CORRESPONDENCE Heat Capacities of Hydrocarbon Gases SIR: I n a previous paper (21) a method of calculating gaseous heat capacities of hydrocarbons at zero pressure was presented. Since that time i t has been desirable t o convert these heat capacity values to one atmosphere pressure; the Berthelot equation of state (24) was used, and may be writ,ten in the form of Equation 1 when converting heat capacities from zero t o one atmosphere pressure: ACp = 5.03 Tf/PeTa
not in line with the conception t h a t the vibrational frequency of a bond increases as t h e binding force increases. It seems best, then, in the light of this theoretical treatment to reassign the values of the acetylenic frequencies as follows: For the valence vibration of the C=C bond Y = 2215 cm.-l, and
TABLE I. HYDROCARBON CRITICALCONSTANTS
(1)
where AC, = molar increase in heat capacity at P, = critical pressure, atmb To = critical temperature, K.
T oK.
Methane Acetylene Ethylene Ethane Methylacetylene Allene Propylene Cyclopropane Propane Dimethylacetylene Butadiene 1-Butene 2-Butene Butane Isoprene Pentylene Pentane Hexane Heptane Octane Cyclohexene Cyclohexane Methylcyolohexane BenEene Toluene Phenylaoetylene S t rene Et%ylbenzene Prop ylbenzene a Calculated by one
Table I contains selected data for the critical temperature and pressure of the hydrocarbons concerned. By means of Equation l and Table I, t h e molar increase in the heat capacity was calculated and added to the heat capacities at zero pressure tabulated in the previous paper ( 2 1 ) . The resulting heat capacities at one atmosphere pressure are presented in Table 11. I n a private communication Herman D. Noether pointed out t h a t the assignment of acetylenic frequencies (91) was not in agreement with those of Crawford (7, 8), or Glockler and Davis (1.8). T h e original frequency assignment was arrived at by taking the experimental heat capacity data of Kistiakowsky and Rice (IS, I C ) , subtracting all the energy except t h a t in the C s C bond, and then distributing this energy between two frequencies to give the best fit with the experimental data. On practical grounds the original frequency assignment came well within the limits of accuracy possible ( d 4 per cent) by this method of calculating heat capacities, but from a theoretical standpoint it is
Tel C. T c , O K. -82.1 191.1 35.9 309.1 9.6 282,s 32.3 305.5 121.6 394.8 120.7 393.9 91.4 364.6 124.6 397.8 370.0 96.8 489.0 215.8 435.0 161.8 433.2 160.0 428.2 155.0 426.0 152.8 474.0 201.0 475.8 202.6 470.4 197.2 234.7 607.9 540.2 267.0 569.6 296.4 525.0 251.8 281.0 554.2 574.7 301.5 288.5 661.7 593.8 320 6 586.0 312.8 646.2 373.0 619.6 346 4 638.8 365.6 of two methods (17,83).
P e , Atm. 45.8 61.7 50.7 48.2 54.7" 53.2" 45.4 54.2 42.0 31.3 42.6 42.1 42.1 36.0 55.6 40.4 33.0 29.5 27.0 25.2 36.6 40.6 34.40 47.8 41.6 40.0 46.1 38.1 32.3
Citation.
a
I
~~
OF HYDROCARBON GASESAT ONE ATMOSPHDRE PRESSVRB (C;) TABLE 11. MOLARHEATCAPACITIES
Ta K,
Allene P r o ylene
C yoPopropane
Propane Dimethylacetylene Butadiene 1-Butene 2-Butene Butane Isoprene Pentylene Pentane Hexane Heptane Octane Cyclohexene Cyclohexane Methylcyclohexane Benzene Toluene Phenylacetylene styrene Ethylbenzene Propylbeneene
250
300
360
400
450
500
600
700
800
900
1000
1100
1200
1300
1400
1500
8.39 8.90 9.67 11.93 13.69 12.57 14.11 14.82 15.71 18.24 16.49 18.03 17.32 19.65 20.18 21.96 23.61 27.71 31.83 35.98 22.92 25.10 29.00 17.97 22.19 24.24 24.61 26.27 30.54
8.89 10.72 10.49 13.16 14.68 13.64 15.63 16.54 17,64 19.67 18.28 20.24 19.64 22.26 22.78 24.85 26.89 31.61 36.35 41.10 26.44 29.00 33.37 20.61 25.50 27.61 28.16 30.23 35.05
9.55 11.48 11.57 14.56 15.79 14.87 17.37 18.42 19.89 21.43 20.28 22-67 22.24 25.27 25.59 28.13 30.65 36.10 41.57 47.05 30.39 33.01 38.26 23.62 29.26 31.33 32.21 34'73 40.27
10.30 12.14 12.69 16.15 16.94 16.16 19.19 20.33 22.24 23.29 22.35 25.35 ~. .. 24.94 28.41 28.48 31.62 34.57 40.78 47.01 53.24 34.40 37.82 43.22 26.66 33.10 35.06 36.28 39.33 44.60
11.08 12.70 13.81 17.70 18.07 17.44 20.99 22.18 24.65 25.12 24.38 27.90 27.55 31.46 31.28 34.82 38.35 45.31 52.26 59.22 38.30 42.23 48.03 29.62 36.79 39.66 40.20 43.76 50.76
11.84 13.14 14.89 19.20 19.16 18.70 22.72 23.91 26.75 26.88 26.33 30.31 30.04 34.36 34.04 37.94 41.95 49.59 57.22 64.83 41.94 46.25 52.52 32.36 40.23 41.98 43.88 47.89 55.57
13.28 13.92 16.87 21.92 21.16 21.01 25.86 27.00 30.70 30.06 29.86 34.67 34.48 39.54 38.69 43.52 48.34 57.20 66.07 74.93 48.38 53.48 60.45 37.19 46.28 47.79 50.31 55.16 64.04
14.59 14.58 18.51 24.30 22.92 23.03 28.57 29.64 34.11 32.83 32.90 38.43 38.29 43.98 42.78 48.28 63.81 63.69 73.56 83.45 53.81 59.60 67.15 -. 41.21 51.24 52.62 55.64 62.20 71.11
15.78 15.16 19.96 26.38 24.54 24.79 30.93 31.92 37.06 35.32 35.53 41.65 41.54 47.81 46.27 52.38 58.49 69.64 79.98 90.72 58.41 64.82 72.82 44.58 55.55 56.69 60.15 66.30 77.05
16.84 15.69 21.45 28.21 25.85 26.33 32.98 33.90 39.64 37.35 37.79 44.28 44.21 51.11 49.27 55.74 62.54 74.02 85.49 96.97 62.33 69.29 77.67 47.40 59.10 59.96 63.90 70.58 82.07
17.79 16.17 22.62 29.82 27,07 27.64 34.76 35.61 41.88 39.19 39.74 46.84 46.78 53.99 51.85 68.93 66.04 78.15 90.26 102.3 65.65 73.08 81.79 49.77 62.11 62.75 67.09 74.21 86.32
18.63 16.60 23.63 31.21 28.12 28.77 36.29 37.10 43.80 40.78 41.42 48.92 48.88 56.48 54.07 61.56 69.06 81.72 94.36 107.0 68.56 76.42 85.39 61.81 64.67 65.13 69.79 77.32 89.97
19.38 17.00 24.51 32.43 29.05 29.76 37.63 38.42 45.50 42.17 42.88 50.74
20.03 17.35 25.26 33.60 29.84 30.61 38.79 39.56 46.96 43.36 44.11 52.28 52.25 60.50 57.63 65.79 73.96 87.48 101.0 114.5 73.20 81.78 91.18 55.04 68.75 68.86 74.07 82.27 95.78
20.60 17.67 25.92 34.42 30.54 31.34 39.79 40.56 48.24 44.41 45.19 53.63 53.60 62.15 59.06 67.48 76.93 89.80 103.6 117.5 75.08 83.94 93.52 56.33 70.38 70.34 75.76 84.25 98.01
21.10 17.95 26.50 35.22 31.13 31 .98 40.66 41.4a 49.35 45.32 46.14 54.81 54.78 63.54 60.30 68.97 77.64 91.83 106. oi 120.1 76.71 85.83: 95.55. 57.44 71 7 9 71 :SO 77.23 85.96 100.k
1303
60.70
58.65 55.99 63.84 71.70 84.82 07.93
iii:o
71.05 79.29 88.50 53 * 54 66.87 67.15 72.10 80.01 93.11
INDUSTRIAL AND ENGINEERING CHEMISTRY
1304
for the deformatim vibration of the C=C bond 6 = 333 cm.-l Using these new frequencies, the acetylenic bonding contributions to the heat capacity are listed for a series of temperatures in Table 111, and should be employed in place of their counterpart in the previous paper (91).
Vol. 35, No. 12
ACKNOWLEDGMENT
It is m y pleasant duty to thank Herman D. ’Puoether for pointing out the shortcomings of the earlier acetylenic frequency assignment, and the Dow Chemical Company for permission to publish this work. LITERATURE CITE0
BONDING CONTRIBUTIONS TO HEAT TABLE 111. ACETYLENIC CAPACITY (CALORIES/MOLE/BOND) Y
T,0 K. e 250 300 350 400 450 600 600 700 4
e
= 2215. = 3178~
0.0009
O.OO5i
0.01~6 0.0446 0.0840 0.1398 0.2821 0.4466 = 1.435
-
6 = 333b
e
478
1 ,4782 1.6152 1.7052 1.7665 1.8103 1.8423 1.8853 1.9114
T,O K .
Y = 2215, 0 = 3178a
d = 333, 8 = 478“
800 900 1000 1100 1200 1300 1400 1500
0.6743 0.7696 0.9104 1.0345 1.1423 1.2356 1.3156 1.3852
1.9290 1.9409 1.9497 1.9560 1.9609 1.9648 1,9679 1,9703
X vibrational frequency.
Calculation of the heat capacity of acetylene with the new frequencies gives results as much as 12.5 per cent lower than the data of Frost (11). This is understandable, for thc theoretical assignment of frequencies in acetylene (60)is considerably different from those for the substituted acetylenes (7, 8, l a ) , on which the new frequency assignment is based. Consequently, the data in Table I1 are those of Frost (11) converted to one atmosphere. Other acetylenic derivatives in Table I1 were from the new frequencies. T h e new data calculated for methylacetylene are 2.8 per cent or less below the experimental (IS)and calculated (8) values; those calculated for dimethylacetylene are 1.4 per cent or less above the experimental values (14). Except for acetylene, the new frequencies reproduce the experimental heat capacities as well as the frequencies first employed (31).
Altschul, 2. physilc. Chem., 11, 577 (1893). Aston, Szasz, and Fink, J . Am. Chem. SOC.,65, 1135 (1943). Beattie, Ibid., 59, 1586 (1937). Beattie, Poffenberger, and Hadlock, J . Chem. Phys., 3 , 96 (1935 Beattie, Su, and Simard, J . Am. Chem. SOC.,61,924 (1939). Calif. Natural Gas. Assoc., Bull. TS-401, 3 (1940). Crawford, J . Chem. Phys., 7 , 555 (1939). Ibid., 8, 526 (1940).
Doss, “Physical Constants of Principal Hydrocarbons’”,4th e d . , pp. 20, 106, New York, Texas Co., 1943. Edmister, I N D .ENG.CHEW.,30, 352 (1938).
Frost, Trans. Exptl. Research Lab. “Khemgas”, Materials
on
Cracking and Chemical Treatment of Craclcino Products (U.S . S . R.),3,27 (1936). Glockler and Davis, J . Chem. Phys., 2,881 (1934). Kistiakowsky and Rice, Ibid., 8, 610 (1940). Ibid., 8, 618 (1940). Landolt-BGrnstein, “Physikalische-Cheniische Tabellen”, 5th.
ed., Haupt Werke I , p. 255, Bcrlin, Julius Springer, 1923. Lespieau and Chavanne, Compt. rend., 140,1035 (1905). Meissner and Redding, IND. ENG.CHEM.,34, 521 (1942). Morehouse and Maass, Can. J . Research, 5 , 306 (1931). Negornov and Rotinyantz, Ann. inst. anal. phys.-chzm. (U.S.S.R.),3, 162 (1926). Stitt, J . Chem. Phys., 8, 56 (1940). Stull and Mayfield, I N D .ENG.CHEM.,35,639 (1943). Vaughan and Graves, Ibid., 32, 1252 (1940). Watson, Ibid., 23, 360 (1931). Wenner, “Thermochemical Calculations”, 1st. ed., p. 19, New York, McGraw-Hill Book Co., 1941. Young, Sei. Proc. Roy. Dublin Soc., 12, 374 (1910). Tan DoW CanMrcAL COXPANY MIDLAND, MICA.
DANIEL R.STWLL
Autoclaves for Pressure-Temperature Reactions SIR: With reference t o the section on “Safety Devices” on page 942 of this article (September, 1943), the folloa‘ing question has been asked: Was it intended that a frangible diaphragm with a rated bursting pressure of one and a half or two times the design pressure of the vessel should be used as the sole safety device? The answer i$ definitely negative, for the A, S. M. E. Code specifies that relief devices shall function a t the design pressure; hence, i t would be permissible to use a safety head with a bursting pressure fixed a t one and a half or two times the design pressure (depending upon operating conditions) only when the vessel is equipped with another safety device set to let go at the design pressure. The discussion in question was strictly limited t o such practice. However, now that the question has been raised, it might be well t o amplify this discussion. First, it might be pointed out that most engineers consider two pressures when designing autoclaves and other pressure vessels-the operating or working pressure and the design pressure; the latter should always be set at least 10 per cent above the operating or working pressure and would correspond to the setting of the usual safety valve. The writer knows of a number of cases in which safety heads are the sole safety device. In such cases the design pressure of the vessel should not be lower than the rated bursting pressure of the rupture disk; even then, in many instances the best practice might call for a safety valve in parallel with the safety head. Further, in such cases the design pressure should be at least 50
per cent above the working pressure, for if operated at a pressure too close t o the rated bursting pressure, the rupture disk may be overstressed. This may result in premature failure which in some cases can entail the loss of valuable batches of chemicals being processed. When vessels are used for comparatively low operating pressures, the design pressure can be 50 per cent higher than the working pressure without a n excessive increase in the cost of the equipment; but for high-pressure autoclaves it is probably decidedly preferable (from the standpoint of initial cost) t o use a safety valve set at the design pressure and then, solely as an emergency safety device, a safety head with a rupture disk having a bursting pressure of one and a half or two times the design pressure. Finally it should be borne in mind that the above remarks apply only t o cases where vessels are being operated a t permissible maximum pressures. I n many instances vessels are actually operated at much lower pressures than those on which design was based. This sometimes makes i t possible t o use a rupture disk with a rated bursting pressure equal to or lower than the design pressure of the vessel but still following the recommended practice of being 50 per cent above the actual operating pressure. D. B. GOOCH BLAW-KNOX COMPANY PITTBBDROH, PBNNA.
