INDUSTRIAL AND ENGINEERING CHEMISTRY
180
TABLE VIII.
EFFECT OF NATURE OF CONTAINER ON OXIDATION OF PEPPERMINT
Container Glass Galvanized iron Stain!ess steel Aluminum
Sample A 53.72 54.55 54.26 54.33
’
Viscosity Sample B 53.54 54.70 54.17 54.71
Average 53.63 54.63 54.22 54.52
TABLE IX. EFFECT OF ANTIOXIDANTS ON OXIDATION OF PEPPERMINT OIL
Untreated oil (3:;pAlcolec N.D.G.A.
Viscosity Increase 8 days 15 days 5.1 9.9 4.6 8.3 3.0 7.2
Cumulative Air Uptake in M1. 8 days 15 days 65.7 103.4 53.7 86.3 44.5 83.1
Table X indicates that 0.1% is a favorable concentration of nordihydroguaiaretic acid.
TABLE X. EFFECT OF CONCENTRATION OF ANTIOXIDANTS Concn. of N.D.G.A.,
%
0.1 0.01 0.005 None
antioxidants obtained from naturally occurring materials. From these nordihydroguaiaretic acid (N.D.G.A.), Alcolec, and e tocopherol were selected for further testing. A summary of the results using 0.1% of each as compared with a control is given in Figure 5. The curves are average values of triplicate runs on five different oils. The efficiency of nordihydroguaiaretic mid is evident from the graph. Alcolec and a-tocopherol are similar i n efficiency and only about one half as effective as nordihydroguaiaretic acid. The same effect can be observed by use of the air uptake measurement as shown in Table IX. The measurement of air uptake is more sensitive and more suitable in the early stages of oxidation. However, it was observed that the course of oxidation was regular enough so that later stages of oxidation could be taken as representative.
Viscosity 6 days a t 35O C. 20 days a t 35’ C. 48.6 50.6 49.9 65.0 49.5 69.3 52.5 73.5
An attempt made to find a useful synergist for nordihydroguaiaretic acid showed that neither ascbrbic acid, a-tocopherol, nor citric acid was effective.
STABILITY AND ANTIOXIDANTS
A study was made of potential antioxidants for peppermint oil. Hydroquinone has been reported to be useful (1). In this present work screening tests were made on several commercial
Vol. 44, No. 1
ACKNOWLEDGMENT
The technical assistance of Robert Clement and William Schipper.who obtained some of the data reported is gratefully acknowledged. The support of Winship Todd and the permission of the A. M. Todd Co. t o publish this work is appreciated. LITERATURE CITED
(1) Baldinger, L. H.,Ellis, N. K., and Fawoett, K . I., J. Am, Pharm. ASEOC., Sci. Ed., 33, 41-3 (1944). (2) Morton, R. A.,Perfumery Essent. Oil Record, 20,258-67 (1929). ( 3 ) Schmidt, H.,Chem. Ber., 80,538-46 (1947). (4) Ibid., 82, 11-16 (1949). (5) Simonsen, J. L., “The Terpenes,” 1st ed., Vol. 11, p. 120,London, Cambridge University Press, 1932. (6) Strausz, H.J., Perfumery Essent. Oil Record, 38,260-3 (1947). (7) Swern, D.,Scanlen, J. T., and Knight, H. B., J . Am. Oil C h i s l a ’ SOC.,25, 193-200 (1948). (8) Swift, L. J., and Thornton, M. H., IND. ENCI.CHEM.,ANAL.ED., 15,422-3 (1943). RECBIVED June 16, 1951.
Compressibilities of Mixtures of Hydroken and Nitrogen above 1 Atmospheres CARROLL 0.BENNETT1 AND BARNETT F. DODGE Chemical,Engineering Department, Yale University, New Haven, Conn.
T
HE properties of gases at high pressures are of interest and importance from both a theoretical and a practical standpoint. I n the field of pressure-volume-temperature relations, the behavior of pure gases below 1000,atmospheresand especially below about 300 atmospheres is known over a considerable temperature range for many of the common gases. The compressibilities of some of the most common gases are also known in the range of loo0 t o 3000 atmospheres. Many industrial processes involve mixtures of gases at high pressures, and design calculations are of course facilitated by a knowledge of the behavior of the mixtures. It is also of importance to know the P-V-T relations of gaseous solutions in order t o perform certain thermodynamic calculations, such as those involving chemical or phase equilibrium. In making the calculations mentioned above, it would be desirable t o be able t o predict the behavior of gas mixtures from the properties of the individual constituents, thus enormously reducing the amount of 1 Present address, School of Chemical and Metallurgical Engineering, Purdue University, Lafayette, Ind.
experimental data required. Several methods have been proposed for doing this, but t o test them, data, of course, are needed on a certain number of actual gas mixtures under various oonditions of pressure and temperature. The compressibility data for gas mixtures are known for several s y s t e m up t o 500 atmospherea and for a few as high as about 1700 atmospheres. The purpose of the present work is to extend the range of pressures for which the behavior of gas mixtures is known in order to test the various methods available for the prediction of this behavior and, in the process, provide some information which may be used to shed some light on such physical topics as the intermolecular attractive forces. Since it was desired t o study a gaseous solution at higher pressures than had been reached previously, it was desirable to choose a system for which data already existed up to a fairly high pressure. In order t o test the methods of prediction, it was also desirable to choose a system whose components had a knowh behavior in the range t o be investigated. On the basis of these considerations it was decided t o study the P-V-2’ relations of
January 1952
I N D U S T R I A L A N D E N G I N E E R I N G CHEMIST RP 4TEE.
181
the most accurate of any existing for hydrogen or nitrogen. &VALVE Bartlett and his coworkers a t 6STOPCOCK the Fixed Nitrogen Research Laboratory in Washington,D. C., from about 1927 to 1938 published many papers concerning the properties of hydrogen, nitrogen, and their mixtures a t pressures up to 1000 atmospheres and over the temperature range -70" to 400" C. (34,G).The work of Wiebe and Gaddy (46)is especially relevant to the present investigation. The system has also been studied by several Russian workers (91,94,96,38) covering the temperature range -50' to 300" C. and pressures as high as 1640 atmospheres. If the reader is interested in other sysQ tems or pure gases, he ia referred t o recent literature surveys by m Bridgman ( I I ) , Comings (IS), Keyes (W),and Sage (40). There are two general procedures which have been used for P-V-Tmeaaurementa. The first of these is known as the constant volume method and was used by the Fived Nitrogen Research Laboratory workers (3-6). In this caw, a quantity of gas at high pressure is confined in a known small volume a t a known temperature. The amount of this gas is then determined by allowing it to expand to a large known volume, again measuring the pressure and temperature; this pressure is low enough so the exact behavior of the gas is known. This method has also been used, Figure 1. Schematic Diagram of A p p a r a t u s with some variations, by J. Mercury U-tube Townend and Bhatt (.&), HolA. Triplex hydraulic pump E . Aminao i n t e d e r , catalog No. 406-159 K. Constant temperature oil bath born (BO), Haney and Bliss (le), L. Safety tubs C. Gas compmsion chamber D . Gas storape cylinder M . Constant temperature water bath and Krichevskil and Markov N. Meraury mandmeter E. (96),all working a t pressures F. Z Z w e i g h t piston gage P. R. Cathetometar Vacuumpump G. Small intermiller for piston gage below 1000 atmospheres. S. M O Mpase E. Cnilletet pump The second method is called the variable volume method. A measured quantity of gas is introduced into a calibrated vessel hydrogen-nitrogen mixtures from 1000 to 3000 atmospheres in and compressed by decreasing the volume of the vessel by forcing the temperature range from 25" to 125' C. Three mixtures in a piston or mercury. Thus a given sample of gas may be 50, and 75% hydrogen in nitrogen. The were studied-25, used to obtain several datum points, but the construction and temperature was kept low in order to decrease the possibilities operation of this type of apparatus are probably more difficult of error due to gas diffusion or absorption in the steel equipment, than for the constant volume type-the method used in this and because the properties of the pure gaaes were known only work. The variable volume method has been used by Michels over a similar range. PREVIOUS WORK and coworkers (91,33)to obtain precise data up to 3000 atmosThe compressibilities of hydrogen and of nitrogen have been pheres. The same principle has been employed by Benedict determined by a large number of workers from the time of Amagat (8) to 6000 atmospheres and by Bridgman (19)to 15,000 atmos(9)t o the present day. In the region of interest in this workpheres, and by Smith and Taylor (&), Sage, Lacey, et al. (39, above lo00 atmospheres-the properties of nitrogen have been ai), and several others a t pressures below 1000 atmospheres. determined most accurately by Michels (34),0" to 150" C.up to The pioneering work of Amagat (9) was performed using the 3000 atmospheres, and by Benedict (8),-175' to 200" C. up to variable volume procedure. 6000 atmospheres. The only precise data on hydrogen above OUTLlNE OF METHOD USED lo00 atmospheres are those of Michels (39)in the range of 0' The method of making a compressibility determination can be to 160' C.up to 3000 atmospheres. Below 1000 atmospheres, the explained by referring to Figure 1. The constant volume method data of Michels and coworkers (91, 39) are usually considered
z
2
INDUSTRIAL AND ENGINEERING CHEMISTRY
182
TABLE I. OBSERVED VALUESOF p v / p s v s FOR HYDROQENNITROGEN h'fIXTURES 25.0% Hydrogen, 75.0% Nitrogen 50° C. 750 P A P A P 3024.55 3020.86 4.2281 4.3489 3004.26 2506.94 4.0313 2493.05 2817.97 3.8259 2027.05 3.6876 2009.84 2476.57 3.3240 1516.04 3.4924 1507.08 2286.86 2.7695 1003 81 1004.64 3.1875 1999,Ol 2.1860 1500.29 2.6477 1006.32 2.0864 1000 c. 125' C. P A P 4 5278 3019.91 2995,79 2514,50 4.0436 2518.87 3.5121 2025,93 2009.56 1499.63 2.9562 1496.74 985.62 2,3695 1005.49 50.5% Hydrogen, 49.5% Nitrogen 50°c. - _ _ _ _ -75" __ ____--- 25O C. W A W A P 3034.07 3.8451 2989.17 3.9111 3028.66 2499.21 3.3856 2488.95 3.4841 2497.34 2.9744 2025.49 3.0645 2006.95 2032.20 1506.71 1518.37 2.5910 1505.60 2.4835 998.03 2.0831 993.99 1007.58 1.9941 1000 C 125OC P A P 3005 95 4 1274 2993 92 2491 47 3 6868 2520 10 2000 70 3 2405 2009 38 1517 44 2 7871 1511 00 995 42 2 2768 997 00 25' C.
75 3% Hydrogen, 24 7% Nitrogen 50' C. 750 ____A A P P 3 5368 3024 59 2995 41 3 4441 2486 79 3 1853 3 0976 2607 04 2 8171 2011 89 2 7193 2019 91 2 4081 1503 82 2 3282 1502 61 999 33 996 15 1 9906 1 8961 1000 c. __ 125' C. A P 2994 57 3 7516 2491 87 3 3563 2028 19 3 0038 1628 15 2 5912 2 1785 1001 20
25' C. P 3001 2519 ,2016 1552 1000
29 53 46
27 27
P 3027 2483 2019 1495 995
48 75 73 71 04
c. A 4.4310 3.9181 3,4090 2.8674 2,2900
feet of 1 / 4 X 1/18 inch chromium-molybdenum steel tubing came to thermal equilibrium almost instantly. As soon as possible after closing valve 13, valve 14 was rautiously opened, admitting the gas in the coil to the glass system which had been evacuated to a pressure of about 0.005 nun. of mercury. This glass system was made of capillary tubing, and each of the three glass bulbs illustrated in Figure 1had a capacity of about 2 liters. The resulting pressure of the expanded gas, between 500 and 1200 mm. of mercury, was indicated by a mercury manometer, X. The bult)s and the manometer were contained in a constant temperature n ater bath maintained a t 25.00' C. The manometer was read through a window in the bath with the aid of a cathetometer. DETAILS O F THE A P P A R A T U S
-4
4.6523 4,1494 3.6292 3,0552 2.4975
c. .4
4.0472 3.5927 3.1446 2.6792 2.1790 -
4 3 3 2
2
-
A 2212 8610 3497 8805 3859
c. A
3 3 2 2 2
3 3 3 2 2
Vol. 44, No. 1
6529 2626 9049 5042
0890
A 8266 4563 1037 7135 2788
was chosen for this work mainly because of its greater simplicity and its more easily attainable accuracy in the volume measurement. The gas being investigated was admitted from the storage vessel, D,at about 100 atmospheres to the compression chamber, C, and any liquid in C was discharged through valve 6. Valve 7' was then closed, and water containing a little sodium chromate and rust inhibitor was forced into the chamber, C , until the desired pressure was obtained a t the Bourdon gage, P". The hydraulic pressure was supplied by the triplex hydraulic pump, A , and the small intensifiel', B. The chamber, C, was equipped with an insulated electrode so that a signal was made as the liquid level neared the top of the compression chamber. Gas mixtures confined over water in C were analyzed after standing 24 hours and did not show any significant change in composition because of the effect of the different solubilities of hydrogen and nitrogen. No gas on which determinations were made R-as ever stored in C more than 10 hours. With valve 14 closed, valve 8 was slowly opened and the gas admitted to the calibrated constant volume coil in the temperature bath, K . The gas in the system was separated from the oil in the dead-weight piston gage, F , by the mercury U-tube, J , equipped with an electrode so the gas-mercury interface could be kept a t a constant level by adding oil from a screw-type injector, H , operating in conjunction with a small intensifier, G, as the oil was compressed and as it leaked out past the piston in the dead-weight gage. When the pressure in the coil was near the desired value, valve 8 was closed, and the necessary weights were placed on the piston-gage pans so that the piston was supported by the oil pressure with the interface in J a t the proper level. The valve I S was then closed slowly, trapping a quantity of gas in the coil. The pressure (now slightly higher because of the decrease in volume caused by closing valve I S ) was detern1iIletl as quickly as possible by balancing the dead-weight piston gage. It n-as found that of the gas in the constant volume coil, about 6 ml. contained in 10
All the valves and tubing used in the high pressure parts of the equipment were standard commercial products; the tubing connections were line-of-contact cone joints. The constant temperature bath heaters were controlled by thyratron tube circuits activated by mercury-in-glass thermoregulators. The temperatures of the baths were read by mercury thermometers calibrated by the U. S. Bureau of Standards. The pressure was measured by a dead-weight piston gage siniilar to that described by Keyes (22). The piston used had a nominal diameter of 3/82inch over a length of 1 inch; the upper part of the piston was 3/8 inch in diameter and acted as a guide for the lower part, since a hardened steel piston of 3/&nch diameter might have failed under the inevitable side thrusts encountered in use. A similar-type gage is described by Bridgman (18). The U-tube used with the ga e was similar to one used by Haney (18) but redesigned for use attigher pressure. It was provided with a lens-ring closure which was very satisfactory and permitted the closure to be broken or resealed very easily. The wall thicknesses of the various vessels were determined using the procedures described by Newitt (36)or Macrae (97). The gas compression chamber was the vessel having the smallest diameter ratio-3 to 1-6-inch outside diameter, 2-inch inside diameter. For this vessel, made of SAE 4140 steel, heat treated to give a yield point of 80,000 pounds per square inch, the maximum shear stress theory indicated that plastic flow should start at the bore at a n internal pressure of 35,000 pounds per square inch. The plastic zone should reach the outside diameter of the vessel, assuming the steel to be purely plastic above the yield point, a t a pressure of 88,000 pounds per square inch. The vessel was subjected to B preliminary hydraulic test to 60,000 pounds per square inch so that a certain amount of plastic flow (autofrettage) took place, and the vessel should undergo no more plastic deformation under subsequent exposures to the maximum working pressure of 45,000 pounds per square inch. The constant-volume coil was also given a preliminary autofrettage treatment a t 60,000 pounds per square inch. However, to
VALUESOF pv/p,v. TABLE 11. SMOOTHED NITROGENMIXTURES Pressure. Atmospheres
25 .O% Hydrogen
50.5% Hydrogen
1000 1500 2000 2500 3000
2.0783 2.6473 3,1877 3,7096 4.2067
1.9862 2,4780 2.9438 3.3911 3.8173 BO0 C. 2.0852 2.5374 3.0414 3.4938 3.9200 750 c. 2.1854 2,6728 3.1405 3.5948 4.0235 1000 c. 2.2844 2,7702 3.2399 3.6943 4.1225 125' C. 2.3891 2.8698 3.3411 2.7986 4,2262
FOR
HYDROQEN75.3% Hydrogen
2.50 c --.
~~
2.1811 2,7512 3,2951 3.8202 4,3160 1000 1500 2000 2500 3000
2.2843 2.8563 3.4011 3.9248 4.4268
-1000 1500 2000 2500 3000
2,3871 2,9567 3.5022 4.0291 4.5322
1000 1500
2.4903 3.0588 3.6025 4.1304 4.6329
2000
2500 3000
1,8959 2.3100 2.7067 3.0842 3.4427
~
1.99402.4059 2,8018 3,1801 3.5400 2.0895 2.5011 2,8959 3.2741 3.6354 2.1829 2.5947 2.9887 3.3681 3,7314 2.2778 2.6905 3,0826 3.4627 3.8301
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1952
183
tained through the courtesy of the Linde Air Products Co. The analysis of the gases as determined by the Linde Co. was as follows: Hydrogen Carbon dioxide Unsaturated hydrocarbons Oxygen Carbon monoxide Saturated hydrocarbons Nitrogen Nitrogen Oxygen Hydrogen Hydrocarbow, carbon monoxide, and carbon dioxide Argon Neon Helium
99.96% 5 p.p.m. 5 p.p.m. 30 p.p.m.
10 p.p.m.
115 p.p.m. 240 p.p.m. 99.99% 9 p.p.m.' 3 p.p.m. 1 p.p.m. 50 p.p.m. 15 p.p.m. 4 p.p.m.
CALCULATIONS
The method of obtaining the compressibility factor from the experimentally determined variables is given below for the point at 3000 atmospheres and 100" C. for the 75.3 mole yo hydrogen mixture. Amagat's compressibility factor, A , was used in this work A = PV/P*V. where p = pressurein atmospheres, v = volume, ml. per grammole,p,vs = pv product in the same units a t 1 atmosphere and 0' C. All pressures are absolute. 1
PRESSURE.
ATMOSPHERES
Figure 2. Amagat Compressibility Factors of Hydrogen, Nitrogen, and Their Mixtures at 25" C .
make sure the subsequent behavior of the coil was as close as possible to elastic, the coil was held a t 300' C. for several hours after the autofrettage (36). The calculation of the distortion of the coil under pressure was then possible acchding to the usual elastic formulas. A detailed discussion of these points is gives by Newitt (36)or Macrae (27). Teflon was used as a packins in the valves at the ends of the coil, since the usual leather packings deteriorated rapidly at temperatures above 75" C . CALIBRATIONS
The dead-weight iston gage may be calibrated as a primary gage by measuring t i e piston diameter and the size of the annular space between the piston and the cylinder as described by Meyers and Jessup (19). The gage can also be calibrated usin the vapor pressure of carbon dioxide a t 0' C. as a standard, carefully determined by several investigators (IO,30,37). Both methods were used to calibrate a 3/le-inch gage in the present work, and this gage was then used to calibrate the 3 / ~ i n c hgage. As a result of these calibrations it is probable that the pressure a t 3000 atmospheres was known to 0.15%. The distortion of the piston and cylinder under the applied pressure was calculated from the usual sim le elastic theory. The vokme of the N i t e r glass bulbs was determined by weighing the amount of water necessary to fill them a t a known temperature, making the required corrections for the buoyant effect of air and the meniscus volumes. The volume of the glass capillary connecting tubing was determined by expanding a known volume of gas from one of the bulbs into the evacuated tubing and noting the decrease in pressure a t constant temperature. The volume of the constant-volume steel coil in the bath K (Figure l),was determined by a calibration with nitrogen, uhng the known compressibility of this gas a t 500 atmospheres (3.4). The procedure was similar to that already described for makin a compressibility measurement; the variable in this case was &e high-pressure volume rather than the compressibility factor. The distortion of the coil under pressure was calculated from Love's formula ( 2 6 ) , and its expansion with rising temperature was determined from a formula given by Haney (18). The hydrogen-nitrogen mixtures were analyzed by slow combustion of the hydrogen over a hot platinum wire, using a Burrell gas analysis apparatus. Useful information on the anal sis technique is given by Altieri ( 1 ) and by Shepherd (49). $he pure gases (99.96% hydrogen and 99.99% nitrogen) were ob-
Weight on dead-weight gage pan Weight of pan Total weight Piston gage constant at 1 atmosphere Correction for distortion a t 3000 atm. Corrected constant Gage pressure (9.3220) (324.06) Atmospheric pressure Pressure Indicated barometer Room temperature Temperature and gravity corrections Barometer at ' 0 C., standard gravity Height of left leg of mercury manometer measurine the exDanded pas as read on the - Dressure cath;tomet& Height of right side of manometer (open to the atmosphere) Indicated gage pressure of expanded gne Correction t o Oo C. and standard gravity Cathetometer scale correction Corrected gage pressure, Oo C., and standard gravity Expanded gas pressure Volume of gas in capillary connections, corrected from room temperature t o 25O C. Volume of gas in left leg of manometer at 25O C. Volume of gas in the constant-volume coil corrected from 100' t o 25O C. Volume of the two bulbs used Volume of expanded gas at 25O C. and 1.3322 atmospheres PO at 25' C. and 1.3322 atmospheres pv/p.vs a t 26O C, for mixture obtained.by linear interpolation from the data of Michels (31, $8) pap, ( p u a t 0" C. and 1 atm.) Volume of high-pressure coil a t 1 atmosphere, 25O C. Volume a t loOD C., 1 atmosphere Increase in volume from pressure effect Volume a t 100" C. and 3027.48 atmospheres p t at looo C. and 3027.48 atmospheres pu/pa~s A
280.73 43.93 324.66 lb. 9.3304 atm./lb.
-0.0084
9.3220 atm./lb. 3026.48 atm.
1 .oo
3027.48 atm. 766.95 a m . mercury 22.9' C. 3 . 1 6 mm. mercury 763.79 mm. mercury
-
289.55 mm. mercury 539.43 mm.
or
1012.45 mm. mercury 1.33217 atm. 27.46 ml. 13.47 5.01 4118.30 4164.30 ml. 5547.56 m1.-atm. 1.09174 5081.39 m1.-atm. 6.2539 ml. 6.2701 0.0287 6.2868 ml. 19063.4 ml.-a&n. 3.7516
RESULTS
The experiwental results are listed in Table I, and the smoothed values of A a t even pressuras are given in Table 11; Figure 2 gives an idea of the variation of A with pressure and composition at constant temperature.
INDUSTRIAL AND ENGINEERING CHEMISTRY
184
Vol. 44, No. 1
PRECISION OF RESULTS
The estimated error of the results can be calculated from the estimated error in each of the measured variables. The high pressure was known to 0.16%' the oil-bath temperature to 0.1' C. (0.03%), and the high pressure volume t o 0.08%. The expanded pressure was known t o 0.25 mm. of mercury or 0.03%, the expanded volume to 0.45 ml. or 0.02%, and the water-bath temperature to 0.02" C. The composition of the gas mixtures was in error by not more than 0.1 mole %; in the worst case this error produced a 0.04% change in the compressibility factor. From these approximations it may be calculated that the estimated error in the compressibility factor was 0.37%. The data were smoothed by fitting an equation for A as a function of pressure at constant temperature and composition t o the data by the method of least squares. idea of the of the data may be obtained by noting the fact that the greatest difference between a smoothed value and an observed value a t any point was 0.15% of A at that point. Table I1 was obtained by calculating the values of A a t even pressures by using the equation mentioned above, which was of the general form (8,4+5)
+ Bp'/a +
A =a where
CY,
8, and
The
Y
(1)
yp2/8
are functions of temperature and composition.
A at 'O0O atmospheres have been by Wiebe Gaddy for Some of the same conditions studied in this work. II1 indicates a good agreement between the Of
two sets of data. The values given for the results of Wiebe and Gaddy have been interpolated from their tabulated data.
TABLE 111. OBSERVED DATACOMPARED WITA THOSE OF WIEBE AND
Pressure Atmoaphdrea
Tgmz.,
1006.32 1003.81 985.62
25 50 100
1007.54 998.03 995.42
25 50 100
1000.27 996.15 995.04
25 50 100
GIDDY
A
wiebIand A(0bsvd.) Gaddy 25.0% Hydrogen 2.0866 2.1862 2.3695
-
A(0bsvd.) A (Wiebe and Gaddy)
A
2.0858 2.8143 2.3669
50.5% Hydrogen 1.9941 1.9937 2.0831 2.0834 1.2788 2.2817 75.3% Hydrogen 1.8961 1.9906 2.1785
1.8957 1.9872 2.1813
--E%
-0.21%
8%
-0:13$
TABLE IV. Preasure,
Atmospheres
ADDITIVE VOLUME LAW
25.0%
Hydrogens
50.5%
75.3%
Hydrogen"
Hydrogen"
1.982 1.986 2.945 2.944 3.823 3.817
1.892 1.894 2.706 2.707 3.447 3.443
2.380 2.389 3 342 3.341 4.238 4.226
2.275 2.278 3.084 3.083 3.835 3.830
25' C. 1000 2000
a000
2.078 2.078 3.194 3.188 4.123 4.207 125O C.
1000 2000 3000 4
2.484 2.490 3.604 3.602 4.647 4.633
The upper value is t h a t oaloulated, the lower one t h a t observed.
DISCUSSION
The measured compressibility factors for hydrogen-nitrogen mixtures between 1000 and 3000 atmospheres from 25' to 125" C. indicate that the mixtures obey Amagat's law in this range. It now becomes of interest to determine whether other mixtures of gases at temperatures far above their critical points alPo approach the additive volume behavior as the pressure is increased. It is to be expected that at very high pressure the effectof the outweigh the effect of the intervolume of the molecu]es molecular attractive forces. Redlich and Kwong (366) have used this general principle, which reduces t o the additive volume law a t very high pressure, in their equation of state for mixtures. At intermediate pressures on both a theoretical and an experimental basis, Amagat's law is not a satisfactory approximation (6, 7'15). The present data should be of some assistance in any future attempts t o formulate an equation of state for gas mixtures. The fugacities of the components in hydrogen-nitrogen mixturea can be calculated from the data using a method outlined by Gibson and Sosnick (16) including the correction suggested by Gillespie and Beattie (17). The fugacities of the components in some mixtures of hydrogen and nitrogen have already been calculated by Bolshakov (9) and by Merz and Whitaker (98) using the data of Wiebe and Gaddy (46)up to lo00 atmospheres. The present data allow the fugacities of the components in the range from lo00 t o 3000 atmospheres to be calculated easiiy. The method of calculation is based on the following well-known relations (1.4)
PREDICTION OF PROPERTIES OF MIXTURES
It was found that Amagat'a law of additive volumes reproduced the data t o about the experimental accuracy (0.257,) in the range considered-1000 to 3000 atmospheres. The calculated values in Table IV are from
+
A , = X N A N SHAH
(2)
A,,, = A of the mixture A N = A of pure nitrogen A H = A of pure hydrogen XR
= mole fraction nitrogen = mole fraction hydrogen
Since V i = v i if the additive volume law is valid, it is clear t h a t
Bartlett's law (14) was found t o be in ermr in all cases by at least 4%. Dalton's law of additive pressures was in error by at least 30% in the cases tested. From the fact that Amagat's law holds, it may be seen by inspection of Equations 1 and 2 that the quantities CY, 8, and y in Equation 1 for a mixture of hydrogen and nitrogen can be obtained from similar quantities for the pure gases by simple linear combination, for example QI
3 .
XNQN
= fugacity of component i in the mixture, atmospheres = mole fraction i ff = fugacity of pure i a t the pressure and temperature of the mixture R = gas constant, ml.-atmospheres per gram mole, O K. T = temperature, O K. specific volume, ml. per gram mole v_s = us = partial molal volume, mi. per gram mole p = pressure, atmospheres XI
where
ZN
where
+
%HUH
(3 )
fi = 1 2 2
for such a mixture, provided that the additive volume law applies from zero pressure up to the pressure in question. If, as is true in the present case, the additive volume law does not apply in the lower pressure range but becomes valid above a certain pressure, then
January 1952
INDUSTRIAL A N D ENGINEERING CHEMISTRY fi = C (a constant)
WA
for all pressures in the upper range where the volumes are additive. C is a function of temperature and composition which oan be evaluated from the P-V-Tmessurements made on this sysem by previous investigators (46). The pressure above which fi/ zifi becomes constant is also a function of composition and temperature as can be seen from the curves given by Mer5 and Whitaker (98). Thus, since the additive volume law has been found in this work to hold in the range of lo00 to 3000 atmospheres, the fugacity of one of %e components in a mixture can be calculated from the value of f,/zi$ given by Merz and Whitaker (98) and by Bolshakov ( 9 ) for the temperature and composition desired at lo00 atmospheres. The value of fp can be found from the data and equations of state of Michels et a2. (SB,34). ACKNOWLEDGMENT
The authors wish t o express their appreciation t o the Research Corp. for the financial assistance of an F. G. Cottrell Grant-inAid which made possible this work. LITERATURE CITED
(1) Altieri, V. J., “Gas Analysis and Testing of Gaaeous Materials,”
New York, Am. Gas Assoc., 1945. (2) Amagat, E. H.,Ann. chim. et phye., (6)29.68 (1893). (3) Bartlett, E. P., J.A n . Chem.SOC.,49,687 (1927). (4) Bartl&t, E.P.,Cupples, H. L., and Tremearne, T. H., Ed.,50, 1275 (1928). (5) Bartlett, E. P.,Hetherington, H. C., Kvalnea, H. M., and Tremearne, T. H., Ibid., 52,1363 (1930). (6) Beattie, J. A., and Ikehara, S., Proc. Am. A d . Arts S&, 64, 127 (1930). (7) Beattie, J. A., and Stockmayer,W. H., Phys. SOC.,Rept. Progresa Physics, 7,195 (1940). (8) Benedict, M.,J. Am. Chem. SOC.,59,2224,2233 (1997). (9) Bolshakov, P..Acta Phusicochirn. U.R.S.S., 20,259 (1945). (10) Bridgeman, 0. C., J. A&. Chem. SOC., 49,1174 (1927). (11) Bridgman, P.W., Rev. Modern Phys., 18,l (1946). (12) Bridgman, P. W., “The Physics of High Pressure," New York, Macmillan Co., 1931. (13) Comings, E. W., Im. ENQ.CHEW.,39,948 (1947). (14) Dodge, B. F., “Chemical Engineering Thermodynamics,” New York, McGraw-Hill Book Co., 1944. (15) Fowler, R. H., and Guggenheim, E. A,, “Statistical Thermodynamics,” Cambridge, England, Cambridge University Press, 1939.
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Gibeon, G. E., and Soanick, B., J. Am. Chem. SOC.,49, 2172 (1927). GUeapie, L. J., and BeatGe, J. A., Phye. Rev., 36,748 (1930). Haney, R. D., D.Eng. diaaertation, Yale University, 1941. Haney, R. D.,and Bliss, R. H., IND.ENQ. CHIDY.,36, 985 (1944). Holborn, L., Ann. Physik., 63,674 (1920). Hazarovaki, Y.S.,Simov, G. B., and Aristov, 0.E., J. Phys. Chem. (U.B.S.R.), 14, 774 (1940). Keyea, F. G., IND, ENQ.CHEW.,23,1375 (1931). Keyes, F.G., Trans. Am. SOC.Mech. Engrs., 70,621 (1948). Krichevskil, 1. R., and Levchenko, G. T o ,Acta Phys., U.R.S.S., 14,271 (1941). Krichevakil, I. R., and Markov, V. P., Ibid.. 12, 59 (1940). Love, E. A. H., “A Treatise on the Mathematical Theory of Elasticity,” 4th ed., Cambridge, England, Cambridge University Press, 1927. Macrae, “The Overstrain of Metals,” London, England, H. M. Stationery Office, 1930. Merz, A, R., and Whitaker, C. W., J. Am. C h a . SOC.,50, 1522 (1928). Meyera, C, H.,and Jeasup, R. S., J. Reeearch Null. Bur. S t a d ards, 6,1061 (1931). Meyers, C. H., and van Duaen, Ibid., 10,381 (1933). Michels, A,, and Gibson, R., Ann. Physik, 87,850 (1928). Michela, A., and Goudeket, M., Physica, 8,347 (1941). Michels, A., Michels, C., and Wouters, H., Proc. Roy. SOC.(London), A153 (1935). Michels, A., Wouters, H., and DeBoer, J., Physica, 3, 686 (1936). Newitt, D. M., “The Design of High Pressure Plant and Properties of Fluids at High Pressures,” Oxford, England, Oxford University Press, 1940. Redlich, O., and Kwong, J. N . S., Chem. Rev..44,233 (1949). Roebuck, J. R.,and Cram, Rev. Sci. Instruments, 8, 215 (1937). R0zen.A. M., J. Phys. Chem. (U.S.S.R.),19.469 (1945). Sage, B. H.,Am. Inst. Mining Met. Engrs., Tech. Pub. 2269 (1947); Petroleum Technol., 10, No. 5 (1947). Sage, B. H., IND.ENQ.CHSM.,42,631 (1950). Sage, B. H., Webster. D. C., and Lacey, W. N., Ibid., 29, 658 (1937). Shepherd, M., J . Research Natl. Bur. Standards, 6,121 (1931). Smith, L. B., and Taylor, R. S., J. Am. Chem. SOC.,47, 3122 (1925). Townend, D. T. A., andBhatt, L. A., Proc. Roy. SOC.(London), A134,502 (1931). Wan, 8. W., personal communication, 1950. Wiebe, R., and Gaddy, V. L.,J. Am. Chem. SOC.,60, 2300 (1938). RBIOEIVED June S. 1051. Based on a diasertation presented by C. 0. Bennett in June 1950 to the faculty of the School of Engineering of Yale Univerrity, in candidacy for the degree of Doctor of Engineering.
Volumetric Behavior of Nitrogen Dioxide in the Liquid Phase H. H. REAMER ANI) B. H. SAGE Calqornia Institute of Technology,Pasadena 4, Calif.
E
XPERIMENTAL information concerning the volumetric and phase behavior of nitrogen dioxide is limited. The vapor pressure was measured by Scheffer and Treub (IO), Baume and Robert (I), Mittasch and coworkers (6),Russ (7),and Ramsay and Young (6), and was recently extended t o temperatures near the critical state (11). The volumetric behavior of the gas phase at low pressures was studied by Verhoek and Daniels (IS) and Bennewitz and Windisch (S),and the specific volume of the saturated gas and saturated liquid was determined b y Mittasch (6). Bennewitz and Windisch (B) measured the specific volume at the critical state and found it to be 0.02810cubic foot per pound at a temperature of 318.8”F. In addition, the specific volume of
the gas phase was determined (11) at temperatures from 70’ t o 310’ F.and at pressures up t o 2000 pounds per square inch for the higher temperatures. The vapor pressure of nitrogen dioxide also was measured. The present measurements established the specific volume of the liquid phase at temperatures between 70’ and 310” F. for pressurea up t o 6000 pounds per square inch. METHODS AND PROCEDURES
The equipment employed in this investigation has been described (11). I n the present study a slightly smaller spherical pressure vessel with a total volume of 0.0087207 cubic foot, at 0’ F. and atmospheric pressure, was used. In principle, the
