JOURNAL OF T H E AMERICAN CHEMICAL SOCIETY VOLUME60
JULY 6, 1938
[CONTRIBUTION FROM THE CHEMICAL
NUMBER 7
LABORATORY OF THE UNIVERSITY OF
CALIFORNIA]
Hindered Rotation of the Methyl Groups in Propane. The Heat Capacity, Vapor Pressure, Heats of Fusion and Vaporization of Propane. Entropy and Density of the Gas BY J. D. KEMP*AND CLARKJ. EGAN Evidence proving the existence of a high potential barrier which hinders the rotation of the methyl groups about the single carbon-carbon bond in has made apparent the need for more experimental data on the hindering potentials in similar molecules. Accordingly, the entropy of propane gas has been obtained experimentally from calorimetric data with the aid of the third law of thermodynamics, and has also been calculated as a function of the height of the potential barrier by means of spectroscopic and molecular structure data. The contributions of a hindered rotator to the entropy, energy, and heat capacity have been given by P i t ~ e r .The ~ height of the potential barrier was determined as that necessary to bring the spectroscopic entropy value into agreement with the experimental entropy value. Purification of Propane.-C. P. propane, of 99.9% purity, from the Ohio Chemical Company, was bubbled through 12 N sodium hydroxide and 36 N sulfuric acid. It was then passed through a tube containing phosphorus pentoxide and condensed in a previously evacuated bulb. The liquid was subjected to two successive fractionations in a vacuum-jacketed fractionating column, (*) Present address: Standard Oil Co., Richmond, Calif. (1) Kcmp and P i t z a , J . Chem. P h y s . , 4,749 (1936); THISJOURNAL, 69, 276 (1937). (2) Howard, Pkrs. h., 61, 53 (1937). (3) Kistiakowsky and Nazmi, J . Chem. P h y s . , 6, 18 (1938). ( 4 ) Piteer, ibid., 6, 469 (1937).
the middle 30% being retained each time. From the course of the heat capacity curve just below the melting point, the amount of liquid-soluble solid-insoluble impurity was estimated to be less than 0.001 mole per cent. The method of making this calculation has been described previously.6 A less accurate value of 0.002 mole per cent. impurity was calculated from the change of the melting point in heating from 5 to 20% melted. Apparatus and Measurement of Amount. The Density of Propane at 1 Atmosphere and 298.10°K.-The calorimetric apparatus and procedure have been described p r e v i o ~ s l y . ~Gold ~~ Calorimeter IV was used for the investigation. The volume of the propane was determined by means of the 5-liter measuring bulb described by Giauque and Johnston.8 A gas density determination was made after each of the three heats of vaporization. The volumetrically measured propane was condensed and weighed in a glass bulb containing pentane, which reduced the vapor pressure of the propane. The molal volume of propane, V , a t T near 298'K. and P near 1 atm. was found to be
s2FT
v=-401 * 7 c c . (1) This gives 1.8325 * 0.0007 g./liter for the density of propane gas a t 298.10'K. and 1 atm.
1521
( 5 ) Johnston and Giauque, THIS JOURNAL, 61, 3194 (1929).
(6) Kemp and Giauque, ibid., 69, 79 (1937). (7) Giauque and Egan, J . Chem. Phys., 6, 45 (1937). (8) Giauque and Johnston, THISJOURNAL, 61, 2300 (1929).
TAHLFTI MELTING POIXTOF PROPASI: 10°C = 2i:j 10°K )
Vapor Pressure.---The procedure used in thc measurements of vapor pressure has been described previously." The observations have been represented by the equation
yo mclted
liquid propane, 166 to 23l'K , CO'C = 273 10°K \ 9.64920 logiJ'(rnt ern H ~ )= -(1325.358/1') 17011895OT 4-0 000013420T2 ( 2 )
+
1 1
211
21 i 211
40
65 Accepted value
35
30
15 *
c, 10
5
0
60 Fig. 1.-Heat
100 13i 200 Temperature, OK. capacity of propane in cal./dcg. per mole.
I'. OH
166.140 173.270 179.792 187.297 195.081 202 860 209 878 214.932 220.209 225.048 228 75t; 231 111'
Pobsd.
-
Tobsd.
-
obsd.
PdCd.
Tdcd.
,1.161 2.200 3.739 6.544 11.103 17.992 28.833 :35.160 45.913 57,889
-0.003 .002 . 000 . 000
+0.028 - ,011 ,000
FX.BlR I i
.2;1
+ -
.1JO5 ,(
I1 I1 1
- .Ul3
. ouo f ,001 - .015 --
-+-
+ + -
.0::2
+ +
OI!
.-
. 000 .o(J:3 ,
(I00
,009
,000 .U(JO
,000 .u10 ,(IO.$
85 45
*
I , oh: thcrmocouplt
heat 85 8.5 85 heat 85 8.5 85 heat
43 43 43 4.j 4.i
44
85 46 heat 85 46
0.05"K.
The boiling point calculated from equation ('3) is 231.04 * 0.05'K. (OOC. = 273.10'K.). Melting Point.-The melting point was observed with various percentages of the propane melted. The results are summarized in Table 11. Table I11 contains a summary of the melting and boiling point temperatures observed by other experimenters. Heat Capacity of Propane.-No measured values of the heat capacity of condensed propane below the boiling point could be found in the literature. 'The heat capacity measurements are given in Table IV. 1.0004 abso330 lute joules was taken equal to 1 Intertiatioiial joule and 4.185 absolute joules equal to 1 calorie. A graphical
T A H L I11 B MELTING A N D BOILIXC POINTTEMPERATURES OF PROPANG
TABLE I
VAPOR PRESSCRB OF LIQUID PROPANE (0°C. = 273.10"K.) Pint. om.
Stopped supply of 8.5 428 8.5 424 83 426 Stopped supply OF 85 434 8.5 430 85 430 Stopped supply of 85 436 Stopped supply of 85 439
1
A summary of the measurements is presented iii Table I. The calculated and observed values are compared in columns 3 aiid 4. Temperatures have been given to 0.001' because of the high relative accuracy. The absolute temperatures may be in error by several hundredths of a degree. Column 3 coritairis values of the rate of change of pressure with temperature calculated from equation ( 2 ) .
0
1 , " K , rcsi4anec thermometer
hl. p . , ?', O K .
(ill ctn. . .. . - __ d T deb-.
0.108
83.2
,187
,392 .A66 ,720 1 .lMj7 1.472
1.827 2.257 3.708 3.092 :3 :392
80 0 85 46
11. p . , ?, OK,
228.1 229.0 228.6 230.98 230.8 230 93 231 0 4
Observer
Olszewskis (1894) Burrell and Robertson1o(1913) Maass and Wright" (1921) Dana, Jenkins, Burdick and Tiinni12(1926) ITrancis and Robbins13 ( 3933) Hicks-Bruun and R r u ~ (1936) n ~ ~ 'This resrrtrch
( 9 ) Olszrwski, Bcr., P7, 3305 (1891). (10) Burrell and Robertson, THIS] U I I K S A L , 37, 2188 (1915) (11) Mansr. and Wright, i b i d . , 43, 1098 (1921). (12) Dana. Jenkins, Burdick and Timm, Rlfiig. Eng , 14, 387 (1926). (l:O I'rancii a n d Robbins. 'I'ins J O U K N A I , . 86, 4339 (1933). (111 Ifirks Bruui? a n d U r i t u n , ihid , 68, 810 (19361.
THEHEATCAPACITY
July, 1938
representation is shown in Fig. 1. Table V contains values of the heat capacity taken from a smooth curve through the data. TABLEIV HEATCAPACITY OF PROPANE Molecular weight, 44.092;15 1.6779 moles in calorimeter. T,
OK.
13.29 16.36 19.60 23.11 26.57 30.51 34.58 38.85 43.68 48.91 54.48 l 59. G 64 87 70.96 77.05 81.32 83.60 83.84 84.75 85.14 85.45 89.67 95.48 101.91 108.45 115.11 121.92 128.85 135.90 142.74 149.69 156.80 164.34 171.97 179.04 185.85 194.23 200.89 207.04 213.05 219.20 224.91 229.76 231.04
C p cal./deg. per mole
0.514 .865 1.504 2.257 2.970 3.864 4.870 5.785 6.682 7.593 8.471 9.328 10.08 10.87 11.69 12.21 12.42 12.60 12.70 13.14 Melting point 20.20 20.25 20.33 20.41 20.60 20.59 20.68 20,84 20.89 21.06 21.19 21.35 21.47 21. G8 21,90 22.17 22.42 22.52 22.80 23.00 23.29 23.48 Boiling point
AT
3.375 2 ..795 3.705 3.315 3.609 4.221 3.915 4.590 5.132 5.219 4.899 5.447 5.947 B ,373 5.733 2.673 1.851 2.551 0,438 .343
Series
I' I1 I' I1 I' I' I' I1 I1 I1 I1 I1 I1 I1 I1 I11 I1 111
I11
5.339 6.134 6.642 6.326 G ,879 6.600 7.119 6.827 G ,578 7.089 6.840 7.910 7.031 6.769 6.547 6.243 6.041 5.a5 5.7117 5.539 5.41
3.941
I I I I I I I I I I I I I I I I I I I I I I
Heat of Fusion.-No measured values of the heat of fusion were found in the literature. The present measurements of the heat of fusion of propane are summarized in Table VI. Heat of Vaporization.-The propane was vaporized from the calorimeter into the 5-liter 115) Int. At. Wt. Committee, Txxs JOURNAL, IS, 219 (1937).
1523
OF P R O P A N E
TABLEV HEATCAPACITY OF PROPANE Molecular weight, 44,092. Values taken from smooth curve through observations. cal./deg. per mole
Cp
T,OK.
15 20 25 30 35 40 45 50 55 60 65 70 75
80 85 86.45
T,O K .
0.662 1.592 2.635 3.765 4.960 5.995 6.923 7.765 8.570 9.342 10.08 10.77 11.42 12.04 12.64 Melting point
90 100 110 120 130 140 150 160 170 180 I90 200 210 220 230 231.04
C p cal./deg.
per mole
20.20 20.31. 20.42 20.55 20.71 20.87 21.05 21.25 21.47 21.73 22.03 22.35 22.70 23.07 23.49 Roiling point
TABLE VI HEATOF FUSIONOF PROPANE Molecular weight, 44.092 Temp. intervat, OK.
Corr. heat input per mote
AH
JCPT cat./mole 130.4 842.1 81.974-87.775 972.5 116.3 842.0 82.208-87.423 958.3 917.7 75.1 842.6 85.082-87.952 Avkrage value = 842.2 * 0 . 8 cal./mole
measuring bulb mentioned previously. A constant pressure regulating device described by Giauque and Johnstons was used. The individual measurements are summarized in Table VII, and are compared with the value calculated from equation (2) and Berthelot's e q ~ a t i o n . ~The value measured by Dana and co-workers12is also included. TABLEV I 1 HEATOF VAPORIZATION OF PROPANE Boiling point, 231.04"K.; molecular weight, 44.092. No. moles vaporized
Time of energy input, min.
0.21634 ,21871 ,21865
38 39 39
AH at 760 mm. cal./mole
4488 4487 4485
*4
Average value = 4487 From vapor pressure equation 2. This includes a Berthelot correction of
- 180
cal./mole Value of Dana, Jenkins, Burdick and Timm
4475 4475
* 4.5
Entropy from Calorimetric Data.-The calculation of the entropy of propane at the boiling point, 231.04'K., from the calorimetric data is summarized in Table VIII.
J . 1). KRMPAND CLARKJ. EGAN
1524
TABLE YIII ENTROPY OF PRQPANE FROM ~ A . L O R l M E l K I CD A r A (1 25 0-15 "K, Debye extrapolation, (hcvlk = 128) Solid, 15-85.45"K., graphical 9 702 9 856 Fusion, 842 2/85 45 Liquid, 88.45-231 04°K , graphical 21 063 S'aporiiation, 487,231 U4 19 421
Vol. 60
where the reduced moment
-IT-)
(Ir)Z= iK)2 ( I - 2K sinz,
(1
-
K = moment of inertia of a methyl group. a = one-half of the C-C--C angle. I , = moment
of inertia about the axis through the center of gravity and perpendicular to the carbon plane. - _____ Iy = moment of inertia about the axis which Entropy of actual gas a t boiling point 61, 29 * 0 1 0 l(i Correction for gas imperfection bisects the C-C-C angle in the carbon plane. - - I , = moment of inertia about the axis through bo 45 cal /deg. Entropy of ideal gas a t 1 atm the center of gravity and perpendicular to both anti 2-31 04°K IWr i l l < J k ? and u" axes. The correction for gas imperfectiuii \\'as obFrom the above data the moments of inertia tairicd from the expression: times 1040 g. cm.2 were found to be I , = 26.9; .S,,ie,l - S',,+,,I= ( X U 1 ?P)/32l.JPL 1, = 96.8; I , = 108.2; K = 5.18; I; = 18.93. The The values of the critical pressure and temperature symmetry number u was taken equal to 18. Kohlrausch and KOppllg have summarized the were taken as T, = 369.9'K. P, = 42.01 atm.I6 Rainan data on propane. They have also inMagnitude of the Potential Barrier.-Although it would be more logical to evaluate the cluded the results of Bartholom620 on the inentropy due to the two degrees of freedom con- frared spectrum of propane. The three vibrations cerned with the internal rotation of the methyl of the carbon skeleton have been identified a t groups and thereby estimate the magnitude of the 373, 867 and 1053 cm.-'. For the calculation of potential barrier, it is more convenient to calculate the vibratlonal contribution to the entropy, the an entropy value with the assumption of free remaining frequencies were estimated as follows : - Sexperlment,ll. seven at 930 cni.-', seven a t 1440 cm.-' and internal rotation and evaluate Sfree eight at 3000 cm.-1.21 With this quantity and a table of Sf,,, - Skliridcrell The sum of the translational, rotational and as a function of the potential barrier, the magnivibrational entropies of freely rotating propane tude of the barrier may be obtained. The values of the natural constants used were was calculated to be (3 83 * 0.25 cal./deg. per those given in the "International Critical Tables.') mole at one atmosphere a t the boiling point, The following data from the electron diffraction 231 04'K. The disagreement of this value with measurements of Bauer" were used to calculate the experimental value, 60.45 * 0.10 cal./deg. per mole, indicates that the rotation of the methyl the rotational contribution to the entropy. groups in propane is hindered rather than free. C-C = 1.503 * 0 02 A. Although lack of equilibrium in the crystal a t low c-H = 1.081 * n.n2 A temperatures has caused discrepancies in the C-C-C -= 11412' The remaining H-C-H angles were assumed to be experimental and spectroscopic entropy values of tetrahedral, namely, 109O28'. Kassel18 has de- several molecules, the reasons for this lack of rived the partition function for freely rotating equilibrium are known and such an explanation propane. The expression for the rotational en- for the disagreement in the case of propane as in the cases of ethane,l tetramethylmethane22and tropy methylaminez3seems very improbable. Pitzer,21 ru.ni,un = R / 2 In (Ix - 2K sin2a)(Iy2 K cos2cu)(l,)(K)z-+- 5/2 R In I' - R In u + 447.599 by interpolating the values of the barriers present in similar molecules, has predicted a hindering may be separated into the usual expression potential of 3400 cal./mole for propane. LLcrIIsI~ rutrtn,i, = R/2 In L I J , 3 / 2 R In 7 The difference, Sfree - Sexperlmrntal, was found R In 2 + 267 649 to be 3.40 * 0.3 cal./deg. per mole a t the boiling plus point This amount of entropy corresponds to a *%rcainternal IOt.tliill = R/2 In(L)z 4- R In T - R In 9 f 179.950 _____ ( I Y i Kohlrausch and Kbppl, Z. physsk Ckcm , Ba6, LO9 (1434)
+
(16) Beattie, I'offenberger and tladlock, J i1936).
(17) Bauer. tbtd., 4, 406 (1936)
('hrm
P h i , 3, W
( 2 0 ) Bartholome, tbtd , BZS, 192 (1933) (21) Pitzer, J Chem P h y s , 8, 473 (1937) ( 2 2 1 4itotl And Messerly, THIS JOURWAL, 68, 2364 (I9d(3) A.tun 'xller a n d Messerly, :bid , 69, 174.7 (1917)
EVIDENCE FOR
July, 1938
THE
barrier of 3300 * 400 ~ a l . / m o l e ,which ~ ~ is in excellent agreement with the predicted value mentioned above. The entropy a t 298.10'K. has been calculated to be 64.7 * 0.3 cal./deg. per mole from molecular and spectroscopic data, the experimental value of the potential barrier and the experimental value of the entropy a t the boiling point. This value a t 298.10'K. is the entropy to be used in thermodynamic calculations. In these calculations the nuclear spin entropy, 8 R In 2 = 11.015 cal./deg. per mole, has been neglected. Table IX contains a summary of the calculations. CALCULATION OF
TABLE IX THE MAGNITUDE OF BARRIER IN PRQPANE T
3/2 R In M 5/2RInT RlnP
Stmna.
-
-
P
231.04"K.
THE POTENTIAL
T
-
298.10°R.
P = 1 atm. cal./deg. per mole
= 1 atm.
4-
2.500
36.02
37.28
20.46
21.22
6.32 1 .05
6.83 2.22
= R/2 In IxIyIs X 10laof 3/2 R
Scrtemnd rot.tion
In T St-
- R In 2
interns1 rotation
- 6.851 = R/2
+
In I,* X l08O 22 In T R In 9 3.050
-
-
Siibrat.
=
z y ,
to
y p ~ SEinntsIn
63.85 60.45
Calorimetric entropy sfre,
- Shlndered
3.40
Entropy of propane with a potential barrier of 3300 cal./mde (nuclear spin entropy not included)
* 0.25
67.55
* 0.3
2.86
* 0.10
64.7
* 0.3
summw The heat capacity of condensed propane has been measured from 15'K. to the boiling point. The melting point was found to be 85.45 * 0.05"K., the boiling point 231.04 * 0.05'R., the heat of fusion 842.2 f 0.8 cal./mole and the heat of vaporization 4487 f 4 cal./mole. Vapor pressure measurements have been made on liquid propane and the results have been represented by the equation (liquid propane, 166 to 231°K. (OOC. = 273.10'K.)) lOgioP(Int,cm.
~ g = )
+
-(1325.358/T) 9.64920 0.0118950T 0.000013420Ta
+
The density of propane gas a t 298.10'K. and one atmosphere was found to be 1.8325 * 0.0007 g ./lit er . At one atmosphere a t the boiling point the experimental entropy of propane (ideal gas) was evaluated as 60.45 * 0.10 cal./deg. per mole. The entropy of propane calculated with the assumption of free internal rotation minus the experimental entropy, Sfree - Sexperimental (at the boiling point), was found to be 3.40 * 0.3 cal./ deg. per mole, which corresponds to a potential barrier of 3300 f 400 cal./mole hindering the internal rotation of the methyl groups. . The entropy of propane (ideal gas, with a 3300 cal./mole barrier) a t one atmosphere and 298.10"K. was found to be 64.7 =t 0.3 cal./deg. per mole (nuclear spin entropy not included), This is the entropy value to be used in thermodynamic calculations. BERKELEY,
(24) Refer to Table I of ref. 4 .
[CONTRIBUTION FROM THE
1525
VALIDITY OF RAOULT'S LAW
CALIF.
RECEIVED MARCH30, 1938
DEPARTMENT OF CHEMISTRY, DUKEUNIVERSITY ]
Vapor Pressure Studies. I. Evidence for the Validity of Raoult's Law. The Systems Benzene-Diphenyl, Benzene-Benzyl Benzoate, Ethyl Acetate-Benzyl Benzoate BY H. H. GILMANN' AND PAULGROSS
Attention recently has been drawn2 to the paucity of direct experimental evidence which is available in support of Raoult's law, In view of its importance for modern solution theory and because of the difficulty of giving a general theoretical foundation to the law, the desirabilitya of adding to this evidence has been emphasized. (1) Part of a thesis of H. H. Gilrnann submitted in partial fulfilment of the requirements for the Ph.D. in Chemistry. (2) Guggenheim, Trans. F a r a d w SOC.,88, 101 (1937). (3) Hildebrand, THISJOURNAL, 69, 794 (1987).
In connection with a study of the stability of addition compounds in non-aqueous systems as indicated by partial pressure determinations, partial pressure data were also obtained for certain binary systems consisting of a volatile and a nonvolatile component. Some of these case9 furnish evidence bearing on the validity of Raoult's law. The systems in question are benzene-diphenyl, benzene-benzyl benzoate and ethyl acetate-benzyl benzoate. Benzyl benzoate boils at 324"
