VISCOSITIES OF
June, 1956
THE
ally a perturbation of the resonance pattern in the phenyl group) than the unsubstituted phenylphosphonic acid, while the constant for the electronyielding p-methoxy- derivative is depressed, that there is a very definite communication of electronic charges across the molecule to the site of ionization. Such a communication can only arise from
BINARY GAS MIXTURES
789
the polarizability of the central phosphorus atom in the acid functional group, operating in concert with the resonance pattern within the phenyl ring. Acknowledment.-We wish gratefully to acknowledge the valuable consultations and many helpful suggestions contributed to us during this study by Dr. A. F. Isbell.
VISCOSITIES O F THE BINARY GAS MIXTURES, METHANE-CARBON DIOXIDE AND ETHYLENE-AR.GON' BY W. MORRISON JACKSON Goodyear A t m i c Corporation, Laboratory Division,Portsmouth, Ohio Received November 36,1066
Experimental viscosities at 25" are reported for the binary gas mixtures, methane-carbon dioxide and ethylene-argon over the composition range from 0 t o 100 mole yoof each component. The measured viscosities are compared with calculated values and their application to quantitative analysis of these gas pairs is discussed.
Introduction Two inert binary gas mixtures for which no previous experimental viscosity data have been reported are methane-carbon dioxide and ethyleneargon. Calculations of the theoretical viscosities showed that for methane-carbon dioxide the change in viscosity with composition should deviate in a positive manner from the additivity of the individual viscosities, while for ethylene-argon the change in viscosity with composition should show a negative deviation. To verify this theoretical difference in behavior, the viscosities of these gas pairs were measured over the entire composition range using the capillary tube method, and the results were compared with the calculated values. Experimental Apparatus .-An automatic-reading capillary tube viscosimeter, previously described by Junkins,Z was used for the determination of the viscosities of the gas pairs, methanecarbon dioxide and ethylene-argon. A straight platinum Capillary with an internal diameter of 0.03 and 100 cm. in length was used in all of the measurements. Materials .-The gases used to prepare the binary gas mixtures were obtained from commercial cylinders of methane, carbon dioxide, ethylene and argon. The impurities present in each gas as determined by mass spectrometer analysis are as follows. Methane: contained 0.1% oxygen, 0.1% propane and 0.7% ethylene; carbon dioxide: based upon a trace of argon observed, a maximum of 0.1% oxygen and 0.4% nitrogen could have been present; ethylene: contained less than 0.17% propane and/or propene and a trace of air. Small amounts of acetylene would not have been detected; argon: contained 0.06% nitrogen and 0.01% oxygen, carbon dioxide and water. The air used was medicinal quality "breathing air" which was dried by passing through a Dry Ice slush trap and drying towers of anhydrous calcium sulfate and anhydrous magnesium perchlorate. Procedure.-Methane-carbon dioxide mixtures of the approximate composition desired were prepared by filling evacuated cylinders with one of the pure gases through a manifold to a predetermined pressure, and then adding the second pure gas at a higher pressure until the desired total pressure was obtained. To ensure thorough mixing, each cylinder was alternately heated and cooled several times and (1) Based on work performed for the U. 8.Atomic Energy Commission by Union Carbide Nuclear Company, Union Carbide and Carbon Corporation, Oak Ridge, Tenneasee. (2) J. H. Junkins, Rev. Sci. Znstr., 28, 467 (1955).
then allowed t o stand about five days before sampling for analysis. The composition of the methane-carbon dioxide mixtures was determined by Orsat analysis. The chemical methods of analysis investigated were found t o be uneatisfactory for ethylene-argon mixtures. Conse uently, ethylene-argon mixtures were prepared in much %e same manner as the methane-carbon dioxide mixtures except that they were mixed with extreme care using a specially designed manifold so as not to exceed a maximum error in composition of &O.l%. For the measurement of the flow time of a gas, whose viscosity was to be determined, the gas was admitted into the capillary forechamber until the pressure was greater than a reference pressure, PI. As the gas flowed through the capillary into a container at a constant pressure, PO, the forechamber pressure dropped until it was lower than a second reference pressure, Pz. The time required for the pressure to drop from P I to PZ was recorded by a timer which was automatically turned on at P I and off at Pa. Measurements were repeated as necessary t o establish the precision. After evacuation of the manifold and capillary, the reference gas was run in the same manner without changing the temperature or pressures PI, PZand PO. The temperature of the bath surrounding the forechamber and capillary and the pressures were noted for each measurement. Relative flow times under different pressure conditions were obtained by changing the reference premures PI, Pz and Pa.
Results Measurements of the viscosity of nitrogen a t 65", made under different pressure conditions of PI, Pz and Po to establish the precision of the viscosimeter and t o determine the effect of varying Reynolds numbers, are shown in Table I. TABLEI
VISCOSITY OF NITROQEN AT 65" Mean pressure,
Pm, om.
Mean Reynolds no. Rem
16.64 18.87 25.29 31.91 37.71
16.5 15.3 40.3 58.3 85.7
Exptl. viscosity of nitro5en. cp0-e
195.3 195.4 195.4 195.5 195.4
Experimental viscosities of methane-carbon dioxide and ethylene-argon mixtures, for the composition range from 0 to 100 mole % of each component, are compared to calculated values in Tables I1 and 111.
W. MORRISON JACKSON
790
Vol. 60
TABLEI1 where p is the density, r the radius of the capillary, VISCOSITIES OF METHANE-CARBON DIOXIDE GASMIXTURES V the linear velocity, M the molecular weight of the gas, L the length of the capillary, R the ideal gas AT 25" constant, T the temperature, q the viscosity, and Methane, mole
Methane, mole %
PI, Pz and Po are initial, final and downstream pressures of gas flowing through the capillary. As shown in Table I, changes in pressures P,, Pz 0 151.0 65.1 132.8 132.3 151.0" and Po which changed the Reynolds number for 2.2 150.9 150.6 128.5 73.0 129.1 nitrogen from 16.5 to 85.7 did not cause a signifi10.3 149.4 149.1 78.9 124.8 125.4 cant change in the viscosities obtained. Thus, it 18.3 147.7 147.4 85.0 122.6 121.8 is concluded that for light gases such as nitrogen, 29.7 145.3 144.6 90.5 119.2 118.3 the critical Reynolds number of the capillary is not 42.1 141.4 141.0 117.4 116.4 93.3 exceeded a t pressures below one atmosphere, and 53.7 111.4" 137.3 137.0 100 111.4 Experimental viscosities of pure gases used in calculat- that the viscosities for other light gases obtained with the same capillary should be independent of ing viscosities for mixtures. pressure. TABLE 111 From the viscosity of nitrogen a t 23", obtained by Yen15the viscosity a t 65" was calculated to be VISCOSITIES OF ETHYLENE-ARGON GASMIXTURES AT 25" Ethvl195.2 p poise. The average viscosity of nitrogen a t -~ ene, Ethylene, 65" obtained during the present experiments was mole Viscosity, ppoise mole Viscosity, p oise % Exptl. Calcd. % Exptl. 8alcd. 195.4 p poises, which is in good agreement with 0 225.2 225.2" 60.0 147.0 145.6 Yen's value. 10.0 211.1 210.1 70.0 135.0 134.5 The experimental and calculated viscosities for 20.0 196.3 195.9 80.0 124.2 124.0 methane-carbon dioxide and ethylene-argon gas 30.0 182.7 182.3 90.0 113.6 113.8 mixtures as shown in Tables I1 and 111 are in rea40.0 169.8 169.5 100 104.2 104.2" sonably good agreement, thus verifying the initial 50.0 158.0 157.3 assumption that the change in viscosity with composition, for the two gas pairs, should be different. a Experimental viscosities of pure gases used in calculating viscosities for mixtures. -The calculated values were obtained using an equation derived by Wilke6 %
Viscosity, ppoise Exptl. Calcd.
Viscosity, ppoise Exptl. Calcd.
Discussion
Myerson and Either* found that the differences between apparent viscosity values for uranium hexafluoride obtained by them and other investigators using the capillary tube method could be explained on the basis of Reynolds numbers. At pressures of one atmosphere or less, the viscosity is independent of pressure. However, Reynolds numbers are a function of pressure, and increase as the mean pressure P, = P I
+ Pz4 + 2PO
(1)
increases, where P I , Pz and Poare initial, final and downstream pressures, respectively, of the gas flowing through the capillary. Since the critical Reynolds number, above which turbulent flow can be expected for metal ~apillaries,~ is much less than for pipes, the possibility of exceeding it is present even a t pressures below one atmosphere. This is especially true when the molecular weight of the gas is large. It is only when the critical Reynolds number is exceeded that the apparent viscosity varies with pressure. Assuming viscous flow, the initial, final and mean Reynolds numbers for a given capillary can be calculated from
Re, =
Rei
+ Ref 2
(4)
(3) A. L. Myerson and J. H. Eicher, J . Am. Chem. SOC.,74, 2758 (1952). (4) W. Ruches, Ann Physik, [ 4 ] 26, 983 (1908).
qm =
I +
( X d X d [l
+
dl (v1/712)'/2
(4/d/2) [1
+
+
(M2/Md1/4I2
(M1/M2)I1/2
where ql and 92 are the experimental viscosities, Ml and M Zthe molecular weights, and X1and X z the mole fraction of the pure components. The precision of the viscosity measurements using the capillary tube viscosimeter was approximately 1 part in 2000. Thus the chief source of error in the determination of viscosities versus composition was in the method of analysis to determine the composition. Check analyses indicated a maximum error of *0.2% in the Orsat analysis of the methane-carbon dioxide mixtures. Since chemical analysis was found to be unsatisfactory for the analysis of ethylene-argon mixtures, the gases were mixed initially to a given composition. For this purpose a specially designed manifold, capable of mixing gases t o a composition of = t O , l ~ o was , used. The difficulty of accurate analysis of a gaseous mixture such as ethylene-argon might be avoided by using viscosity values as a measure of composition. Application of such a method would require that there be a difference between the viscosities of the two gases and no maximum in the composition range of interest. Mixtures of methane-carbon dioxide and ethylene-argon satisfy these conditions as can be seen from Tables I1 and 111. Having obtained a standard curve of viscosity versus composition, then the composition of any unknown mix(5) K.L. Yen, Phil. M a g . , 38,582 (1919). C. R. Wilke, J . Chem. Phys., 18, 517 (1950).
(6)
June, 1956
MOLTENSALTMIXTURES
ture of the two gases could be determined quickly and accurately using an automatic-reading capillary tube viscosimeter to determine the viscosity. Acknowledgment.-The author expresses his appreciation for the cooperation and assistance
79 1
which he has received during the course of this work. Recognition is given to Dr. E. J. Barber for his direction of this work and to Mr. J. H . Junkins for his many helpful suggestions related to the design and operation of apparatus.
MOLTEN SALT MIXTURES. PART 2. THE REFRACTIVE INDEX OF MOLTEN NITRATE MIXTURES AND THEIR MOLAR REFRACTIVITIES BY H. BLOOMAND D. C. RHODES Department of Chemistry, Auckland University College, Auckland, New Zealand Received November 88, 1966
A method has been developed for the accurate measurement of refractive index of molten salts. Measurements of refractive index have been carried out over a temperature range of about 100' for pure molten NaNO,, NaNOa, KN02, KNOI and AgN03. The molar refractivity of each salt has been calculated. The refractive indices of molten mixtures of NaNOsKNOI, NaNO,-AgNOa and KNO3-AgNO3 have similarly been investigated and their molar refractivities calculated. The plot of molar refractivity versus mole fraction is for the NaN08-AgNOs and KN03-AgNOs systems linear within experimental error. For the NaNOa-KNOa system the deviations from the linear relation are slightly outside the limits of experimental error.
T o explain the conductivity minima observed in isotherms of electrical conductivity of certain molten salt mixtures, such as the CdC12-KC1 system, Bloom and Heymann,' Bloom, et U Z . , ~ and Harrap and Heymann3 assumed that complex anions are present in such systems. Van Artsdalen and Yaffe4 have pointed out, however, that a conductivity minimum is observed in the system LiCl-KC1 in which the formation of complex ions is very unlikely. They drew attention to the danger of explaining such minima by the formation of complex ions, if there is no supporting evidence from other physical properties. I n certain systems, e.g., PbClrKCl and CdC12-KC1, the presence of complex ions has been qualitatively established by the large negative deviations from additivity, of electrical conductivity, together with a maximum value of the energy of activation for ionic migration, in the plot of property against composition. Such qualitative evidence, as well as that arising from considerable positive deviations of molar volume from additivity, does not yield quantitative information on the structure of the complex ions present. The investigation of refractive index and molar refractivity of molten salt mixtures was undertaken in an attempt to find a physical property which is likely to be affected considerably by the presence of complex ions and which can give quantitative information about such complexes. Refractivities of ions both in the free gaseous state and in infinitely dilute aqueous solutions have been obtained by F a j a n ~ . ~ Similar data on molten salts can be used to give information about the mutual influence of ions in a melt. I n order to minimize experimental difficulties, the investigation of relatively low melting salts was first undertaken. For the systems selected, (1) H. Bloom and E. Heymann, Proc. Roy. SOC. (London), 188A, 392 (1947). (2) H. Bloom, I. W. Knaggs, J. J. Molloy and D. Welch, Trans. Faraday Soc., 48, 1458 (1953). (3) B. S. Harrap and E. Heymann, ibid., 61, 259 (1955). (4) E. R. Van Artsdalen and I. S. Yaffe, THISJOURNAL,68, 118 (1955). (5) K.Fajans. 2. p h y s i k . Chem., 2 0 , 103 (1934).
electrical conductivity and density studies have shown that their mixtures exhibit only minor departures from ideality. No measurements of refractive index of molten salt mixtures have yet been published but there have been some determinations of the refractive index of pure fused hydroxides, nitrates and other fairly low melting salts. Meyer and Hecks determined the refractive indices of KNOI, NaN03, KOH and NaOH and calculated their molar refractivities. Their method was to make cross-wires and their image coincide Using an autocollimator. A beam of light illuminating the cross-wires was directed into the melt and made to strike an immersed inclined mirror. The angle of the mirror was adjusted so that the cross-wires and their real inverted image coincided. From the angle of the mirror and that of the measuring telescope, the refractive index could be evaluated. Wagner' modified the apparatus slightly and determined the refractive index of a number of alkali and silver nitrates and other oxy-salts. His results did not agree very well with those of Meyer and Heck. Experimental The chemicals used were all of analytical reagent quality and gave colorless clear melts. Silver nitrate was kept out of light to prevent photolysis. Mixtures of salts were made up by weighing lumps of the solidified previously fused salts, directly into the container, Method.-Two sets of fine platinum cross-wires were rigidly supported a t a distance of 2.5 inches apart by means of Pyrex glass rods. They were fixed firmly in a furnace which consisted of a stainless steel tuhe ( 3 inch diameter, 24 inches long) heated by a Nichrome V element fitted in an insulated case. The cross-wires were illuminated by light of a sodium vapor lamp just above the furnace tube and were viewed by means of a transit theodolite which was mounted about three feet from the furnace in such a way as to allow three dimensional adjustment. By alternately focussing the telescope on the upper and lower cross-wires and making suitable adjustments to the angle of inclination of the theodolite telescope, the angle of inclination of the cross-wires could be determined accurately. The melt which was contained in a Pyrex tube (2 inch diameter, 7 inches long) could be raised and lowered in the furnace. The surface of (6) G. Meyer and A. Heck, i b i d . , 100, 316 (1922). (7) 0.H. Wagner, ibid., 131, 400 (1928).
