P-V-T Relations and Derived Quantities for Hexanes E. A. KELSO' WITH W. A. FELSING The University of Texas, Austin, Texas
The molal volumes of liquid 2,3-dimethylbutane for different pressures at loo', lW', S O ' , 175', 200°, and 225' C. have been determined. The pressure-volume-temperature relations for gaseous hexane are reported at 250' and 275' C. The experimental data on n-hexane, 2-methylpentane, and 2,3-dimethylbutane have been utilized to evaluate Z values and the fugacity coefficients, which are presented in tables.
TABLEI. MOLALVOLUMES ILloles/ Liter
Pressure, Atm.
1 0 0 . 0 0 ~c. 6.769 5.60 6.796 13.50 6.887 48.91 7.006 101.82 7.112 154.07 7.202 206.70 7.285 252.36 7.358 311.81 175.00' 5.587 5.851 6.123
C. 16.14 48.92 101.52
Moles/ Liter
OF LIQUID 2,3-DIivfETHYLBUTANE
Pressure, Atm.
Moles/ Liter
C. 6.93 13.51 48.92 101.53 154.07 206.70 259.37 311.82
6.058 6.236 6.436 6.591 6.721 6.832 6.930
13.51 48.92 101.53 154 08 206 71 259.37 311.82
225.00° 4.422 4.781 5.416 5.736 5.961 6.140 6.287
C.
125.00° 6.422 6.449 6.577 6.731 6.854 6.963 7.060 7.147
200.00~c. 5.076 5.390 5.788 6.035 6.218 6.499 6.372
26.65 48.91 101.51 154.06 206.69 311.80 259.36
Pressure, Atm.
150.00° C.
37.21 48.91 101.51 154.06 206.69 259.35 311.80
ECENTLY the authors (11) published experimental ::i+i :{: data on the pressure-volume-temperature relations for ;: :!; 3-; n-hexane and 2-methylpentane. Since then t similar data have been obtained for 2,3-dimethylbutane; these data are here reported. The increasing TABLE 11. P R E S S U R E - V O L ~ ~ ~ - T E MDATA P ~ RON A TGASEOUS U~ 2,3-]DIMETRYLBUTANB demand for a more extended knowledge of .the properPressure, Atm. Density Pressure, Atm. ties of individual hydrocarbons has prompted the Density calculation of the familiar Lewis 1.1 values (14) (desMoWLit'er 250.00° C. 275.00° C. Moles/Liier 250.00° c. 275.000 c. 1.5 34.53 39.71 4.0 52.78 75.23 ignated in this paper by 2) and fugacity-pressure 2.0 38.12 46.59 4.5 68.03 98.15 ratios for the three hexanes investigated thus far 2.5 40.46 50.49 5.0 100.97 141.70 3.0 42.68 55.72 5.5 167.26 221.73 in this laboratory. 3.5 46.02 62.98 6.0 289 41 Many hydrocarbons were investigated in the past before the advent of modern methods of purification by fractionation, crystallization, etc. Relatively few the International Temperature Scale. In the liquid state modern P-V-T data exist for hydrocarbons; those investigated the compressibilities were determined a t convenient pressure by precision methods include methane (12, ld), ethane (3,6, in the gas phase the pressures were measured a t go), ethylene ( I ) , propane (4, 9, 19), propylene (84), butane (6,10, 81), isobutane (17), pentane (16, 18), isopentane (M), exact densities* The O d Y comparisons which may be made with the results cyclohexane (16), and %-heptane (22). I n addition, Thomas of this investigation are the data of Young (26) on the and Young (28)reported measurements on *hexane a t tendensity of 2,3-dimethylbutane in the liquid state under its peratures from 1700 to 2800 c. and at pressures up to 37 own vapor pressure. The density of the liquid under its atmospheres. own vapor pressure was obtained from the intersection of the liquid curve with the vapor pressure line of large-scale Experimental Data graphs of specific volume vs. pressure. The results are given The apparatus employed in this investigation was dein 'I1* scribed in detail elsewhere (11); the dead-weight piston gage was patterned after the one described by Beattie (8) and was TABLE 111. SPECIFIC VOLUMES OF LIQWIDDIM DIM ETHYL BUTANE calibrated by the method of Bridgeman (7). The average UNDER ITSOWN VAPOR PRESSURE millimeter equivalent of 1 gram on the piston was 2.00107. Specific Volume The 2,3-dimethylbutane was prepared in this laboratory Young Kelao and Felsing Difference, % Temp., C. from acetone by a slight modification of a method described 1.7172 0 04 1.7179 100 by Brooks, Howard, and Crafton (8). The final product, 125 1.8093 1.8089 1.9234 1.9229 00 .. 0 0 23 150 after careful fractionation through a Stedman column, had 175 2,0851 2.0848 0.02 the following characteristics: = 1.37484; boiling point 200 2.3397 2.3390 0 03 (760mm.) = 67.97 * 0.02' C.; d (grams/cc. a t 0-30' C.) =
R
;;;
O
0.67970 - 0.00091t.
The data are presented in Tables I and 11; pressures are expressed in normal atmospheres, and temperatures are on 1
The density data for 2,3-dimethylbutane are believed to be accurate to 0.05 per cent a t the lower and to 0.1-0.2 per cent at the higher temperatures and pressures. The m e r -
Present address, Humble o i l and Refining Company, Baytown, Texas.
161
INDUSTRIAL AND ENGINEERING CHEMISTRY
162
TABLE IV. Z
~
1
AND
-
flp VALUESAT DIFFERENT TEMPERATURES
PO = 30.0 Atm.; t o = 234.8O C. Z = PV/RT f / P pr PV/RT
,--Hexane; .pi 0
0.0807 0.0807 0.1867 0.4500 1.6303 3.3840 5.1357 6.8903 8.6453 IO.3937 c -
0,2460 0.2460 0.4500 1.6298 3.3833 5.1348 6.8880 8.6445 10.3923
0.3617 0.5857 0.5857 0,8873 1,6293 3,3830 5.1347 6.8887 8.6440 10,3923 r-25O.0O0 0,4210 0,8520 1,2210 1,2723 1.3617 1.5680 2.0863 3.2493 5,5887 9.9260
0
.
0 c.-0
0.9053 0.0118 0.0271 0.0650 0.2329 0.4758 0.7120 0.9435 1.1712 1.3945
--150.00" 0.2951 0.2961 0.4401 1.5935 3.3071 5.0188 6.7332 8.4485 80.1569
~
0.9304 0.9304 0.4255 0.1769 0.0663 0.0410 0.0345 0.0328 0.0331 0.0349
0.1450 0.1450 0.1867 0.4500 1.6300 3.3837 5.1353 6.8897 8.6453 10.3937
150.00° . C
1
2
7 -
0.7960 0.0352 0.0641 0.2262 0.4561 0.6771 0.8918 1.1012 1.3058
0.8471 0.8471 0.4772 0.1532 0.0935 0.0776 0.0727 0.0725 0.0751
0.8440 0.7367 0.7367 0.5072 0.3137 0.1913 0.1585 0.1474 0.1458 0.1497
0.7947 0.6161 0.0894 0.1321 0.2316 0.4620 0.6599 0.8605 1.0653 1.2443
0.3900 0.3900 0.5370 1,6300 3.3833 5.1350 6.8893 8.6450 10.3930
Q ,8553 0.8553 1.0630 1.6280 3.3817 5.1330 6.8873 8.6430 10.3910
5
.
0 C-. 0
0.8534 0,0208 0.0266 0.0643 0,2283 0,4640 0,6920 0.9149 1.1331 1.3464
f/P ~ 0.8919 0.8919 0.6972 0.3037 0.0976 0.0600 0.0500 0.0472 0.0473 0.0508
0.7185 0.0567 0.0777 0.2280 0.4520 0.6663 0.8735 1.0758 1.2719
0.8832 0.7331 0,6079 0.5911 0.5631 0.5080 0,4143 0.3150 0.2501 0.2394
0.8360 0.5954 0.3413 0.2963 0.2719 0,2740 0.3240 0.4543 0.7100 1.1561
0.9004 0.0153 0,0270 0.0649 0.2319 0.4732 0.7075 0.9372 1.1627 1.3840
0.8045 0 . 8045 0.5966 0.2334 0,1425 0.1181 0.1101 0.1093 0.1127
0.4707 0.1501 0.1736 0.2438 0.4563 0.6571 0.8504 1.0373 1.2188
0.6574 0.6574 0.5481 0.3943 0.2413 0.1996 0.1855 0.1828 0.1869
0.0920 0.0920 0.1741 0.4203 1.5234 3.1623 4.7991 6.4387 8.0795 9.7135 0.2250 0.2250 0.4203 1.5234 3.1620 4.7991 6.4387 8.0795 9.7135 0.6330 0.6330 0.8299 1.5234 3.1623 4.7991 6.4387 8.0795 9.7136 7 -
0.9920 1.5687 1.7207 1.9430 2.3460 3.1337 4,6463 7.5120
0.6617 0,4184 0,3826 0,3702 0.3911 0,4644 0.6212 0.9109
0.7558 0.6136 0.5805 0.5380 0.4789 0.4060 0.3370 0.3009
0.1808 0.1808 0.2251 0.4401 1.5935 3.3071 5.0185 6.7328 8.4485 10.1569
0.8460 0.0265 0.0330 0.0641 0.2277 0.4617 0.6880 0 . 9086 1.1245 1.3354
1.0632 1.1754 1.2542 1.3327 1.4536 1.7196 2.2844 3.4804 5.8467
p e = 32.10 Atm.; t c = 228.0° C.f/p pr Z = PV/RT f/P
c.-
100.00~ 0.9006 0.0166 0.0274 0.0660 0.2358 0.4805 0.7185 0.9514 1.1806 1.4047
0.9317 0.9317 0.5045 0.2097 0.0857 0.0528 0.0447 0.0425 0.0430 0.0454
150.00° C-. 0.8245 0.0297 0.0654 0.2210 0.4620 0.6843 0.9001 1.1105 1.3160
0.8465 0.8465 0.5516 0.2005 0.1212 0.1012 0.0951 0.0954 0.0993
2 0 0 . 0 0 ~c.0.6000 0.1138 0.1385 0.2386 0.4601 0.6688 0.8698 1.0647 1.2643 250.00° C-. 0.5299 0.4396 0,3750 0.3322 0.3105 0.3215 0.3797 0.5204 0,7948
-125.00° 0.1716 0.1716 0.1741 0.4203 1.5234 3.1623 4.7991 6.4387 8.0795 9. 7135
0.8421 0.0230 0.0271 0.0652 0.2316 0.4693 0.6991 0.9230 1.1420 1.3556
0.8820 0.8820 0.3760 0.2738 0.0995 0.0612 0.0515 0.0487 0.0490 0.0514
0.4270 0.4270 0.5019 1.5231 3.1620 4.7991 6.4387 8.0792 9.7132
175.00° C -. 0.7011 0,0649 0.0802 0.2316 0.4687 0,6742 0.8822 1,0847 1.2814
0.7766 0.7766 0.6665 0.2841 0,1739 0.1447 0.1354 0.1357 0.1405
0.6916 0.6916 0.5455 0.3360 0.2062 0.1714 0.1589 0.1609 0.1687
--225.00° 0.9125 0.9125 1.1592 1.5234 3.1623 4.7994 6.4387 8.0795 9.7135
C. 0.4251 0.1514 0.2123 0.2565 0.4671 0.6683 0.8617 1,0492 1.2313
0.5882 0.5882 0.4950 0.3920 0.2464 0.2000 0.1862 0.1885 0.1930
0.6955 0.6606 0.6367 0.6107 0.5758 0.5129 0.4263 0.3376 0.2807
-------275.00° 1.2274 1.4143 1.5732 1.7483 1.9972 2.4474 3.2639 4,7928 7.5779
C -. 0.5840 0.5047 0.4491 0.4160 0.4073 0.4366 0.5176 0,6841 0.9833
0,7039 0.6600 0.6242 0.5879 0.5433 0.4830 0.4151 0.3553 0.3280
--
C-.
tainty in the measurement of pressure is less than 0.01 per cent, and in the measurement of volume from 0.05 to 0.1 per cent.
c.-
0.8846 0.8846 0.7114 0.3707 0.1333 0,0801 0.0669 0.0630 0.0631 0.0659
Treatment of Results The data of this investigation and those for n-hexane (11) and 2-methylpentane (11) were used to evaluate the values of 2 (= pv/RT) and of the fugacity-pressure ratios ( j / p ) . The latter evaluations were made by a graphical integration of the relation,
~ 1 7 5 . 0 0 C-. '
C -. 0.7883 0.0433 0,0642 0.2259 0.4543 0.6733 0.8868 1.0934 1.2959
7 -
c -
p , = 30.70 Atm.; t o = 227.4' C.-------125.00~ 0.9214 0.9214 0.5394 0.2240 0.0892 0.0539 0.0453 0.0429 0.0429 0.0453
.--Z-Methylpentane; PT Z =v / R T
7 -
175.00'C.-
C.-
-2,3-Dimethylbutane; --loo, 000 c.0.1033 0.1033 0,1824 0.4397 1.5931 3.3068 5.0185 6.7328 8.4481 10.1566
~
Vol. 34, No. 2
0.8349 0.8349 0.5727 0.2060 0.1237 0.1029 0.0962 0.0960 0.0993
~ 2 0 0 . 0 c.-0 ~ 0.6730 0.6730 0.8681 1,5931 3.3065 6.0182 6.7325 8.4481 10.1563
0.5857 0.1073 0.1352 0.2337 0.4518 0.6576 0.8561 1.0484 1.2357
0.6818 0.6818 0.5432 0.3341 0.2006 0.1668 0.1555 0.1537 0.1581
1.1248 1.2417 1.3179 1.3902 1.4990 1.7192 2.2160 3.2889 5.4482 9.4270
0.5362 0.4440 0.3769 0.3315 0.3063 0.3075 0.3522 0.4703 0.7084 1.1237
0.6917 0.6579 0.6352 0.6137 0.5830 0.5300 0.4470 0.3534 0.2864 0.2728
0.4560 0.4560 0.5257 1.5935 3.3068 6.0185 6,7328 8.4485 10.1569
0.6937 0.0684 0.0786 0.2274 0.4509 0.6632 0.8685 1.0685 1.2626
7 2 2 6 . 0 0 0 0.9687 0.9687 1.2120 1.5932 3.3065 5.0182 6.7325 8.4478 10.1563
,--1.2935 1.4850 1.6446 1.8150 2.0515 2.4505 3.1971 4.6156 7.2225
0.7620 0.7620 0 .e628 0.2724 0.1636 0.1360 0.1268 0.1256 0.1295
c.-
0.3801 0.1961 0.2059 0.2503 0.4585 0.6571 0.8482 1.0333 1.2133
0.5648 0.5648 0.4732 0.3833 0.2331 0.1938 0.1802 0.1778 0.1818
275.OO0C.------0.5885 0.5069 0.4491 0.4129 0.4000 0.4182 0.4849 0.6301 0.8962
0.7063 0.6636 0.6282
0.5948 0.5529 0,4976 0.4298 0.3657 0.3284
from pr = 0 to each experimentally demanded value of p,, where p , is the reduced pressure, equal to p / p c , and p , is the critical pressure. This was made possible by means of large-scale plots of - (' against pr. These calculated values are presented in Table IV.
[ ir"1
Acknowledgment This investigation was made possible by a grant from the University of Texas Research Institute as Project No. 1. The authors wish to express their thanks to George M. Watson for the aid given in the graphical evaluation of the fugacity coefficients.
Literature Cited (1) Amagat, Ann. chim. phus., 29, 68 (1893). (2) Beattie, Proc. Am. Acad. Sci., 69,389 (1934). (3) Beattie, Hadlock, and Poffenberger, J . Chem. Phys., 3, 93 (1935). (4) Beattie, Kay, and Kaminsky, J. Am. Chem. SOC.,59, 1689 (1937).
February, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
( 5 ) Beattie, Sirnard, and Su, Ibid., 61, 26 (1939). (6) Beattie, Su, and Simard, Ibid., 61, 929 (1939). (7) Bridgeman, Ibid., 49, 1174 (1927). (8) Brooks, Howard, and Crafton, J . Research Nail. Bur. Standards, 24, 33 (1940). (9) Deschner and Brown, IND. ENG.CHBM., 32,836 (1940). (10) Kay, Ibid., 32,358 (1940). (11) Kelso and Felsing, J . Am. Chem. SOC.,62,3132 (1940). (12) Keyes and Burks, Ibid., 49, 1403 (1927). (13) Kvalnes and Gaddy, Ibid., 53, 394 (1931). ENG.CHEM.,28,257 (1936). (14) Lewis, IND. (15) Rose-Innes and Young. Phil. Mag., 151 47, 353 (1899).
163
Rotinjanz and Nagornow, 2. physik. Chem., A169, 20 (1934). Sage and Lacey, IND. ENG.CHEM.,30,673 (1938) Sage, Lacey, and Schaafsma, Ibid., 27, 48 (1935). Sage, SchaafRma, and Laoey, Ibid., 26, 1218 (1934). Sage, Webster, and Lacey, Ibid., 29,658 (1937). Ibid., 29, 1188 (1937). Smith, Beattie, and Kay, J. Am. Chem. SOC.,59, 1587 (1937). Thomas and Young, J . Chem. Soc., 67, 1071 (1895). Vaughn and Graves, IND. ENG.CHEM.,32,1252 (1940). Young, in International Critical Tables, Vol. 111, p. 345, New York, McGraw-Hill Book Co., 1928. (26) Young, 2.physik. Chem., 29, 193 (1899).
(16) (17) (18) (19) (20) (21) (22) (23) (24) (25)
Calculation of Viscosity from Stormer Viscometer Data J. A. GEDDES AND D. H. DAWSON Krebs Pigment & Color Corporation, Newport, Del.
B
ECAUSE of its simplicity of operation and ease of cleanbration of the Stormer viscometer in absolute units. We ing, the Stormer viscometer has long been used for realized that appreciable correction factors would need to be consistency measurements of paints and allied prodapplied, and that these might be valid only over a limited range. This difficulty was not considered too serious, howucts. Consistency is a measure of the flow of materials which exhibit permanent deformation ever, because present recomunder applied shearing stress. mendations on the Stormer visThis term will be used not only cometer hold the speed of the for plastic materials, but also rotating paddle between relaTo explore the possibility of describing the in cases where the viscous natively narrow limits. Krebs ture of a substance has not been units are measured only beconsistency of paints in more fundamental established. Consistency is tween times of 24 and 40 units, use of the modified Stormer viscomenot always a definite physical seconds per hundred revoluter on truly viscous oils has been studied. quantity, since its value may tions, while the American It has been found possible to correlate the depend upon the stress applied, Society for Testing Materials viscosity of these oils with Stormer data, or upon the previous history suggests a paddle speed of 200 of the sample. Viscosity is der.p.m., interpolated frommeasprovided a correction for kinetic energy fined in the usual manner (8’). urements varying over a range losses is made. I n spite of the extensive not greater than 27-33 seconds The fork-type paddle ordinarily used on use of the Stormer viscometer, per hundred revolutions (1, 2). the modified Stormer viscometer has been little effort has been made to replaced with a newer “submerged” paddle, express the results obtained in Apparatus and Materials absolute units. It has been which allows more reproducible readings. The modified Stormer viscomcustomary to present such data The formula developed for calculation of eter as described in Perry’s handby giving the weight-time relabook ( 5 )was used, with a further viscosity of truly viscous liquids is limited tion (9,B ) , or the Krebs units modification in the paddle emwith respect to several variables, including ployed. The old forked type (6, 6)read from a weight-time required calibration and marking temperature and container size (pint cans chart. of each individual paddle before These arbitrary methods are preferred). It is suggested that maximum use and, in addition, very careopen to criticism for several ful setting to ensure the proper tolerances of *O0.25O C. be imposed in all depth of immersion in the liquid reasons. The principal objecliquid and paint measurements. Although being measured. tion is that even in the case of The newer submerged paddle Containers from half-pint size upward may truly viscous liquids, a straight( 6 ) is not subject t o these limibe used, measurements made in containers line relation between weight tations, since it can be supplied already marked by the manuand reciprocal of time on the of different sizes cannot be intercompared facturer, and the depth of immermodified Stormer viscometer without correction. sion is determined on a relatively does not exist. A curve consmall center shaft. It is thereFurther application of the kinetic energy cave toward the weight axis is fore much easier to set, and the correction to measurements of yield value obtained, and the apparent viserrors from incorrect settinp are minimized. Paddles of this and mobility of paint systems with the cosity depends upon the stress type have been used for some applied. Stormer viscometer is under consideration. years in this laboratory withcomIt was therefore considered plete success. A recent compariadvisable to attempt a calison of the forked and submerged
