TemDerature Coefficient of Density and Refractive Index for Hvdrocarbons in the Liquid State I
J
J
11. H . LIPKIN AND S. S. KURTZ, JR., Sun Oil Company, iMarcus Hook, Penna.
us. density, and a single curve of fl US. density. Since each hydrocarbon type has a curve of its own, the accuracy of a single curve for hydrocarbon mixtures is seriously dependent on composition. Jessup (10) confirmed this when he found that two oils of the same specific gravity but from different sources differed more than 30 per cent in their thermal expansion. Figure 11 of Ward and Kurtz (22) shows the aromatics, especially those of low molecular weight, to be widely divergent from the curve corresponding to the National Standard Petroleum Oil Tables.
Using the equation
dt/4 = d20/4
+ a(t - 20) + @(t- 20)2
a single curve of a us. molecular weight and a single curve of p us. molecular weight have been found applicable to all types of hydrocarbons with very few exceptions. From these curves the temperature coefficient of density of a liquid hydrocarbonat atmospheric pressure can be predicted from the molecular weight within *0.00002 gram per CC. per O C. The only definite exceptions to this relation are benzene, pentaethylbenzene, and hexapropylbenzene which show coefficients 0.00010 gram per cc. per ' C. higher than the predicted values. The curves are also applicable to hydrocarbon mixtures. This relation is more general than any previously published for predicting the temperature coefficient of density. The corresponding relationship between compressibility and molecular weight is being investigated. Since Ward and Kurtz have shown that for hydrocarbons A n = 0.60 Ad
s 9
an accurate method of calculating density change also provides a satisfactory method for calculating change in refractive index.
T
HE change of volume and density of hydrocarbons with change of temperature has been the subject of a number of careful investigations. The commonly accepted equation for change of density with temperature is dt/4 =620/4 + a(t - 20) P ( t - 20)' (1)
DENSITY AT 20.C
FIGURE1. TEMPBRATURE-DENBITY COEFFICIENTS us. DENSITY FOR %PARAFFINE4
+
Calingaert, Beatty, Kuder, and Thomson (3) developed a correlation between a and /3 and number of carbon atoms for the normal and branched paraffins up to 20 carbon atoms. The present work is an amplification of their work and provides a single correlation between cr and p and molecular weight for hydrocarbons of any structure, and applies to all data now available, including compounds of high molecular weight. Using this correlation the change of density with temperature can usually be predicted within *0.00002 gram per cc. per
where a is the temperature coefficient, Ad/At, of the liquid density, d a t 20" C., and one atmosphere pressure, and fl covers the variation of Adlilt with temperature t. The problem has been to correlate a and fl with other properties, so that change of density with temperature can be predicted. Early work in the field by Bearce and Peffer (2) was based on a plot of a and p against density. Recently Beale (1) proposed a new attack by plotting the cubical coefficient of expansion against boiling point. Paraffins, naphthenes, and aromatics form lines of similar curvature based on the data used by Beale. This type of plot is convenient, since cubical coefficient a t 20" C. X density a t 20' C. equals Ad/& Kard and Kurtz (22) derived a plot of density coefficient us. density a t 20" C. using a plot of cubical coefficient of expansion us. boiling point, and a boiling point-density plot. The plot of density us. density coefficient (Figure 11,22)reveals separate and -Jery different lines for different hydrocarbon types. It is known that the naphthene lines on this graph will require some revision, but that the paraffin and aromatic lines are essentially correct. The National Standard Petroleum Oil Tables used in the petroleum industry for correcting the specific gravity of oils for temperature change are based on a single curve of a
O
c.
The derivation of the general relation between molecular weight and the a and p coefficients is simple. The smoothed values of a and /3 for the normal paraffins of 5 to 12 carbon atoms; which have been calculated by Calingaert and cowere workers (3) from the data of Dornte and Smyth (4, plotted against density, d20/4. As shown in Figure 1 very good straight lines were obtained. Consideration of physical property relations made it seem probable that a plot of a and /3 against molecular weight might give a single relation for both paraffins and naphthenes, and perhaps for other classes of hydrocarbons. The equation of Calingaert and coworkers (3) relating molecular weight to molecular volume and density was, therefore, used to convert the density co291
INDUSTRIAL AND ENGINEERING CHEMISTRY
292
ordinate in Figure 1 to molecular weight. In order to correct the resulting curve so that it would be representative of average paraffins rather than just normal paraffins, the data of Edgar and Calingaert (6) were used. These data indicate that the average Ad/At for all nine isomeric heptanes is 1.5 X unit higher than the value for the corresponding normal compound. The CY coordinate of the graph of molecular unit. The graph weight us. CY was, therefore, shifted 1.5 X thus obtained is shown as Figure 2 and numerical values for constructing such a graph are given in Table I.
TABLE I. DATANECESSARY FOR CONSTRUCTION OF CURYESOF cy AND 5 ,' COEFFICIENTS PLOTTED AGAINST MOLECULAR WEIGHT Molecular Weight 0 x 106 B x 10' 720 85 120 140 160 180 200 225 250 275 300 350 400 450 500 600 700 800
-4
@
I
L
-97.1 -91.5 -86.7 -82.0 -78.6 -75.8 -73.7 -71.9 -70.3 -69.0 -67.9 -66.8 -65.2 -63.8 -62.8 -62.0 -60.8 -60.1 -59.5
100
'"I\ .4
Vol. 13, No. 5
-8 1 -6 4 -5 0 -3 7 -2.6 -1.8 -1.2 -0.7 -0.2 fO.2 +0.5
+o.s f1.3
+1.6 +1.9 +2.1 4-2.5 +2.7 4-2.8
Curve not recommended for less than 72 molecular weight.
coefficient. Furthermore, there is little systematic error since the deviation of the average (taking sign into consideration) is zero.
I \
UNSATURATED
CYCLlCS
0 MONOCYCLIC 50
,
150
I
250
I
I
I
350 450 550 MOLECULAR WEIGHT
I
I
650
750
-60
FIGURE2. TEMPERATERE-DENSITY COEFFICIENTSus. MOLECULAR WEIGHTFOR HYDROCARBONS
In the derivation of Figure 2 the equation of Huggins (9), relating molecular weight to molecular volume for the normal paraffins, can be used in place of the Calingaert equation. If this is done the curves obtained are identical with those shown in Figure 2 up to 450 molecular weight, but there is a small increasing deviation above this point, in a which a t 700 molecular weight amounts to 1 X and 2 x lo-* in p. Since neither Calingaert nor Huggins claims accuracy for his density-molecular weight relations above 282 molecular weight (20 carbon atoms), and since the data for the higher molecular weight pure compounds are not sufficient to provide completely definite empirical evidence, we cannot yet be sure which relation is best. The authors have arbitrarily used the Calingaert relation in this work. Having obtained a relation between the CY and /3 coefficients and molecular weight for paraffins as shown in Figure 2 and Table I, it was necessary to determine the accuracy of this generalization for paraffins, and whether or not it could be used for other classes of hydrocarbons. Examination of density data (6, 7, 11) a t the two temperature extremes for all types of hydrocarbons on which densities are reported a t two temperatures, a t least 20" C. apart, provided the data which are presented in Table 11. Inspection of Table I1 makes it clear that by using Equation 1 and Figure 2 the change of density with temperature can be calculated accurately for paraffins, naphthenes, aromatics, and a variety of unsaturated compounds. [Francis @ A ) gives an equation for the density coefficient of paraffins which is essentially in agreement with this paper.] The average calculated density change for 98 compounds for an average temperature change of 74" C. is correct within *0.0012 gram per cc., and the average calculated density coefficient agrees with the experimentally determined density coefficient within *0.00002 gram per cc. per " C. This is about .t3 per cent uncertainty on either the density change or the temperature
0 POLYCYCLIC
-70 -90
UNSATURATED
I-\
NON-CYCLICS
0 MONOOLEFINS 0 DIOLEFINS
X ACETYLENES
- 70 -60
-0
AROMATICS
L?
NAPHTHENES
-100 a
0 X
d
0 MONOCYCLIC
-80
-701 - 60
0 POLYCYCLIC
-
O
PARAFFINS
I O
0 NORMALS 0 ISOMERS
-70 -60
I 50
I
I
I
I
I
150
250
350
450
550
MOLECULAR
WEIGHT
FIGURE 3. AGREEMENTOF DERIVED AND OBSERMD a FOR HYDROCARBONS
ANALYTICAL EDITION
May 15, 1941
293
TABLE11. COMPARISON OF CALCULATED AND EXPERIMENTAL CHANGEOF DENSITY Maximum Deviation of Anv Single Compound Corresponding Deviation of Ad x 106 Ada ~
Hydrocarbon Type
No. of Compounds
Average Deviation Regardless of Sign Ad x 10' Ada
Average Temperature Range, O C.
l'ara5ns 39 94 0,0015 2 Saphthenes 6 55 0.0010 2 Mono Poly 3 59 0.0012 2 .\romatios .Mono 1Sb 62 0 0005 1 Di 3 67 0.0023 4 Olefins 9 69 0.0012 2 Mono Di 6 48 0.0017 4 Acetylenes 2 55 0.0013 3 Unsaturated cyclics 12 62 0.0007 1 All hydrocarbons 98 74 0.0012 2 a Ad = (dr, dt, observed) (dr dr calculated). b Benzene, toluene, pentaethylbeniene, ahd hexapropylbenzene omitted from average
-
-
-
Deviation of Average Taking Sign i n t o Account Ad" +0.0004
- 0,0008 - 0.0012
0
+0,0065
+3
-1 -2
- 0.0019
-0.0021
-3 -3
+0.0001
0 +1
+0.0011 -0,0033
+3 -4
- 0.0008
-1
t0.0002
-0.0001 -0.0001 -0.0001 0
-1
0 0 0
- 0.0047
+0.0030
-5 1-7 -3 4
+ O . 0065
+3
+0.0032
-0.0014
Only a few compounds show poor agreement with the avercompounds of unusual structure may not agree with this genage data. Benzene, pentaethylbenzene, and hexapropyleral system of correcting density. Table I11 was, therefore, gram per cc. per benzene are badly out of line ( + l o X prepared to show that for a specific group of varied compounds ' C.). Toluene is slightly out of line (+ 4 X gram per the agreement is good-that is, approximately *0.001 gram co. per O C.). Some of the large rings synthesized by Ruzicka per cc. or less for 50" C. change in temperature. are also out of line, while others check very well. Additional Also, using the limiting density of Kurtz and Lipkin (16) precise data on such compounds are needed. All the other for the paraffin homologous series, and Figure 1 corrected for data are in good agreement. The above-mentioned comthe isomer effect, we obtain a value of Ad!At a t 20" C. = pounds were omitted from the average in Table 11. All 5.5 X 10-5 gram per cc. per O C. The best estimate of data other reliable data, where the data cover an appreciable for hydrogenated rubber indicates Ad/At to be 5.7 X temperature range, have been included, and the worst degram per cc. per " C. which checks the limiting value satisfactorily. viations in each group have been indicated in the last two columns of Table 11. The worst deviations in density change in the paraffin and naphthene groups correTABLE 111. DENSITY CHANGEWITH TEMPERATURE FOR SOMEIXTERESTING spond to *0.00003 gram per cc. per COMPOUNDS Deviation O C., or about =t5 per cent on the Ad Molecular Temperature coefficient, The worst deviation in Range, C Ada At Weight any group is about 10 per cent on the c-Ca-c 72 120 +a 002s +o.oonoi n-Pentane coefficient and probably represents poor data. A further cross check on the accuracy of Equation 1and Figure 2 was Cyclooctane 112 5s -0.0005 -o.ooont obtained by assuming that the /3 curve was correct, and taking all the difference between observed and calculated density change as error in the a Hydrindane 124 58 -0.0009 -0.00002 coefficient. These observed a values (assuming /3 is correct) are plotted in 128 97 -0.0033 -0.00003 Figure 3 for the same data as shown in Table 11. Figure 3 makes it very Naphthalen? clear that with the exception of the four aromatic compounds already men66 -0.0005 -0.00001 136 tioned, the agreement obtained is excellent and there are no svstematic ~dl-a-Pinene deviations. C One rather surprising thing about the data for paraffins which is shown by 138 167 4-0.0006 +O.OOOOl C Figure 3 is that the normal paraffin C data agree very exactly with the curvp, d-Limcnene although in its derivation a distinction 224 65 -0.0003 -0.00001 C=C-Cia-C between normal and average paraffins Hexadecene-1 was made, and the curve was adjusted 98 0.0000 0.00000 281 C-cls-c n-Eicosane to agree with what the authors believe to be the best data for average paraffins. At any rate the final curve obtained 51 0.0001 0.00000 (Figure 2) has excellent empirical justification, and is recommended for Octadecahydrocarotene normal paraffins as well as for all Ad = (dr, - dt, observed) - (d!l - dt, calculated). other hydrocarbons. The question may be raised, that O
(->
/?\
\
