Homologous Series of Alkanes DENSITY AND ITS TEMPERATURE COEFFICIENT *
GEORGE CALINGAERT, HAROLD A. BEATTY, ROBERT C. KUDER, AND GEORGE W. THOMSON Ethyl Gasoline Corporation, Detroit, Mioh.
through the points for each of P R E V I O U S p a p e r (1) Selected, smoothed values of the temperafrom this laboratory dethe eight hydrocarbons, and ture coefficients of the density for normal scribed a linear alignment the changes in density for each and branched-chain alkanes have been of the number of carbon atoms c o n s e c u t i v e 20" range were obtained from a collection and alignment of and the molecular volumes in taken from the curves. The the literature data. The molecular voldifferent homologous series of coefficients were then plotted branched-chain alkanes. This against their mean temperaumes in the liquid state at 20' C. of the tures, giving slightly curved was obtained by constructing normal alkanes from butane to eicosane an arbitrary ordinate scale such lines. Straight lines approxiare adequately given by the simple equamating these curves a t 20" were that the values selected for the tion : drawn for each hydrocarbon, the molecular volumes of the normal slope of each line was plotted alkanes gave a straight line when V = 30.392 16.375 N 74.44,lW against the number of carbon plotted. I n practice, the exeratoms, N , and a smooth curve cise of this method has proved where N = number of carbon atoms. was drawn through the Doints. useful in estimating the densities As shown in T a b 6 I, this' curve of various branched-chain alThe molecular volumes in different is adequately expressed simply kanes $or which no reliable homologous series of branched-chain bv: values, if any, were available -* . alkanes, with the possible exception of the and also in detecting erroneous initial member of each series, differ from log ( - b ) a -5*300 - o.loo N values previously reported. A revision of this chart is now those of the corresponding normal isomers Extrapolation of this function in order, owing t o the subby a constant amount, characteristic of the sequent publication of a numup to = 20 should not be series. The use of this alignment method seriously in error: this has been ber of new or more accurate to detect erroneous or suspicious density done, and the values obtained density data. I n addition, it has proved possible to convert values in the literature is illustrated. are listed in Table I. For liquid propane and butane the exthe graphical method to one which employs simple mathetrapolation itr probably not rematical equations only, with a consequent greater ease of liable, since the data of van der Vet (7) give values of b which handling and, perhaps, accuracy. As a preliminary to this are, respectively, three and four times those calculated from revision, a general survey and selection was made of the the above function. temperature coefficients of the densities of the liquid hydrocarbons. I n this selection, as well as in that of the densities of the normal alkanes, emphasis has been placed on the fact TABLEI. VARIATION OF TEMPERATURE COEFFICIENT WITH TEMPERATURE that the properties in question are expected t o vary in a smooth and continuous manner throughout the homologous N 5 6 7 8 9 1 0 1 1 1 2 - b X 10' series. Accordingly, values taken from smoothed curves have .58 1.25 0.96 0.70 0.60 0.53 0.40 0.33 been used in preference to those from individual points. I n %% 11.58 1.26 1.00 0.79 0.63 0 . 5 0 0.40 0.32 view of the considerable degree of uncertainty associated with almost all of the individual data, it is felt that this procedure affords the best method of selection. For the branched-chain alkanes there are practically no data adequate t o determine reliable values of b, other than Temperature Coefficients those of Smyth and Stoops (6) for the 2,2-dimethyl, 3-ethyl, If we write Dt = D*O a(t - 20) (b/2)(t - 20)* then a and 2,2,4-trimethylpentanes. An analysis of these and of the is the temperature coefficient of the density, D , a t 20" C., and few other scattered data available was made as described above and indicated about the same values of b as found for b is the small but appreciable variation of this coefficient with the normal alkanes of equal N . Fortunately, owing to its temperature, t . DETERMINATION OF b. For the normal alkanes the only small size, the value of b is of little significance in the determination of P o and the temperature coefficient, a. suitable set of data is that of Dornte and Smyth (2) who deDETERMINATION OF a. For normal alkanes all the available termined the densities of pentane to dodecane a t 20" C. indensity data from a given author a t two or more temperatures tervals over 100-2UO" C. ranges. Their values were plotted for the liquids from N = 3 to 20 were collected, and the coron large scale against temperature, smooth curves were drawn
A
+
+
+
+
103
104
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
responding values of a were computed (using the above mentioned valuea of b for the slight correction for temperatures remote from 20” C.). At the same time an estimate of the reliability of these values was made. Plots as a function of N were then made of a, l/u, log a, a times the molecular volume, and a times the molecular weight. The last of these proved to be linear from N = 7 to 20 and slightly curved below A‘ = 7. Since nearly every individual value of a, including the most reliable ones, did not depart from this line by more than the estimated uncertainty in the value, it was considered that values read from the line constituted the best selection. These values are listed in Table 11. For the branched-chain alkanes, in like manner, the values of a were computed from the literature data, multiplied by the corresponding molecular weights, and plotted. Most of these points were scattered on both sides of the line for the normal alkanes, with a departure from the line less than the estimated uncertainty in the points. Hence, the corresponding value for the normal hydrocarbon was taken as the best selection in general for each isomer. The only pronounced exception was isobutane, for which the value of a assigned was 0.00123 instead of that of %-butane, 0.00109. That this correspondence is not strictly correct is shown by the one set of data which is sufficiently accurate for intercomparisonthat of Edgar and Calingaert (5)for the nine isomeric heptanes. Their values of a for the branched-chain compounds vary from 0.000838 to 0.000856 (average, 0.000850), compared with 0.000835 for n-heptane, and are [‘almost certainly correct” to 0.000007. A similar dilatometric comparison of other pure branched-chain hydrocarbons with their normal isomers would be of interest.
Molecular Volumes
Vol. 33, No. 1
separate values, since the true value is more probably near one or another of them. Therefore each separate selected value was retained, but one of them in each case was designated as the first choice for use in the subsequent fitting of a n equation. These separate values are given in Table 11, the first choices being in bold face type. For the densities from N = 13 to 20, the data are far less reliable, and a different method of selection was used. The individual data were corrected to molecular volumes, the increments between each of them and its adjacent values were plotted, and a plausible smoothed increment curve was drawn, from which smoothed molecular voIumes and, in turn, densities were derived. These last are given in Table 11; with the exception of ,V = 14 and 16, they agree with Egloff’s selections (4)within two units in the fourth place. The selected densities were converted to molecular volumes, V , using the atomic weights C = 12.010 and IT = 1.0081, and plotted against Ai. As was expected, the resulting curve approached a straight line, but even a t N = 20 the curvature was still di3tinct. For further use it was desired to represent this curve, with the warranted precision, by a simple mathematical function. The type of function preferred was one which would become BN f(N), where linear a t high values of N (i. e., V = A f(N) approaches zero with increasing iV). Aleo, it was felt that the number and accuracy of the data did not m-arrant the use of more than four constants. After consideration of several different types of function, it was concluded that the most satisfactory was:
+
+
f ( N ) = CN-r $. DN-8
A systematic test of various values of r and s showed that the optimum values lay very close to r = 2 and s 7 0, and therefore the simple three-constant equation,
NORMAL ALKANES. For the present purpose it is desirable to select the densities of the normal alkanes as reliably as V =A BN C/Na possible, since they are to serve as the standard of compariwas adopted. The three constants were evaluated by a series son. It might be supposed that these values are known with of judicious selections of three fixed points and observations of a considerable degree of certainty, a t least from iV = 4 to 12, but this is by no- means the case, as shown by comparison of the various published selections of “best” values. For example, the densiAND THEIR TEMPERATURE COEFFICIENTS FOR TABLE11. DENSITIES ties for N = 4 to 12 selected by Grosse and WORiVAL ALKANES 0 2 0 DPP Egloff (5), and a year later by Egloff (0, differ Temp. Coeff. at 20°a Calculatedb Selectrd Calcd. up to several units in the fourth decimal place; from M i nus D20 Liieratnrec Selected Alkane N --ax102 -bxi06 v both sets differ more or less from the values Propane 3 1.300 .. .. 100.644 87.788 0.502 0.498 0.004 previously selected (1) in the present study. Butane 4 1.093 0.5781 0.5778 0.0003 0.5789 Accordingly, it was decided to make a new and Pentane 5 0.972 1.58 115.245 0.62603 0,62606 -0.00003 independent selection. 0.62623 0.62681 For this purpose the individual literature Hexane 5 0.897 1.26 130.710 0.65927 0.65930 -0.00003 0.63944 values were taken and corrected when neces1.00 146.530 0,68379 Heptane 7 0.848 0.68362 0.00000 sary to 20” C. by coefficients a and b of Table 11, 0.68379 0.79 162.555 0.70269 0.70P3R 0.00012 Octane 8 0.812 and a careful appraisal of the probable purity n- . 7. 0- 9-4-5 0.70257 of the compound and accuracy of the deter0.70278 mination was made for each. Values for pro178.680 0,71775 9 0.785 0.63 0,71770 0.00005 Nonane 0.71780 pane and butane determined a t 20” (i. e., 0.73006 0.72993 0,00013 Decane 10 0.763 0.50 194.886 0.73014 above normal pressure) were converted to 11 0.746 0.40 211.132 0.74032 0.74025 0.00003 Undecane atmospheric pressure by means of the coefficients 0.7410 227.409 0,74901 0,74908 -0.00007 12 0.731 0.82 Dodecane of compressibility (7); values for propane a t 0.7511 Tridecane 13 0.718 0.25 243.707 0,7565 0.7567 -0,0002 -42” C. were not used, owing to the magni260.022 0.7630 0.7632 -0,0002 14 0.707 0.20 Tetradecane tude and uncertainty of the temperature cor276.348 0.7686 0,76855 -0.0002.~ 16 0.697 0.16 Pentadecane Hexadecane 16 0.088 0.13 292,683 0.7737 0.7738, - 0,0001, rection. 0.10 309.025 0.7781 0.7783-0.0002Heptadecane 17 0.681 Examination of these densities showed that 0.7821 0.782% -0.0001 325.372 18 0.674 0.08 Ooiadccane 341.723 0.7858 0.7857 0.0001 19 0.669 0.06 Nonadeoane for each hydrocarbon from N = 4 t o 12, a 0.05 358.078 0,7890 0.7838 0.0002 Eicosane 20 0.664 selection could be made of two or more sepa+ b / 2 ! U-2O)z; for N 7 to 20, --a = (0.0298 + 0.00788 a From Dt = D O + a;f-20: rate values which differed from one another N,/(2.0162 + 14.0262 N ) ’ log - b = - - 5.300 - 0.100 N b From I/ = 30.392 + 1’6.375 N 7 4 . 4 4 / X 2 and D2D = (‘2.0162 + 14.0202 N ) / V . by considerably more than the presumptive c Values in bold iace type are the first choice oi the two or more selections; values for N = 13 i o 20 are from a smoothed curve. error in each. I n this situation there seemed to be no reason for taking a mean of these
+
+
,
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1941
the resulting deviation curves, comparing the calculated with only the first choice of the selected values. (With data of the present type this method compares favorably with the use of least squares from the viewpoint of precision and permits the data t o be weighted as a group rather than singly.) The values of the constants are given in Table 11,together with the calculated molecular volumes and densities. Comparison of the selected and calculated densities shows satisfactory agreement, except for propane for which this is scarcely to be expected. The deviations found are: propane, 0.004; butane, 0.0003; N = 5 to 12, maximum 0.00013 and average 0.00006; N = 13 t o 20, maximum 0.00025 and average 0.00017. I n view of the uncertainty in the individual values, it appears that the calculated densities are nearly as good an approximation to the true values as can be obtained a t this time. BRANCHED-CHAIN ALKANES. I n the previous study (6) i t was found that when different homologous series of branchedchain alkanes (with the exception of the initial member of each series) were plotted on the (V - N ) chart, they gave straight lines parallel to the 45" straight line of the normal compounds. Put in mathematical form, this means that if V = f ( N ) represents the normal alkanes, then V = f(N A N ) represents a particular series of branched-chain alkanes, where the functions are identical and AN is a constant characteristic of the given series. On this basis, the function selected above for the normal series becomes for a given branched-chain series
+
V =A
TABLE111. DENSITIES OF BRANCHED-CHAIN ALKANES Dao
=
A
+ AA + B N + C / N 2
where AA is the constant characteristic of the series. Owing to the smaller number and lower degree of reliability of the densities in a series of branched-chain compounds (compared with the series of normal alkanes), it is not possible to say which of the above two functions gives the better fit; both are apparently adequate. Accordingly, in view of its simpler form and more obvious physical significance, the second of these functions is chosen. It may be expressed in words as follows: I n any given homologous series of branched-chain alkanes, the molecular volumes a t 20" C. differ from those of the corresponding normal isomers by a constant amount, with the possible exception of the initial member of the series. For each of the branched-chain alkanes, the density data. were collected, converted to 20 O , and appraised for reliability, and a best value was selected and assigned a degree of reliability or weighting factor of 0, 1,3,8, or 25. The compounds were then classified into different homologous series. For each series where there were two or more values (in addition to that of the first member of the series) having some degree of reliability, the above equation was applied and the best value of AA was computed. I n most of these series the initial member (the homolog with the least possible N ) characteristically did not line up with the others and therefore was not used in determining A A . Altogether eleven different series were calculated in this manner, with the results given in Table 111. Only two of these-the 2-methyl and 3-methyl derivatives-contain more than four individual members each; these display a satisfactory alignment, with an average deviation (for the values with reliability factors of 3, 8, or 25) of less than 0.0005 in density, and there are no systematic deviations. For the 2methyl series (with the exception of isobutane), a careful estimate indicates that the calculated densities are reliable to
Dm
sT:y$d
N
Compound
Calculateda &Ed V Dl0 Literatureweight
2-Meth yl Series: (2-Methyl ropane) 4 101.67 2-Methylgutane 5 116.38 2-Methyl entane 6 131,84 2-Meth ylE exane 7 147.67 2-Methylheptane 8 163.69 2-Methyloctane 9 179.82 2-Methylnonane 10 196.02 2-Methylheptadecane 18 326.50 20 359.21 2-Methylnonadecane
AA = 0.5717 0.6199 0.6536 0.6785 0.6978 0.7132 0.7258 0.7794 0.7866
1.13 0.5582 0.6199 0.6530 0,6791 0.6971 0.7132 0.7281 0.7806 0.7863
0 25 8 8 3 3 1 1 1
3-Methyl Series: AA = -0.84 6 129.87 0.6635 0.6643
3-Methyl entane leth ylgexane fethylheptane
78
8 3 8
145.70 161.72
$:& Selected
0 : 0000 0.0006
- 0.0006 0.0007
0.0000 -0.0023 -0.0012 0.0003
-0.0008 0.0008
8 1
0.0006 0.0003 -0.0001 -0.0010
AA = -0.49 0.7048 0.7043 0.7197 0.7200 0.7319 0,7323 0.7420 0.7422
8 1 8 1
0.0003 - 0.0004 0.0002
2,Z-Dimethyl Series: AA = 2.08 (2,2-Dimethylpropane) 5 117.33 0.6149 0.600 2 2-Dimethylbutane 6 132.79 0.6489 0.6493 2'2-Dimethyl entane 7 148.62 0.6742 0.6738 2:Z-DimethylEexane 8 164.64 0.6938 0.6943 2,Z-Dimethylheptane 9 180.77 0.7095 0.7105
25 25 1 1
0
- 0.0004 0.0004
1
4-Methyl Series: 8 162.07 9 178.20 10 194.40 11 210.64
4-Methylheptane 4-Methylortane 4-Methylnonane 4-Methyldecane
2,l-Dimethyl Series:
0.0005
....
0005 --00.0010
AA = -2.33
0
25 1
+ B ( N + AN) + C / ( N + A N ) *
Since the third term is much smaller than the second term, and AN proves to be within 0.25 of zero, it is possible to drop AN from the third term and write the function simply a s
V
105
1
1
2,CDimethyl Series: AA P 0.53 7 147.07 0.6813 0.6730 (2 4-Dimethyl entane) 2,i-Dimethylferane 8 163.09 0.7004 0.7002 2.4-Dimethylheptane Q 179.22 0.7156 0.7160 2 4-Dimethyloctane 10 195.42 0.7281 0.7246 2:4-Dimethylnonane 11 211.66 0.7385 0.7340
0 3 1
0 0
- 0:0002
0.0007 0.0023 0.0015
....
0.0002 -0.0004 0.0035 0.0045
2,2'-Dimethyl Series: AA = 2.25 6 132.96 0.6481 0.6617 (2.3-Dimethylbutane) 2.4-Dimethyl entane 7 148.79 0.6734 0.6730 2,5-Dimethylkenane 8 164.81 0.6931 0,6941 2,6-Dimethylheptane 9 180.94 0.7088 0.7089 2 7-Dimeth loctane 10 197.14 0.7217 0.7228 Z:ll-Dirnet$ldodeoane 14 262.27 0.7564 0.7691
25 8 1
2,3'-Dimethyl Series: AA 2.3-Dimethyl entane) 7 146.98 0.6817 2,4-Dimethyl~exene 8 163,OO 0.7008 2.5-Dimethylheptane 9 179.13 0,7160 10 195.33 0.7284 2,6-Dimethyloctane
= 0.44 0.6950 0.7002 0.7139 0.7295
0 3 1 3
0.0021 -0.0011
3.3-Dimethyl Series: AA 3 3-Dimethyl entane 7 144.53 0.6933 3:3-D/methylgexane 8 160.55 0.7115 8 3-Dimethylheptane 9 176.68 0.7259 3:3-Dimethyloctane 10 192.88 0,7377
-2.01 0.6932 0.7110 0,7258 0.7390
8 1 1 1
0.0001 O.OOO5 0.0001 -0.0013
2.2.2'-Trimethyl Series: AA (2 2 3-Trimethylbutane) 7 149.05 0.6723 2'2'4-Trimethyl entane 8 165.07 0.6920 2:2:5-TrjmethylRexane 9 181.20 0.7078 2.2.6-Trimethylheptane 10 197.40 0.7208
= 2.51 0.6900 0,6919 0.7077 0.7225
0 25 3 1
0.0001 0.0001 -0.0017
AA = -2.29 0.6946 0.6983 0.7127 0.7129 0.7271 0.7272 0.7941 0.7935
0 3 1 1
-
(3-Ethyl entane) 3-Ethy1Rexane 3-Ethylheptane 3-Ethyloctadecane
From V = 30.392 14.0262 N ) / V . a
3-Ethyl 7 8 9 20
Series: 144.25 160.27 176.40 355.79
+ AA f 16.375 N f 74.44/1V4 and
0 25
8
Dl0
....
O.ooo1 --0.0010 0.0001 -0.0011 - 0.0127
....
O.OO06
....
-
.... --0.0001 0.0002 0.0005 (2.0162
+
0.0005 or better; for the 3-methyl series the results are a little less certain, especially since the initial member of the series (3-methylpentane) has been included, and a reliability of about 0.0008 is indicated for the calculated densities. For the remaining nine series tested, each containing from, two to four individual members with reliability factors greater than zero, it is more difficult to estimate the accuracy of the alignment. Three of these series-the 4-methyl, the 2,2-.
106
INDUSTRIAL AND ENGINEERING CHEMISTRY
BETWEEN PREDICTED DENSITIES TABLE IV. DISCREPANCIES AND VALUES FROM Tnn LITERATURE
from Literature Present authors 0.74070 0.7250d 0.7139 0.7281 0.7246C 0,7390s 0.’7229 0.7225 0.734e 0.734c 0.7691 0.7691C 0.7750 0.77409 Dl0
Compound 4-Ethylhe tane 2,3-D/metEylheptane 2,5-Dimethylheptane
DSo Ca1cd.a 0.730b 0.727 0.716 0.7258 0.728 0.7377 0.721 0.7385 0.7564 0,773851
Egloff (4) 0.7407 0.7235 0.7147 0.72805 0.724fY
nlHexadeca6e a From Tables I1 and 111. b See text. c Only one literature value ava/lable. d Difference in selected values is due t o the new value available to present authors. 8 Caloulated t o 20’ by present authors. f Selected value (see text): equation gives 0.7737. a Value selected without reference to values for other n-alkanes.
dimethyl, and the 2,2’-dimethyl derivatives-appear t o be as definitely aligned as the 3-methyl series, and a similar accuracy of 0.0008 in the calculated densities is indicated. (The primed numbers refer to the positions from the opposite end of the chain: thus, the 2,2’-dimethyl series is 2,3-dimethylbutane, 2,4-dimethylpentane, 2,5-dimethylhexane, etc.). The other series (2,3-, 2,4-, and 2,3‘-dimethyl, 2,2,2’-trimethyl, and 3-ethyl derivatives) are also as well aligned as it is
Vol. 33, No. 1
reasonable to expect from the data available, and their calculated densities are probably accurate to 0.0010-0.0015. The interrelations between the different series also suggest other approximate alignments which may be useful in estimating densities for compounds outside of these series. For example, the estimated AA values for 3-ethylpentane and 5ethylnonane are each about -3.00, so that a similar value can be predicted for 4-ethylheptane, giving it a calculated density of 0.730. In general, substitution of a given single group in any position more than two removed from the ends of the chain has approximately the same effect on the molecular volume. To illustrate the utility of the alignment equations in detecting erroneous or suspicious literature data, Table IV compares (for a number of hydrocarbons) the densities predicted by the alignment method with those taken by Egloff (4) or by ourselves as the best selection from the literature.
Literature Cited (1) Calingaert and Hladky, J. Am. Chem. Soc., 58, 153 (1936). (2) Dornte and Smyth, Ibid., 52,3540 (1930). (3) Edgar and Calingaert, Ibid., 51, 1540 (1929). (4) Egloff, “Physical Constants of Hydrocarbons”, Vol. 1, New York, Reinhold Pub. Corp., 1939. (5) Grosse and Egloff, Universal Oil Products Co., Booklet 219 (1938). (6) Smyth and Stoops, J . Am. Chem. Sac., 50, 1883 (1928). (7) Vet, van der, Proc. dnd Wortd Petroleum Congr., Paris, 2, Sect. 2 , 515-21 (1937).
Heat Conductivitv of Zinc Oxide J
Produced by Flash Calcination of Zinc Sulfite H. F. JOHNSTONE, H. G. JACOBSON, AND G . W. PRECKSHOT University of Illinois, Urbana, 111.
HE flash calcination of hydrated zinc sulfite produces an oxide of extremely low bulk density as shown in Table I (1). This suggests that the powder should have a low heat conductivity and perhaps be useful as an insulating material.
T
OF CALCIWED ZINC OXIDE TABLE I. DENSITY
Compression Load K g . / s q . om. Lb./sq. in.
Density Grank/cc.
Lb./cu. p.
Measurements of the heat conductivity were made in a guarded-disk type calorimeter in which the temperature drop across the powder, the thickness of the powder, and the power input to the heater disk were measured. The apparatus was the same as that used by Kistler and Caldmell (g) in their study of the heat conductivity of aerogels. A detailed description may be found in the earlier paper. Since standardization had previously been made, the accuracy of the method was not rechecked. The heat conductivity of several samples of commercial Celotex were measured for comparison. The
results agreed closely with the values given in the literature for this material. The zinc oxide was a sample collected dry from the calciner constructed in the pilot plant for recovery of sulfur dioxide from waste gases ( 1 ) . The oalciner consisted of a 10-foot section of 4-inch 0. d. 11-gage stainless steel tubing. This was surrounded by cylindrical firebrick tile, 6 inches 0. d. and 1 inch thick, for protection against the direct action of the gas flames used for firing. The outer wall of the furnace was constructed of 4.5-inch firebrick with nine burner ports arranged for tangential flames. The temperatme of the wall of the calciner was recorded by a six-point recording pyrometer operating on thermocouples peened into the metal. Calcination of the zinc sulfite used for these tests was made at a wall temperature of 750” C. (1382” F.) and a t a feed rate of 1.12 grams per minute per sq. cm. (2.3 pounds per minute per square foot). The original zinc sulfite was prepared by adding sulfur dioxide t o a suspension of pure zinc oxide until the zinc sulfite first formed was entirely dissolved. The solution was then evaporated in a vacuum oven, and the crystals of reprecipitated zinc sulfite were collected and dried. The analysis of this product corresponded to the partially dehydrated hemipentahydrate: ZnO 45.7 per cent, SO2 33.7, total sulfur as SO2 35.2; calculated for ZnSOa.21/2Hz0: ZnO 42.8, SO, 33.6. Before calcination the crystals were
