber and a slow evaporation of the liquid to maintain full vapor pressure.
FIG. 1. ISOTHERMALCALORIMETER
The thermel B connects with the reference unit. The stirrer E of glass extends through a long bearing to the water level. The glass shaft is cemented to a brass rod which rotates in a bearing several centimeters above the cover. The heat generated in the bearing is prevented by the thermostat from reaching the calorimeter. The chimney G, for the admission of reacting materials, extends to the water level where it is provided with a stopper. The heating coil C of 50 cm. bare No. 28 constantan wire is wound on a glass tube and soldered to leads of No. 16 copper wire. The leads are set in paraffin in long snugly-fitting glass tubes passing through the thermostat water.
i
A N ISOTHERMAL CALORIMETER FOR SLOW REACTIONS
3
The cooling unit A is a cylinder of sheet copper containing carbon tetrachloride through which air is bubbled. Other inert liquids of different vapor pressures may be more suitable under other conditions. For high temperatures a higher boiling liquid is better. The mercury trap D is introduced to insure the same conditions a t the beginning and at the end of a determination. A small glass tube (not shown) passes down through the exit tube and ends near the mercury level. By turning a stopcock, air is forced down through this tube and all the vapor beyond the mercury seal is swept out. The air sent through the cooling unit must be dry and free.from any substance which might be adsorbed by the silica gel. The rate of flow is regulated by four stopcocks drawn down to capillaries of different apertures. Connecting thesa in parallel, it is possible to send air through at any rate from ten to several hundred bubbles per minute. The air is dried by passing it through concentrated sulfuric acid, calcium chloride, phosphorus pentoxide, and silica gel, It is brought to the temperature of the calorimeter by passing through three glass tubes, 2 cm. in diameter and 80 cm. long, filled with copper turnings and immersed in the thermostat. In the last tube is an additional section of phosphorus pentoxide. The amount of carbon tetrachloride evaporated is determined by adsorbing in two glass-stoppered U-tubes, each containing about 75 grams of silica gel. When the second tube increases in weight by more than about 1mg. the first tube is rejuvenated by placing in an oil bath a t 150”to 170°C. and drawing through dry air for two or three hours. The thermostat of 750 liters capacity is kept constant within about 0.001” with the help of efficient stirring and a mercury regulator of the oscillating type. The contact wire dipping into the mercury in the capillary is forced up by a spring against the under side of a horizontal pulley wheel. The under side of the wheel is partly cut away so that the contact wire moves up and down for a distance of about 2 mm. during one revolution, thus making and breaking the circuit and insuring certain contact with the mercury. The thermel, which indicates a difference in temperature between the “variable” and ‘ I reference” units, consists of two ll-junction elements. Each is used independently of the other and one acts as a check on the other. Constantan wire (No. 28) and copper wire (No. 24) were used. The resistances of the thermels were 39.92 and 40.29 ohms. When used with the galvanometer, having a sensitivity of 5 mm. per microvolt, a deflection of 1 mm. corresponded to 0.00025”C. The two thermels always agreed within 3 mm. A reversing switch was useful in correcting for possible stray potentials in the circuits. Other switches enabled the operator to use either one of the two thermels or to connect the galvanometer with the potentiometer for use with the heating coil. All connec-
I
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E. D. COON AND FARRINGTON DANIELS
tions and switches were well insulated and mounted on grounded copper shields. PROCEDURE
The thermostat is first brought to the desired temperature (25”C., for example). The reference unit is brought to a temperature slightly lower and the whole calorimeter is set in the thermostat. The temperature of the “reference” is then brought t o the temperature of the thermostat by means of the heating coil. The final temperature adjustment is effected simply by means of stirring. The galvanometer is then connected to one of the main thermels connecting the two units, and the temperature of the “variable” unit is brought to the same temperature, using either the heater
FIQ. 2. RATEOF THERMAL LEAKAGE Calories per hour. A = 0.25, B = 0.12, C = 0.06, B’ = 0.12, C’
=
0.07.
or the cooler as necessary, These adjustments can be effected in a short time, but in order to insure complete equilibrium the system is left undisturbed for several hours,-preferably over night, when both thermels should read within 0.5 cm. of zero. The next step is the establishment of a reproducible condition in the cooler. Air is bubbled through the carbon tetrachloride, and the vapor that passes through the mercury trap is washed out by a stream of air from the inner tube. The temperature is brought back with the heater until the galvanometer reads zero. The silica gel tubes are weighed separately and connected to the outlet of the cooling unit. The reacting material is then introduced through the chimney, and
AN ISOTHERMAL CALORIMETER FOR SLOW REACTIONS
a
5
during the course of the determination the temperature is maintained as nearly isothermal as possible. The galvanometer deflections of the therme1 are kept within 3 or 4 cm. of the zero point and the times of the positive and negative deflections are kept about equal. With slow reactions evolving less than 3 or 4 calories per hour this control is not difficult, and with reactions involving more heat the control becomes relatively less import ant. At the end of a determination the vapor in the exit tube of the cooler is again swept out and if necessary the original temperature is restored. The silica gel tubes are weighed and the heat of reaction determined by the amount of carbon tetrachloride adsorbed; 0.0206 gram is equivalent to 1 calorie as shown below. It is easier-and also sufficiently accurate-to apply a small correction a t the end of the experiment than to bring back the galvanometer exactly to zero. Experiments with the direct input of electrical heat showed that a deflection of 1 cm. corresponded to 0.357 calorie in the empty calorimeter and to 0.372 calorie when the calorimeter contained reacting material in a certain glass tube. The errors introduced by thermal leakage when the calorimeter is not exactly balanced, are shown in figure 2. Tangents to these experimental curves give the rates of cooling or heating. A deflection of 1 cm. of the thermel-galvanometer indicates that the temperature of the variable unit differs from that of the reference unit and the thermostat by 0.0025°C., and that the transfer of heat then amounts to 0.06 calorie per hour. CALCULATIONS
The input of electrical heat was determined by standard methods with a type K potentiometer. The heat of stirring constitutes the least accurate part of the measurements but the correction is small-about 0.1 calorie per hour. In slow reactions it is necessary to maintain stirring only for a portion of the time, and in more violent reactions the total evolution of heat is large compared with the heat of stirring. After a rapid change in temperature it is necessary to stir for at least ten minutes to insure thermal equilibrium. The heat of vaporization of carbon tetrachloride It was not the object, in this investigation, to find the true heat of vaporization but rather to determine the heat of vaporization under the conditions of this calorimeter so that exothermic heats of reactions may be calculated from it. It is possible that a slight Joule-Thompson effect at the mercury trap and some loss of spray have prevented the determination of the true heat of vaporization. Nevertheless the value obtained here is not greatly in error and the method can be adapted easily for exact
6
E. D. COON AND FARRINGTON DANIELS
measurements of the heats of vaporization of liquids at various temperatures. The carbon tetrachloride was purified by refluxing for 2 hours with potassium dichromate and sulfuric acid. It was fractionally distilled and the portion boiling between 75.18”C. and 75.20”C. a t 734.2 mm. was used. The rate of flow of air through the cooler was adjusted so that the heat absorbed in evaporating the carbon tetrachloride practically offset the electrical heating. The average value of the current through the heating coil was obtained by plotting the current against time and estimating the median height. The value obtained is at least one decimal place beyond significant figures. A small “end correction” was applied for failure to reach complete “isothermality” at the end of a determination. Several experiments were carried out using a current of about 0.1 ampere for times ranging between fifteen and thirty minutes and evaporating 0.25 to 0.5 gram. It was found that a t 25°C. the evaporation of 0.0206 f 0.0002 gram of carbon tetrachloride is necessary to offset the evolution of 1.00 calorie (15” calorie) of heat. No calorimetric determination of the heat of vaporization of carbon tetrachloride at 25°C. is available in the literature as a check on this value. In fact most heats of vaporization have been determined only a t the normal boiling point; a few a t 0°C. A value of 0.0200 gram per calorie was obtained from the Clausius-Clapeyron equation, using the vapor pressure data from the International Critical Tables. Heat of neutralization of hydrochloric acid The accurately known heat of neutralization of hydrochloric acid by sodium hydroxide was chosen to test the calorimeter, even though such a fast reaction as this can be determined more accurately with other, simpler types of calorimeters. It was thought that a satisfactory check using only 2 cc. of 0.5 N hydrochloric acid would give confidence in measuring unknown heats of reaction. Exactly 2.00 cc. of 0.4942 N hydrochloric acid was placed in the thin glass vessel shown in figure 3 and sealed off. A slight excess of 0.5 N carbonate-free sodium hydroxide was placed in the upper compartment and the whole vessel was brought t o the temperature of the thermostat and then submerged in the calorimeter. When thermal equilibrium was established the tip of the inner tube was broken with a long rod and the upper solution allowed to flow down. Mixing was effected by gentle shaking. The reaction was so rapid that in attempting to keep the temperature constant, too much carbon tetrachloride would often be evaporated. In such cases it was necessary a t times to use the heating coil. The results are summarized in table 1. The values in the last,
7
AN ISOTHERMAL CALORIMETER FOR SLOW REACTIONS
column are obtained by subtracting the sum of all the corrections from the calories absorbed by the vaporization of carbon tetrachloride. Considering the small amount of material used the average value of 13.39 is in very good agreement with the best values in the literature obtained with large quantities. Recalculation of the data of Richards and Rowe (7) and of Richards and Hall (8) and a correction from 0.55 N give 13,909 calories for the heat of neutralization per mole in 0.50 N solutions a t 20°C. Correcting to 25OC. this value becomes 13,642 calories per mole
FIG. 3. MIXINGVESSEL
WEIGHT
CCla
1
TABLE 1 T h e heat of neutralization of 2 cc. of 0.4942 N hydrochloric acid
CALORIES EQUIVALENT
cc,~
gram
0.4287 0.3701 0.2772 0.2886 0.3256
20.81 17.96 13.44 14.00 15.80
1
HEATING COIL
1
TIME OF BTIRRING
H E A T OF STIRRING
calories
minutes
7.196 4.666
55 40 40 37 55
none 1.00
2.67
E N D CORRECTION
TOTAL CORRECTION
HEAT OF NEUTRALIZATION
calories
calories
calories
calories
0.11 0.08 0.08 0.07 0.11
$0.145 0.20 0.10 0.48 0.48
7.45 4.54 0.18 1.59 2.30
13.36 13.42 13.26 13.41 13.50
-
and 2.00 cc. of 0.4942 N hydrochloric acid then evolve 13.48 calories when neutralized with 0.50 N sodium hydroxide. Heat of hydrolysis of methyl acetate The reaction CH3COOCH3 H?O ( N HC1) = CHICOOH CH30H ( N HC1) was chosen for study because it is a typical, slow reaction which can be readily followed by titrations. The reaction was catalyzed by normal hydrochloric acid. It is known that the reaction involves very little thermal change because the equilibrium is nearly independent of temperature. Subtracting the heats of combustion of the reactants from those of the products the reaction appears to be slightly
+
+
+
+
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E. D. COON AND FARRINGTON DANIELS
exothermic, the exact heat evolved differing greatly with the various values accepted for the heats of combustion. A slight error in any of these large quantities makes a large relative error in their difference. As carried out in the present investigation, the reaction proved to be endothermic. The cooling effect was counter-balanced with the heating coil and it was unnecessary to vaporize carbon tetrachloride in the cooler. Ninety cc. of N hydrochIoric acid was pIaced in the thermostat and 10 cc. of methyl acetate was added. Ten cc. of the resulting solution was placed in the calorimeter and 2 cc. samples were withdrawn at intervals
I
u 0'
1
1
2
3
4
5
Tme in hours
FIQ.4. HEATABSORBEDI N
T H E H Y D R o L Y s I a O F METHYLACETATE The vertical lines represent measured heat supplied by electric heating coil. 0 Titration data. X Calorimetric data
from the remaining solution for titration. The course of the reaction was thus followed simultaneously for a period of 3 hours and 42 seconds, by thermal analysis and by chemical analysis. The difference between the titrations at the beginning and end of this period showed that 0.00513 mole of methyl acetate had been hydrolyzed in the calorimeter during this time. To maintain the temperature constant it was necessary to add 5.61 calories from the heating coil. The heat of stirring was 0.405) so that the reaction absorbed a total of 6.015 calories, or 1170 calories per mole.
AN ISOTHERMAL CALORIMETER FOR SLOW REACTIONS
9
The course of the thermal reaction in a single determination is shown in the upper graph of figure 4, in which the four vertical lines represent the addition of heat-at approximately 0.1 ampere for intervals ranging from 1.5 to 2.5 minutes. The true hydrolysis reaction is complicated by the presence of the hydrochloric acid, for as the reaction proceeds the reacting substances are removed from the solution and the products are added. Corrections for these heats of mixing were determined experimentally using the vessel shown in figure 3. Five-tenths of 1 cc. or 0.0065 mole of methyl acetate was added to 10 cc. of N hydrochloric acid, this quantity representing nearly the amount removed during the reaction in the calorimeter. The heat evolved was 11.45 calories, corresponding to 1763 calories per mole. Check determinations were 1800, 1793, and 1762 giving an average of 1779 calories. Similarly, when 0.00705 mole of glacial acetic acid, purified by freezing, was added to 10 cc. of N hydrochloric acid solution, the heat evolved per mole was respectively 258, 232, 237, and 227, giving an average of 239 calories. Adding 0.00748 mole of methyl alcohol to 10 cc. N hydrochloric acid, the heat of evolution was 1423, 1421, and 1422 calories per mole. The thermal change following the addition of a similar amount of water to N hydrochloric acid was negligible. The summation of the several reactions is then as follows: Removal Removal Addition Addition
of of of of
1 mole 1 mole 1 mole 1 mole
methyl acetate from N HCI.. . . 1779 calories absorbed water from N HCl.. ............ 0 calories methyl alcohol t o N HCl.. . . . . . 1422 calories evolved acetic acid t o N HC1.. . . . . . . . . . 239 calories evolved
-
Total heats of mixing .............................. 118 calories absorbed Total reaction as measured.. ...................... 1170 calories absorbed Heat of reaction per mole, excluding thermal effects with N HCI.. ................................. 1052 calories absorbed
One other direct determination of this reaction is reported in the literature (9), giving an absorption of 1070 calories per mole. Heat of fermentation of yeast The growth of yeast is an example of the type of reaction for which this calorimeter is uniquely suited. It is an exothermic reaction which proceeds too slowly for accurate measurement in an ordinary calorimeter. I n each experiment three culture tubes of yeast and glucose having identical concentrations were prepared. Two were pasteurized at the time the third was placed in a tube in the calorimeter. At the end of the determination this culture was pasteurized also. All were titrated for glucose
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E. D. COON AND FARRINGTON DANIELS
content and the difference gave the amount of glucose destroyed during the fermentation.2 The fermentation caused the temperature to rise slowly and every hour or so air was passed through the cooler, evaporating carbon tetrachloride and bringing the temperature slightly below the normal value. The course of determination I is shown in figure 5, where the vertical lines represent these periods of cooling,
I
2
3
+
5
7
6
a
9
10
Time in hours
FIG.5. HEATEVOLVEDIN THE FERMENTATION OF YEAST The vertical lines represent the measured cooling effect produced by evaporating knonpn quantities of carbon tetrachloride.
The heat of fermentation is calculated from the data of determinations I and I1 as follows: I1
I
Weight of carbon tetrachloride. . . . . . . . . . . . . . 0,4452 21.60 Heat compensated. . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Time of stirring.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10 Heat of stirring.. . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.1777gram 8.64 calories 5.5 hours .66 calories
20.50 Heat of fermentation., .................... Correction for vaporization of water.. ....... 0.59 Corrected heat of fermentation.. . . . . . . . . . . 21.09 Weight of glucose a t beginning., . . . . . . . . . . . . 0,260 0.1617 Glucose consumed.. ......................... Calories per gram of glucose consumed.. . . 130,4
7.98 calories .23 calories 8.21 calories 0.1575 gram 0.0632 gram 129.9
The average value of 130.1 calories per gram of glucose is in good agreement with the value 133.3 reported by Rubner (10) using a “microbiocalorimeter” and a Beckmann thermometer. The correction necessitated by the carrying away of water vapor by the carbon dioxide liberated is calculated from the vappr pressure of water 2 The authors are indebted t o Dr. P. W. Wilson of the Department of Agricultural Bacteriology for the yeast cultures and their analyses.
A N ISOTHERMAL CALORIMETER FOR SLOW RPACTIONS
11
(23.7), the volume of the gas, and the heat of vaporization (582 calories per gram). The reaction of fermentation Cr,H1206-+2C02
+ 2CzHsOH
should evolve 147.9 calories per gram of glucose according to data on heats of combustion (11). The fact that the observed value differs from this value by 17.8 calories may be due in part to the heats of solution of glucose and ethyl alcohol in water and in part to the fact that other fermentation reactions are occurring also. An unsuccessful attempt was made to measure the heat of bacterial growth, but the cultures of Azotobacter were not large enough to give a reliable value. Less than 0.2 calorie was evolved during a period of 6 hours. Thermal studies of the decomposi~onof nitrogen pentoxide in liquid nitrogen tetroxide will be published later. SUMMARY
1. An isothermal calorimeter is described, capable of measuring continuously for many hours reactions which evolve less than a calorie an hour. 2. Evolution of heat is compensated by evaporating carbon tetrachloride, or other liquid, absorbing the vapor in silica gel, and weighing. Absorption of heat is compensated by measured electrical heating. 3. Special precautions, including the elimination of rubber, are necessary in maintaining an organic liquid in a calorimeter at exactly the same temperature as its surroundings. 4. At 25"C., 48.5 calories was required to offset the vaporization of 1 gram of carbon tetrachloride. 5. Using only 2 cc. of solution, values for the heat of neutralization of 0.5 N hydrochloric acid in close agreement with accepted values have been obtained. 6. The hydrolysis of methyl acetate has been found to absorb 1052 calories per mole, after correcting for the heat of mixing with N hydrochloric acid. 7. The heat of fermentation of yeast at 25°C. has been found to be 130.1 calories per gram of glucose consumed. REFERENCES (1) KEYESAND BEATTIE:J. Am. Chem. Soc. 46, 1753 (1924). (2) WATERMAN: Phys. Rev. 4, 161 (1896). (3) HIROB:J. Faculty Sci. Imp. Univ. Tokyo, Sect. I, 6, part 4. (4) WARTENBERG AND LERNER: z. physik. Chem. 122, 113 (1926). (5) TITAN:Compt. rend. 178, 705 (1924).
12 (6) (7) (8) (9) (IO) (11)
E. D. COON AND FARRINGTON DANIELS
BERENGER-CALVERT: J. chim. phys. 24, 325 (1927). RICHARDS AND ROWE:J. Am. Chem. SOC.44, 699 (1922). RICHARDS AND HALL:J. Am. Chem. SOC.61,735 (1929). J. chim. 24, 325 (1927). BERENGER-CALVERT: RUBNER:Arch. Hyg. 67, 193 (1906). WILSON AND PETERSON: Chem. Rev. 8, 455 (1931).
