August 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
5 . The decreasing absorbance at 5.73 p indicated the loss of carbonyl groups. T h e rate of decrease in this region was more or less uniform throughout the entire exposure for the linseed oil film. A slight increase in absorbance after a 2-hour exposure was noted for t h e dehydrated castor ail with a uniformly decreasing rate for t h e remainder of the exposure. 6. The loss of t h e individual groups as indicated by the infrared spectra agreed with the total weight loss of both oil films. This loss is apparently sustained by a breakdown of the.film at severrd points-e.g., OH-group, CH2 groups in the chain, and carbonyl groups-and is greatly accelerated by the ultraviolet light in t h e presence of oxygen. T h e breakdown products are apparently highly voIatile me,teria.ls which escape and have not yet been identified. LITERATURE CITED
(1) .idams, K., Auxier, R. W., and Wilson, C . E.,
Ofic.Dig. Federation Paint & V a r n i s h Production Clubs, No. 322, 669 (1951). (2) Coffey, S., J. Chem. SOC.,119, 1152;60 (1921). CHEW.31, ( 3 ) Deatheraget F. E., and Mathill, FI: A., IXD. 1425 (1939). (4) Dugan, L. R-3 Jr.9 Beadle, B. and Henick A. s.3 J . Am. oil Chemists' Soc., 26, 681-5 (1949). (5) Ellis, B.A., and Jones, R.A., Analyst, 61, 812 (1936). (6) Elm, A. C., IND. ENG.CHEM.,23, 8 !1-7 (1931). (7) Fahrion, W.. 2. Angew. Chem., 23: r22--6 (1910).
w.,
1649
(8) Farmer, E. H., Trans. Faraday SOC.,42, 228 (1946) (9) Farmer, E. H., and Sutton, D. A., J . Chem. SOC.,1943, p. 119. (10) Farmer, E. H., Koch, H. P., and Sutton, D. A , , Ibid., 1943, p. 541. (11) Frank, W., and Jerchel, D., Liebigs Ann. Chem., 533, 46 (1938). (12) Honn, F. J., Bezman, I. I., and Daubert, B. F., J. Am. Chem. soc., 71, 812 (1949). (13) Kass, J. P., and Burr, G. O., Ibid., 63, 1060-3 (1941). (14) MFrcusson, J., 2. angew. Chem., 38. 148 (1925). (15) Nicholls, R. V. V., and Hoffman, W. H., Ofic.Dig. Federation Paint & Varnish Production Clubs, No. 327, 245 (1952). (16) Overholt, J. L., and Elm, A. C., IND.ENG. CKEM.,32, 378 (1940); 32, 1348 (1940); 33, 658 (1941). (17) Paquot, thesis, "Autoxydation et Oxydation Par I'Oxygen," University of Paris, 1943. (18) Powers, P. O., IND. ENG.CREM.,41, 305 (1949). (19) Powers, P. O., Overholt, J. L., and Elm. A. C.. Ibid., 33, 1257 (1941). (20) Prill. E. A , , Oil & Soap, 19, 107 (1942). (21) Sheppard, N., J . Inst. Petroleum, 37, 95 (1951). (22) shreve, 0 , D., Heether, N. R.,Knight, H, R., and Swern, I>., Anal. Chem., 23, 282 (1951). ~paraday ~ sot., ~ 41, ~ 286 (1946). . (23) Sutherland, G , B. B,, T RECEIVED for review October 22, 1954. ACCEPTED February 23, 1955. Presented before Division of Paint, Plastics, and Printing Ink Chemistry. 126th Meeting, ACS, New York, September 1954.
Thermodynamic Functions of Carbon Dioxide ENTHALPY, ENTROPY, AND ISOBARIC HEAT CAPACITY AT 100" TO 1000" C. AND 50 TO 1400 BARS DONNA PRICE ,Vaual Ordnance Laboratory, White Oak, Silver Spring, Md.
T THE present time, tables of thermodynamic functions based on pressure-volume-temperature ( P - V - T ) measurements of carbon dioxide gas are available in t h e ranges 25' t o 150" C., 1t o 3000 atm. ( 6 , 7 ) ,and 0" t o 600" C., 1 t o 50 atm. ( 4 ) . Recently P-V-T d a t a have been determined b y Kennedy at higher simultaneous temperatures and pressures ( 2 ) . These data have been used in t h e present work t o compute thermodynamic functions in t h e range 100" to 1000' C., and 50 to 1400 bars
The Kennedy P-V-T data ( 2 ) have a precision of 2/1000; these d a t a were obtained b y the use of reference values from the 150" C. isotherm determined b y Michels and others (8, 10) (precision of 1/10,000), and agree t o O.2Y0 or 0.0001 gram per cc. with the d a t a of MacCormack and Schneider ( 9 ) (precision of 1/10,000). T h e two sets of data of higher prccision agree in t h e region of overlap. with each other t o about o.lE17~ Diffcrence tables of Kennedy's data ( d ) indicated that a functional smoothing in two variables should be made. This was donra b v plotting t h e compressibility. = PV/RT
COMPUTATION OF THERMODYNAMIC PROPERTIES
T h e enthalpy was computed by
H(T,P )
SMOOTHING O F DATA
Z
Table I contains the smoothed values of the pressure-volume product, PV, as a function of pressure and temperature. T h e terminal points and their sources are indicated. Most of the changes introduced b y the smoothing were well within the precision limit of O.2YO. A few were larger but none exceeded the maximum shift of 0.4% ( 8 ) .
(1)
as a function of density, p, t o form a mesh of isobars and is+ therms. T h e data of higher precision ( 3 , 8, 10) and a temperature extrapolation of the MacCorniack and Schneider data (11) were used t o obtain fixed terminal points. T h e remaining points, a t corners of t h e mesh, were adjusted so t h a t the smoothed values g a w a satisfactory graphical net and also satisfied Equation 1.
=
H ( T , 50.66)
+
and the entropy by
where P is in bars, T in 'K., and V in Amagat units. T h e zero points for both entropy and enthalpy have been chosen at 0' C. and 1 atm. T h e constants used for this adjustment are those of MacCormack and Schneider ( 4 ) and are included in t h e 50.66-bar (50-atm.) starting values. T o obtain the starting values a t 50.66 bars, the correction t o t h e value a t 1 atm. was plotted against temperature. Values for 75" t o 150" C. ( 7 ) were assumed correct; those for 200" t o 500' C. ( 4 )and for 600' t o 1000' C. ( I I ) , approximately correct, with greater weight given t o t h e values a t higher temperature. T h e final curve was visually chosen t o pass through the first
Val. 47, No. 8
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
1650
Table I. Pressure, Bars
150 1.467la 1 ,3570 1.2672 1.208Zc 1.1890c 1.2O4ac 1.2455c l.3OlGc 1.36690 1 4377c
100
1.2255a 1 ,0469 0.8908 0.8214c 0.8383< 0.8947c 0.9664c 1.044lC 1.124fiC 1.2063c I.3703 1.5888 1,5332 1.7446 1. 6943c 1 ,9019: 1 ,8530 2 . 0 5 8 7 2.0100 2.215Ic 2.164gC 2.37OZc 2.317SC 2.5236c 2.469OC 2.6757E 2.618Gc 2 . 8 2 6 4 c
50
100 160
200 250 300 350 400
450 500
600 700 800
H
900 1000 1100 1200
1300 1400
Smoothed Values of Pressure-Volume Product [PY (bar-Amagat unit) I
~Temperature, C. _ _ _ _ _ ~ 200 250 3JO 350 400 450 500 600 700 800 900 1000 1. 69Oga 1.9040a 2.1100a 2.3127" 2.5113a 2 . 7O7la 2.9019a 3 2895= 3.67386 4.05526 4.4366b 4.81706
I.6181
1.8563
1 . 5609
I . 8204
1.5256 1.5106 1.5174 1.5418
1 8034 1.8014 1.8116 1.8334 1 ,8640 1.9034 1.9516 2,0776 2.2159 2.3648 2.5161 2.6679 2.8212 2.9747 3.1272 3,2787
1.5816
1.6340 1.6943 I ,8287 1 9774 2.1305 2.2843 2.4372 2.5913 2.7444 2.8980 3,0492
2.0829 2.0630 2,0578 2.0682 2.0843 2,1097 2.1438 2.1844 2.2284 2.3343 2.4596 2,6025 2.7548 2.9044 3.0560 3.2094 3.3583 3.5070
2.3010 2.2936 2.2952 2.3086 2.3346 2,3669 2.4048 2,4472 2,4913 2,5903 2,7046 2.8412 2.9922 3.1417 3.2914 3.4444 3.5912 3.7393
2.5088
2 5147 2 5252
2.5430 2.5685 2.6063 2.6499 2.6964 2.7436 2.8429 2.9536 3.0828 3.2258 3.3738 3.5234 3.6756 3 8235 3.9705
2.7137 2.7243 2.7412 2.7664 2.7998 2.8416 2.8885 2.9371 2.9870 3.0880 3,1.993 3,3236 3.4602 3.6023 3.7504 3.9012 4.0474 4.1992
2,9154 2.9320 2,9529 2.9826 3.0211 3,0672 3.1177 3.1695 3.2216 3.3280 3.4415 3.5627 3,6914 3.8270 3.9726 4.1209 4,2707 4.4178
3.3134 3.3393 3.3670 3,4046 3.4479 3.4962 3,5492 3.6058 3.6630 3.7760 3.8965 4,0221 4.1475 4.2790 4.4106 4.5541 4.6999 4.8426
3.7078 3.7388 3.7736 3.8110 3.8600 3.9106 3.9643 4,0232 4.0816 4.2032 4.3269 4.4519 4.5825
4.7148 4.8437 4.9792 5.1201
5.2592
4.0950 4.1311 4.1719 4.2166
4.2614 4.3156 3.3711 4,4309 4.4924 4.6154 4.7425 4 8674 5 0011 5.1282 5.2604 5.3932 5.5249 5 6611
4.4803 4,5194 4.5652 4.6125
4.8638 4.9084 4.9554
4.6656
6.0573 5,1117 B.1680 5.2253 6.2843 6.4054 5,5292 5.6577 5.7803 6.9067 6.0373 6.1671 6.3015 6.4279
4.7189 4.7750 4.8335 4.8948 5,0184 6.1470 5.2701 5.3989 5.5279 6.6584 5.7859 5.9145 6.0527
6,0050
From ( 3 ) . b From (11). From ( 7 . 0).
(1
Table 11.
Ideal and Initial Values of Thermodynamic Properties for Carbon Dioxide Zero Pressure
Temp.,
Enthalpy, cal./mole 0
c. 0
100 150 200 260
300 350 400 450 500 600
700 800
a
900 1000 Scale for
913 30 1406 23 1920 01 2452 57 3002 07 3566 98 4145 90 4737 69 5341 20 G579 42 7863 64 9158 69 I0488 2 11839 4 zero point a t 0' C. and 1 atm.
Entropy, cal./mole-deg. 0
50-Atm. Pressure Heat capacity, cal./mole-deg.
2.8409 4.0801 5,2273 6.2970 7.2999 8.2446 9.1383 9.9862 10.7932 12.2987 13.6800 14.952 16.136 17.243
four points and t o give the best fit for the rest of the data. Correction values from the curve were then combined with newly available data on ideal gas properties ( 1 4 ) . The ideal gas term was obtained by linear interpolation and combination of the data of Woolley (14). Table I1 contains the ideal gas and starting values so obtained. T h e isobaric heat capacity was obtained by numerical differentiation of the enthalpy. C P
=
(%)
(4)
Differentiation of PV Tvas done numerically, and a graphical smoothing of the derivative was also carried out. All integrations were done numerically. The procedures are discussed by Price ( I f ? ) . Tables 111, IV, and V contain the enthalpy, entropy, and heat capacity, respectively, as functions of pressure and temperature. The conversion factor for PV in units of bar-Arnagat unit t o calories per mole is 531.97, derived from the value of MacCormack and Schneider ( 4 ) . DISCUSSION
I n general, these functions follow t h e trends in pressure and temperature expected from the law of corresponding states. They qualitatively check the entropy and enthalpy values predicted by Sweigert and others ( 1 3 ) up t o 3000 pounds per square inch. I n the intermediate temperature region of the higher isobars, the curves b ( P V ) / b T us. IT, while smooth, showed unexpected
Enthalpya, cal./mole
Entropya cal./mole-dg.
588.8 1166.6 1738.6 2312,6 2892,l 3480.2 4076.7 4683.0 5296.8 6550.8 7837.8 9153.3 10491.2 11849.5
- 5: 564
-4.110 -2.838 -1.679 -0 617 0.363 1.278 2.144 2.965
4.495 5.888 7.170 8.362 9.475
Heat capacity cal./mole-deg.
11.834 11.335 11.340 11,485 11.663 11.857 12.051 12.228 12.403 12.726 13 017 13.268 13.485 13.670
shallow variations. These irregularities are, of course, reflected in the thermodynamic functions. They appear in difference tables for pressures above 500 bars and temperatures of 300" t o 35OOC. Values obtained for the 100' and 150' C . isothernw can be compared with those of Michels and others. Although the initial PV values were the same in both cases, the treatment and the effect of adjoining data differ. For t h e lower temperature, t h e present entropy and enthalpy values are practically identical with those of Michels and DeGroot (7); the heat capacity differs b y amounts up to 1. cal. per mole-degree (1). For the 150" C. isotherm, the present values of entropy and enthalpy depart from those of Michels and DeGroot ( 7 ) at about 200 bars and parallel them at 600 bars and above. Again the heat capacity values may differ b y up t o 1 cal. per mole-degree. Examination of the isobars shows t h a t the present values of mtropy and enthalpy join smoothly with those of Michels and DeGroot at all pressures. The present heat capacity values ,join smoothly at 150" C. t o those of Michels and DeGroot ( 7 ) up to about 400-bar pressure. At higher pressures, a smooth join can be made only a t higher temperatures b y extrapolating values ( 7 ) t o 200" or 250' C . Recent work a t the National Bureau of Standards (6) has correlated all available earlier P-TI-T data for carbon dioxide and from these data and from very accurate measurements of heat capacity has developed virial equations of state for t h e range 1 to 100 atm. and 300" t o 1500' K. T h e heat capacity in this range was computed from the equation of state; the entropy and enthalpy were computed by integration of the appropriate functions involving t h e heat capacity
August 1955
INDUSTRIAL AND ENGINEERING CHEMISTRY
original data is taken as its accuracy. T h e first derivative would then be expected t o have a n error of 2 % or less; t h e second derivative, of 20% or less. On this estimate, the maximum error in entropy would amount t o 2% of t h e pressure correction increment; the maximum error in heat capacity, t o 20% of the pressure correction increment. T h e error in t h e enthalpy correction varies throughout t h e table and would have to be computed from the integrand of Equation 2 a t t h e point of interest. I n general. it is found t h a t the smaller the correction term for pressure effect, the larger the percentage of possible error in this term is a p t t o he, but, at the same time, the percentage error in the total functional value is smaller. On t h e basis of size of t h e pressure correction increment, examination of difference tables of the thermodynamic properties, and comparison of the present values with other computed values ( 1 , 5, 7 ) in t h e small region of overlap, a certain variation of probable accuracy with pressure and temperature conditions is indicated. The experimental regions, in order of increasing accuracy of the total functional value seem t o be:
This work, of course, involved a temperature extrapolation, since only comparatively low temperature data were available for the correlat,ion. T h e least accurate region was thought t o be above 10 atm. and below 500' K. I n the region 300" t o 1000" C., the C, values of Masi (5) and those obtained from Table V agree t o within 0.1% at 50 at n. and within 0.670 a t 100 atm. Below 300" C., t h e maximum difference is a t 150" C.; i t amounts t o 1% C, at 50 atm. and 2.3% a t 100 atm. This is also, of course, the difference between t h e values of Masi (5)and DeGroot and Michels ( 1 ) . T h e final comparison of enthalpy and entropy values with tliose of Masi (6) cannot be made until the computation of integration constants, now in process, has been completed However, a preliminary comparison may be obtained by using the 150" C. values of Michels and DeGroot (7') together with the subsequent increments with temperature computed h y Masi (6). When this is done, the agreement with t h e values of Tables I11 and IV is good. For enthalpy the difference is within 0.1% a t 50 atm. and within 1% (0.1% above 500" C.) a t 100 atm. For entropy, the values agree within 1% (0.2y0 above 500" C.) a t 50 atm. and t o a constant 0.1 cal. per mole-degree a t 100 atm.
1.
ERROR ESTIMATE
2'
3.
hlong isobars, PV approximates a linear function of temperature. Therefore, each differentation might be expected t o increase the error b y a factor of 10. T o obtain a n order of magnitude for a n error a t any given point, the 0.2% precision of t h e
Table 111.
1651
{
450-1400 bars, 100-350 C . 50- 400 bars, 100-350° C. 450-1400 bars, 400-1000° C. 50- 400 bars, 400-1000° C.
Finally, some error may have been introduced in the starting values of Table 11. This can be simply remedied b y replacing
Enthalpy as a Function of Temperature and Pressure [ H a (cal./mole)]
Prrssure, Bars 50
100
- _ _ _ ~
200 1170.0 1741 2 593.6 907.7b 1546 8 l98.Ob 100 638.5 1360 5 1 RO - 255.5 390.0 1185 7 -- 625.2 200 186.2 1028 1 - 845 1 250 33 4 892 4 300 - 988 6 77 0 782 5 -1058 9 3 50 698 9 -- 1120.4 -156 6 400 -211 7 636 0 450 - 1146.8 -251 7 088 8 500 -1178.4 -301 5 526 0 600 - 1200.0 -323 1 494 7 700 - 1199.8 483 5 -1189.1 -326 8 800 485 3 -1167.5 -318 4 ROO 49G 7 -1141.3 -300 7 1000 515 5 1100 - 1108.3 -276 2 -246 6 040 1 1200 - 1073.3 -213 1 569 4 1300 - 1033.5 602 4 1400 - 992.9 -176 4 a Scale for zero point at 0' C. and 1 atm. 150
C. 450 4683.9 4620.0 4561.1 4608.3 4462.0 4420,O 4382 7 4351.2 4323.0 4296.5 4282.9 4222.7 4205.8 4203.7 4214.8 4235.3 4262,7 4295.1 4331.4
Temperature,
250 2314 6 2164.2 2020.1 1885.7 1763.1 1654.0 15%59. 5 1479.3 1414.4 1362.2 1290.0 1252.7 1237.4 1235.6 1243.3 1268.6 1280.1 1306.8 1337.6
300 2893 7 2775 2 2660 2 2552 5 2456 2 2367 2 2289 7 2221 1 2161 6 2112 0 2040 2 2000 0 1982 2 1978 5 1984 8 1999 0 2019 6 2045 4 2075 4
350 3481.5 3387 9 3296.8 3211 2 3134 4 3064 7 3003,O 294Q,7 2903.3 2862.6 2798.7 2768.6 2739.1 2735.2 2742.7 2758.1 2779.5 2805.9
2836.4
400
4077.7 4001.5 3929.0 3862 8 3803.8 3749.2 3700.5 3658.8 3622.3 3689.4 3535.6 3458.6 3478.7 3475.2 3484 3 3601.9 3525.8 3554.7 3687,6
500 5297 5 5243 6 6194 9 5151 9 5114 4 5081 2 5052 7 5029 5 5009 1 4989 8 4958 6 4938 7 4928 4 4929 3 4942 3 4964 6 4994 2 5029 1 6067 9
600 6551 3 6512.7 6478 9 6449 3 6423.7 6401.9 6384.7 6372.5 6363.9 6357.2 6348.4 6347.4 6353.3 6365.4 6384.3 6410.3 6443.0 6481 4 6524 1
700 7838 2 7812 1 7790 1 7770 9 7754 3 7740 6 7731 3 7726 2 7724 7 7725 9 7733 6 7747 5 7766 7 7790.9 7820 0 7853 5 7891 4 793* 3 7981 3
800
9153.6 9135.6 9121.9 9110.3 9101.o 9094.1 9090.9 9091.5 9095.4 9102.0 9120.5 9144.8 9174.2 9208.8 9248.0 9290.2 9335.7 9384.7 9436 3
900 10491.4 10479.2 10471.7 10466.2 10462.7 10461.9 10464.5 10470.3 10478.8 10489.9 10518.5 10554.5 10595.7 10641 . O 10690.4 10742.7 10796.6 10851.8 10908.2
1000
From (6).
Table IV. Pre6sure, Bars 50
100 150 200 - 5.528 - 4 078 - 2.808 100 - 7.726h - 5.921.6- 4.617 - 9 520 - 7 368 - 5.7,58 150 -10,853 -8.611 -6.634 200 250 -11.711 - 9.232 - 7.351 300 -12.295 - 9.865 - 7.950 -12,713 -10 368 - 8.448 350 400 -13,051 -10,768 - 8.860 -13.322 -11,098 - 9,206 450 500 -13,563 --11.378 - 9.503 600 -13 955 -11,843 - 5.998 700 -14,273 -12,217 -10,394 -14,551 -12 532 -10,726 800 ROO -14 791 -12,805 -11,015 1000 -16,010 -13,046 -11,271 1100 -15.208 -13.263 -11,501 1200 -15,389 -13,461 -11,710 1300 -15,556 -13.643 -11,902 1400 -1B.715 -13,813 -12,080 a Scale for zero point a t 0' C. and 1 atm. b
From (6).
Entropy as a Function of Temperature and Pressure [Sa(cal./mole-degree) 1 Temperature,
250 - 1.650 - 3.371 - 4.427 -5,222 - 5.869 - 6.414 - 6.881 - 7.286 - 7.636 - 7.943 - 8.456 - 8.864 - 9.205 - 9,501 - 9.764 -10.001 -10.216 -10.413 -10 595
300
-0.589 -2.251 -3.254
-4.000 -4.600 -5.107 -5,843 -5.927 -6.268 -6.571 -7.084 -7.498 -7.843 -8.142 -8.408 -8.647 -8.864 -9.063
-9.247
350 +0.391 -1.231 -2.195 -2.904 -3.469 -3.944 -4.353 -4.711 -5.030 -5.318 -5.817 -6.231 -6.579 -6.879 -7.143 -7.380 -7.596 -7.794 -7.977
400 1306 -0 289 -1.224 -1.903 -2.441 -2.892 -3.281 -3.621 -3 924 -4.200 -4.684 -5.093 -5.442 -5.741 -6.002 -6.236 -6.448 -6.642 -6.821
C. 450 2.171 0.555 -0.320 -0.979 -1.499 -1.932 -2.304 -2.630 -2 922 -3.189 -3.658 -4.057 -4.401 -4.698 -4.957 -5.187 -5,394 -5.583 -5.758
500 2.992 1.429 0.528 -0.118 -0.626 -1.047 -1.408 -1.723 -2 005 -2.262 -2.715 -3.101 -3.437 -3.730 -3.986 -4.213 -4.417 -4.603 -4.774
600 4.552 2.977 2.095
1.466
0 973 0 566
0,219 -0.082 -0.349 -0.550
-1.015 -1.377 -1.693 -1.973 -2 222 -2 445 -2.640 -2.827 -2 951
700 5.915 4 384 3.514 2.896 2 413 2.015 1 677 1.384 1.125 0.892 0.485 0.139 -0.162 -0.428 -0.666 -0.881 -1.076 -1,253 -1.415
800
7 197 5.674 4.812 4.201 3.725 3.334 3.002 2.714 2.460 2.233 1.837 1.501 1,210 0,954 0,726 0.520 0,332 0,161 0,004
900 8.389 6.871 6,015 5,410 4 939 4.553 4.226 3.943 3.693 3.470 3.083 2.757 2.476 2,229 2.010 1.813 1.633 1.468 1.315
1000 9.502 7.987 7.136 6.535 6.069 5.687 5.364 5.084 4.837 4.617 4.238 3.923 3.652 3.415 3.205 3.017 2.845 2.1386 2.537
1652
Table V.
Isobaric Heat Capacity as Function of Temperature and Pressure IC,( TP),cal./mole-degree]
PI08-
aure. ___ Bars 100 150 50 11.82 11.32 100 15.87" 13.07" 150 21.91 15.80 200 23.02 17.72 250 22.22 18.46 300 21.17 18.57 350 20.15 18.28 400 19.60 18.07 450 19.00 17.77 500 18.67 17.61 600 18.04 17.24 700 17.57 16.95 800 17.24 16.74 900 16.97 16.56 16.78 16.40 1000 16.61 16.26 1100 16.50 16.16 1200 16.44 16.05 1300 16.28 15 97 1400 From (I). ~
200 11.31 12.46 13.56 14.64 15.52 16.02 16.24 16.23 16.17 16.04 15.82 15.68 15.57 15.48 15.38 15.28 15.20 15.13 15.07
250 11.47 12.24 12.90 13.52 14.11 14.61 14.96 15.12 15.15 15.12 15.02 14.93 14.87 14.82 14.77 14.72 14.68 14.65 14.62
300 11.65 12.22 12.74 13.21 13.66 14.05 14.38 14.67 14.88 18.00 15.10 15.07 15.03 15.01 15.01 15.02 15.02 15.01 15.01
350 11.85 12.26 12.68 13.10 13.48 13.82 14.10 14.38 14.63 14.81 15.00 15.03 15.01 15.01 15.04 15.08 15.11 15.14 15.17
Temperature, C. 450 400 12.04 12.22 12.31 12.44 12.63 12.65 12.96 12.88 13.27 13.09 13.55 13.31 13.79 13.51 14.01 13.70 14.18 13.86 14.32 13.98 14.52 14.20 14.62 14.38 ' 14.65 14.47 14.66 14.51 14.70 14.55 14.75 14.61 14.82 14.67 14.88 14.74 14.95 14.80
these values with a more accurate set when such data become available. DEFINITIONS AND CONVERSION FACTORS
V
volume (A.U.) = volume/volumeNTp = density (A.U.) = density/densityprTp =
p
p
=
_____---.-___
500 12.40 12.54 12.72 12.90 13.05 13.21 13.36 13.50 13.64 13.77 14.01 14.20 14.34 14.42 14.47 14.51 14.56 14.60 14.66
600 12.72 12.84 12.97 13.09 13.18 13.28 13.36 13.45 13.54 13.65 13.85 14.02 14.18 14.30 14.38 14.44 14.47 14.51 14.55
700 13.02 13.12 13.22 13.31 13.39 13.46 13.53 13.59 13.65 13.72 13.85 13.97 14.08 14.20 14.30 14.38 14.45 14.50 14.55
800 13.27 13.37 13.41 13.48 13.54 13.60 13.66 13.72 13.77 13.82 13.92 14.02 14.13 14.23 14.33 14.43 14.51 14.57 14.62
900
1000
13.48 13.53 13.59 13.64 13.70 13.76 13.81 13.86 13.90 13.94 14.04 14.16 14.28 14.40 14.50 14.61 '14.70 14.77 14.82
13.67 13.71 13.77 13.82 13.88 13.93 13.97 14.01 14.04 14.08 14.18 14.30 14.42 14.55 14.68 14.79 14.90 14.99 16.05
LITERATURE CITED
(1) DeGroot, S. R., and Michels. A., Physica, 14, 218-22 (1948). (2) Kennedy, G. C., Am. J . Sci., 252, 225-41 (1954). (3) MacCormack, K. E., and Schneider. W. G., J. Chem. Phys., 18, 1269-72 (1950). (4) Ibid., pp. 1273--5. ( 5 ) Masi, J. F., private
communication. Preliminary incomplete version of chapter, "Thermodynamic Properties of Carbon Dioxide," for Bureau of Standards compilation. (6) Michels, A,. and DeGroot, S. R.. A p p l . Sci. Research, lA, 94-
v-1
N T P indicates 0" C. and I atm. = 505.833 p (gram/cc.) (mole/cc.) = 4.49202 X 10-6 p (A.U.) R = 82.0567 cc.-atm./mole-degree = 83.1357 cc.-bar/mole-degree = 1.98719 cal./mole-degree P(bars) = 0.98692 P(atm.) PV(bar-A.U.) = 0.98692 PV (atin.-A.U.) PV(bar-A.U.) = 531.97 c*al./mole p p
Vol. 41, No. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
(A.U.)
102 (1948). (7) Ibid., pp. 103-6.
( 8 ) Michels, A,, and Michels, C., PTOC.Roy. Soc. (London), 153A, 201-14 (1935). (9) Ibid., 160A,348-57 (1937).
(10) Michels, A., Michels, C . , and Wouters, H. H., Ibid., 153A, 214-24 (1935). (11)
ACKNOW LEDGltl ENT
The writer wishes t o thank Elise Fisher, Applied Mathematics Division, Naval Ordnance Laboratory, for assistance with this work; most of the computation was carried out on an I.B.M. card-programmed calculator.
Price, D., Naval Ordnance Laboratory, Rept. 2876 (1953).
(12) Ibid., 3876 (1954). (13) Sweigert, R. L., Weber, P., and Allen, R. L., IND. ENG.CHEM., 38, 185-200 (1946). (14) Woolley, H. E., J. Research Natl. Bur. Standards, 52, 289-92 (1954). ACCEPTEDFebruary 21, 1955. RECEIVED for review December 11, 1954. Work of G. C. Kennedy supported by Bureau of Ordnance under contract NOrd-10449, Task 5, with Harvsrd Univemity.
Measurement and Correlation of Vapor Pressure Data for High Boiling Hvdrocarbons 1
J
€I. S. MYERS' AND M. R. FENSBE College of Chemistry and Physics, The Pennsylvania State University, University Park, Pa.
F
OR some time the petroleum industry has shown an increasing interest in better utilization of high boiling residua. As a result, the vacuum unit is rapidly becoming an integral part of nearly every refinery. This introduces a need for reliable vapor pressure data for high boiling hydrocarbons. I n designing and operating a vacuum unit, boiling points must be converted from one pressure t o another b y means of a vapor pressure chart. A search of t h e literature shows many vapor pressure charts Present address, C. F. Braun Br Co.. Alhambra. Calif.
and nomographs. B u t very few of these correlations agree cloaely, and some of them are widely different, particularly in the high boiling region. For example, suppose a hydrocarbon oil boils a t 575' F. a t an absolute pressure of 1 mm. of mercury. T h e vapor pressure nomograph developed b y Lippincott ( 4 ) predicts a boiling point of 1060" F. a t atmospheric pressure. T h e nomograph of Maxwell (6) predicts 1020" F., t h a t of Kelson ( 6 ) , 980' F., and that of Brown and Badger ( 2 ) , 970" F. This particular example, then, shows a discrepancy of 90" between . correlations.
