I S D USTRIAL A S D E-VGIIVEERING CHEMISTRY
August, 1931
(43) Orlov, J . Russ. Phrs. Chem. Soc., 42, 658 (1910). (44) Rhodes and van Wirt, IND. ENG. CHEM., 16, 1135 (1923); 16, 960 (1924). (45) Salway, J. Soc. Chem. I n d . , 39, 324 (1920). (46) Scheiber, Farbe Lack, 1927, 75. (47) Scheiber, Zbid., 1926, 295. (48) Scheiber, 2. angew. Chem., 40, 1279 (1927). (49) Scheiber. Chem. Umschau Feffe, O d e , Wachse Harze, 34, 1 (1927). (50) Scheiber and Sandig, “Die kunstlichen Harze,” Leipzig, 1930. (51) Scheiber and Sindig, Zbid., p. 60. (52) Slansky. Chem. Umschau Felte, Oele, rt’achse Harze, 34, 148 (1927).
(53) (54) (55) (56) (57) (58) (59) (60) (61) (62) (63)
887
Slansky, Z . angew. Chem., 36, 389 (1922). Slansky, I b i d . , 32, 533 (1921). Smit, Rec. trau. chim., 49, 675 (1930). Stutz, Nelson, and Schmutz, I N D . ENG. CHBM.,17, 1138 (1925). Tschirsch, Chem. Umschau Felle, O d e , Wachse Hame, 32, 29 (1925). Vollmann, Farben-Ztg., 33, 1531, 1599 (1928). Werthan, Elm. and Wien, I N D .ENG. CREM.,22, 772 (1930). Wolff, Farben-Ztg., 31, 1239, 1457 (1926). Wolff, Chem.-Zfg., 48, 897 (1924). Wolff, Farbe Lack, 1928, 262. Wolff, Chem. Umschau Felte, Ode. Wachse Harse, 36, 313 (1928).
Generalized Thermodynamic Properties of Higher Hydrocarbon Vapors’ J. Q. Cope, W. K. Lewis, and H. C. Weber DEPARTMENT OF CHEMICAL ENGINEERING, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASS.
All available, direct, experimental determinations of deviations from the gas laws for the saturated vapors of hydrocarbons having more t h a n two carbon atoms per molecule, when plotted against the ratio of reduced pressure to reduced temperature, fall on a single curve within a maximum deviation of about 3 per cent. Analysis of the data available leads to the conclusion that, up to moderate pressures, the deviations from the gas laws of hydrocarbons having more than three carbon atoms per molecule are approximately the same for equal values of reduced temperature and pressure whether the vapors are saturated or not. These relations, shown graphically, are valid up to a value of RT/P,V = about 4.0, but not beyond. They make it possible to estimate the vapor volume and vapor density of a hydrocarbon under any given conditions of temperature and pressure
from a knowledge of molecular weight and critical pressure and temperature alone. These graphical relationships may be expressed by approximate algebraic forms corrected by graphical functions obtained from the original data, from which, by graphical integration, the internal energy and total heat of hydrocarbon vapors as functions of temperature and pressure are obtained. With these it is possible to compute the heat consumption and energy changes of various processes. Granting additivity of volumes and total heats when, mixing vapors a t constant pressure and temperature, it is possible to estimate the volumetric and thermal relations of vapor mixtures. The material presented may be considered as a graphical method of estimating the volume and the thermal properties of the vapor of any higher hydrocarbon up to and somewhat beyond its critical conditions.
N THE processing of hydrocarbons, the trend of industrial
three carbon atoms per molecule, the ratio is remarkably constant at approximately 3.85, as is shown by Table I based on Young’s data. Furthermore, for these compounds the critical density is practically constant, indicating a critical volume proportional to the molecular weight. Ring compounds have a somewhat lower value of RT,/P,T’,, but even in the case of the aromatics this value falls only to about 3.7. If one wishes to use an average value of 3.78, it seems safe to conclude that a deviation of the ratio RT,,’P,T‘, of more than about 2 per cent from this value need not be anticipated.
I
practice is toward higher pressures and temperatures. From the point of view of engineering design, this introduces serious difficulty, because little is known regarding the properties of hydrocarbons under these conditions. Indeed, the limited data available are restricted to hydrocarbons of relatively low molecular weight, so that, in the case of higher boiling compounds with which the engineer deals predominantly, one is a t present restricted to methods of estimation which may be far in error. It is the purpose of this article to present certain generalizations regarding the P-T’-T relationships and the thermal properties of vapors of higher hydrocarbons, which, it is believed, offer a sounder basis for estimation in the solution of the problems of design involving these materials at high temperatures and pressures than any hitherto available. P-V-T Similarities a t Critical Point
It has long been appreciated that, in certain respects, the various hydrocarbons are extraordinarily similar in their P-V-T relationships. Thus Young’s data (12) on the hydrocarbons emphasize the fact that, at the critical point, the ratio RT,/P,T7, varies but little, particularly if compounds with less than three carbon atoms per molecule are not considered. This ratio indicates, of course, the extent the compound in question deviates from the gas law at the critical point. In the case of normal paraffins containing more than 1
Received April 9, 1931.
T a b l e I-Critical HYDROCARBON
TC
c. n-Pentane n-Hexane %Heptane n-Octane Isopentane Diisobutyl Hexamet hylene Diphenyl Benzene
197 234 266 296 187 276 280 281 526 288
2 8
85 20 80 8 7 5
PC Atm. 3 3 00 29 60 26 80 24 65 32 95 24 55 39 8 40 4 41.3 47 9
Relationships RT, VC
PC
Cc./g. mol
311.0 367,O 429.0 491 308 484 306.5 311.0 490 256.7
~
PCV,
0.232 0.234 0.234 0.2327 0.234 0.236 0.270 0.2735
3 762 3.83 3 845 3 860 3 73 3 795 3 71 3 72
0.3045
3.74
...,
For a series such as the normal paraffins above propane, for which the critical density is constant, the constancy of RT,IP,V, is equivalent to the constancy of the ratio MP,/T,. Data on this ratio, from International Critical Tables and Landolt-Bornstein-Meyerhofer Tabellen, are given in Table 11. It will be noted that for normal paraffins above propane the maximum deviation from 5.01 is * 0 . 1 1 4 . e.,
INDUSTRIAL AND ENGINEERING CHEMISTRY
888
about 2 per cent.2 As discussed below, benzene shows the highest experimental value, 6.94, whereas other hydrocarbons are intermediate, as is clear from the table. The higher values for hydrocarbons other than normal paraffins are, of course, due to higher densities of these hydrocarbons at the critical point.
P-V-T Similarities of Saturated Vapors
Vol. 23, No. 8
ture where the reduced pressures are very low and the percentage differences between them become very great. The differences in Pr shown in Table I11 are far beyond any possible experimental errors, but had that table been constructed a t temperatures near the critical, this would not have been obvious. None the less, Table I11 demonstrates that there can be no universal reduced equation of state for hydrocarbons along the saturation line.
Inasmuch as the various hydrocarbons have values of RT/PV so nearly identical at their respective critical points, corresponding similarity below the critical would be anticipated. The simplest assumption would be that, a t the same reduced temperatures, the saturation pressures of the different hydrocarbons, expressed as reduced pressures, would be identical. Table 111, made up for the normal paraffin hydrocarbons from ethane to octane, inclusive, shows nearly an eightfold variation in the saturation pressures thus expressed, a t a reduced temperature of 0.5. This table demonstrates that for such hydrocarbons there can be no simple, general, reduced equation of state along the saturation line. of M P J T c f o r Hydrocarbons'
T a b l e 11-Value
MP,
HYDROCARBON
INVESTIGATOR
TO
Propane
Pickering Olsyewski Lebau Butane Pickering n-Pentane Young n-Hexane Young Altschul n-Heptane Young n-Octane Young Altschul n-D ecane Altschul Isobutane Pickering Youne Isopentane Diisopropy I Young Diisobutyl Young Ethylene Van der Waals Dewar Olsyewski Cardoso Pickering Propylene Pickering Acetylene Ansdell Cardoso - ~~. Hexamethylene Young Benzene 6.64 Young 6.97 Sajotscbenski 6.95 Altschul 6.89 Scbamhardt Naphthalene 6.77 Guye and M d l e t 6.46 Altschul Toluene o-Xylene 6.2 Altschul m-Xylene 6.14 Altschul #-Xylene 6.01 Altschul Diphenyl 6.37 Guye and Mallet Dural [CaHz(CHa)r] 5.75 Guye and Mallet D a t a taken from International Critical Tables and Landolt-BornsteinMeyerhofer.
5.15 5.25 5.32 4.90 5.06 5.03 5.10 4.98 4.95 5.05 6.02 5.20 5.15 5.29 5.10 5.75 5.05 5.11 5.02 5.20 5.21 5.7 5.2 6.05
Table 111-Saturation
Pressures of N o r m a l Parafan H y d r o c a r b o n s f r o m E t h a n e to O c t a n e
(TI= 0.5) HYDROCARBONT e
c.
Ethane Propane n-Butane n-Pentane n-Hexane n-Heptane ?%-Octane
33.3 96.7 153 197.2 234.65 266.85 296.3
T
P A h .
PI
-119.7 88.2 60.0 37.9 19.2 - 3.1 11.6
0.135 '0.094 0.062 0.028 0.019 0,0133 0.0091
0.00280 0,00214 0,00172 0.000850 0.000638 0,000495 0.0003655
PO Atm. 48.3 44 36.0 33.04 29.8 26.9 24.9
c.
-
Since the reduced pressures of all 'substances necessarily become identical a t Tr = 1 at the value Pr = 1, it is clear that if the vapor-pressure curves of different substances are plotted as Pr against T,, these curves must all converge a t the critical point. I n fact, for the hydrocarbons they come close together long before the critical is reached. Because of this, Table I11 was constructed a t a low reduced tempera-
* Young's
data would indicate a trend, his values for pentane being
5.06 and for octane 4.95. However, Altschul's data ( 1 ) for octane are 5.05 and for decane 6.02, while Pickering (10) gives 4.90 for butane. In other words, both of these investigators reverse the trend shown by Young. I t seems reasonable t o assume an average value of 5.01 for normal paraffin hydrocarbons above propane.
Figure 1
It is clear that whatever the P-V-T relations of a material, they can be represented by the expression PV = pRT, provided one employs at each point the proper value of p. Obviously also, p = PVIRT, and is the correction factor to the gas laws, where P, V , and T are the actual values of these variables for the material under consideration at the point in question, and R is the gas constant, Inspection of the data makes it clear that the deviation is a function of pressure as well as temperature, and, since the reduced pressures for the various hydrocarbons are so widely different for the same values of reduced temperature, the deviation for the saturated vapor cannot be a function of the reduced temperature alone. The most extensive data available on the densities of saturated vapors are the measurements of Young. A study of these data showed that if the correction factor /I = PV/RT be plotted, not against reduced temperature, but against the ratio of reduced pressure to reduced temperature, Pr/Tr, the differences between the various hydrocarbons largely disappear. I n Figure 1 are plotted all direct experimental determinations known to the authors on hydrocarbons above ethane. It must be remembered that density measurements in the neighborhood of the critical are subject to considerable uncertainty. On this plot the only serious percentage errors are encountered in this region, At values of Pr/Tr less than 0.98, the maximum deviations of the points from the curve are about 3 per cent.3 Data are available on one other hydrocarbon, diphenyl. Chipman and Peltier (4) measured the vapor density of this 8 The data are plotted without any modification whatever, except that, for benzene the value 6.94 was used for the ratio MPJT,. Young's data give 6.64 for this ratio, hut the literature contains three other determinations of the critical point of benzene which average the higher ratio given above, the lowest value being 6.89 and the highest 6.97 (Table 11). I n view of the fact t h a t Young's value for the shove ratio at the critical differs from the average of the other investigators six times as much as the maximum deviation of any of the others from that average, i t seems justifiable to conclude t h a t Young's figure for benzene a t the critical is in error.
August, 1931
INDUSTRIAL, AND ENGINEERING CHEMISTRY
hydrocarbon by the Dumas method at a pressure of 740 mm. and a temperature about 5" above the saturation point. They made five independent experimental determinations and report a density of 3.615 * 0.01 gram per liter. They corrected this result to the saturation line by means of the gas laws, reporting 3.75 grams per liter at the akmospheric boiling point, 265.25" C. This gives a value of p = 0.949 at P,/Tr = 0.046, whereas the Young curve gives p = 0.95. This point checks Young's data almost perfectly. Note-There has recently appeared a table of the vapor properties of diphenyl u p t o the critical point ( 5 ) which does not check the Young relationship. The dotted line of Figure 2 shows the data from this table plotted on the Young curve. The Cunningham table does not check the experimental determinations of Chipman and Peltier, their experimental determination of the density at atmospheric boiling point corresponding to 0.2335 pound per cubic foot, whereas Cunningham's table gives 0.210,a figure 10 per cent lower. At these conditions the density calculated from the gas laws is 0.22 pound per cubic foot. Thus, while Chipman and Peltier's determinations correlate with the experimental data of Young, Cunningham's table would indicate t h a t a t low pressures the saturated vapor of diphenyl occupies a volume considerably higher than that corresponding to the gas laws. As far as the writers are aware, no known substance exhibits this phenomenon. Furthermore, Cunningham's table gives for the critical point of diphenyl a temperature of 526.7' C. and a pressure of 41.3 atmospheres. At least this is the point a t which the table shows a latent heat of zero. Guye and Mallet (7) determined the critical point of diphenyl experimentally, obtaining T, = 495.6' C. and P,: = 31.8 atm. Because of these discrepancies between the Cunningham table and the literature, the writers feel that, until Cunningham's figures :are more adequately substantiated, they should not be looked upon as invalidating the Young relationship. Even as they stand, the maximum deviation between the values calculated from Cunningham's table and those shown by the curve of Young is less than 15 per cent.
The curve of Figure 1 is equivalent to a universal reduced equation of state along the saturation line, but as pointed out above, no such relationship exists. The experimental data plot so satisfactorily on Figure 1 because at moderate values of P , the deviations in T , for the various hydrocarbons are small. Thus, for the normal paraffins from methane to octane inclusive, at values of P, = 0.05, the deviations in
889
this point the deviations from the gas laws become slight. Had one plotted not p, but 1 - p, the deviation from the gas laws itself, the percentage errors a t the low pressures just referred to would have been very great indeed. Figure 1 must be looked upon as a relation which may be practically useful, but which, on rigid, theoretical grounds, is untenable. While the data for all hydrocarbons cannot fall on a single curve, it is doubtful if the deviations are greater than the precision of the data at present available. Figure 1makes it possible to obtain the density of the saturated vapor of any hydrocarbon at any temperature, provided its molecular weight, critical pressure, critical temperature, and saturation pressure at the temperature in question be known. It can be looked upon as a correction curve to the gas laws for saturated vapors. It is perhaps well to call attention to the fact that vapor volume at the critical calculated from the gas laws would be 3.8 times the actual value-i. e., would involve an error of 280 per cent. Although this error decreases rapidly below the critical, it is none the less large at pressures of a few atmospheres. In Figure 1, besides the data of Young, are included the data of Dana, Jenkins, Burdick, and Timm (6). These investigators determined the yapor densities of propane, n-butane, and isobutane. They likewise computed the vapor densities by the use of the Clapeyron equation. Except a t high pressures, the checks are excellent, although the computed values of specific volume show a decided tendency to exceed the experimental. At their highest pressures the computed specific volume exceeds the experimental by as much as 7 per cent. Their experimental determinations fall on the Young curve with a maximum deviation of 3 per cent, but their computed values are, of course, low values of MP/T. In their final tables the computed rather than the observed values are used. It must be remembered that Figure 1applies only to hydrocarbons and even then only to compounds of more than two carbon atoms per molecule. Consequently, it should be used for other materials with r e ~ e r v e . ~The relationship is purely empirical. It represents only a method of plotting the available data. The method is, however, dimensionally sound, and the curve can be used for whatever units of pressure, temperature, and volume may be employed, on either a weight or a molal basis, provided the corresponding gas constant be used.
P-V-T Similarities of Superheated Vapor Granting the validity of a relationship such as that just presented for saturated vapors, it would be surprising if some similar relationship did not apply in the superheated region. Meissner and Keyser (9) found that in the region of moderate pressures the P-V-T relations of a number of gases could be represented by the formula PV/RT = e -
RTf/Pcv
=
p
(1)
In this formula, the quantity f was claimed to be a unique function of the reduced temperature. It will be noted that the equation is dimensionless, so that any desired units may be employed. It is convenient to represent the quantity RT/P,V by a new variable, z, so that Equation 1 may be written in the alternative form - RTf pcv = RT=p=e
PV
T , are less than 5 per cent from the mean, and as Pr increases the deviations in T , become smaller still. Therefore, the curve of Figure 1 can be looked upon as p plotted against P,, corrected for variations in Tr that are quite minor. Below P, = 0.05, the variations in T,become large, but below
e -d =e -
PTf/!J
(2)
Althoughf is not the same function of the reduced temperature for all substances, for the majority of non-associating compounds the differences are apparently not great. For 4 However, even for carbon dioxide the deviation from this curve is apparently only about 5 per cent, and for water 10 per cent.
890
INDUSTRIAL AND ENGINEERING CHEMISTRY
such materials as hydrogen, helium, and water, f will deviate widely from the values given by other substances. Meissner and Keyser claimed that this relation holds up to about z = 2.5, but not above. Obviously, for the higher hydrocarbons, at the critical point z = 3.78. Consequently, this equation breaks down below the critical, although the percentage error is not great. Indeed, it was suggested that the valueof f at the critical, fa, be modified so as to make the equation fit the c r i t i c a1 densityi.e.,so as to make zc = 3.78. However, since the first a n d second partial derivatives of pressure with respect t o volume o b t a i n e d from the equation a r e n o t zero, a n equation of this sort cannot apply a t the critical point. T o extend the range of a p p l i c a bility of Equation 1, and particularly Figure 3 to make it more dependable in the neighborhood of the critical point, it was modified by adding to the exponent a correction term, 9. The data indicate clearly that, a t temperatures above the critical, 4 varies with reduced temperature as well as with z, but, at the critical and below, @I is small in any case, and varies but little with T,. As a preliminary approximation up to values of z = 4.0, its variation other than with z may be neglected-i. e., 4 is assumed to be a function of z only. The modified equation, therefore, becomes
Vol. 23, No. 8
curve through the points. Attention is called to the fact that in the above equation the only specific constants characteristic of the individual hydrocarbons are P , and T,. Although the vapors of the different compounds follow the Meissner relationship as long as they remain vapors, the Meissner equation gives no indication when, at any given temperature, the vapor of any hydrocarbon will reach its saturation pressure. The equation is otherwise general for all hydrocarbons to which it is applicable. Furthermore, as is clear from the discussion of Figure 1, it applies within the experimental error to the data on saturated vapors, despite the fact, already noted, that no general, reduced equation of state can possibly represent the properties of the saturated vapor. Table IV-Exponential
Correction T e r m for Meissner E q u a t i o n
5
$10
2.429 2.5 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
0.0 0.00013 0.000555 0.00259 0.00609 0,0109 0.01716 0.02471 0.0335 0.0435
Table V-Coefficients of Meissner E q u a t i o n (S = negative slope of curve In Tr against In f)
T,
S 4.36 4.36 4.36 4.36 4.36 4.36 4.36 4.34 4.07 3.82 3.71 3.66 3.50 3.16 2.74 2.74 2.74 2.74
fi0
1.5 1.45 1.4 1.35 1.3 1.25 1.2 1.15 1.1 1.05 1.0 0.95 0.9 0.85 0.8 0.75 0.7 0.65
0.032 0.036 0.042 0.0485 0,05585 0,06577 0.07834 0.09441 0.1138 0.1346 0.1614 0.1982 0.2409 0.2911 0,3482 0,4164 0.4938 0.5714
Table VI shows calculated values for n-octane obtained by Equation 4 and the values observed by Young.
-
10
- + ZflO
$10
Table VI-Values
was calculated from the data available and values of 4 are given in Table IV. This relationship should probably be restricted to higher hydrocarbons. Unfortunately, there are in the literature no adequate data above the critical point for the higher hydrocarbons. Meissner showed that Amagat’s ( 2 ) data on ethylene check well with data on most compounds. I n developing the relationship between f and temperature, Amagat’s data on ethylene have been employed for points above the critical. For points below, one has available the data on the vapors of saturated hydrocarbons. Figure 3 shows the data for f versus T,, plotted logarithmically. Below the critical are found points representing data on propane, n-butane, isobutane, n-pentane, isopentane, n-hexane, n-heptane, n-octane, diisopropyl, diisobutyl, hexamethylene, and benzene. It will be noted that the divergence increases a t low values of T , and high numerical values off. This is because f is a measure of the deviations from the gas laws, and under these conditions, when the pressures are very low, the deviations are small and the precision of determining the deviations extremely poor. The relation between f and T, can be represented throughout the range from high values of Tr to low, by a continuous smooth curve, the coordinates and the logarithmic slope, S , of which a t various points are listed in Table V. Intermediate points may readily be obtained by interpolation or from a g5
for N o r m a l O c t a n e O b t a i n e d b y E q u a t i o n 4
( T c = 569.2, P c = 24.63 atm.)
(4) T
Tt
P
Pr
RT/PcV
0.0345 0,0760 0.148 0.263 0.4387 0.692
0.0372 0.0848 0.1735 0.3325 0.634 1.20
f
Z
PV/RT Obsd. Calcd. DEVN.
% 393 423 453 483 513 543
0.69 0.851 0.743 1.875 0.796 3.65 0.848 6.48 0.902 10.81 0.954 17.07
0.5321 0 0.4266 0 0.352 0 0.292 0 0,239 0 0 0.194
0.957 0.91 0.870 0.800 0.706 0.585
0.955 0.920 0.871 0.807 0.695 0.585
0.2 1.1 0.1 0.9 1.6
0.0
Av. 0 . 6 5
To apply Equation 4 to a given hydrocarbon the value of its critical temperature and pressure must be known, and to get its density, its molecular weight. If not available, the first two constants can be estimated, provided one has the vapor-pressure curve, by extrapolating this curve by any of the usual methods and taking advantage of the fact that a t the critical point M P J T c is approximately 5.0 for normal paraffin hydrocarbons, rising apparently to approximately 6.9 for aromatics with no side chains and having no rings connected other than by common carbon atoms. Since Equation 4 is dimensionless, one can employ any desired units of pressure, temperature, and volume, provided only pressures and temperatures are absolute and the corresponding perfect gas constant is used. Inspection of the equation (4)
INDUSTRIAL AND ENGINEERING CHEMISTRY
August, 1931
shows that it is implicit in V . Figures 4 and 5 enable one to solve Equation 4 graphically. Equation 4 may be written log Pr - log z = fioz 810,or log PP fioz = log z 410 = log x ( 5 ) Log % is thus obviously linear in z, -fro being the slope of the line. As log x is a function of z only, a very definite relationship exists between 2: and log z t h a t must always he satisfied. It may be represented by the curve obtained on plotting log x against 8. Since all possible relationships between log x and e are represented by this curve, its intersection with the line given by Equation 4 is the particular solution of Equation 4. A semilogarithmic plot may he constructed with the curve mentioned, with suitable intercept (P,) and slope (Tr) scales which enable one to solve the equation for a without interpolation.
+
+
-
I n using Figure 4 it must be remembered that the curves for temperatures below the critical have been extrapolated beyond the saturation pressures and hence beyond the experimental data into the region of superheated vapors. Thus, on the left hand curve, T, = 0.65, the highest reduced pressure of a saturated vapor a t this temperature is 0.042 corre-
89 1
Obviously, at values of T , less than unity, where q5 is negligible, F becomes unity. The expressions assume as the datum of internal energy that of the hydrocarbon in question, present as liquid under its own vapor pressure and at some suitable datum temperature, To,preferably chosen low enough so that at this temperature the deviation of the vapor from the gas laws is negligible.6 At these low pressures the internal energy of the saturated vapor a t datum temperature is obviously the heat of vaporization less the external work, and the increase in internal energy above this temperature is
The last term in the expression for internal energy given in Equation 7, it will be noted, is the correction term for the deviations from the gas laws. Where these deviations are zero, the correction is, of course, also zero. Although below the critical temperature F may be taken as unity, above the critical it rapidly becomes of considerable magnitude. Values of F , determined by graphical integration, are plotted in Figure 6. In the practical use of these equations it is necessary to know the heat of vaporization a t the datum temperature. In the absence of dependable data for the hydrocarbon in question, the Hildebrand function can be employed. Data indicate that the deviations of pure hydrocarbons from the curve
I l l I l l I l l I l l 1 1 1 1 I 1 1
't
Figure 5
values for P and (;+)V may be substituted and an expression obtained which gives for the internal energy, U = Mro - RTo
+
L:
MCV dT
+ ( S - l)FRTA(p - 1 ) (7)
and the total heat:
jTol n m
H = Mro
- RTo +
In these formulas,
and S = -d Inf/d
M C V dT
(S
In Tr,
+
- 1 ) FRTA(p - 1 ) + A P V
(8)
shown on Figure 7 are at the most only a few per cent, probably little if any greater than the experimental error of other than the most careful measurements. Dependable information as to the specific heat a t constant volume is necessary if one wishes to use Equations 7 and 8. This laboratory published a proposed equation some years ago which is satisfactory for hydrocarbons of low molecular weight, but when it was published data on compounds of high molecular weight were lacking, particularly as to the temperature coefficients. Since that time, Bahlke and Kay (5) have published their determinations. They indicate for high molecular weight a temperature coefficient of approximately 0.5 in all cases. The former equation has been modified and generalized in the light of these more recent data and the authors now tentatively recommend the following expression:
+ 1.587%+ 1 . 2 6 7 +~ ~(-0.0027 + 0.0048% + 0.00197m)t F. 1.74 + 1.74%+ 1.33m + (-0.00486 + 0.00864% + 0.003545m)t ' C.
MC, = 1.826
5 If desired, the deviation of the saturated vapor a t datum temperature can be calculated from the above formula for H and a corrected value of Mr RTo obtained.
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
892
Table VII-Thermal
P r o p e r t i e s of S a t u r a t e d Ethane Vapor APV = H S JMCudf pRT Pr CORRECTIONb Calcd.
T P PIIT? Ir F OK. Afm. 1 0.9135 2.74 184.46 0.034 1 1.34 0.955 2.74 0,044 1 190 2.2 0.937 2.74 0.069 1 200 0,912 3.4 2.74 0.101 1 210 0.890 2.74 4.55 220 0.138 1 0.828 2.74 0.253 9.7 240 1 0.788 2.96 0.323 13 1 250 0.745 3.16 0.409 17 260 1 22 0.689 3.40 0.510 270 1 28 0.625 3.54 280 0.625 1 35 0.555 3.65 290 0.755 1 42.5 0,468 3.69 0.886 1 300 48.8 0.264 1 1.23 3.71 306.3 a Estimated values ( 1 1). b (S l ) F R T A ( P V / R T - 1) = (S l ) F R T A ( p - 1).
-
Vol. 23, No. 8
0 49.9 141.6 235.2 330.5 527.0 628.0 731.0 835,O 942.0 1052 1163 1218
355 360 372 380 389 395 39 1 385 369 348 319 279 159
-
0.0205 0,0275 0,0451 0.0697 0 0994 0,1988 0.2365 0.3485 0.4515 0.5741 0.7170 0.8710 1.0
22.3 29.5 43.5 63.8 83.6 -142.5 -206.1 -284.5 -400.5 -529.8 -682.0 -853.0 - 1486
3395 3442 3532 3613 3698 3842 3875 3893 3865 3822 3751 3651 2953
-
H Obsd.
DIFP.
3325 3390 3502 3605 3703 3861 3923 3962 3975 3947 3849 3566. 3050''
f
++ 705230
+ 8 - 5 - 19 - 48 - 69 -110 - 125 - 98 85 97
+-
-
Unfortunately, there are no data available on the thermal properties of higher hydrocarbon vapors to test adequately these methods of computation. However, there were published last year direct determinations of the total heat of the saturated vapors of ethane from its boiling point at atmospheric pressure up to the critical (11). While the relations here presented do not apply to ethane, as indicated by the fact that ethane has a value of RT,/P,V', = 3.59 rather than the value of 3.78 which has been used as the basis of these plots, none the less, since the difference in these two values is only 5 per cent, it seems advisable to calculate the thermal properties of saturated ethane vapor by these methods and compare the results with the experimental determination. This has been done in Table VII. This table assumes for ethane T o = 305.3 and P o = 48.81. Datum temperature is 184.46O K., the atmospheric boiling point, the lowest temperature employed in the data of Wiebe Hubbard, and Brevoort. At this temperature the value of Mro/To from Figure 7 is 18.4, corresponding to Mro = 3395. The first column gives the absolute temperature, the second the pressure in atmospheres, and the third P,/T,.
as the deviation of this ratio for ethane from the average used for the higher hydrocarbons. I n other words, this method of computation enables one to compute the thermal properties of the saturated vapor of ethane up to the critical point, using no data whatever on that particular hydrocarbon except 30
29 2"
24 21 LO 18
lb
k8 io
io
,000
P
-7.-
Figure 7
its vapor-pressure curve. The small deviations encountered are in the direction one would anticipate in view of the difference of behavior of ethane a t the critical from that of the higher hydrocarbons for which these graphs are intended. Nomenclature P T R
= = = =
V
P, = T, =
c
V, w
= =
z
=
f
=
4
=
F
M S
n 2
Figure 6
The fourth gives the corresponding value of p as read from Figure 1. The fifth shows the value of F taken from Figure 7, and the next, 8, from Table V. The remaining columns should be self-explanatory, After the values of the total heat of the saturated vapor thus calculated the experimental values reported by Wiebe, Hubbard, and Brevoort are given. It will be noted that the maximum deviation of the two is 4 per cent. With a single exception, a t high pressures the computed values of total heat are less than the observed. This is to be anticipated in view of the fact that the compressibility of ethane is less than that of the higher hydrocarbons as shown by its low value of RT,/P,V,. Furthermore, the percentage deviation is approximately the same
= = = =
m
=
C,
= = =
C, r A
=
absolute pressure (any units) absolute temperature (any scale) gas constant (units depending on units of P , V , and T ) molal volume (any units) reduced pressure = P / P c reduced temperature = T / T c reduced volume = V/V, PV/RT RT/P,V function of T , (obtained graphically) function of z (obtained graphically) see Equation 8a molecular weight - d In f / d In T , number of carbon atoms per molecule number of hydrogen atoms per molecule specific heat a t constant pressure specific heat a t constant volume latent heat of vaporization work-heat conversion factor
Literature Cited (1) (2) (3) (4) (5) (6) (7) (S) (9)
(10) (11) (12)
Altschul, 2. physik. Chem., 11, 577 (1893). Amagat, Ann. chim. p h y s . , 29, 68 (1893). Bahlke and Kay, IND. ENG.CHEM.,21, 942 (1929). Chipman and Peltier, I b i d . , 21, 1106-08 (1929). Cunningham, Power, 72, 374-7 (1930). Dana, Jenkins, Burdick, and Timm, Refrigerating Eng., 12, 402-3 (1926). Guye and Mallet, Compf. rend., 133, 1287 (1901). Lewis and McAdams, Chem. M e f . Eng., 36, No. 6, 336 (1929). Meissner and Keyser, Mass. Inst. Tech., Chem. Eng. Thesis, 1930. Pickering, Bur. Standards, Sci. Paper 641 (1926). Wiebe, Hubbard, and Brevoort, J. Am. Chem. Soc., 52, 611-22 (1930). Young, Proc. Roy. Dublin Soc., 12, 374 (1910).
