Calculation of Molecular Volumes OVER A WIDE RANGE OF TEMPERATURES AND PRESSURES S. S. KURTZ, JR., AND ALBERT SANICINl Sun Oil Co., Marcus Hook, Pa.
T
HE problem of calculating the molecular volume of hydro-
carbons is of importance. This is true because, in the molecular weight range of lubricating oils, we cannot hope to synthesize more than a small proportion of the total number of compounds which theoretically might exist ( 7 , 8 ) . A reliable method for calculating molecular volumes would make it possible to map out by calculation the density trends for a wide variety of s h e tures, and then synthesize a limited number of key compounds to check the calculated data. The molecular volumes in milliliters per gram mole of liquid hydrocarbons at 20" C. and 1 atmosphere can be calculated using the equat'ion:
M.V.
= 16.28Ni
4- 13.1592
+ 9.7Sa - 6.2N4 + 31.2
gas. From pressure measurements and a knowledge of the bulb volume without the hydrocarbon present, the volume of the hydrocarbon was calculated. As the weight of hydrocarbon in the bulb was known, density and molecular volume could be calculated. The work was done a t the Reichsanstalt and published in 1930. There is every reason to believe that it is reliable.
TABLEI. DATAOF HEUSEFOR MOLECULAR VOLUMEO F 10 ALK.4NEs I N S O L I D STATE AT
Measured Mol. YOL, -253O C. 30.8 40.0 54.6 66.4 81.6
(1)
where
NI Nz
N8= number of carbon atoms a t ring junctions Kh = number of double bonds 31.2 = molecular volume constant at 20" C. and 1 atmosphere
3IOLECULAR VOLUME OF HYDROCARBON
In order to generalize Equation 1 it is necessary to have good data on the molecular volume of hydrocarbons over a wide range of temperatures and pressures. It has been shown (20) that the change of density with t,emperature is a simple function of molecular weight for a wide variety of hydrocarbons. This provides a basis for adjusting Equat,ion 1 to other temperatures by calculation. However. a good set of experimental density dat,a for a wide variety oi hydrocarbons at, a temperature well removed from 20' C. is highly desirable as a check on the form of the molccuiar volume equations. Table I presents the data of Heuse (6) for 10 alkanes in t.he crystalline state, which were obtained at, 20" absolute ( -253" C.). The technique used hji Heuse involved freezing t.he hydrocarbons in a bulb, degassing, and then int,roducing a noncondensing 1
c.
Mol. Calcd.' vp1.5 ~ o i . Minus Vol., 13.15 N I Eq. 2 17.6 29.0 13.7 42.1 15.1 56.3 13.8 68.4 15.8 81.6
Compound CH2" AVa Methane .., -1.8 Ethane 9.2 ~ 2 . 1 +0.7 Propane 14.6 n-Butane 11.8 +2.0 n-Pentane l5,Z 0.0 Isopentane (crystalline) 82.7 (163) ... 81.6 (-1.1) Isopentane (supercooled) 85.1 (18.7) , , . 81.6 (-3.5) +O.l 15.7 91.7 n-Hexane 94.6 13.0 107.8 -2.1 17.8 n-Heptane 109.Q 15.3 15.6 121.0 +0.2 120.8 10.9 n-Octane 134.2 -1.8 n-Nonane 138.0 15.2 17.4 Average of normals 13 15b 16.83 a Calculated for present paper. b Average of four high and four low increments, represents a mean value.
= number of chain carbon atoms = number of carbon atoms in rings
Statistical data supporting this equation were given in 1941 ( 7 ) . More recently (8) it has been shown that molecular volumes of 423 hydrocarbons tabulated by API Projects 42 ( 1 , 16) and 44 (a, 16) agree with an average deviation of about 1.8 ml. Equation 1 does not allow for differences in the volume of isomers. The principles on which it is based are such that additional terms for isomer effects can undoubtedly be developed using t,he principles of Wiener (19-21) and Platt ( l a ) . For the published BPI 42 data on compounds of high molecular weight, the average deviation bet.ween determined and calculated molecular volume is about f0.570. Equation 1 seems adequate for calculating molecular volumes a t 20" C. and 1 atmosphere pressure, particularly for hydrocarbons of high molecular weight. Generalizing this equation so that it could be used over a wide range of temperature and pressure would clearly increase its value. The present paper shows t,hat this can be done. It is believed that the form of the equations used is basically sound, and that the numerical coefficients proposed are good preliminary values.
-253"
Column 3 shows a reasonable constancy in CH, increment, a i t h some alternations between the odd and the even members of the series. Using an average CH, increment for normal paraffine from methane to nonane gives the following equation:
+
AI.V. 13.15~1~1 15.8 (2) which agrees well with the data. Even methane fits into the pattern with no great deviation. The other data of Heuse are given in Table 11. These data, and the data in Table I, have been used in deriving Equation 3 for hydrocarbons in the crystalline state a t -253' C. &I.V. a t - 253 ' C. = 13.15aV1 11.13A'Z 8.9Ws - 4.0A'a 15.8 (3)
+
+
+
TABLE11. DaT.4 O F HEUSEFOR 3'IOLECUL.IR VOLUME CYCLIC A N D UKSATURATED HYDROCARBONS Compound Cyclohexanea
hIolecular Volume Measured, Calod., -253O C. Eq. 3 82.6 82 6 35.9 34.1 69.3 70.6 83.6 83.8
Ethylene Benzene Toluene 96.9 97.8 E thylbenzene 96 9 n-Xylene 88.5 110.0 n-Propylbenzene 116.0 110.0 Mesitylene 110.9 102,6 102.6 Naphthalene b a Used t o establkh CH? increment. b Used to establish ring junction increment.
Present address, Pennsylvania Gtate Cniversity, State College, P a .
2186
AV
0.0 -1.8 4-1.3 +0.2 +O.O -1.6 (-6.0) -O.R 0.0
OF
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1954
Equation 3 for crystalline hydrocarbons a t -253’ C. corresponds to Equation 1 for liquid hydrocarbons a t 20’ C. The similarity of Equations 1 and 3 suggests the possibility of developing a generalized equation for the molecular volume of hydrocarbo5s in the liquid state, which will approach Equation 3 as a limit a t very low temperatures. I t is recognized that any such general equation will be inaccurate for the solid state, except a t temperatures which are so low that the volume change on crystallization is no longer large. Comparison of Equations 1 and 3 reveals that the biggest change is in the “molecular volume constant.” This increment is therefore referred to as the “molecular increment of volume” (M.I.V.), as i t is constant only when temperature and pressure are constant. Table I11 shows the ratios of the various increments and the per cent decrease.
TABLE 111.
COMPARISON OF ATZOOAND
Chaincarbons, Nia Rinacarbons.Nzb Ring junction carbons ivs Double’bond, AT, Average NI,to N4 Molecular incrementofvolumec
INCREMENTS
16.28 13.15
13.15 11.13
1.238 1.181
0.8078 0.8465
3.13 2.02
19.2 16.1
9.7 6.2
8.9 4.0
1.090 1.55 1.264
0.9176 0.64 0.8029
0.8 2.2
.. .
8.2 35.4 19.7
1.975
0.5064
15.4
49.3
,
..
31.2
...
15.8
I
Chain carbons may be -CHs, b
MOLECULAR VOLUME -253°C.
Ring carbons may be CHz, -dH
I
-!XI
-CHa,
I
t
1
or -C--.
I
1
or
--A-.I
Rings containing more than
eight carbons in one ring have not been investigated from this point of view. Molecular increment of volume is preferable to molecular volume constant, as i t is not constant when temperature or pressure changes.
The average change for the increments for N1 to Na, inclusive, is numerically close t o the change for Nt. -4s a first approximation it is, therefore, reasonable to use the ratio of change for N I as the ratio of change for NzJ iVa, and N d . As the ratios for -VI under various conditions can be derived using experimental data for normal paraffins, which are relatively plentiful, this is a helplul simplification. The simple relation between molecular weight and density coefficicnt (9, IO) for all types of hydrocarbons in the liquid state also suggests that it is reasonable to apply a single ratio of change to the increments for chain carbons, ring carbons, ring junction carbons, and the removal of two hydrogens to form a double bond. The more general equation may therefore be written:
+
M.V. at t o C. = KIN% KgNz
+ KaNa + K ~ N +I Kg
(4)
in which K 1 . etc., are the appropriate volume increments which can be tabulated as a function of temperature, and Ka is the molecular increment of volume. DEIVSITY CHANGE AND COEFFICIENT OF EXPANSION
To summarize briefly the point of view of the authors in regard to density change and coefficient of expansion, the normal paraffins may serve as an illustration. I n the crystalline state x-rav studies indicate a perfectly regular linear equation for chain length of normal paraffins, and a uniform cross section. From a molecular volume point of view, this means that in the crystalline state the molecular voIumes of normal paraffins are correctly represented by a simple linear equation, such as Equation 2, in terms cf number of carbon atoms, and a molecular increment of volume. On going over to the liquid state, the data ( 7 , 8) agree reasonably well with the hypothesis that there is no change in the increment of length per CHZ group, but that there is a change in the increment of cross section per CH1 group. In other words,
2187
the rotation around the carbon-carbon bonds in the liquid state is sufficient to cause the molecule effectively to occupy more space. The smaller amount of space occupied by ring carbons, and ring junction carbons, is a direct measure of their lesser freedom to movc by rotation around bonds. The molecular increment of volume for liquid hydrocarbons has been found to be relatively constant except for hydrocarbons of very low molecular weight. This may mean that the molecular increment of volume is a simple function of the kinetic energy of motion of the molecule as a whole. All hydrocarbon molecules in the liquid state a t the same temperature should have about the same kinetic energy. This seems a reasonable basis for the approximate constancy of the molecular increment of volume at any particular temperature and pressure. Each molecule by kinetic impact of the molecule as a whole creates for itself a certain free space; this is the molecular increment of volume. Green’s discussion of the kinetic energy of molecules in the liquid state ( 4 ) agrees with what has been said thus far. Although the authors’ approach to the subject differs from that of Moore, Gibbs, and Eyring (II), it is believed that the two approaches supplement each other and do not lead to any disagreement. The advantage of the concept of molecular increment of volume is that it makes possible a simple quantitative treatment of this part of the “free volume” or “holes” that exist in liquids. As molecular weight increases, the increment of volume per CHn approaches B constant or limiting value. In the case of very large molecules such as hydrogenated rubber, the total molecular volume is so great that the molecular increment of volume becomes negligible. One can therefore obtain the average volume of a CH1 increment merely by dividing the molecular weight for CHa (14.026) by the density for giant hydrocarbon molecules such as hydrogenated rubber. The density of hydrogenated rubber a t 16” C. as given by Staudinger ( 1 7 ) is 0.8585. Correcting to 20’ C. gives 0 8563, from which 16.379 ml. is obtained as the limiting increment for CH, at 20’ C. This increment of volume will change with temperature, because in theee large molecules there is an increase in chain vibration even though the molecule is so large that, considered as a whole, it is static. The change in limiting density with temperature is therefore a measure of the motion of segments in big molecules, and not of the molecule as a whole. As shown in Figure 13 of (a), the limiting density for repetitive series containing “an appreciable amount” of ring structure, such as polystyrene or hydrogenated polystyrene, will be greater than the limiting density for hydrocarbons consisting predominantly of chain CHZ groups. Presumably the change of density with temperature will also be different, and will depend on the average structure. The general relation between density coefficient and molecular weight (9, IO), which works well for most hydrocarbons, will have to be replaced in the case of repetitive series having an unusual limiting density coefficient by more specialized equations. The need for such specialized equations was noted by Griswold and Chew ( 5 ) . As molecular weight decreases, the over-all density coefficient increases as a linear function of the reciprocal of molecular weight, as shown in Figure 3 of (8). In the equation
t 20 d- = d x 4 01
+
01(t
- 20)
+ P ( t - 20)’
(5)
and p can be evaluated with the following equations: cy
x
3516 wt. 941 2 p X 10’ = 4.0 mol. wt. 106 = -55.3
- mol.
+ 12
-
The latter equation is not good below a molecular weight of 200. The constant term can be thought of as representing ro-
2188
INDUSTRIAL A N D ENGINEERING CHEMISTRY
tational effects within the molecule and independent of the motion of the molecule as a whole. In other words, one can relate the constant terms to the limiting volume increment for CH2, etc., and the molecular weight term to the molecular increment of volume. hlore exactly, the molecular weight term measurea the rate at which the molecular increment of volume becomes negligible a8 molecular weight increases.
-100 0 '100 DEGREES CENTIGRADE
'200
Figure 1. Relation of Volume I n c r e m e n t to T e m p e r a t u r e
Vol. 46, No. 10
These data are shown in Table V. It is clear that the molecular increment of volume is constant over this molecular weight range, but decreases rapidly with decreasing temperature. The values for the molecular increment of volume from Table V are plotted in Figure 2 along with the values for IC to K,. These data also extrapolate Tell to the experimental value derived from Heuse's data a t -253' C. Curves such as those in Figure 1 can be used for obtaining values for Ki or the molecular increment of volume at othcr temperatures. Values of K I and the molecular increment of volume were not calculated below -100" C. or above 200' C. because a t present there is some uncertainty about the use of Equations 5 , 6, and 7 beyond this range. Table VI shows the agreement of Equation 4 with data for normal hydrocarbons from ethane to pentane at -100" C. (-148" F.), and for methane to n-pentane a t their respective boiling points. The calculated values tend to be a little high for temperatures below the boiling point, but as the boiling point is approached, the calculated values become too small. This is discussed in connection with Figure 3. Table VI1 illuatrates the calculation of molecular volume of two complex hydrocarbons synthesized by API Project 42. For these two compounds, the worst deviations are only about 0 2% on the molecular volume. Table VI11 compares experimental molecular volumes at 210" F. for 121 compounds synthesized by API Project 42 with the corresponding values calculated using Equation 4, and the constants from Tables IT7 and V. The average deviation is about 0.6% and the worst deviation is 2.8%.
Nearly 30 years ago Richards (IS, 14) published a relation betveen coefficient of expansion and the ratio obtained by dividing numbers of atoms in a molecule by the molecular volume. This would imply a simple relation for hydrocarbons between molecular weight and coefficient of expansion or density coefficient, TABLE IT'. LIMITIIUG I N C R E U E N T FOR CHp AND CORRESPOXDINU but the hint was neglected. VALUESFOR COEFFICIENTS IN EQUATION 4" Using Equations 5 , 6, and 7 , the values for the limiting volume Ratio of of the CH2 increment have been calculated for the range - loOD Volume a t Temperature L/mitt o C. t o to +200" C. and are given in column 2 of Table IV. Each value Volume a t 0 c. 0 F. &tb 20° C. KI Rz Ka K4 in column 2 of this table represents 14.026 divided by the density 18.220 1.1124 14.63 10.79 6.90 4-200 392 18.11 calculated with Equation 5 using 0.8563 for hydrogenated rubber 1.0511 13.82 212 10.20 6.52 17.216 17.11 + 100 as the limiting density at 20' C., and assuming that a t a molec10.19 6. 51 7.205 1.0504 13.81 210 17.10 98.9 6.50 17.165 1.0480 1 3 , 7 8 10.16 203 17.06 ++ 95 ular weight equivalent to the limiting density, the molecular 9.89 6.32 16.698 13.40 1.0193 122 16.59 50 6.20 9.70 16.379 13,l5 16.28 ++ 20 68 1.a000 weight terms in Equations 6 and 7 are negligible. 16.327 0.9899 13.13 16.23 6.18 60 9.67 15.6 The corresponding values of the volume increments K1 to 6.12 16.166 0,98699 12.98 32 9.57 0 16.07 12,55 5.82 0.05464 9.26 15.636 15.54 -- loo 50 - 58 15,107 Kd are also tabulated. These were calculated by multiplying 8 . 9 5 5.72, 15,02 12,l3 0.92234 -148 - 253 - 487 13.15C 0.80285 13.15C 1 l . l a C 8.9OC 45 .. 00d the K values at 20' C . by the ratios shown in column 3 of Table 7.8d 10.62d IV. If cubic Angstroms per molea Units of volume are ml per gram mole. I n Figure 1the values for & to K , are plotted against temperature from -253" to +200° C. The values for Ki form a smooth are desired' 14.026, by mo4. 1 Limiting CHz = -where d; = 0.8663 - 55.3(1 - 20) f 4 O(1 curve. The values for Ka, &, and K, at -253' C. obtained by d 4i ratios from the K I value were used in this graph in view of the 20)9. limited amount of data available at -2.53' C. C Heuse d a t a experimental d Calculated irom 20" C. &lues using ratio [ % - 2 5 3 ) / K i (20' C ) I I n order to evaluate the 0.80774. m o l e c u l a r i n c r e m e n t of volume, the molecular volume O F hlOLECULAR INCREMENT OF J'OLUME, Ks, AT VARIOUS TEMPERATURES" TABLEV. EVALUATION of average hydrocarbons havAv. Kt ing 20 and 30 carbon atoms, Calcd. Mol. Calod. nioi. for Mol. Vo1.b Incr. of Mol. Vo1.b Incr. of Range 20respectively, were calculated Temperature a t t o C., 20x1 Vol., a t t o C., 30K Vol., 30 Carbon c. O F. Ca Table I V Ka Cao Table 11' Ka Atoms for the same temperatures as 60.2 shown in Table IT', using both 608.5 543.3 62.2 58.2 362.2 392 420.4 +zoo 40.3 40.0 553,3 513.3 40.6 342.2 382.8 212 +98.9 100 the a and 8, coefficients as 4 0.1 3 9 . 8 513.0 5 5 2 . 8 40.4 342.0 382.4 210 39.5 551.1 511.8 39.3 39.8 341.2 381 .O 203 -I-95 given by Equations 6 and 7 , 34.6 3 4 . 8 632.5 497.7 34.4 331.8 366.2 122 50 31.2 31.2 519.6 488.4 and correcting the density us31.2 325.6 356.8 20 30.8 30.5 517.8 487.9 30.8 324.7 355.5 15.6 ing Equation 5. From the 29.5 482.1 29.5 511.6 n 29.4 321.4 380.8 32 26.0 492.3 466.6 26.1 25.8 310.8 336.6 - 56 -- 148 58 molecular volumes thus cal23.1 450.6 23.3 473.9 22.9 300.4 323.3 100 culated, the volume of 20K1 If cubic Angstroms per molecule are desired, multiply by 1.6604. If Units of volume, ml. per gram mole. or 30K1 was subtracted to cubic inches per pound mole are desired, multiply by 37.24. b Calculated using Equations 1, 5 , 6, and 7. leave the molecular increment of volume.
+
'
-
O
++
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1954
2189
TABLEVI. MOLECULAR VOLUMESOF NORMAL HYDROCARBON TABLEVII. EXAMPLE OF CALCULATIONS USINQ EQUATION 4 SERIES FROM METHANE TO 12-PENTANE A P I 42 Compound PSC 110
Molecular Volume a t Molecular Volume at C. (-148' F.), Boiling Point, Ml./G. Mole Ml./G. Mole Calcd., Calcd., -100'
Compound Methane Ethane Propane n-Butane n-Pentane
"4"'
E ~ p t l . Dif.b ~
...
52.3 68.5 83.7 98.9
...
63.0 68.3 82.2 97.9
...
-1.3 +0.2 4-1.5 +1.0
"4"'
Exptl.0
34.5 54.0 73.4 93.7 115.3
37.7 54.9 75.4 96.4 118.6
Tz>-.-j;c.
struoture B.P C:'
D3.b -3.2 -0.9 -2.0 -2.7 -3.5
Formula CNHM
-161.6
- 88.0 - 42.1 0.5 +- 36.1
t, t.
c.
0 E". Ki X 20 Ka X 6
M.I.V. Mol. vol. calcd. Mol. vol. exptl. Difference
0 32 321.4 64.9 29.5 415.8 416.5 -0.7
20 08 325.0 65.75 31.2 422.6 422.9 -0.3
37.8 100 327.4 66.3 33.2 427.1 428.8 -1.7
98.9 210 342.0 69.1 40.1 45i.a 451.0 0.2
37.8 100 131.0 225.4 -37.0 33.2 352.0 a53.3 - 1.3
98.9 210 136.8 234.8 -39.1 -I-40.1 372.6 369.1 a.6
A P I 42 Compound PSC 120
60 Formula CrsHir t , c. t QF.
MOLECULAR INCREMENT OF VOLUME
i40
9
0
8 Kz X 17 K4 X 6
i
20 68 130.2 223.0 -37.2 $31.2 347.8 348.8 - 1.0
32 + 128.6 +220.7
kl x
M.I.V. Mol. vol. aalcd. Mol. vol. exptl. Difference
36.7 +-342.1 29.5
-
344.0 1.9
.+
i $3 lL
0
d 501-
L ,/'9
0
W
wND-K~
0
0
z %53 -200
-I00 0 400 DEGREES CENTIGRADE
Figure 2.
Relation of Volume Increment to Temperature
0
- 253°C.
0
1.260
The data in Table VI11 show that Equation 4 can be used to calculate molecular volumes for a wide variety of compounds. However, Table VI11 also indicates that this type of calculation can undoubtedly be further refined, which will improve the agreement. The authors will have to leave this improvement to others. The relation between the increment for the chain carbon atoms, (ITl), used in Equation 4 and the limiting volume for this group is worth a little more discussion. In Table I X are shown some molecular volumes of normal hydrocarbons having from 5 to 40 carbon atoms, the increment of chain carbon atoms, and the molecular increment of volume obtained by subtracting N times the limiting CHs increment, 16.38, from the molecular volume. Inspection of this table indicates that the value for the limiting CHa increment based on hydrogenated rubber may possibly be low by about 0.02 ml. The more important thing that Table I X shows is that, as we go down the series below 10 carbon atoms, there are a systematic increase in molecular increment of volume and a corresponding decrease in the apparent CHI increment. The average value for chain CH2increment used in Equations 1 and 4 corresponds approximately to the CH2 increment in the
3
8 ' i i i i i dr Figure 3.
I 10
I
I
15
20
NUMBER OF CARBON ATOMS
Molecular Increment of Volume for Normal Paraffins
10- to 15-carbon atom range. This is an intentional compromise in setting up an approximate equation which will give good values for a wide variety of hydrocarbons, and a wide range of molecular weights. If paraffins of high molecular weight are considered, better agreement between calculated and experimental molecular volumes can be obtained if the limiting CH, increment is used. Figure 3 shows the molecular increment of volume based on da1,a for normal paraffins from Heuse ( 6 ) , API 44 ($), and Bridgman (3) from metharie to eicosane, and from -253' to +95" C. I t is clear that a t low temperature, the molecular increment of volume is relatively constant farther down the homologous series than a t higher temperatures. The apparent increase in the molecular increment of volume near the boiling point may be due to end over end rotation of the molecules, as suggested by Moore, Gibbs, and Eyring (11). The pattern of the lines in this graph fits in with the concept that the molecular increment of volume is related to the kinetic energy associated with motion of the whole molecule. This increase in the apparent molecular in-
2190
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 10
limiting volumes for the chain CH2 increment, K,, in order to Dev. c of get a limiting molecular increAv. .IT. b Av., Ml. Max. ment of volume. s o of Mol Weight Mol. Dev., (Ca1cd.Dev., Cpds. Min. .\lax. Av Vol. Ml. Exptl.) M1. Tspe The atmospheric pressure P-araffins 37 170 535 343 457.4 2.0 -1.7 + 4.9 data of Rridgman %re ehonn Naphthenes 21 196 547 366 466.5 1.2 +0.5 Monocyclic in Table X and the correDicyclic 12 194 433 317 387.8 3.4 p z +-i l 48l .. 702 T-r-._i i n v r_.__ lio 8 2 4._ 8 261 228 283 3 A-. A_ _ _ _l-.sponding data under pressure Tetracyclic i 429 429 429 484.1 5.8 +i:i +'5:b in Table XI. 42 ... ... ... 417.9 2.5 +2.3 11.7 Average for Naphthenes Average for a11 satuThe data in Table X show 79 170 547 345 442.0 2.4 -0.2 +11.7 rated hsdrocrrrbons Aromatics that the average CH, incre188 429 320 391.9 Monocyclic 23 2.0 0.0 ++ 66 .. 26 ment, K1 for the range C5 to 292 Dicyclic 351 329,9 182 2.7 t2.7 346 353.1 234 316 5.1 Tricyclic -5.1 +T 77 .. 55 CIOis considerably smaller than 429 182 313 36 372,7 All aromatics 2.6 f1.3 351 357.6 182 Sonaromatic olefins 278 6 2.5 -0.3 the limiting CHz increment. ++11.7 5.1 417.2 170 911 hydrocarbons 332 121 547 2.5 f1.2 The molecular increment of All data published by API 42 in 1946 (25) have been used. More recent data obtained by API 42 have only volume is c o r r e s p o n d i n g l y lbeen circulated privately and mere not available for use in this table. b Average deviation means sum of differences obtained by subtracting experimental mol. volume from calculated larger. This should be kept mol. volume disrenarding sign and dividing by number of data. in mind in considering the 'c Deviatidn of &erage means sum of differences obtained as above, b u t taking sign into account. For parafhns ,experimental average mol. volume for 37 compounds is 467.4. Calculated value is 455.7; difference 1.7 is shown data in Table XI which are as 'deviation of average. all for the average C, to Clo increment. Table XI shows that there is a high degree of regularity in the data, and that a t 10,000 kg. wemen% of volume near the boiling point is not allowed for in per eq. em. both the CHZincrement, and the molecular increment Equation 4. so as the boiling point is approached, the calculated of volume are of the same order of magnitude as a t -253" C. and molecular volumes tend to be a little low. atmospheric pressure. The effect of pressure on molecular volume has been investiI n order to apply a correction to Equation 4 t o t,alce care of gated with the aid of Bridgman's data ( 8 ) . I n a few cases these the effect of pressure: it seemed desirable to consider the Csto have been extrapolated a little either graphically or by the careful C10 increment rather than the Cg t o CIOincrement, since as shown use of increments. Bridgman has provided data a t 0", 50", and in Table I X the average CH, increment, 16.28, in Equations 1 9.5' C. for nornial paraffins having 5, 6, 7j 8, and 10 carbon atoms. and 4 corresponds to the CH, increment a t ahout the 10-carbon Data for isopentane and four hexane isomers are also given. atom level. Data for this range are shoivn in Table XII. The Because the authors are not aware of data on the compressilogic of this approach is that if a pair of hydrocarbons is chosen bility of hydrogenated rubber or other material of high molecfor which t.he CIL increment K1, oorresponde to the increment ular weight 75-hich would apply to the effect of pressure on the K1 in Equations 1 and 4, the effect of pressure on the other inlimiting CHZ increment, the constants in Equation 4 were evalucrements ( K z !K I , K,, Kg) a-ill aleo correspond. Theee data have ated using Bridgman's data for the Cg to Clo normal paraffins. been plotted and the graphs used as the basis for Table XIII, His data a t atmospheric pressure were also calculated using
TABLE VIII. BPI 42 HYDROCARBOYS 9T 210' F."
I--
s
@
TABLE IX. hfOLECULAR INCREMENT O F VOLUME CALCCLATED FROM LIMITING VALUE FOR CHQA X D NORMAL P.4RAFFIX DATA OF API 44 ( 2 ) 'No. of Carbon Btoms, N1 4
5 6
7 8 9 10 15 20
25
Mol. Volume, 200 c. 100.4 115.2 130.7 146.5 162,6 178.7 194.9 276,4 358.5b 440.2b 522.1s 604.2b 686.2a
Mol. Incr of Volume, Mol. Vol. Minus 16.38 N i 34.9 33.3 32.4 31.8 31.6 31.3 31.1 30.7 30.9
EQUILIBRIUM
PRESSURE
0 50 Q5
16.4Za 16.34' 16. 3Sa 1 6 ,4Za 16.40a
c 6 9 c7, c8, AYD
D.4TA O F BRIDGM.4K FOR Cj, c,, ci, Cs, KORYALPARAFFIXS UXDER PRESSURE
1000 Kg./Sq. Cm. Av. $Io'. CHz incr. incr., of Cs-Cio volume 15.64 l5,95 16,l5
5000 Kp./Sq. Cm. Bv. >Iol. CHz incr. incr., of CdLo volume
22.6 25.5 28.7
14.65 14.62 14.95
AND
clo
10,000 Kg./Sq. Cm. Av ?201. CHI sncr. incr., of Cr-C:a volume
14.17 16.63 16.51
1i:b 13.89
14:80 1.i.17
TABLEXII. BASIC DATAUSED IN PREPARING CORRECTION FACTORS FOR EFFECT OF PRESSURE SHOWN IK TABLE SIV
16.30a
Pressure, ~ ~ , / Temp., Cm. or C. 1 Atm.= 0 1 atm.' 1,000 2,000 5,000
CiO
(1
N O R M 4 L P-4RAFFISS AT N O R X A L PRESSURE
OR
c.
14.8 15.5 15.8 16.1 16.1 16.2
29.0
TABLEX. DATAO F BRIDGXAK FOR co,
Temp.,
CHa Increment
30.7 30 30.9 35 31.0 40 a Average for preceding interyal of 5 carbon atoms. b For supercooled liquid state.
TABLE XI.
ATMOSPHERE) CORRESPOXDING TO ISDIC.4TED
50
TEMPERATURE
Molecular dverage Molecular Llmiting CHe Increment CH2 Increment Temp., Increment, of Increment, of c. Table IT' Volume Ca-Cx T'olume 15.81" 32.7 16,166 29.9 0 15 84 41.8 16.695 35.6 50 15.76 52.8 17.216 42.2 95 a As example of variation within range, niin. value = 15.46 a t Oa C., mas. value = 15.92.
1 atm.Q 1,000 2,000 5,000
10.000 95
1 atni.& 1,000 3,000
5;OOO
~
10,000 a
s ~Molecular ,
Volume Cs Cia 159.0 190.8 148.0 179.0 141.9 ... 131.2 .. .
CH2 Increment 7c of value at 1 MI. atm.
Molecular Incr. of Voluiu5b7"of value at 1 All. atm.
15.91 15.50
100.0 97.4
31.7 24.0
...
...
...
...
,..
100.0
38.4
100.0 74.0 63.3 53.6 49.0
...
...
168.4 153.5 146.3 134.0 123.2
200.9 184.7 176.7 162.3 149.3
14.17
13.05
93.8 87.2 80.3
178.5 158.1 149.8 136.6 125.8
211.4 189.9 180.6 165.6 152.5
16.40 15.90 15.41 14.46 13.32
100.0 97.0 04.0 88.2 81.2
16.25 15.63 15.24
96.2
28.4 24.3 20.6
18.8
47.4 30.9 26.5 20.0
19.3
1 atmosphere = 1.0338 kg./sq. om. = 14.696 lb./aq. inch. Evaluated with data for n-decane.
100.0
75.7
...
100.0 65.3 56.0 44.2 40.5
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1954 TdBLE
Mri!t,i-..~ Presplier sure, Fi for L b . 1 ~ ~K ., t o K~ Inch + a t Any 1000 Temp. 1.0 0.0147 3 . 5 0.990 0.982 7.1 14.2 0.965 0.960 21.3 0.938 28.4 4 2 . 7 0.915 0.895 56.9 0.875 71.1 0.839 106.7 142.2 0.807 ~
PressUreb, Kg./Sq. Cm. 0.99 250 500 1000 1500 2000 3000 4000 5000 7500
10000
EFFECT O F PRESSURE“
XIII. ~
Multiplier O’C. 1.0 0.900 0.840 0.755 0.690 0.665 0.600 0.680 0.560 0.530 0.510
h for Molecular Increment of Volume, Ka
20°C. 1.0 0.900 0.835 0.750 0.685 0.660 0.595 0.575 0.550 0.530 0.510
50°C. 1.0 0.890 0.840 0.735 0.670 0.640 0.590 0.660 0.540 0.515 0.490
95O C. 1.0 0.850
0.760 0.660 0.605
0.560 0.510 0.475 0.440 0.420 0.400
looo
C.
1.0 0.845 0.745 0.650 0.595
0.550 0.490 0.455 0.425 0.410 0.390
a Derived from Bridgman’s d a t a for normal Cs and normal Cio, with Borne extrapolation. See Table XII. b 1 Kg./sq. om. = 14.223 lb./sq. inch.
TABLE XIV.
2191
1. A molecular increment of volume which represents the space generated by kinetic impact on its neighbors of the molecule as a whole. The molecular increment of volume is a function of molecular weight, but not of structure. 2 . A portion which represents the combined volume occupied by the constituent atoms of the molecule because each atom enjoys a certain amount of freedom to move. This portion d e pends upon the structure of the molecule, but not on the molecular weight. LITERATURE CITED
(1) American Petroleum Institute, Research Project 42, Pennsyl-
vania State University, State College, Pa. (2) American Petroleum Institute, Research Project 44, Carnegie Institute of Technology, Pittsburgh, Pa. (3) Bridgman, P. W., “Physics of High Pressure,’’ pp. 128-30. New York, Macmillan Co., 1931.
OF DATAOF BRIDGMAN’FOR SATURATED HYDROCARBONS WITH EQUATION 8 COMPARISON
(Deviations in M l . ) a l b
M.V., 00 C.
kg./sq.
%-Pentane Isopentane
111 7 112 8
-0.3 -3.0
%-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane
127 2 128.4 126,3 129.2 126.8
-1.3
%-Heptane %-Octane n-Decane
143,O 159,O 190.8
No. of d a t a Av. deviation Dev. of average Max. dev.
om.
00 c. 5000 kg./sq. om. +0.5 -1.8
10,000’ kg./w.
cm.
+0.6
-2.0 -2.2 -0.7 -3.8 -0.9
... ... -0.3 ... ...
-1.0 -0.9 -0.9
-1.9
.. .. ..
10 1.4 -1.4 -3.3
8 1.7 -1.6 -3.8
-2.5
-0.4 -3.3 -0.9
...
...
...
2 0.4 +0.2 +0.6
c.
l b
kg./sq. om. -1.5 -4.5 -2.0 -3.6 -1.2
500 5000 kg./sq.
om. +3.5 +1.0
4-0.8
f0.8
...
+2.5 -0.9 +2.1
-1.2 -1.0
f1.5
-1.7
-0.5
9 1.9 -1.9
-4.5
Calcd. mol. vol. - exptl. mol. vol. b 1 Kg./sq. cm. actually means 1 atmosphere or equilibrium pressure at indicated temp.
+1.0 t . .
9 1.6 f1.4 +3.5
950
10,000 kg./sq. om. +3.5
16
...
kg./sq. om. -6.1 -7.8
+0.5 f0.6 f2.1
-5.0 -6.6 -3.9
c.
5000 kg./aq. cm. +2.5
-0.2
0.0
10,000 kg./sq. om. +2.8
...
+0.1 0.0
+2:2
...
-4.1
-0.1 +1.5 -1.5 +1.1
f1.3
-3.6 -2.8 -1.9
fO.9 +0.1 +0.8
...
9 4.6 -4.6
10 0.9 +0.5 +2.5
8 1.1 +0.7 +2.8
. . I
... 6
1.7
+1.7 +3.5
-7 8
f1.7 -1.9
4-1.4 +1.1 +O.P
a
which provides values for F I and F5 which can be used to correct Equation 4. A general equation is as follows:
M.V. at t
’ C. and P F,K,N,
pressure
=
+ P1Kz~’z f FIKJ‘~ - F1K4fVa + F&F,
(8)
N , , N z , Na, and N a , and K,, Kz, Ks, K4, and KF,have the same significance as in Equation 4. Values for the K I to K4 increments can be obtained from Table IV, values for Kb from Table V, and values of F1 and F5 from Table XIII. For the present Fz, Fa, and Fd are taken as equal to K . The equation is believed to be good a t 1 atmosphere over the range -253’ to +200° C. In the range 0” to 100’ C., it is good from 1 atmosphere to 10,000 kg. per sq. em. Data for checking Equation 8 are not plentiful. Table XIV shows the agreement of this equation with Bridgman’s data for 10 saturated hydrocarbons from pentane to decane. Except at 95” C. and equilibrium pressure, the data agree within 2%. The pressure coefficients in Equation 8 and Table XI11 have also been checked with unpublished data from API Project 42 (18); results indicate that the equation used is basically sound for correlating pressure data. CONCLUSIONS
The change of volume of hydrocarbons due to changes in temperature and pressure can be treated in a very general and relatively simple manner. I n order to do this i t is necessary to consider the molecular volume of any hydrocarbon as consisting of two parts.
Low pressures were not reported by Bridgman.
( 4 ) Green, H. C., “Molecular Theory of Fluids,” pp. 30-3, New
York, Interscience Publishers, 1952. (5) Griswold, J., and Chew, J. N., IKD.ENG. Cam
