ALFRED W. FRANCIS Research and Development Laboratory, Socony Mobil Oil Co., Inc., Paulsboro,
N. J.
Pressure-Temperature-Liquid Density Relations of Pure Hydrocarbons N e w equations expressing densities of hydrocarbons as functions of pressure a n d / o r temperature can be used to estimate densities of oils at temperatures above boiling points and at high pressures
&~SITIES of coexisting liquid and vapor phases of organic compounds including hydrocarbons are commonly plotted as oblique “parabolas” with “rectilinear diameters” (Figure 1). This relation, noted by Cailletet and Mathias (ZO), is general, though not quite accurate. T o increase accuracy quadratic equations have been used for the “diameters.” The relation serves to detect discrepancies in observed data, but it is not well adapted for calculating density of either phase in the absence of observations on the other one. I t has been employed for that purpose ( 2 2 ) but by a circuitous route.
Saturated liquid Densities above Boiling Points Quadratic equations are given in the “International Critical Tables” (50) and elsewhere for densities of organic liquids, including hydrocarbons as functions of temperature. These show good agreement with observations u p to the boiling points and sometimes a little beyond. They are not of suitable form to correlate liquid densities a t ternperatures approaching the critical temperature. The curvatures of the density curves increase rapidly in that region. Published equations for the range between the boiling point and critical temperatures are not entirely satisfactory. The relation of Fales and Shapiro (35, cf. 57, 58) employs seven constants (for the two equations required) and shows discrepancies averaging 0.27% for hy-
drocarbons. The equation of Ferguson and Miller (47)involving a decimal exponent is somewhat awkward to use, and its range of good agreement with observations falls short of the critical temperature by about 70’ C . The form of Equation 1 is here devised for this purpose and holds over wide ranges of temperature u p to within 5’ to 20’ C. of the critical temperature.
c D, = A - Bt - E - t In this equation D, is the density of the saturated liquid-i.e., under its own vapor pressure; t is the temperature in ’ C.; A is a constant, generally about 0.06 higher than the density a t 20’ C.; 3 is the slope coefficient, a little lower than the expansion coefficient a t ordinary temperature; C is an integer, generally from 6 to 10; and E is a number generally 34’ C. above the critical temperature for nonaromatic hydrocarbons and a little higher still for aromatics. The plot of the equation includes the dashed curve a t the right in Figure 1. The constants of Equation 1 have been evaluated for each of 44 hydrocarbons, including all those for which observations on density appreciably above the boiling point were found published and some others observed in this investigation or calculated indirectly from published data. They are listed in Table I along with pertinent properties. The average deviation of observations on density frsm the equations is less than 0.0007 or about 0.1%. Even
these discrepancies may be due largely to observational error. The hydrocarbons with the most refined observations over a wide range in temperature, propane and butadiene, show an average deviation of only 0.00024. I n evaluating constants for a compound, a working table is made with temperatures in column 1, preferably at intervals of loo or 20’ C. Column 2 lists observed or interpolated densities at those temperatures. Column 3 is obtained by adding C / ( E - t ) to column 2. E is usually 34’ C. higher than the critical temperature (to the nearest degree) and C is an integer which seems appropriate from Table I . Column 4 is obtained by adding Bt to column 3. B is selected to make the items of column 4 nearly equal near the boiling point and a t a temperature about 30’ C. below the critical temperature. The entire column 4 should be nearly uniform. If so, its mean is constant A . If the items of column 4 bulge, a larger integer is tried for C, and the process repeated. If they sag, a smaller integer is tried. No advantage appeared in using more significant figures for any of the constants than those shown in Table I . More refined data may change this situation. The same form of equation has been found satisfactory for 64 nonhydrocarbons, 20 of them inorganic. The observed densities for each of the hydrocarbons were taken from several investigations covering various temperature ranges, and these were often somewhat inconsistent. The greatest weight was assigned to selections by American VOL. 49, NO. 10
0
OCTOBER 1957
1779
,e:.
m
'0
1780
INDUSTRIAL AND ENGINEERING CHEMISTRY
DENSITY OF HYDROCARBONS Petroleum Institute (API) Hydrocarbon Research Project 44 in the temperature ranges given by them and for moderate extrapolations of those ranges. These tables give densities u p to the boiling points for paraffins and olefins and for monocyclic aromatic hydrocarbons ( 4 ); but for naphthenes the selections are for 20' and 25' C. only ( 3 ) . They extend appreciably above the boiling point only for propane (up to 2.0' C.). The early observations of Young (52, 53, 65, 707) for nine hydrocarbons u p to their critical temperatures are fairly consistent with modern ones in cases which have been tested. Those of von Hirsch (48, 53, 65) on four aromatics have a more limited range, and some of them are definitely low. Those for p-xylene are about 10% low, judging by the API Project 44 selections at lower temperatures (Table I1 and Figure 2). New observations on densities of pxylene as a function of temperature were made by two methods. I n one, a glass pressure dilatometer with graduated stem was charged with a sample, which was boiled to remove air, sealed, and weighed. I t was heated in a bath to the critical temperature and cooled slowly with simultaneous readings of temperature and volume (from the level in the ~~
0.7 0.6
i a5 I \
5 0.4 (3
0.3
5
z
x 0.2
O
C.
I
I I
0.I 0
mXylene
140
180
160
200
220
Figure 1.
.
~~
280
300
Orthobaric densities of n-octane
calibrated stem). Corrections were made for weight of vapor and expansion of borosilicate glass. The other method employed sealed, hollow glass floats of calibrated low ~~
260
240
'C.
TEMPERATURE,
densities; the temperatures a t which they just floated while still completely submerged were noted (43). Floats of density below 0.55 gram per ml. were too fragile for the corresponding high
~
Observed Liquid Densities of Hydrocarbons 2,3-Di-
Obsd.o
...
0.6711 0.6598 0.6515 0.6425
0.6903 0.6841 0.6755 0.6667
0.8088 0.8005 0.7916 0.7823
0.7971 0.7872 0.7782 0.7687
140 150 160 170
0.6348 0.6258 0.6163 0.6077
0.6592 0.6524 0.6436 0.6356
0.7739 0.7640 0.7545 0.7433
0.7593 0.7494 0.7376 0.7263
0.7330 0.7220
180 190 200 210
0.5969 0.5876 0.5776 0.5675
0,6268 0.6176 0.6081 0.5994
0.7327 0.7209 0.7102 0.6966
0.7149 0.7027 0.6910 0.6786
220 230 240 250
0.5573 0.5467 0.5358 0.5226
0.5901 0.5808 0.5705 0.5607
0.6842 0.6717 0.6578 0.6433
260 2 70 280 290
0.5093 0.4950 0.4802 0.4636
0.5499 0.5389 0.5266 0.5142
300 3 10 320 325
0.4458 0.4260 0.4016 0.3875
a
120
100
100 110 120 130
... ... ... ... ... ...
I I
~~
nn0Decane Dodecane Xylene
330 335 340 350 360 370
I I
Table II.
Temp.,
i
p-Xylene
(4)
Calcd.b
... ... ...
2,4-Di- 2,2,5-Tri- Methyl-
Temp., methyl methyl- methylo C. pentane pentane hexane
...
cyclohexane
Toluene
0.7340 0.7228 0.7162 0.7076
0.8229 0.8128 0. 8029 0.7926 0.7829 0.7720 0.7602
...
...
60 70 80 90
0.6598 0 + 6507 0.6423 0.6332
0.6355 0.6252 0.6165 0.6065
...
0.7533 0.7423 0.7312 0.7199
100 110 120 130
0.6236 0.6126 0.6036 0.5931
0.5965 0.5863 0.5758 0.5650
0.6221 0.6121
0.6984 0.6895 0.6798 0.6703
0.7070 0.6966 0.6843 0.6717
(48) 0.620 0.612 0.603
0.7083 0.6965 0.6845 0.6722
140 150 160 170
0.5811 0.5703 0.5584 0.5445
0.5544 0.5415 0.5295 0.5148
0.6022 0.5919 0.5812 0.5709
0.6598 0.6493 0.6386 0.6263
0.7485 0.7341 0.7254 0.7136
0.6670 0.6537 0.6397 0.6244
0.6596 0.6473 0.6343 0.6196
0.594 0.585 0.575 0.562
0.6595 0.6464 0.6328 0.6185
180 190 200 210
0.5325 0.5179 0.5055 0.4873
0.5004 0.4858 0.4700 0.4505
0.5599 0.5486 0.5358 0.5235
0.6151 0.6034 0.5909 0.5768
0.7012 0.6881 0.6746 0.6615
0.6297 0.6157 0.6009 0.5850
0.6099 0.5938 0.5771 0.5581
0.6040 0.5873 0.5699 0.5510
0.548 0.534 0.520
0.6035 0.5874 0.5701 0.5512
220 230 240 246.5
0.4684 0.4461 0.4207 0.3996
0.4254 0.3978 0.3830
0.5077 0.4930 0.4764
0.5618 0.5468 0.5300
0.6471 0.6331 0.6168
0.5017 0.4882 0.4733
0.5667 0.5446 0.5237
0.5375 0.5135 0.4876
0.5304 0.5038 0.4757
0.5301 9.5058 0.4771 0.4605
2 50 253 260 270
0.4572
0.5113
0.5981
0.4362 0.4103
0.4906 0.4690
0.5775 0.5562
0.4574
0.5000 0.4812
0.4556
0.4409 0.4212 0.3968
0.4417 0.4202 0.3950
275 280 285 290 300 305
0.4375 0.4225 0.4062
0.5330
...
... 0.4405
~
...
0.4214 0.3980 0.3749
... ... ... ...
... ... ...
... ... ...
... ... ...
... 0.7430
...
... ... ...
0.7902 0.7810 0.7718 0.7625 0.7531
...
. I .
... ... ... ...
... ... ... ... ... ... . a .
... ... ...
08 .;'5
... ...
...
... ... ... *.. ...
... ...
... ... ... ... ... ... ... I . .
... ... ... ... e . .
... ...
0.3946 0.3772 0.354
I . .
... ... ...
...
...
...
...
...
*.. ... ...
...
0.5069 0.4735 0.4548
Interpolated between observations by two methods. De
=
0.9240
- 0.00093t -
10 387 - t
VOL. 49, NO. 10
OCTOBER 1957
178 1
0.80
I
I
I
I
I
I
I
A P I 44 VON HIRSCH x FRANCIS 0 FRANCIS
I
I
1
-
0
0.76
A
FLOAT METHOD DILATOMETER METHOD
0.72 0.68 0
9
",-0.64
t m
A
A
5 0.60 n
A A A A \
0.56 0.52 0.50 100
I
I
A
I
120
140
I
160
180
I
I
I
I
200
220
240
260
TEMPERATURE,
Figure 2.
Table 111.
2,4-Dimethylpentane
c.
m-Xylene
248.5 247.1
124.1 124.084 174.1 174.123 216.1 216.278
296.7 348.2 (346)" 391.5 (386)"
- 126.593
100.9 100.934
300 299.1
(9)
- 94.991
110.65 110.625
320.8
Obsd. (9)
-26.3 -25.182
144.1 144.411
358 359
Obsd.
- 49
-47,872
139.1 139.103
347 346
+13.0 +13.263
138.35 138.351
346 345
Obsd. Obsd. Obsd. Obsd. Obsd.
Obsd. (8)
(I
Estimates.
1782
c.
80.7 80.50
(3)
p-Xylene
O
- 119.242
(9, 69)
o-Xylene
Temp.,
Glass
(3)
Methylcyclohexane
c.
264 264.6
(3)
n-Dodecane
...
O
Critical
89.8 89.784
Obsd. (3) Obsd.
(3)
n-Decane
320
Properties of Hydrocarbons Studied Experimentally Melting Boiling Point, Point,
(3)
2,2,5-Trimethylhexane
280 300
OC.
by their properties in comparison with literature values. Observations by Kay (59, 58) on the saturated densities of the hexanes and four of the naphthenes are not listed in his papers explicitly but only by complex equations and (for the naphthenes) graphical deviations. These were computed, and correlated by the new Equation l . The new observations on methvlcvclohexane (Table 11) agree within 0.1% with those of Kay (58). No saturated density observations are published on neopentane above 20" C., nor on tetramethylbutane (melting
Hydrocarbon
2,3-Dimethylpentane
\
Density observations on p-xylene
pressures. Some floats were lost by collapse. The method had a limited range, especially for nonaromatic hydrocarbons, and was used only on p-xylene. New experimental density observations arc presented in Table 11. Those for p-xylene are compared in Table I1 and Figure 2 with values calculated from Equation 1 using the constants listed in Table I. The selections of API Project 44 up to 140" C. (4) and those of von Hirsch (48) at 190' to 280' C. also arc listed. The purity of the samples is indicated in Table I11
Toluene
A
A
point, 100.69O C.) except a t 100' (subcooled) and 110' C. ( 3 ) . For ethane there is a gap in observations from - 74O (68) to 0' C. (55). [The table in the "International Critical Tables" (57) includes only estimates based partly on an obsolete value for critical density.] Some saturated densities for these three hydrocarbons are here calculated by short extrapolations of virtually straight isochors (Figure 3) from pressurevolume-temperature studies (7, 74, 39, 84) downward to the vapor pressure curves. This method was used also to obtain additional "Observations" of saturated density on cyclohexane (87) and several other hydrocarbons. These arc listed in Table IV. Attempts to calculate liquid ethane densities below 0' C. by this method were unsatisfactory because the long extrapolation required from data at higher temperatures (84, 93) gave inconsistent results. Density observations on czs-2-pentene and 2-methyl-2-butene are published up to 80' C. (37, 96). These arc omitted from Table I, however, because the values at 20' C. differ by about o.7y0 from those chosen bv API Project 44 ( 3 ) . It is concluded that the samples were impure. The densities listed at 60" and 70' C. arc out of line for both hydrocarbons. Apparently the values a t these temperatures were interchanged for the two hydrocarbons. Seyer's observations on trans-2-pentene (96) showed good agreement and were accepted. The temperature ranges listed in Table I for trans-2-butene, trans-2-pentene, 2,2,3,3-tetramethylbutane,and n-nonane fall far short of the critical temperatures because of lack of observations. Quad-
INDUSTRIAL A N D ENGINEERING CHEMISTRY
... ...
- 105.73 -29.7 -29.681 -9.9 -9.587 * e .
...
...
...
DENSITY O F HYDROCARBONS ratic equations would suffice for the ranges covered, but Equation 1 constants were derived for them so that the equations could be expected to hold with fair precision a t much higher temperatures than those listed. Densities for naphthalene are published up to 470' C. (708); but they are erratic, about 0.01 low at 400' and 460' C., 0.02 low a t 420' and 440' C., and 0.01 high at 470' C., according to the equation. The densities from 200' to 380' C. from Zhuravlev (708) and those calculated from the graphs of Russell and Hottel (88) are not very consistent (mean discrepancy 0.0053) ; but their averages give excellent correlation with the equation. The low listed mean deviation, 0.0003, may be misleading in this case. The temperature ranges listed in Table I are those for which the equations hold within the mean deviations listed. The upper limit was made as close to the critical temperature as possible. Omitting five hydrocarbons (including naphthalene) lacking in observations, the average shortage is 12' C. The lower limit of coverage is either near the boiling point or lower if the equation holds. Consistency of the constants with structure and low mean deviation were preferred to excessive lowering of the range, however.
Saturated liquid Densities Near Critical Point The similarity of the orthobaric density curves-e.g., Figure 1-to parabolas suggests a simple relation between excess of liquid density above the critical density, D, - D,,and the difference in temperature below the critical, t, - t. If a curve were a true parabola, the square of the formerwould be a linear function of the latter. Tests showed, however, that exponent h in Equation 2 is between 2 and 3 for all the hydrocarbons:
The average is 2.55. This relation results in curves which are flatter nosed than parabolas (cf. 48). It is somewhat similar to that for the difference between liquid and vapor densities of carbon dioxide stated by Michels and coworkers (72) to be "well-known" in form. The latter has the same limitations in application mentioned above for rectilinear diameters. The constants of Equation 2 have been evaluated for all 44 of the hydrocarbons and are listed in Table I. The consistencies of the equations with the observations are comparable to those of Equation 1 down to about 50' to 100' C.
70
v)
60
W E
a
50
v)
0
I40
2
30 w
E
20 w
B1:
a 10 0 120
140
160
tb
180 200 220 240 260 TEMPERATURE, 'C. Figure 3.
Table IV,
Compound Ethane (14,84)
n-Butane (13)
Isobutane (8, 89)
Isobutene (9) Neopentane (7) 2-Methylpentane (60)
a
280
300 320 tc
lsochors of n-octane
Saturated Liquid Densities Calculated from lsochors Temp., O C. +12.4 18.4 21.9 25.5 29.5 85.8 103 117.8 128.9 138.1 144.8 148.7 67.9 75 81.3 83.8 87 92.4 97.4 102 106.4 110.55 111.7 114.5 118.3 127.7 113.07 131.3 127.6 150.45 174.3 194.5 211
Density, Gram/ MI. 0.367 0.347 0.333 0.316 0.300 0.4937 0.4646 0.4356 0.4065 0.3775 0.3485 0.3194 0.4936 0.4808 0.4700 0.4650 0.459 0.448 0.437 0.428 0.418 0.4075 0.4068 0.3975 0.387 0.3487 0.4478 0.3927 0.432 0.360 0.4739 0.4308 0.3877
Density, Gram/ c. M1. 130 0.6667 0.6250 165 0.5882 192 0.5556 215 231.5 0.5263 242 0.5000 252.8 0.4762 0.4651 256 0.4545 259 265.35 0.4348 0.4167 269.7 271 0.4082 273 0.4000 275 0.3846 279.7 0.3571 195.5 0.5014 94.4 0.6588" 96.1 0.6570" 102.4 0.6514 106.3 0.6485 108.2 0.6468 112 0.6414 114 0.6332 116 0.6378 118 0.6357 128 0.6234 137 0.6196 142.4 0.6143 150.4 0.6056 155.5 0.6002 158.3 0.5966 172.4 0.5851 184 0.5708 188.7 0.5654 195.5 0.5562 199 0.5510 206.6 0.5467 214.6 0 * 5359 227.4 0.5139 236.6 0.4904
Temp., Compound
Cyclohexane (87)
%-Heptane (97) 2,2,3,3-Tetramethylbutane (37)
Extrapolated (liquid).
VOL. 49, NO. 10
OCTOBER 1957
1783
below the critical temperature. There is thus substantial overlap in coverage for the two equations for every hydrocarbon listed except 2-butene and 2-pentene. For the five hydrocarbons lacking in reliable observations near the critical temperature, densities calculated by Equation 1 were used in evaluating constants for Equation 2. The equations are less reliable in those cases. Exponents h are affected considerably by the selections o i critical densities, which are difficult to observe with precision. Some of them listed in Table I (enclosed in parentheses) are only estimates. The API Project 44 estimate (5) for p-xylene, 0.29, was reduced to 0.27 because at all lower temperatures p-xylene in the lightest isomer. This value is more consistent with Equation 2, which can be used in reverse to estimate critical density. For five hydrocarbons an additional value of critical temperature is listed in Table I in parentheses. These are not actual critical temperatures, but are the values of to to be used in Equation 2 and give more consistent results. For the xylenes, these artificial critical temperatures narrow the gap between that of o-xylene and those of its isomers. This gap is much larger than would be expected from boiling point differences. One possible explanation is that for the five hydrocarbons mentioned, and possibly for some others, the orthobaric density curves (such as Figure 1) are excessively flattened at the nose by mutual solubility of liquid and vapor, giving abnormally low critical temperatures.
tions of isochors from straight lines far exceed possible experimental error in the extreme range in pressure studied by him. Although his conclusion is probably correct, at least for polar compounds, his table in support of it is somewhat equivocal. Some of his isochors are convex and some concave. These curvatures are sometimes reversed in different pressure ranges, and bear no perceptible relation to structure. Thus, isochors of normal paraffins C j to C8 are convex, concave, concave, and convex, respectively. Edulgee, Newitt, and Weale (30) could find no deviations from straight lines for three of these four normal paraffins in the same pressure range.
1.4
1784
o BRIDGMAN EDULGEE x FELSING 8. WATSON
,c'
2 1.2
A
IQ
'. 1.0 a 5 0.8 Ld
v)
& r lx
I
0.6 0
0.4
;
Q
0.2
a
1
I
I
I
I
I
I
1
I
6 4 5 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 DENSITY, GRAMIML.
Liquid Densities at Higher Pressures At temperatures approaching the critical temperature a liquid becomes increasingly more compressible. Investigations have been published, several by Sage and coworkers, giving volumes or densities at various temperatures and pressures for many substances, mostly hydrocarbons. Publications are in the form of extensive tables using various units for pressure, temperature, volume, or density. Accurate interpolation is difficult because of the high curvature of isotherms, isobars (lines of constant pressure), and curves for pressurevolume values. O n the other hand, isochors or lines of constant density or specific volume (called also isometrics, isopycnics, or isosteres) are almost straight, not only for gases a t low pressure but also for gases at high pressure and for liquids to enormous pressures. O n a pressuretemperature plot the isochors fan out from both the lower (vapor) and upper (liquid) side of the vapor pressure curve (Figure 3). Bridgman (78) considered that devia-
ated for 27 hydrocarbons for which data are available, and are listed in Table V. All but isoprene are included among the 44 hydrocarbons of Table I. The degree of correlation is illustrated in Figure 4 for n-octane, with observations taken from three different investigations. There is, of course, some scattering of the points; and Bridgman's observations (76, 77) which reach the highest pressures, up to 12,000 atm., give an aberage of 2 to 370 lower values of IT than do the other investigations. This is not due to the higher pressures, however, as the same discrepancies occur at the same pressures in overlapping regions. The same form of equation has been found satisfactory for un-
Figure 4.
Slopes of isochors of n-octane
Other papers (25, 47, 700) have presented temperature functions of volume only. Westwater, Prantz, and Hildebrand (704) gave a relation equivalent to a = S T V 2 between slope of the isochor, absolute temperature, and molar volume. It holds well for the pressure range observed by them, up to 20 atm., but not a t much higher pressures. A more empirical relation is developed here, as expressed in the following equation : log S = K D
-
F
(3)
in which D ( = l / V ) is the density in grams per milliliter; S is the slope of the isochor (dP/dt), in atmospheres per O C.; F is a constant, which is 1.0 for several gasoline hydrocarbons; and X i s a constant, roughly two thirds of the critical volume in milliliters per gram. Constants F and IC have been evalu-
INDUSTRIAL AND ENGINEERING CHEMISTRY
published data on 22 high boiling hydrocarbons. Equation 3 can be combined with Equation 1 or 2 and also a n approximate function of the vapor pressure (57-5.3, 99) to give pressure at a selected ternperature and density or temperature for a selected pressure and density. To get density or volume for a selected temperature and pressure it would be expedient to use trial densities and to interpolate. Calculations are illustrated by the following examples : Find the pressure necessary to hold benzene at a density of 0.7 gram per ml. at 200' C. First, solve Equation 1 for d (Table I ) . D , = 0.9314 - 0.00036t - 10/(327 t ) = 0.7 when t = 173.6' C., vapor pressure = 9 atm. Next, solve Equation 3 for S (Table V) ; log S = 2.3370 - 1.0 = 0.636. 5' = 4.325.
DENSITY OF HYDROCARBONS Hydrogen BRIDGMAN AMAGAT
0
a
0
1.6
CURVE C A L C U ~ A T E D FROM WOOLEY
I
w
sa LL
0
Hydrogen is included in these correlations because at high pressures it behaves in miscibility relations like a hydrocarbon of zero carbon atoms. Pressure-density-temperature relations for hydrogen have. been studied with high precision by many investigators. Wooley, Scott, and Brickwedde (706)
/-I
1.0 -
0.6 -
log S function is presumably a measure of the compressibility of the molecules, as suggested by Bridgman (79). At lower pressures and densities the hydrogen molecules are mobile. The density a t the break of the curve in Figure 5 is near to that estimated by extrapolation by Dewar (28) for liquid hydrogen a t absolute zero, 0.0834 gram per ml.
I
I 0.6 -
'.
d
s
Table V.
0.4-
0.2-
Hydrogen (above 2000 atm.) Methane Ethane Ethylene
0 I
0
I
I
I
0.02 0.04 0.06 0.08 0.10 DENSITY, GRAMIML.
Figure 5.
,
0.12
0.14
Slopes of hydrogen isotopes
Then, AP = S(At) = 4.325 (200 173.6) = 114 atm. P = 114 f 9 = 123 atm. Find the temperature a t which the pressure of cyclohexane is 50 atm. a t a density of 0.5 gram per ml.: First, solve Equation 1 (Table I) for t. D, = 0.8275 - 0.00095t - 7/(315 - t ) = 0.5 when t = 242.7' C., vapor pressure = 25 atm. Next, solve Equation 3 (Table V) for S; l o g s = 2.5380 - 1.0 = 0.269. S = 1.86. Then, At = A P / S = (50 - 25)/1.86 = 13.4'; t = 242.7 13.4 = 256.1' C.
+
a
Find the density of n-pentane at 100' C. and 100 atm.: It is necessary to find by trial (cf. Figure 3) an isochor through the selected conditions which intersects the vapor pressure curve at a temperature at which D, has the same value as D of the isochor. First, assume D = 0.6; then from Equation 3 (Table V), log S = 2.760 0.9 = 0.756, S = 5.7; vapor pressure = 3.9 atm. (by trial). At = A P / S = (100 3.9)/5.7 = 16.9' C. This isochor would intersect the vapor pressure curve (3.9 atm.) a t 16.9' below 100' C. or 83.1' C. (first trial temperature). D, = 0.6762 - 0.00087t - 7/(231 - t ) = 0.5564, a discrepancy of -0.0436. Or, assume D = 0.56, then proceeding as above, S = 4.42; vapor pressure = 3.4 atm. At = (100 3.4)/4.42 = 22.0' C. t = 78' C. D,= 0.5624. The discrepancy, +0.0024, is only 5.5% as great as in the first assumption. Interpolating, D, = D = 0.5624 - 0.055 (0.5624 0.5564) = 0.5621.
-
-
-
-
All three answers could be derived instantly from appropriate large-scale graphs similar to Figure 3.
lsochors for Compression of Pure Hydrocarbons above Their Critical Densities" K Hydrocarbon F 22.0 3.63 3.22 2.87
0.885 0.41 0.64 0.53
Propane Propylene n-Butane Isobutane
2.90 2.877 2.88 2.90
0.73
1-Butene Isobutene n-Pentane Isopentane
2.77 2.775 2.76 2.94
0.8 0.82 0.9 1.0
Neopentane Isoprene %-Hexane 2-Methylpentane
2.905 2.304 2.83 2.82
0.95 0.56 1.0 1.0
3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane n-Heptane
2.75 2.795 2.78 2.754
1.0 1.0 1.0 1.0
n-Octane 2,2,4-Trimethylpentane 2,2,3,3-Tetramethylbutane n-Nonane
2.964 2.65 2.63 2.95
1.17 1.0 1.0 1.2
n-Decane Cyclohexane Benzene Naphthalene
2.91 2.538 2.337 1.899
1.2 1.0 1.0 1.0
log S = K D
0.73 0.85 0.85
'
- F.
have smoothed these in the form of a table over the temperature range 0' to GOO0 K. and extending to 500 Amagat units in density (0.045 grams per ml.). Bridgman's observations (78) a t 30' and 65' C . and from 2000 to 12,600 atm. give isochors with densities higher than 0.08 gram per ml. Plots of their slopes fall close to a straight line (Figure 5) as with the hydrocarbons (Figure 4). They correspond to the equation l o g s = 2 2 0 - 0.885
(4)
Slopes of isochors from all of the observations at lower densities fall on a smooth curve which meets the Bridgman line but shows a sharp break a t the intersection. No single equation could reproduce both sets of data even approximately. Nor can the reliability of the observations be seriously questioned. Corrections of over 50% in density would be necessary to bring the points to a single smooth curve. The straight-line
The curve in Figure 5 was derived from the densities given by Wooley (706) a t 300' and 320' K. and so shows the slopes of the isochors as a function of density at 310' K. or 36.84' C. The pressures are reproduced within 0.04% by Equation 5.
S
= 40.680
+ 4000' + 250005
(5)
Equation 5 is satisfactory also for the observations of Amagat (7) u p to 0.085 gram per ml, In the pressure range below 1000 atm. a t least, the hydrogen isochors are slightly convex, in contrast to those of water, which are slightly concave, and those for most substances including hydrocarbons, which are practically straight. That is, the slope for hydrogen isochors decreases with rising trmperature. Temperature corrections can be applied to the coefficients of D2 and D3 in Equation 5 . VOL. 49, NO. 10
OCTOBER 1957
1785
J’ = 40.680
+ (320 -+ 22,200/770’ + (800,000/T)D3 (6)
Equation 6 shows the pressure-temperature-density relations vary generally for hydrogen u p to 1000 atmospheres, and from 200O to 600’ K., though with slightly less precision (about 0.270) than does Equation 5 a t a single temperature ( T in OK.)
Literature Cited (1) Amagat, E. H., Ann. chim. phys. 29, 68 ( 1 893). (2) Ambrose, n., Trans. Faraday Soc. 52, 772 (1956). (3) American Petroleum Institute, Carnegie Institute of Technology, Pittsburgh, Pa., Project 44, “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” pp. 36-71, Carnegie Press, Pittsburgh, Pa., 1953. (4) Ibid., pp. 290-8. (5) Zbid., pp. 326-35. (6) Armstrong, G. T.,Brickwedde, F. G., Scott, K. B., J . Research Natl. Bur. Slandards 55, 39 (1955). (7) Beattie, J. M., Douslin, D. R., Levine, S. W., J . Chem. Phys. 20,1619 (1952). (8) Beattie, J. M., Edwards, D. G., Marple, S., Jr., Ibid., 17, 576 11949’). . - ,(9) Beattie, J. M., Ingersoll, H. G., Stockmayer, W. H., J . Am. Chem. Snc. 64, 547, 549 (1942). (10) Beattie, J.M., Kay,W.C.,Kaminsky, J.. Zbid.. 59. 1590 (1937). ( 11) Beaitie, J.‘ M.’, Marple, S.; Jr., Ibid., 72, 1449, 4144 (1950). (12) Beattie, J. M., Mnrple, S., Jr., Edwards, D. G., J . Chem. Phys. 18, 127 (1950). 113) Beattie, J. M.. Simard. G. L., Su, G-J.; J . Am. Chem. ‘SOC.61, 27 f 1939). (14) Begttic,‘J. M., Su, G.- J., Simard, G. L., Ibid., pp. 924, 926. (15) Bekkedahl, N., Wood, L. A., Wojciechowski, M., J . Research Natl. Bur. Sfandards 17,.883 (1936). (16) Bridgman, P. W., Proc. Am. Acad. Arts Sci. 66, 185-223 (1931). (17) Bridgman, P. W., Ibid., 67, 19-21 (1932). (18) Bridgman, P. W., “Physics of High Pressure,” p. 139, G. Bell and Sons, Ltd., London, 1949. (19) Bridgman, P. W., Rec. trav. chim. 42, 570- .(1023). . (20) Cailletet, L:, Mathias, E., Compt. rend. 102, 1202 (1886); 104, 1563 (1887). (21) Carmichael, L. T., Sage, B. H., Lacev. W. N.. IND.ENG.CHEM. 45. 2698 (1953). \ - -
~
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’’,_
ll.’.,
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RECEIVED for review September 7, 1956 ACCEPTED February 11, 1957 Division of Petroleum Chemistry, 131st Meeting, ACS, Miami, Fla., April 1957.
