110
INDUSTRIAL AND ENGINEERING CHEMISTRY
The following azeotropes were found, composition in weight per cent being given in parentheses: water (29.0)-2-methyI-3butyn-2-ol (71.0) boils at 91.0 o C. at 770 mm., and water (60.7)-3-hydro~y-3-methyI-2-butanone (39.3) boils at 98.6 at 755 mm. The vapor pressure-temperature relations were determined for the methylbutynol and hydroxgmethylbutanone. The refractive index-composition relations for the two binary systems studied were determined.
Vol. 42, No. k
LITERATURE CITED (1) Carlson, H.C..andColburn, A.P., IND.EXG.C H E M . ,581 ~ ~ (1942), ,
(2) Conner,A. z., Elving, P. J.,and Steingiser, S . , I b i d . , 40,497 (1948). (3) Gilmont, R., and Othmer, D. F., I b i d . . 36, 1061 (1944). (4) "International Critical Tables," Val. 111, p. 211-212, New York. McGraw-Hill Book Co., 1927. (@ Othrnerv D . F.i CHEhf., 351 (1943). (6) Reilly, J., and Rae, W. N., "Physico-Chemical Methods," Vol 11,pp. 9-10, New York, D. Van Nostrand Co., 1939. (7) Wohl, K., Trans. Am. Inst. Chem. Engrs., 4 2 , 2 1 5 (1946)
RECEIVED January 10, 1949.
Isobaric Heat Capacities at Bubble Point PROPENE, NEOHEXANE, CYCLOHEXANE, AND ISO-OCTANE C. E. AUERBACH, B. H. SAGE, AND W. N. LACEY California Institute of Technology, Pasadena, Calif. T h e isobaric heat capacity at bubble point has been determined at temperatures from 80" to 160" F. for propene and at temperatures from 80" to 200" F. for neohexane, cyclohexane, and iso-octane. The isobaric heat capacity at bubble point was calculated from the directly measured isochoric values by use of supplementary volumetric data. The latter data were obtained from the literature when available, or estimated from the law of corresponding states. The results are presented in graphical and tabular form.
T
HE information available concerning the heat capacity of propene, neohexane (2,2-dimethylbutane), cyclohexane, and iso-octane (2,2,4-trimethylpentane) in the liquid phase is limited to measurements below 95" F. Powell and Giauque ( 2 0 ) have reported heat capacities for liquid propene a t temperatures from -103" to -43" F. Kilpatrick and Pitzer ( 1 2 ) carried out measurements upon the heat capacity of liquid neohexane in the temperature range from 44' to 62' F., and Douslin .and Huffman (4)made similar measurements in the range from 27' to 73 ' F. The heat capacity of liquid cyclohexane was investigated in the temperature interval between 44" and 7 1 " F. by Aston et al. (I), between 44" and 80" F. by Ruehrwein and Huffman ( $ I ) , and between 50" and 78" F. by Parks and eo-workers (19). Heat capacities of liquid iso-octane have been presented by Parks et al. ( 1 9 ) in the temperature range from 35" to 72" F. and by Osborne and Ginnings (18) in the range from 50" to 95' F. As a result of the absence of such data a t the high temperatures, an investigation of the isobaric heat capacity of bubble-point liquid has been carried out in the temperature interval from 80' to 160" F. for propene and from 80" to 200 O F. for neohexane, cyclohexane, and iso-octane. The measurements were made in the two-phase region utilizing a constant-volume calorimeter. The energy required to raise the temperature of the calorimeter bomb and contents through a predetermined interval was measured and the isobaric heat capacity at bubble point was calculated from these data by means of a relationship resulting from a thermodynamic analysis of the process. The calorimetric measurements were carried out for at least two different quantities of the pure hydrocarbon in the calorimeter. The following equation applying to a pair such measurements has been derived (16,2.4):
r
1
Equation 1 requires certain volumetric data concerning the material in question and also the isobaric heat capacity of the dew-point gas. The thermal quantities in Equation 1, !,/dt and Pz/dt, represent the net energy required per unit temperature change of the calorimeter bomb and its contents. These thermal quantities must include corrections for the radiation losses from the calorimeter. The volumetric data for propene were obtained from Farrington and Sage ( b ) ,and are estimated to represent the actual behavior of propene within 0.3%. The volumetric and vapor pressure data for neohexane were taken from Kay (11). As there were no volumetric data available for the superheated region, the behavior in this region was estimated from the known dew-point volumes and the assumption that the behavior of the fluid was analogous to that of similar substances for which volumetric data were available. It is believed that the quantities so obtained represent the actual behavior to within 1% The volumetric data for cyclohexane were taken from Young (28). Volumes in the superheat region were estimated in the same manner as for neohexane. Vapor pressure data were obtained from the International Critical Tables (9). Volumetric data for gaseous iso-octane a t temperatures ranging from SO" to 200" F. were not available in the literature. They were estimated from the Clapeyron equation d_ P" dT
-
AH
-W V
utilizing the relationship of Nutting (I?') AH
8 ( T 0 - T)l's
(31
January 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vapor pressure data and a value of the latent heat of vaporiaation
at one temperature were obtained from Smith (86). The bubblepoint volumes were taken from the International Critical Tables ( I O ) . The isobars in the superheat region were estimated by the law of corresponding states. The heat capacity of the dew-point gas for each material was obtained from the literature (7, 13, 14, 16, 86). These data were accurate to within 0.2y0.
transfer was established w t h reasonable accuracy and it is believed that the uncertainties resulting from thermal losses were not greater than 0.2% in the corrected values of the,energy added to the calorimeter. The measurement involved the addition of a known weight of the particular hydrocarbon under investigation to the calorimeter and determination of the net energy required to raise the tempvature of t h e calorimeter and contents through a known temperature interval. For the purposes of these calculations it was assumed for the small temperature interval in question t h a t the following equation was applicable: q/dT = & / ( Y E- T A )
120 loo
140 TEMPERATURE,
180
I80
OF.
Figure 1. Experimental Results for Neohexane
The only item of information involving a significant uncertainty is the isobaric volume-temperature derivative a t the dew point in the case of neohexane, cyclohexane, and iso-octane. A consideration of Equation 1 indicates that the influence of this quantity on the heat capacity of the bubble-point liquid is relatively small. This results from the fact that the ratio of the specific volume of the bubble-point liquid to that of the dewpoint gas is small except in the vicinity of the critical state. For this reason, relatively large uncertainties in the isobaric volumetemperature derivative for the dew-point gas do not influence appreciably the resultant values of the isobaric heat capacity of bubble-point liquid.
111
(4)
The left-hand side of.Equation 4 was considered t o apply a t the mean of the initial and final .emperatures. After completion of one such sel'ies of measurements extending over the entire temperature interval investigated, additional material was added to the calorimeter and the sequence of measurements was repeated. For the most part the quantity of energy added electrically was adjusted to yield an over-all temperature rise of approximately 6" F. An effort was made to carry out each set of determinations in accordance with a standardized procedure. The period established for the attainment of equilibrium after the addition of energy was used as the conditioning period for the next step. The temperature of the contents of the calorimeter was measured a t the beginning of the energy addition, and a t the end of the calming period with an accuracy of =t0.005' F., giving an uncertainty of 0.275 in the measurement of temperature rise. The samples were added to the calorimeter by high vacuum and weighing bomb methods (23). It is believed that the weight of the sample was known within 0.0270. I n order to check this quantity and to ascertain that no loss occurred, the samples were withdrawn after the completion of each set of measurements. It was found in all cases that agreement between the weight of material added and that withdrawn was within 0.1%.
APPARATUS AND PROCEDURE
ir
P
The calorimetric equipment used in these studies was substantially the same as that employed in earlier investigations (3, $8, 24). In principle, the equipment consisted of a cylindrical steel container provided with hemispherical closures within which the hydrocarbon liquid was confined. Energy was added electrically t o the interior of the calorimeter by means of a short length of glass-insulated constantan wire encased iyithin a stainless steel tube approximately 0.05 inch in diameter. The ends of the steel tube were brought through the wall of the calorimeter and were sealed t o it a t the point of egress. The quantity of electrical energy added to the calorimeter was determined by conventional volt box and standard resistance techniques. A potentiometer was employed to measure the electromotive force applied and the current flowing through the calorimeter heater. It is believed that the rate of energy addition to the calorimeter was known with an uncertainty of less than o.05~0'0. Energy was added to the calorimeter for approximately 500 seconds in the case of each measurement. The uncertainty in the determination of the total energy added to the equipment was less than 0.1%. The timing of the other events associated with the measurement of heat capacity was sufficiently accurate as to introduce only a negligible uncertainty in the result ($7). In order t o decrease the thermal losses the calorimeter was surrounded by an adiabatic jacket, and the space between the jacket and the calorimeter was evacuated. Arrangements were provided for the automatic maintenance of the average temperature of the interior surface of the jacket a t substantially that of the exterior surface of the calorimeter. Measurements were carried out to establish the magnitude of the thermal losses as a function of the measured temperature difference between the calorimeter and the wall of the jacket. The energy transfers between the calorimeter jacket were in almost all cases less than 1% of the energy added to the unit. The magnitude of this
Figure 2.
Isobaric Heat Capacity of Propene a t Bubble Point MATERIALS
The propene used was purchased as research grade from the Phillips Petroleum Company with analyses which indicated that it contained 99 mole yo propene. This material was subjected to a low temperature-atmospheric pressure fractionation a t a 40 to 1 reflux ratio. The initial 15% of the overhead and final 20% in the still were discarded. The resulting material boiled within a range of 0.1"F. The propene was then subjected to a partial condensation a t liquid air temperature t o remove any dissolved noncondensable gas. The neohexane was of technical grade purchased from the Phillips Petroleum Company. The analysis of the substance showed that it contained not less than 95 mole yo neohexane. It was fractionated twice a t atmospheric pressure in a high temperature-bubble plate column a t a reflux ratio of 5 to 1. Approximately 15% of the overhead was discarded a t the beginning of each fractionation. The variation of the boiling point was less than 0.1"F. during the fractionation. The index of refraction was observed and agreed with values cited in the literature (2,6, 8) within 0.020J0. The cyclohexane was of technical grade and obtained from the Eastman Kodak Company. Analysis showed it to be 97% pure,
112
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLEI. HEAT C A P A C I T Y Temp., OF.
O F C A L O R I M E T E R AWD CONTENTSO
ddT, l3.t.u.p R.
E'.
Propene
.... ,...
,... ,...
,...
....
,...
....
....
,...
.... , . . .
0 ,14716 Lb.6 95.78 96.26 98.37 101.39 103.61 106.47 108.78 109.45 119.02 121.06 126.04 169.16 131.22 134.24 136.34 136.35 141.20 141.36 146.06 150.88
,...
.... .... ....
....
0.3947 0.3965 0,3947 0,3974 0,4026 0.4025 0,4040 0.4017 0.4117 0.4097 0.4154 0,4147 0,4146 0.4199 0.4180 0.4210 0.4223 0.4235 0.4294 0.4270
Neohexane 0.01650 Lb.6 0.2892 85.90 0.2909 93.39 0.2902 100.81 0.2973 108.30 0.2975 116.08 0.2979 123.26 0.3008 130.27 0,3006 137.21 0.3025 144.27 0.3042 151.23 0.3069 158.12 0.3097 164.91 0.3086 171.69 0.3150 185.05
,...
....
,...
.. .. .. .. ....
,... ,... ,...
.... .... .... .... .... .... ,...
0.4110 Lb.6 87.78 0.4985 92.10 0.5034 96.47 0,5040 100.81 0.5043 105.94 0.5086 110.21 0.5065 0.5084 114.50 118.72 0.5141 122.92 0.5135 127.10 0.5116 131.29 0.5139 135.51 0.5127 139.68 0.5191 143.80 0.5188 147.84 0.5232 151.89 0.5250 155.93 0,5265 0,5297 159.98 0.5355 163.95 167.98 0.5328 171.94 0.5359 0.5361 175.91 0.5360 179.86 0,5396 183.81 0.5377 187.78 199.40 0.54fifi
.... .... .. .. .. .. .... ....
.... Iso-octane
0.05687 Lb.b 86.70 0.3089 94.27 0.3124 0.3119 101.32 0.3183 108.18 0.3180 114.93 121.82 0.3179 128.66 0.3182 135.37 0.3218 141.93 0.3218 148.59 0.3237 0.3239 155.25 161.88 0.3266 168.84 0.3306 0.3302 176.27 183.98 0.3317 191.63 0.3328
0.06890 Lb. b 82.49 0.3086 96.54 103.06 109.69 116.23 122.67 129,09 135.51 141.95 148.30 154.58 160.88 187.08 173.22 179.38 185.43
a
0.3135 0.3166 0.3183 0.3200 0.3230 0.3230 0.3187 0.3231 0.3255 0.3258 0,3292 0.3292 0.3317 0.3341 0.3359
0.3495 Lb.b 98.76 105.46 111.88 118.74 125.65 131.97 138.18 144.48 150.72 156.90 168.57 174.55 180.50 186.53 192.58
0.4591 0.4641 0.4678 0.4704 0.4707 0,4744 0,4745 0,4779 0.4808 0.4833 0.4882 0.4915 0.4935 0.4930
....
0.5C
2i
0.4'0
TWY%ATU~L;F.
Figure 3. Isobaric Heat Capacities of Neohexane, Iso-octane, and Cyclohexane at Bubble Point
with benzene as the probable impurity. It was fractionated in the same manner as was neohexane. The material boiled over a range of less than 0.1 ' F. The index of refraction was observed and agreed with values found in the literature (8)within 0.05%. It is estimated that the impurity was less than 0.1 mole %. The iso-octane was of technical grade (97 mole % minimum) and was obtained from the Eastman Kodak Company. It was distilled at atmospheric pressure in a Claissen flask, which was fitted with glass beads to prevent entrainment. The material boiled over a range of less than 0.1 F. The index of refraction was checked with values in the literature (8) and found to agree within 0.05%. The impurity was estimated to be less than 0.1 mole %. O
EXPERIMENTAL MEA SUREM FAT S
The experimental values obtained for the heat capacity of the bomb and contents a t several temperatures for two different quantities of each hydrocarbon are tabulated in Table I. A sample plot of these values for neohexane is presented in Figure 1. The average deviation of the experimental points from the curves as drawn, expressed as a percentage of the difference between the two curves drawn for each substance is 5% in the case of propene, 1.2% for neohexane, 1.0% for cyclohexane, and 0.6% for is* octane. RESULTS
Values of the isobaric heat capacity at bubble point for propene, neohexane, cyclohexane, and iso-octane are recorded in Table 11. A consideration of the accuracy of the measurements of the individual quantities involved indicates an uncertainty in the tabulated values of about 3% in the case of propene and about
0.3482 Lb. b 110.80 0,4426 116.67 0.4467 122.42 0.4493 128.21 0,4496 133.99 0.4521 139.77 0.4554 145.37 0.4590 150.98 0.4600 156.62 0.4597 162.22 0.4663 167.78 0.4686 173.28 0.4702 178.73 0.4704 184.20 0.4748 189.63 0.4744 195.09 0.4764
Total volume of oalorimeter 0.0142 c u . ft. of material in calorimeter.
b Weight
0.55
ddT, B.t.u./' R.
Temp.,
0 . 08225 Lb. b 0,3592 88.29 0.3662 98.89 0.3703 104.60 0.3759 114.96 0.3801 120.54 0.3835 126.08 0.3873 131.50 0.3889 136.91 0,3925 142.25 0.3962 147.55
,...
Vol. 42, No. 1
Figure 4. Volumetric Corrections as Defined by Equation 4
January 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
113
NOMENCLATURE
TABLE 11. ISOBARIC HEATCAPACITIESOF PROPENE, NEOHEXANE, CYCLOHEXANE, AND ISO-OCTANE AT BUBBLE POINT Temp.,
Propene Neohexane Cyclohexane Iso-octane F. 0.5615Q 0.5312 80 0.4378 0.4980 0.5747 0.6373 90 0.4445 0.5035 0.5917 0.5429 100 0.4505 0.5094 110 0.6102 0.5485 0.4570 0.5153 0.6329 0.5543 120 0.4641 0.5212 130 0.4700 0.5273 0.6607 0.5601 0.6985 0.5662 140 0,4764 0.6333 0.7607 0.5723 150 0.4835 0.5395 0.8608 0.6781 160 0.4899 0.5457 0.4961 0.5525 0.5836 170 0.6900 0.5034 0.5584 180 0.5960 190 0.5108 0.5650 0.6045 200 0.5189 0.6717 Isobaric heat capacity a t bubble point, B.t.u./(lb.)(O R.). a
.... .... .... ....
a
1% in the case of the other hydrocarbons. These data are presented graphically in Figures 2 and 3. The sharp increase in the isobaric heat capacity near 140’ F. in the case of propene is in accordance with the proximity of the critical state. Included in these plots are the data of earlier investigators (1, 4, 12, 1821). Most of these measurements were made a t lower temperatures and can only be compared with extrapolations of the present work. The values of Osborne and Ginnings (18) for iso-octane at 50’ to 95” F. shown in Figure 3 were calculated by adding the volumetric correction developed in this work to their reported values of & / A T A m in an isochoric system at the arithmetic mean temperature. Their values are about 0.6% higher than the values obtained in this study. In general, the discrepancies between the extrapolated data of the present work and published data are less than the combined uncertainties of the various sets of measurements. Equation 1 permits the evaluation of the isobaric heat capacity at bubble point from the measured thermal quantities recorded in Table I. I n order that the magnitude of these corrections as established from available volumetric data may be more readily indicated they have been resolved into a single term. This term is defined by the following expression:
(5) C -
The values of the quantity C are related to the state of the system and the pertinent derivatives indicated in Equation 1 in the following way:
%) +
V d dT - vb d V b Vd
(
C, = isobaric heat capacity, B.t.u./(lb.)( O R.) H = specific enthalpy, B.t.u./lb. m = weight of material in calorimeter, lb. P = pressure, lb,/sq. inch absolute - = heat associated with process, B.t.u. Q
?
=
heat associated with infinitesimal change in state, B.t.u.
T = thermodynamic temperature, O R. V = specific volume, cu. ft./lb. p = constant of proportionality in Equation 3
Subscripts A , B = state A and state B 6 = bubble point c = critical state d = dew point 1, 2 = conditions with different quantities of sample in calorim eter Superscript = two-phase state LITERATURE CITED
(1) &ton, Szasz, and Fink, J . A m . Chem. SOC.,65, 1135 (1943).
(2) Brooks,Howard, and Crafton, J. Research Natl. Bur. Standards, 24, 33 (1940). (3) Budenholzer, Sage, and Lacey, IND. ENG. CHEM., 35, 1214 (1943). (4) Douslin and Huffman, J. A m . Chem. Soc., 68,1704 (1946). (5) Farrington and Sage, IND.ENG.CHEM.,41, 1734 (1949). (6) Felsing and Watson, J. A m : C h a . Soc., 65, 1889 (1943). ENG.CHEM.,34. 360 (1942). (7) Gilliland and Parekh, IND. Hodgman, C. D., Ed., “Handbook of Chemistry and Physics,” 26th ed., Cleveland, Chemical Rubber Publishing Co., 1943. “International Critical Tables,’’ Vol. 111, p. 222, New York, McGraw-Hill Book Co., 1927. Ibid.,p. 145. Kay, J. Am. Chem. Soc., 68, 1336 (1946). Kilpatrick and Pitzer, p. 1066. Ibid., p. 1071. Kilpatrick and Pitzer, J. Research Natl. Bur. Standards, 37, 163 (1946). Kiperash and Parks, J . Am. Chem. SOC.,64, 179 (1942). Lacey *and Sage, “Thermodymmics of One-Component Syaterns,” Calif. Inst. of Tech., 1847. Nutting, IND.ENG.CHEM.,22,771 (1930). Osborne, and Ginnings, J . Research Natl. Bur. Standarde, 39, 453 (1947). Parks, Huffman, and Thomas, J. A m . Chem. Soc., 52, 1032 (1930). Powell and Giauque, Ibid., 61, 2366 (1939). Ruehrwein and Huffman, I b i d . , 65, 1620 (1943). Sage, Evans, and Lacey, IND.ENG.CHEM.,31,763 (1939). Sage and Lacey, Trans. Am. Inst. Mining Met. Engra., 13a 136 (1940). Schlinger and Sage, IND. ENG.CHEM.,41,1779 (1949). Smith, J. Research N d l . Bur. Standards, 24, 229 (1940). Spitzer and Pitzer, J.A m . Chem. SOC.,68,2537 (1946). White, Phys. Rev., 31,545 (1910). Young, Sci. Proc. Roy. Dublin SOC.,12,374 (1910).
RECE~VED April 4. 1949.
The values of this quantity as a function of temperature for each of the materials investigated are presented in Figure 4 and with the exception of propene they are of relatively small magnitude and do not appear to decrease the accuracy of the data recorded in Table 11. ACKNOWLEDGMENT
The financial assistance of the California Research Corporation and the interest of H. G. Vesper of that organization have made this work possible. The equipment employed was developed as a part of the activities of Project 37 of the American Petroleum Institute. The cooperation of the American Petroleum Institute in permitting the use of the calorimeter equipment in this investigation is acknowledged as is the assistance of T. J. Connolly in preparing the manuscript.
