Physical and Chemical Properties of Petroleum Fractions 11. Relations between Molecular Weight and Concentration in Dilute Solution HARRY T. RALL AND HAROLD M. SMITH, Petroleum Experiment Station, Bartlesville, Okla.
which may be rearranged as
The molecular weights of oils as usually calculated from either cryoscopic or ebullioscopic data generally change uniformly with concentration. This necessitates a series of determinations so that the curve through the determined values may be extrapolated to zero concentration. There appears to be a relation between the slope of the molecular weight-concentration curve and the value of the extrapolated molecular weight. If this relationship is equated with the formula connecting the concentration and molecular weight, the result is an equation that will give the value of the extrapolated molecular weight from one determination. Equations of this character are given for benzene and ethylene bromide. Comparisons of calculated and actual results are also given which show that for the data presented the suggested method applies fairly well.
( KT -) 2 6
M = m
(3)
where M is the extrapolated value of molecular weight, m the observed molecular weight as calculated by Formula 1, w/W the concentration in grams of solute per gram of solvent, M. the molecular weight of the solvent, K the molar cryoscopic constant, and A the depression in degrees Centigrade. It appears that Equation 3 implies a definite percentage decrease over Formula l for each oil per degree depression, the percentage varying with the solvent, being smaller the larger 900
/
LEG E‘ND
,/’
CYCLOHEXANE --- -BENZENE ETHYLENE BROMIDE---
/,/
800
/
OIL 0-1
/
/ 700
600
I
T HAS long been observed, in the determination of molecular weights of petroleum fractions by the cryoscopic method in benzene, that the apparent molecular weight of the solute as calculated by the ordinary formula
E
r t-
M
4
‘$ 500 Y I
P
J
increases with the concentration of the solute. Equally true, but perhaps less commonly known, is the case of solvents in which the deviation is negative, as for cyclohexane in the cryoscopic method and carbon tetrachloride or cyclohexane in the ebullioscopic method. So far as the authors can ascertain, no adequate explanation of these departures from theoretical solution laws has been made. However, the reason for these deviations is not the subject of this paper; rather it is recognized as a fact, and an attempt is made to utilize it t o simplify the determination of the molecular weight of petroleum fractions.
u
w
1 . ’
400
/
I - ’*/ /
________ ___------------ OIL
-/A -
0-3
5--=---- - --________ 1----- --______
300 -
i
DOTTED LINES INDICATE EXTRAPOLATION BEYOND DATA -/)---‘OIL 0-4 /-
-------
-c----__-______ --- ---___ //----
______----------_
Empirical Relationships FitzSimons and Thiele (1) report an attempt to devise a formula from which the extrapolated molecular weight could be calculated from a single observation of molecular weight by the freezing point depression method. Their formula, stated to be applicable to benzene and cyclohexane, is given as
.o I .02 .03 CONCENTRATION, C = $
.04
FIGURE 1. RELATIONSHIP BETWEEN OBSERVED MOLECULAR WEIGHT AND CONCENTRATION FOR THREE CRYOSCOPIC. SOLVENTS 436
NOVEMBER 15. 1936
ANALYTICAL EDITION
437
125 the cryoscopic constant. The experience of this laboratory is that such a simple correction will not apply generally to all oils or to all solvents. It definitely cannot be applied to solvents in 100 which the slope of the molecular weight-concentration curve is negative. During the past few years this laboratory has 75 had occasion to make numerous molecular weight determinations by both the cryoscopic X and ebullioscopic (Mendes-Wright) methods m 50 with pure and impure solvents and with and bJwithout dehydrating agents (2). It has been a 0 -I observed that the slope of the molecular weightv, 25 concentration curve depends for the most part upon the molecular weight of the solute. This observation is probably not precisely true, but it is believed to be sufficiently exact for the 0 intended use of the relationship. Further work, if it does not completely invalidate the equations developed on this assumption, will only - 25 '00 200 300 400 500 600 700 800 correct them. T h e e q u a t i o n s a r e entirely MOLECULAR WEIGHT hA empirical and are subject to correction or FIGURE2. SLOPE-MOLECULAR WEIGHT RELATIONSHIP FOR SEVEN SOLVENTS abandonment as more and more data are accumulated. Figure 1 shows curves obtained by plotting observed various solvents) from which M can be determined in terms cryoscopic molecular weights as calculated by Equation 1 of known quantities. Thus the equation against concentration of solute for four different oils in three different solvents (8). The discrepancy between the extrapolated values of molecular weight of the four oils in the various solvents may be due to impurities and moisture and will be disregarded; the slope of the curves is the point to which attention will be directed. It will be observed that the is obtained for benzene (cryoscopic). It might be mentioned slope for benzene and ethylene bromide increases and for that the equation cyclohexane decreases as the molecular weight of the oils increases. 1.125 C K - 200 Table I gives the equations of all the curves of Figure 1 and M (7) 1.125 C 1 0.889 c also those for six ebullioscopic solvents. The method of averages was applied to the cryoscopic and ebullioscopic data accommodates the authors' own data somewhat more closely in the derivation of these equations. From inspection of the than Equation 6. This equation does not include the origin equations in Table I the thought occurs that there might and therefore assumes some slope for zero molecular weight possibly be some relation between the extrapolated value of which it is believed is not in accord with the general trend of molecular weight, M , and the slope, S, of the curve. Figure the data for the several solvents studied (Figure 2). 2 shows the result of plotting S against M . While there are several irregularities in the data from which this family of TABLEI. SLOPE-MOLECULAR WEIGHT RELATIONSHIPS FOR curves was derived, there seems to be a definite tendency for SEVENSOLVENTS the slope to increase or decrease as molecular weight increases, Method Equations Solvent and all curves appear to originate at the origin. Thus when M S benzene i s used as a solvent in cryoscopic determinations the Oil 0-1 linear equation, calculated by the method of least squares Cryo. m = 763.7 + 855.2 C
1s
rT
+
8 = 1.15M
(4)
passes through the origin and satisfies all the points for this solvent fairly well. In a like manner the relation, not necessarily linear, between slope S and molecular weight M could be determined for each solvent, provided the molecular weights of sufficient oils were determined to make the equation certain. Once this relation is known it becomes simply a problem in algebra to apply it in developing an equation from which 144 can be determined from a single observation of rn on any other sample of unknown molecular weight. Referring to Figure 1, assume that the apparent molecular weight of such an oil has been determined and the point P located. It is apparent that the extrapolated molecular weight can be represented by the equation M = m-SC (6) which is a transposed form of those equations reported in Table I. This equation can be rewritten to evaluate S and this value substituted in Equation 4 (or similar equations for
Isopropyl ether Isopropyl alcohol Eth lene bromide C a d o n tetrachloride Benzene (A-1) Benzene (A-3) Cyclohexane (B-I, B-2) Cyclohexane (B-3) IsouroDvl ether 1soLrobj.l alcohol Etl.ylene bromide Ethylene chloride Benzene (A-2) Benzene (A-3) Cyclohexane (B-2) Cyclohexane (B-3) Ethylene chloride Ethylene bromide Benzene (A-2) Cyclohexane (B-2) Ethylene bromide a C = concentration = 2 W.
+
Ebull. Cryo. Ebull. Ebull. Ebull. Ebull. Cryo. Ebull. Oil 0 - 2 Cryo. Ebull. Cryo. Ebull. Ebull. Ebull. Cryo. Ebull. Oil 0 - 3 Cryo. Ebull. Cryo. Ebull. Ebull. Cryo. Oil 0 - 4 Cryo. Cryo. Cryo.
m = m = m = m =
m m
= =
m = rn =
-
705.6 215.0 C 722.6 1674.0 C 716.1 948.0 C 7 2 5 . 1 4- 1363.0 C 743.0 310.0 C 738.1 2446.0 C 626.5 -t 1160.0 C 704.9 2166.0 C
--
+-
m = 490.6 m = 459.8 m = 451.5
m
=
455.6
m = 468.9
m = 457.7 m = 438.0 m = 484.6
4-
430.5 C 35.0 C 208.0 C 229.0 C 31.3 C 1270.0 C 4920.0 C 4- 6 2 6 . 0 C
+-
++-
+
535.4 C 325.9 -t 121.7 C 328.9 595.5 C 326.9 47.1 C 336.8 542.2 C m = 318.7 4-2500.0 C m = 333.4
m m m m
= = = =
+-+
= 209.3 -4400.3 C m = 207.9 25.5 C m = 197.6 4- 1606.0 C
n~
-
VOL. 8, NO. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
438
TABLE 11. APPLICATION OF EQUATION 6 TO MOLECULAR WEIQHT DATA Oil 0-1 ( K ;m ? )=
7
(+) C
, $ MI : ;
C (%)
Oil 0-2
Oil 0-3-
M glm6 )(; C
m = (K;?)
( K ;m ? )=
&M;
- ,
( 5C )
Oil 0-4 m = (K%%)
M from
Eq.6
..... ..... ..... ..... .....
... ...
... ... ... .. .. ..
.....
483.6 482.6 481.7 478.6 494.6 487.8 484.2 484.8 488.8 492.9 484.0 485.2 482.1 482.2
760.3 763.7 766.0 756.3 764.2 763.9 765.4 761.2
...
Extrapolated values for M Average
763.7 762.6
763.7 805.6
.....
490.6 486.2
490.6 509.2
.....
Table I1 gives the results of cryoscopic molecular weight determinations in benzene made on four oils calculated according to the usual equation and according to Equation 6. In Figure 3, where these same data are plotted, the effect of applying Equation 6 is apparent, and the curves indicate that the result probably is fairly adequate for the purpose. However, it is believed that additional data, carefully obtained, might lead to an even better formula universally applicable to the determination of the molecular weight of petroleum and its fractions with benzene in the cryoscopic method. It is realized that several laboratories have reported molecular weight vs. concentration curves not in harmony with some of those presented in this paper. Data from other petroleum laboratories working with apparatus similar to the authors’ have been examined and considerable agreement has been found.
Application of Equations to Data The applicability of Equation 6 to some such data is shown in Figure 4 where the results obtained by eight laboratories as well as the authors’ are graphed for the four oils (2) reported in Table I. At intervals are shown curves that represent the ideal slope all data would have to assume to accommodate Equation 6 perfectly. Any data falling on these ideal curves or roughly parallel to them would give the extrapolated
350 340
330
01
02
03
04
05
2001
01
1
I
02
03
t: 530
w 520
4 3 510 Y
_I
0 500 I
490 480
CONCENTRATION, C-
CONCENTRATION,C =
+
FIGURE 3. APPLICATION OF EQUATION 6 TO MOLECULAR WEIGHTDATAIN BENZENE
388.3 340.1 342.8 341.6 344.1 334.0 335.1 335.3 337.8 338.0 331.1 333.3 332.5 333.4
..... .....
333.4 346.3
0.00719 0.01391 0.02140 0.00546 0.01054 0.01602 0.02468 0.01091 0.00485
.....
..... ..... ..... .....
.....
333.4 337.0
.....
212.8 215.5 217.3 214.9 213.2 215.8 218.8 206.4 214.0
211.1 212.1 212.1 213.6 210.6 211.9 212.8 205.3 211.3
...
... ...
209.3 214.3
209.3 211.2
..*
... ... ...
molecular weight, M , of any sample from cryoscopic data in benzene if calculated according to Equation 6. The agfeement is not perfect but it is encouraging. It is assumed in the case of benzene (cryoscopic) that the relation between S and M is linear. This assumption is probably near enough to fact for the purpose of formulating Equation 6, but additional data would probably show it to be a curve. Most of the other data of Figure 2 cannot be represented suitably by straight lines. Thus the equation of the parabola S = 0.0482 ( M
-
170)’
+ 1550
(8)
is in agreement with the authors’ data for ethylene bromide. The curve, however, does not pass through the origin and therefore cannot apply to data below M = 250, as can be readily understood by inspection of Figure 2. An equation for ethylene bromide corresponding to Equation 6 for benzene can be developed from Equation 8.
M=
( 1 6 . 3 9 C - l ) + d l -(32.78-0.1928m)C-298.9C’ 0.0964 C (9)
This formula corrects all the data obtained in ethylene bromide so nearly perfectly that any single determination might have been accepted with confidence that in no case would the error from the extrapolated value be very great, considering that the rise in apparent molecular weight (as calculated by the ordinary formula) with concentration is unusually great. Of course, the result cannot be any more accurate than is the single determination itself. If it is in error (datum does not lie on the molecular weight-concentration curve) then the results of applying the above formula will also be in error by a corresponding amount plus any additional error that might be incorporated in the formula itself. The latter is small in this particular case. Table I11 gives the result of applying the formula to the data from one of the oils. Equation 9 is entirely too cumbersome for convenience, but it indicates what can be done even in the case of such B solvent as ethylene bromide, where the increase of apparent molecular weight with concentration is exceptional. Figure 5 shows clearly how Equation 9 reduces the data obtained for oil 0-1 in ethylene bromide to nearly a horizontal line. Since Equation 8 fits the data points for oils 0-2, 0-3, and 0-4 as accurately as it does the data point of 0-1 (Figure 2 ) , it is obvious that molecular weight data for these oils will plot just as nearly horizontal if calculated by Equation 9 as do the data for oil 0-1. Tables I1 and I11 indicate the error possible in accepting an “average” molecular weight when calculated by the usual formula, particularly where large
NOVEMBER 15, 1936
ANALYTICAL EDITION
439
1300 EQUATION (6) COOPERATING LABORATORIES ---.B U R E A U OF MINES ---------
1200
MOLECULAR WEIGHT AS CALCULATED B Y : E Q U A T I O N ( I ) -0-
EQUATION (9)
860
540
I100
820
E
$ 500 W
l-”
1
2 1000
780
3 760
5
740
43 720
CT
4
2
0
700
900
w J
8 690
0
I
660
800
640 620 6000
4
8
12
16 CONCENTRATION. C x 100
CONCENTRATION, C x l O O
FIGURE4. GRAPHICAL COMPARISON OF DATA FROM NINE LABORATORIES WITH EQUATION 6
concentrations of solute are employed or solvents giving a steep molecular weight-concentration curve are used. CONCENTRATION,
Discussion
It should be understood, of course, that these equations are entirely empirical and are based upon the molecular weights of the four petroleum oils studied. They are therefore subject t o revision or rejection as further data are accumulated. However, the attention of all petroleum laboratories is directed to these equations and their development in the hope that confirmation or conflict may be discovered in data of these laboratories. These equations are recommended for use primarily where only one determination of apparent molecular weight is made. The procedure of determining apparent molecular weight at various concentrations and extrapolating to zero concentration is still to be considered the safest practice. However, if only one determination is made, equations such as 6 and 9 appear to the authors to be a logical approximation, particularly if in that determination a high concentration of oil is used or a solvent whose slopemolecular weight curve deviates rapidly from the molecular weight axis.
C=G
FIGURE5. APPLICATION OF EQUATION 9 TO MOLECULAR WEIGHT DATAIN ETHYLENE BROXIDE
Considering the curves shown in Figure 2, it would seem that some idea could be obtained of the relative desirability of the solvents when used in cryoscopic or ebullioscopic determinations. Thus, ethylene bromide swinging sharply away from the molecular weight axis indicates a rapid departure from ideal solution laws as the molecular weight increases. Conversely, those curves lying near the molecular weight axis would indicate less deviation from solution laws. From this standpoint benzene used either cryoscopically or ebullioscopically should be the preferred solvent. However, other factors might also influence the choice of solvent, such as the solubility of water and of the sample to be determined, the value of K, the convenience of the freezing or boiling point, and probably numerous other conditions, some of which might be peculiar to special laboratories or equipment. Thus, in the authors’ apparatus (8) cyclohexane is a satisfactory cryoscopic solvent. The authors do not believe it would be as satisfactory as benzene in the usual type of apparatus because TABLE111. APPLICATION OF EQUATION 9 TO MOLECULAR its low heat of fusion necessitates good agitation and rapid WEIGHT DATA determination of freezing point before the concentrating of the solvent due to crystallization becomes appreciable. (Oil 0-1in ethylene bromide) c m = Similarly, from inspection of Figure 2, isopropyl ether would M from seem to be as satisfactory an ebullioscopic solvent as benzene. (K$+) Equation 9 However, the property of frothing and the limited solubility 609.8 of petroleum oils in this solvent are serious objections to its 614.0 627.4 use in the Menzies-Wright apparatus. 628.5
Extrapolated value for M Average
626.5 834.1
638.7 601.8 630,O 628.4 630.9 635.8 628.9 583.6 622.9 625.0 663.5 645.9 626.5 626.3
Literature Cited (1) FitzSimons, O., and Thiele, E. W., IND.ENG.CHEM., Anal. Ed., 7, 11 (1935). (2) Rall, H. T., and Smith, H. M . , Ibid., 8, 324 (1936). RECEIVED June 27, 1936. Presented before the Division of Petroleum Chemistry at the 91st Meeting of the American Chemical Society, Kansas City, Mo.,April 13 to 17, 1936. Published by permission of the Director, U. S.Bureau of Mines. (Not subject to copyright.)
