THE APPLICATION OF T H E THIRD LAW OF THERMODYNAMICS TO SOME ORGANIC REACTIONS BY QEORGE S. PARKS AND KENNETH K. KELLEY
Preliminay Discussion Probably the most satisfactory statement of the proposed third law of thermodynamics is that of Lewis and Gibson’: “If the entropy of each element in some crystalline form be taken as zero a t the absolute zero, the entropy of any pure crystal at the absolute zero is zero, and the entropy of any other substance is greater than zero.” The last portion of this statement was prompted partly by theoretical considerations and partly by evidence adduced from the data of Gibson, Parks and Latimer? on the specific heats of ethyl and n-propyl alcohols and their equimolal mixture. From these data i t appeared that a t o°K. the entropy of a solution probably exceeds that of the pure components by a small finite value and the entropy of glassy ethyl alcohol may possibly exceed that of the crystals by about 1.08 units per mol. More recently this comparison between the glassy and liquid states has been made in a more convincing fashion in the case of glycerol. I n studies upon this substance by Simon3, by Gibson and Giauque4, and finally by Simon and Lange5 the heat capacity measurements have been carried down to 10.6’K. with the result that the estimated entropy of the glass a t o°K. exceeds that of the crystals by 4.6 ( rt0.3) units per mol. New data on the heat capacities of the glass and crystals in the cases of both ethyl6 and n-propyl’ alcohol point to the same conclusion: namely, that the entropy of a glass a t the absolute zero exceeds that of the corresponding crystalline form. Considerations such as these have led Eastmans to suggest that a pure crystalline substance has a positive, tho probably small, value for its entropy a t the absolute zero, if the unit of structure of the crystal contains a large number of atoms. I n this respect such a compound would bear a general resemblance to a glass and would differ from it merely in degree. Such compounds with complex cell units and finite positive entropies a t o°K. would probably be found largely in the field of organic chemistry. However, more recently Padding and Tolman9, applying the methods of statistical mechanics, have deduced the conclusion that (‘the entropy of a perfect crystal ’Lewis and Gibson: J. Am. Chem. Soc.,42, 1533 (1920). Gibson, Parks and Latimer: J. Am. Chem. SOC.,42,I j42 (1920). Simon: Ann. Physik, (4)68,260 (1922). Gibson and Giauque: J. Am. Chem. SOC., 45,93 (1923). 6 Simon and Lange: Z. Physik, 38, 227 (1926). a Parks: J. Am. Chem. SOC.,47,341 (192j). ’Parks and Huffman: J. Am. Chem. SOC., 48,2791 (1926). Eastman: J. .4m. Chem. SOC.,46,43 (1924). Pauling and Tolman: J. Am. Chem. Soc.,47,2156(1925). 2
APPLICATION OF THIRD L A W OF THERMODYNAMICS
73 5
at the absolute zero is not dependent on the complexity of the unit of crystal structure”, in distinct contradiction to this suggestion by Eastman. From a practical standpoint the first portion of the preceding statement of the third law of thermodynamics, that providing for zero entropy for a pure crystalline substance at the absolute zero, is of such importance to physical chemistry that it should be thoroly tested experimentally. This may be done in the case of a given reaction at a definite temperature by comparing the entropy change, A S , calculated from heat capacity data on the assumption of the third law with the corresponding value for A S calculated indirectly from the free energy change ( A F ) and the change in heat content ( A H ) by means of the fundamental relationship, AF = AH - T A S . (1) Such a comparison, in order that i t may have any real significance, requires very accurate data; since several types of experimentally measurable quantities are involved and even moderate errors in these, if cumulative, may produce astonishing discrepancies. For inorganic reactions involving pure crystalline substances a considerable number of these tests have been made and in general it has been found that the more reliable the data obtainable the better is the agreement with the requirements of the third law. Thus, for instance, Lewis and Gibson’ in 1917,reviewing the data for nine such tests, found an average discrepancy of 1.6 entropy units; while a few years later Lewis, Gibson and Latimer2, using the extremely accurate electromotive force measurements of Gerke, found in the case of three of these reactions involving chlorides that the average apparent deviation from the third law had been reduced tenfold. Hence, insofar as simple, crystalline, inorganic compounds are concerned, the third law as stated at the beginning of this paper seems to have been placed on a very firm basis. I n the field of organic chemistry the situation is quite different. Organic compounds in general do not lend themselves to simple, reversible reactions involving the elements and suitable for the measurement of equilibria. Still fewer of them are involved in such reactions as may be studied by electromotive force measurements with a reversible galvanic cell. Hence, the third law of thermodynamics, if valid, serves as a very valuable tool for the calculation of the free energies of organic substances by the sole use of thermal data, such as heats of combustion and low temperature heat capacity values. We say “if valid” because i t is precisely in the field of organic compounds that the tests of the third law have been fewest a n a least satisfactory. I n 1923, when the present investigation was undertaken, the only earlier work on this question was that of Gibson, Latimer and Parks3 dealing with the following three reactions: CO HzO. = HCOzH (1) Hz 0 2 C = HCOzH (11) PHZ I/Z 0 2 N2 C = CQ(NHz)z (111)
+ + + + + +
‘Lewis and Gibson: J. Am. Chem. Soc., 39,2580 (1917). *Lewis, Gibson and Latimer: J. Am. Chem. SOC., 44, 1014(1922). Gibson, Latimer and Parks: J. Am. Chem. Soc., 42, I 533 (1920).
736
GEORGE S. PARKS AND K E N N E T H K. KELLEY
For the purposes of the moment we have now revised and corrected their data in the light of the later information given by Lewis and Randall’. The final results are summarized in Table I. I n the case of the first two reactions the values for AF0298 calculated by Lewis and Randall have been corrected by means of vapor pressure data recently obtained for formic acid by Ramsperger and Porter2. The AS,,, values found by Equation I appear in the fourth column of the table. The corresponding values (Column 5 ) calculated on the assumption of the third law have been obtained by use of the latest table for the entropies of the element^.^ I n all cases we have attempted to estimate the maximum errors in these A S figures.
TABLE I Summarized Data for Earlier Tests of the Third Law Reaction
I I1 111
AF’m cal.
+
4,100
-85,000 -47,280
AH238
Assqs, cal./degree
cal.
by equation
- 5,200 -99,700
- 31.2(+6) - 49.3(*7)
-44.5(*
-78,800
-105.7(&8)
-88.7(&10)
I
by third law 4)
-28.4(*
4)
A comparison of the AS results obtained by the two different methods shows that in the case of all three reactions the agreement is within the limits of maximum error in the quantities involved. However, these possible errors are very large and from the data just given we are only justified in concluding that the third law is roughly valid for organic reactions. This situation, in view of the increasing t,endency to assume the exact validity of the third law in the case of organic reactions, calls for further and, if possible, more accurate tests. The present study has been undertaken to partially fill the need. Perhaps, before proceeding further, it will be well to analyze the probleni so that we may see wherein the uncertainties in the AS values are apt to arise. A S calculated by Equation I obviously depends upon the accuracy of the values for AF and AH. Now A F in these tests is ordinarily the result of equilibria measurements and in some cases can be determined with a fairly high degree of accuracy, especially if only one reaction is involved and the temperatures concerned are close to that of the room. If on the other hand, as in reactions I1 and 111, the value for AF is the result obtained by the addition of several equations and their corresponding A F quantities, the errors may be cumulative and the uncertainty in the final value will mount with surprising rapidity. Thus, in reaction I1 a possible error of z I O calories in the free energy of formation of C 0 4 alone contributes thereby an uncertainty of 0.7 entropy unit in the final result. Equally important are errors in the A H values. I n some reactions the change in heat content, AH, may Lewis and Randall: “Thermodynamics,” pp, 578, 585 (1923).Here and thruout the remainder of this paper we shall employ their notation and methods. *Ramsperger and Porter: J. Am. Chem. SOC.,48, 1272 (1926). Lewis, Gibson and Latimer: J. Am. Chem. SOC.,44. 1016(1922). 4 Eastman and Evans: J. Am.Chem. SOC., 46,902(1924).
APPLICATION OF THIRD LAW OF THERMODYNAMICS
73 7
be obtained directly by a calorimetric method or indirectly from measurements of the e.m.f. of a galvanic cell or of equilibria over a range of temperatures. These indirect methods are frequently of greater accuracy than the calorimetric. Especially is this likely to be true in the case of organic reactions in which heats of combustion are used, because most of the combustion data now available is from early work and may involve errors of one per cent or more. Thus, in the case of reactions I and I1 an error of 600 calories ( I %) in the heat of combustion of formic acid produces an equal error in the A H values and an error of 2 . 0 units in the entropy change in Column 4. On the other hand, considering the AS values calculated by the third law. we find that they are probably good to about one or two per cent when entirely dependent on accurate specific heat data. However, in cases such as the entropies of formic acid and urea the experimental data did not go below liquid air temperatures and i t was necessary to use the “n formula” of Lewis and Gibson’ for extrapolation to o°K. This relationship when applied to organic compounds constitutes, we believe, only a first approximation and may involve errors of even 2 5 % in estimating the entropies below 90°K. Thus, for instance, we estimate that the entropy of formic acid, obtained by this formula, may possibly be in error by 3.0 units. I n view of all these considerations, the reaction which we in 1923 selected for again testing the third law was the following: (CH3)?CHOH,liquid = (CH~)ZCO, liquid
+ Hz, gas.
Sabatier2 had shown that this reaction in the gaseous phase was reversible and later RideaP had measured the equilibria involved over a range of temperatures by means of a static method. His results, however, were rather uncertain, owing to the great possibility of side reactions with such a procedure. We in the present study have employed a dynamic method and have obtained the equilibrium constant a t several temperatures. From this series and ~ AH298 for the of equilibrium constants we have finally obtained A F ’ Z ~ above reaction. We have also measured the heat capacities of iso-propyl alcohol and acetone from 70” up to 298’K. and in this way we have been able to calculate the corresponding entropies at 298” on the assumption of the third law. Of course, in estimating the entropy increases for these compounds from oo to 70°K. we have been forced to employ some extrapolation method and so have had recourse to the afore-mentioned formula of Lewis and Gibson. However, as we are later concerned with the difference between the entropies of these two compounds in obtaining any error arising from use of the “n formula” is minimized in this case and is probably not greater than 1.0entropy unit. The entropy of a mol of hydrogen a t 2 9 8 ’ K . is also involved but this is probably known with considerable accuracy; in fact, Lewis, Gibson and Latimer consider their figure to be good to better Lewis and Gibson: J. Am. Chern. SOC.,39, 2565 (1917). Sabatier (Reid): “Catalysis in Organic Chemistry,” p. 236 ( 1 9 2 2 ) . 3 Rideal: Proc. Roy SOC.,99A, 153 (1921).
1 2
738
GEORGE 8. PARES AND KENNETH K. KELLEY
than one-tenth of a unit. All in all, then, this organic reaction serves as a very promising test of the third law’. Within the last few years sufficient data have accumulated in the literature to provide for another very good test in the case of the reaction: C B H ~ ( O H solid ) ~ , = CEH~OZ, solid
+ Hz, gas.
This chemical change is very similar in principle to the preceding one. Therefore, we shall briefly consider it after first presenting our data for the isopropyl alcohol, acetone reaction.
Experimental The experimental work owing to the nature of the problem resolved itself into two distinct parts, which here will be considered separately. Materials. During the course of the investigation several samples of isopropyl alcohol were prepared and used. I n our purification process “refined” iso-propyl alcohol was first dehydrated by two successive distillations over lime in the ordinary manner. In each instance the resulting product was carefully fractionated and the middle portion, about 60% of the total, was selected for the measurements. The average density of these middle portions was 0.78093 at 2 5 O / 4 O l which corresponds to 99.96y0 alcohol on the basis of the criteria* previously employed. Pure, absolute acetone, obtained from the National Aniline and Chemical Company, was used without further purification for the heat capacity determinations of Part I. For the equilibrium measurements of Part I1 the ordinary C.P. acetone of commerce was purified by treatment with anhydrous calcium chloride as in the work of Parks and Chaffee.3 After the final fractionation process, the middle portion representing about one-half of the total was selected for use. It distilled between 56.1’ and 56.2OC. and had a density of 0.7855 at 25’14’. Part I : Heat Capacity Data I n principle, the method of Nernst was employed with an aneroid calorimeter in determining the “true” specific heats and the fusion data. A measured amount of heat was supplied by an electric current to the substance 1 I n connection with this test of the third law there is one point which should be noted. If the entropy of hydrogen a t oo K be taken aa zero, then according to Eastman’s argument it i~ conceivable that the two compounds in question, iso-prop 1 alcohol and acetone, may have small positive entropies, possibly of the order of two or txree tenths of a unit, a t the absolute zero. Furthermore, if this be true, these values will more or less cancel one another in the subsequent calculation of ASlpaand the result will not differ appreciably from that obtainable on the basis of zero entropies a t oo K. Hence, our present test cannot be used to either prove or disprove Eaatman s speculations, aa the possible experimental error in our A&w value obtained from the heat capacity data is a t least 1.0 entropy unit or, perhaps, five times the magnitude of an such hypothetical effect. However, Eaatman’s argument is reall of theoretical rather t k n of practical interest insofar as the simpler organic compoun& are concerned, and in the present p a r we are primarily involved with the uestion of the applicabilit of the third law aa a airly accurate, uaeful tool for the calcaation of free energies. d r t a i n l y for such a practical purpose the above reaction serves very well for testing the (at least approximate) validity of the third law in the field of organic chemistry. 2 Parka and Kelley: J. Phys. Chem., 29, 728 (1925). a Parks and Chaffee: J. Phys. Chem., 31, 440 (1927).
APPLICATION OF THIRD LAW OF THERMODYNAMICS
739
contained in a copper calorimeter] which was suspended in a vacuum and surrounded by a silvered copper cylinder in order to diminish the conduction and radiation of heat to and from the surroundings. A thermocouple in the center of the calorimeter measured the rise in temperature. The entire apparatus and details of experimental procedure have been fully described in other places.' I n view of the accuracy of the various measurements involved]
TABLE I1 Specific Heat Values for Iso-Propyl Alcohol Crystals Temp., "K Cp per gram
Liquid Temp., "K
Cp per gram 0.443
0.192
195.4 198.5 199.1
88.5 88.9
0.201
227.0
0.472
0.201
275.3
0.55.3
92.2
0.208
275.6
0.554
92.7
0.207
284.0
0.576
0.582
70.7
0.172
76.6
0.I82
82.7
0,446 0.447
93.0
0.208
287.6
95.2
0.212
290.2
0.592
95.9 99.7
0.212
290.3
0.590
0.219
293 ' 1
0.601
100.9
0.221
101.3
0.220
106.5
0.227
111.6
0.235
152.5 153.2
0,307 0.308
TABLEI11 Specific Heat Values for Acetone CryStSl.3 Temp., OK. Cp per gram
Liquid Temp., "K
CP per Rram
0.218
'93.2
0.480
0.227
196.6
0.480
0.237
200.I
0.482
0.248
210.3
0.485
90.8
0.256
217.5
0,485
91.2
0.258
276.9
0.505
95.2
0.264
279.3
0.505
100.I
0.271
104.3
0.277
283.4 286.4 289.4
0.507 0.510
69.9 74.2 79.9 85.6
105.3
0.280
151.2
0,349
I53 .o
0.351
0.510
1 Parks: J. Am. Chem. SOO., 47, 338 (1925);also Parks and Kelley: J. Phys. Chem., 30, 47 (1926).
GEORGE 6. PARKS AND KENNETH K. KELLEY
7 40
the absolute error in the experimental values is probably less than 1%. Thus in the case of iso-propyl alcohol two samples were studied with different thermocouple thermometers, lead-wire connections, etc. The results of the two sets of determinations, made over a year apart, agreed to 0.5% or better and served to indicate the reproducibility of the values obtained. The specific heats and the fusion data, expressed in terms of the 15' calorie and with all weights reduced to a vacuum basis, appear in Tables 11-IV.
TABLE IV Fusion Data Substance
Iso-Propyl Alcohol Acetone
Me1ti:g
point
K. 184.6 177.6
Heat of fusion (cal. per gram) Ist, result 2d result Mean
21.03 23 47 '
21.14
21.08
23.37
23.42
Part I1 : The Equilibrium Measurements Method.' As stated before, a dynamic method was used in studying the equilibrium between iso-propyl alcohol, acetone and hydrogen in the gaseous phase. Briefly it was as follows. Pure electrolytic hydrogen, stored in a cylinder, was passed slowly thru two drying towers containing phosphorus pentoxide and then into an empty condensing tube immersed in liquid air, a precautionary device to extract impurities such as carbon dioxide or hydrocarbons; however, none of these were found. From here the hydrogen passed thru two bubblers, each containing 2 5 to 40 cc of iso-propyl alcohol or acetone or of a mixture of the two, depending on the direction from which the equilibrium point was being approached. These bubblers were kept at the temperature of the melting point of ice when the iso-propyl alcohol or a mixture was used and a t the boiling point of liquid ammonia when filled with acetone. There were two reasons for this: first, it was desirable to have the concentrations of the iso-propyl alcohol and acetone low so that the partial pressures would follow the perfect gas law; and second, it was found by experiment that equilibrium could not be obtained with a convenient rate of gas flow if the concentrations were high. These bubblers sufficed to saturate the hydrogen with the vapor of the liquid. After saturation the gas passed into the reaction tube which will be described subsequently. Here in the presence of the catalyst the reaction took place and the resulting gaseous mixture then passed into a condensing tube immersed in liquid air, which solidified the isopropyl alcohol and acetone. After a I or z cc sample of these had been formed by condensation (a process which took six to twelve hours), it was removed and analyzed by the refractometer method previously used by Parks and 1 The method and resulta of this investigation of the e uilibrium between iso-propyl alcohol, acetone and hydrogen were re$r,ted by,one of us (I!.K.K,.) in a paper r a d before the chemical section meeting of the acific d~vmonof the Amencan Association for the Advancement of Science at Mills College, California, June 18, 1926.
APPLICATION OF THIRD LAW OF THERMODYNAMICS
741
Chaffee.’ This method involved simply the determination of the index of refraction of the sample by a Zeiss-Pulfrich refractometer. The resulting value, when referred to a chart on which we had plotted the refractive indices for known mixtures of acetone and iso-propyl alcohol against the corresponding molal compositions, gave the molal composition of the condensate sample to within 0.6%. As this analytical procedure was easy and rapid and required less than I cc of liquid, it was ideal for our purposes. The Reaction Tube. The reaction tube consisted of a Pyrex U-tube about 90 cm. long and 1.2 cm. in diameter. The side thru which the reactants entered was almost completely filled with catalyst, while that thru which the products passed out was one-third full; by this arrangement the emerging gases were well removed from the catalyst before any temperature change was encountered. The reaction tube was suspended in a long Monel metal can which served as a container for the vapor bath and the boiling liquid in equilibrium therewith. This cylindrical can was wound with a heating coil and covered with sheet asbestos and a 2 . 5 cm. layer of “85% magnesia” insulation. The bath liquid was heated partly electrically and partly by a micro burner. The temperature of the vapor around the reaction tube was measured with a single element copper-constantan thermocouple and a White potentiometer. Finely divided copper was used as a catalyst, since Sabatier had found that it did not appreciably catalyze side reactions such as dehydration. This catalytic copper was prepared partly from cuprous oxide and partly from copper gauze by repeated oxidations and reductions. The first reductions were made with hydrogen and the last with iso-propyl alcohol. Air was used as the oxidizer. These repeated oxidations and reductions, about twenty in number, were made a t progressively decreasing temperatures, the final one being a t about 100°C. This process gave a catalyst which proved to be sensitive and made it possible to obtain the equilibrium mixture of gases from either the iso-propyl alcohol or the acetone side, altho at the lower temperatures the equilibrium point lies well over toward the alcohol side and more consistent results were always obtainable by starting from this direction. The Equilzbrium Constants. The equilibrium measurements were made by use of aniline, naphthalene and ethylene glycol as bath liquids. Of these substances the first two were very satisfactory; the ethylene glycol, however, decomposed more or less on prolonged heating with a resulting rise of the boiling point. Above 190°C. the gas entering the reaction tube consisted of either hydrogen and pure iso-propyl alcohol or of hydrogen and pure acetone. At the temperature of boiling aniline (184.3’C.), on the other hand, it was not possible to obtain equilibrium by using hydrogen and pure acetone, so a mixture of mol fraction 0.I I acetone to 0.89 iso-propyl alcohol vias placed in the saturation bubblers when approaching equilibrium from the acetone side. ParksandChaffee: J. Phys. Chem., 31,442 (1927).
742
GEORGE S. PARKS AND KENNETH K. KELLEY
I n the vapor of this mixture a t 0%. gcetone was present a t least to the extent of 50 mol per cent as indicated by the results of Parks and Chaffee. When equilibrium was approached from the alcohol side, hydrogen and pure isopropyl alcohol were used as a t the higher temperatures. Under our experimental conditions all the gases involved approximate to the perfect gas behavior and their fugacities are equal to the corresponding partial pressures. Hence, the equilibrium constant for the reaction (CH3)2C€IOH, gas = (CH~)ZCO, gas
+ H2, gas
is given by the equation, K = P,P3/Pl where Pz/PIis the ratio of the partial pressures of acetone and iso-propyl alcohol and P3 is the partial pressure of hydrogen, measured in atmospheres, The ratio, Pz/PI,is equal to the molal ratio of acetone to iso-propyl alcohol in the condensate and was evaluated by the refractometer analysis, The partial pressure of hydrogen was found by subtracting from the total pressure (barometric) the vapor pressure of the liquid employed in the saturation bubblers before the reaction tube, as the change in composition due to the reaction does not affect the third significant figure of the hydrogen pressure obtained in this manner. Our results appear in Tables V-IX. I n all cases the prefix “a” before the number of a determination indicates that equilibrium was approached from the alcohol side and the prefix “b” that it was approached from the acetone side.
TABLE V Equilibrium Constants at 184.3% Determination Total PreRsure in mm. of Hg
a 1 765 a 2 766 a 3 766 a 4 764 764 a 5 a 6 764 a 7 762 a 8 762 a 9 762 a IO 764 Mean of the “a” values b I 766 b 2 766 b 3 766 b 4 766 Mean of the “b” valucs
PdPI
0.342 0.351 0.406 0.360 0.368 0.342 0.360 0.360 0.368 0.368 0.406
0.368 0,342
0.389
Pa
in atm.
0.997 0,999 0,999 0.996 0.996
0.996 0,993 0.993 0.993
0.996 0.986 0.986 0.986 0.986
743
APPLICATION OF THIRD LAW OF THERMODYNAMICS
TABLE VI Equilibrium Constants a t 218.oOC Determination Total Pressure PI PdPL in mm. of Hg.
a 1 756 a 2 756 a 3 758 a 4 758 a 5 760 a 6 759 a 7 760 a 8 766 a 9 766 a IO 765 a II 765 765 a 12 Mean of the “a” values b r 763 b 2 762 b 3 762 b 4 761 b 5 759 b 6 758 7 56 b 7 b 8 760 b 9 759 759 b IO b 11 7 59 Mean of the “b” values
I , I.
14 14
I . I2
1.12
1.07 I . 14 1.12 I
.os
19 I . 17 I . 19 I . 19 I.
1.17 I ,
14
1.22
I . 19 1.14 1.17 1.19 I . 19 1.18 1.18
1.17
0,986 0.986 0.988 0.988 0.991 0.989 0.991 0,999 0.999 0,997 0,997 0,997 0,993 0.992 0,992 0.991 0.988 0.987 0.984 0.989 0.988 0,988 0.988
1.12
1.12 1.11 1.11
1.06 I . 13 1.11 I
19 1.17 I . 19 1.19 I . 13 I . 16 1.13 1.21 1.18 I.
1.17 1.18 1.17
1.17
1.16 1.16
Equilibrium Constants a t a Mean Temperature of 196.4OC
a a a a a
2 3 4 5 6
a 7
a 8 Mean
PdPl
13
1.15
TABLEVI1 Determination Total Presaure in mm. of H g .
.os
I.
GEORGE S. PARKS AND KENNETH K. KELLEY
744
TABLE 1'111 Equilibrium Constants a t a Mean Temperature of 2oo.1OC Determination Total Pressure in mm. of Hg.
a 1 a 2
760
762
0.678 0.613
a 3
760
0.587
a 4 a 5
758
0.6jo 0.692 0.686 0.667
762 762 764
a 6 a 7
Pa
PP/PI
K
0.993 0.991 .o.991 0.988 0.993 0.993 0.996
P&'s/Pi
0.673 0.607 0.582 0.642 0.687 0.681 0.664 0.648
Mean
TABLE IX Equilibrium Constants a t a Mean Temperature of 201.8~C Determination
b b b b
r z 3 4
b5 b6 Mean
Total Pressure in mm. of Hg.
PdPI
Pa
7 60 760 759 760 762 759
0.692 0.692 0.650 0.664 0.678 0.692
0.980 0.984 0.980 0.982 0.989 0.987
K
P,Pa/P,
0.678 0.681 0.637 0.652 0.671 0.683 0.667
Calculations and Discussion by the Third Law. According to the statement of the third lam of thermodynamics a t the beginning of this paper, the entropies of the pure crystalline acetone and iso-propyl alcohol are zero a t the absolute zero. Then the entropy of each compound in the liquid state at 298" K. (Le. 2 5 " C.) is given by the equation, A S 2 9 8
S298
=
1"
d_& T '
For convenience in the calculations this may be expanded as follow, SZ98
1;
CP
i c F t a l s ) dT
A B (fusion) T'
+
C p (crystals) +
11;
dt
+
C P ( y d ) dT
where T' is the melting point. The first integral in this expression,
APPLICATION O F THIRD LAW O F TH~RMODYNAMICS
745
cannot be evaluated directly from the experimental data and therefore the “n formula” of Lewis and Gibson has been utilized for the extrapolation. By application of their methods to the data for iso-propyl alcohol, the values n = 0,357 and S ~ O = 10.41cal./degree heve been obtained. This entropy result is undoubtedly too high and possibly the absolute error in it is two or three units. However, for the purposes of a comparative study of the entropies of iso-propyl alcohol and acetone the value will be retained as given above, since without doubt the application of the Lewis-Gibson extrapolation method to this alcohol and to acetone involves comparable errors which will be largely eliminated in obtaining AS, the entropy increase in the reaction. The remaining three terms on the right-hand side of Equation 3 can be evaluated with much greater certainty. The quantity AH (fusion)/T’ is obtainable directly from the experimental data of Table IV. The two integrals were determined graphically by plotting the values of Cp per mol as ordinates against In T as abscissas and measuring the area under the curve. The results for both substances appear in Table X.
TABLE X Entropy Data Substance
Iso-Propyl Alcohol Acetone
Entropies per mol Crystals Fusion Liquid 0-70” Above 70”
10.41 14.35
14.57 15.90
6.86 7.65
14.28 14.76
SWS
46.1 52.7
The entropy of a mol of hydrogen is 29.4 units a t 298’ K. according to Lewis, Gibson and Latimer. Therefore, for the reaction (CH&CHOH, liquid = (CHs)zCO, liquid H2, gas, AS298 = 5 2 . 7 29.4 - 46.1 = 36.0 cal./degree on the assumption of the third law. The error in this value for AS is probably less than 1.5 entropy unit,s. ASzss from the Equilibrium Data. TVe shall now consider the equilibria data and compare the value for AS298thereby obtainedwith the preceding one. The rate of change of AH (Le. the heat absorbed) with respect to the temperature for any reaction is given by the equation,
+
+
(F)
=
ACP
where ACp in the present case is the heat capacity of one mol of gaseous acetone plus that of one mol of hydrogen minus the heat capacity of one mol of gaseous iso-propyl alcohol, since here we must consider the reaction in the gaseous phase as in the equilibria measurements. The equations for the heat capacities of acetone and iso-propyl alcohol as functions of the temperature are not known. That for hydrogen, calculated from values given by Partington and Shilling,’ is per mol CP = 6.65 0.00070T. Altho the heat capacity of iso-propyl alcohol is probably somewhat larger than that for acetone, it seems reasonable on the basis of existing data for various substances to believe that the difference is not great. Therefore, in the present
+
1
Partington and Shilling: “Specific Heats of Gases,’’ p.
206
(1924).
GEORGE S. PARKS AND KENNETH K. KELLEY
746
reaction we shall take ACp as equal t o 4.0 calories. This procedure is admittedly somewhat arbitrary. However, it does not greatly affect our calculations of A S or our conclusions, as any error in ACp causes practically compensating errors' in O F and AH. Integrating Equation 4 on this assumption for ACp, we obtain the expression A H T = AH,
+ 4.0 T
(51,
where AH, is the constant of integration. For the free energy change in a reaction, the following general relation exists, =-- A H (6).
[Qp]T2 P
Substituting the value for A H given by Equation 5 , integrating and then multiplying thru by T, we obtain the expression A F T = AH,
- 4.0 T In T
+I T
(7)
where I is the constant of integration. The constants, AH, and I, can be evaluated by use of two values for A F T obtained a t different temperatures. These in the present caw can be calculated from the measured equilibrium constants a t the respective temperatures of boiling aniline and boiling naphthalene by means of the equation A F T = -R T In K. The essential data are:
K
= 0.36
K
= 1.15
a t 184.3"C. or 457.4' K.;A F = 933 cal. a t 218.0' C.or 491.1'K.;A F = -137 cal.
Substituting these values of A F in Equation 7 and solving the two simultaneous equations, we obtain I = -2.6 and AH, = 13,310cal. Therefore Equations 5 and 7 become AHT AFT
= 13r310 13,310
+ 4.0 T
- 9.21T log T -
(9)
2.6 T,
and (10)
from which the changes in heat content and free energy for the reaction may be obtained a t any temperature. As a check upon the validity of these equations we have also used the equilibrium constants obtained for the ethylene glycol temperatures to calculate the corresponding free energy changes ( A F ) , which then afford us alternate values for I when substituted in Equation IO. For a complete consideration of the problem we have treated Rideal's data obtained by his static method in the same way. All these results appear in Table XI. 1 Thus, for instance, we have also carried out all our calculations on the assumption that ACP = 6.0 cal. (an improbably high value, we believe), with the result that our final entropy change becomes 34.9, instead of 35.9 aa shown subsequently.
APPLICATION OF THIRD LAW O F THERMODYNAMICS
747
TABLE XI
Parks and Kelley
Rideal
Equilibria Data T 457.4 491.1 469.5 473.2 474.9 378.1 423 ’ 1 448.1 473 ’ 1 498.1 523.1
548.1
and the Constant I K 0.36
I -2.6
1.15
0.533 0.648 0.667
-2.5
0.00028
+o.z
-2.7
-2.5
0.0204
+0.5
0.I 7 7
-1.8
0,523
-2.3
1.35
4.82
- I ,640 -2,710
12.0
-2.4 -3; 5 -4.0
Examination of the values for I shows that our data obtained by the dynamic method are very concordant and that Rideal’s data over the temperature range 448’-523’ K. inclusive are in fair agreement with our own. However, this is not true for his two lowest temperatures, and his result for the highest temperature is also indicative of an increasing departure from - 2.6,our mean value. We believe that the correct explanation for this situation is to be found in a failure to obtain equilibrium a t the lower temperatures and to secondary decomposition of the acetone a t the higher temperatures. To quote his own words, “it was found in general that slight decomposition could not be avoided and that, although the decomposition curves could be repeated, the values obtained for the process of hydrogenation were by no means regular. If sufficient time were given for the system to arrive a t equilibrium, secondary decomposition occurred relatively rapidly a t high temperatures, and after two or three hours contact a t low temperatures.” Therefore, using Equations 9 and IO, we calculate for the reaction a t 298’ K. and I atmosphere pressure, H?, gas, (a) (CH+CHOH, gas = (CH&CO, gas A H = 14,500cal.
+
AF
= 5,750
”
However, it is customary to take the liquid state as the standard state of iso-propyl alcohol and acetone, fiince that is the ordinary form for these substances a t 298’ K. and I atmosphere pressure. Now for the process, (b) (CH?)iCHOH,liquid a t I atm. = (CHs)&HOH, gas a t I atm., AH298 = 10,620 - 300 = 10,320 cal., where 10,620cal. is the heat of vaporization1 of iso-propyl alcohol a t 25’C under its own vapor pressure, 44.0 mm. of mercury, and - 300 cal. is our estimate of the Joule-Thomson effect for compressing the resulting vapor isothermally from 44 to 760 mm.; and AFBR= R T In 760/44 = 1690 cal.
* Parks and Barton: J. 4m.Chem. Soc.,S?, 26 (1928).
7 48
GEORGE S. PARKS AND K E N S E T H K. KELLEY
In like manner for the process, (c)
(CHI)ZCO,gas at
I
atm.
=
(CH)~)ZCO, liquid at
I
atm.,
+
AH298 = - 7590 2 0 0 = - 7,390 cal., where 7,590 cal. is the heat of vaporization' of acetone a t 2 5 T under its own vapor pressure, 226.5 mm.,* and 2 0 0 cal. is our estimate of the Joule-Thomson effect for expanding the vapor isothermally from 760 to 226.j mm.; and AFm = R T In 226.5,'760 = - 7 2 0 cal.
+
Finally, combining Equations a, b and c, we obtain for the standard state reaction, (CH?)aCHOH, liquid = (CHS)~CO, liquid Hz, gas,
+
AH298 = 17,430 cal.; and AF'29g = 6,720 cal. For the entropy change, these results give by Equation I : AS,,, = 3 j . 9 cal./degree. This value for AS,,, is probably good to within 2 . 0 entropy units and is in excellent agreement with the result, AS,,, = 36.0 ( + I . s ) , obtained by means of the third law. While the check in the present instance is undoubtedly somewhat fortuitous, it seems reasonable to claim that this is a much better test of the third law in the case of an organic reaction than any heretofore proposed. The Hydroquinone, Quinone Reaction
As mentioned before, the reaction, C E H(OH)Z, ~ solid = CsHaOz, solid
+ Hz, gas
provides us with another test of the third law. Lange3 has determined the heat capacity of crystalline hydroquinone and quinone from liquid hydrogen temperatures up to that of the room. Without doubt his results are reasonably accurate and will serve excellently for estimating the respective entropies of these two substances a t 285'K. 6.e. 12'C) on the assumption of zero entropy a t zero absolute. Thus, by plotting his values for the mold heat capacity of hydroquinone against the natural logarithms of the corresponding temperatures, we obtain by graphical integration 3 1.3 units for the increase in entropy between 20' and 285'K. There are no heat capacity data for this substance below 20' but the work of Simon4 has indicated that the Debye T3law holds for organic substances up to about IZ'X and that above this point the heat capacity changes gradually so as to become at first proportional to the square of the temperature and finally, in the neighborhood of liquid air temperatures, directly proportional to the temperature. With this information we have estimated the entropy increase for hydroquinone between 0' and 20°K to be 0.8 unit per mol. Then, on the assumption of the third law, the total entropy a t z8j°K is 32.1 units per mol. Felsingand Durban: J. Am. Chem. SOC.,48,2893 (1926).
* Parks and Chaffee: J. Phys. Chem., 31, 442 (192f).
Lange: Z. physik. Chem.. 110, 350 (1924). Simon: Ann. Physik, (4) 68, 260 (1922); Z. Physik, 38,227 (1926)
APPLICATION O F THIRD LAW O F THERMODYNAMICS
749
I n similar fashion we have estimated the entropy increase for quinone to be 1.4 cal./degree in going from '0 to ZOOK. From 20' to 285'K the increase, obtained by graphical integration, amounts to 36.4 units per mol. Thus the total entropy a t 285'K is 37.8 cal./degree. -4s stated before, the entropy of a mol of hydrogen a t 298'K is 29.4 units. = 29.4 - 6.85 C, for hydrogen a t room temperature is 6.85 cal. and hence In 298/285 = 29.1 cal./degree. By the third law we then find for the above reaction, ASZE,= 37.8 29.1 - 3 2 . 1 = 34.8 ( f 1 . 0 ) cal./degree. The electromotive force, E, andits rate of change with temperature, dE/dT, have been determined by Conant* and by Schreinerz for a galvanic cell involving this particular reaction. These results have not been obtained directly but represent indirect determinations from a study of the quinonequinhydrone and the quinhydrone-hydroquinone electrodes. However, in all probability these values are very reliable, as the cells employed were reversible and reproducible. Conant obtained 0.690 volts for the e.m.f. associated with the reaction under consideration and 0 . 0 0 0 7 2 for dE/dT at 285.6"K. Similarly Schreiner found E = 0.6905 and dE/dT = 0.000770 a t 285'. The two values for E are in excellent agreement, altho unfortunately the respective results for the temperature coefficient differ by over 6%. AS for a reaction is related to d E / d T by the simple equation
+
Hence, for this reaction AS,,,= 33.2 according to Conant's data and 35.5 cal. , degree according to the data of Schreiner. The mean of these two results, 34.4, is probably accurate to within 2 . 0 units and is in excellent agreement with the value previously obtained from the heat capacity data on the assumption of the third law of thermodynamics. Thus we have here another very good check on the third law in the case of an organic reaction.
-S The present status of the proposed third law of thermodynamics has been reviewed with special reference to its applicability to organic reactions. I n this connection it has been pointed out that none of the earlier tests of this principle in the field of organic chemistry may be considered adequate. 2. I n view of this situation, we decided in 1923 to again test the third law, using the reaction, (CH3)2CHOH, liquid = (CHs)&O, liquid Hz,gas. I.
+
Accordingly, we have measured the heat capacities of iso-propyl alcohol and acetone in the crystalline and liquid states from jo' to 298'K. We have also determined the heat of fusion of each substance a t its melting point. From these thermal data AS,,, has been calculated on the assumption of the third law. 'Conant and Fieser: J. Am. Chem. Soc., 45,2198 (1923). * Schreiner: Z.physik. Chem., 117, 77 (1925).
750
GEORGE S. PARKS AND KENNETH K. KELLEY
The equilibrium constants for this reaction in the gaseous phase have been measured with copper as a catalyst over the temperature range, 184O-218OC. With the aid of these results we have calculated AF298 and AHw for the reaction involving liquid iso-propyl alcohol and acetone. The value for AS298 thereby obtained is in good agreement with that calculated from the thermal data. This check indicates the validity of the third law in the field of organic chemistry. 3. Recent data pertaining to another organic reaction,
Cd&(OH)z, solid
=
C B H ~ Osolid ~,
+ Hz, gas,
have been utilized in obtaining a second very accurate test of the third law. Stanford University, California, November 3,1937
