1536
J. 0. HALFORD AKD GEORGE A. MILLER
The evidence for either of these is not complete, but it is known from the work of Howard,l8 that NaAlF4 exists. Sodium aluminate, NaAlO2, has been identified by X-ray in the rapidly quenched salt, particularly from NaF rich melts.l* Finally, Xray and infrared absorption of quenched samples show structures that are indicative of oxyfluoride compounds.12 The first scheme above also was proposed in part by Boner,I4 based largely on the work of others. Both the consumption of cryolite and the production of the four-coordinated fluoroaluminate ion (13) E. H. Howard. J . A m . Chem. Sot.. 76, 2041 (1954). J. E. Boner, H e h . Cham. Acta., 33, 1137 (1950).
(14)
Vol. 61
would act still further to reduce the fluoride ion concentration from the sodium fluoride. Thus, the prediction would be that the addition of alumina would reduce the conductivity of the solution to a greater extent than would be expected by the addition of a non-conducting diluent. This was the experimental observation oi Edwards, et al." It is not possible to reduce the fluoride ion concentration to zero by the above mechanisms. However, it is not unreasonable to assume that the remaining fluoride might be immobilized by long range attraction to the fluoroaluminate or aluminum oxyfluoride ions. This might be regarded as a tendency for aluminum to exhibit a still higher coordinate number.
STANDARD HEAT CAPACITIES OF GASEOUS METHANOL, ETHL4NOL, METHANE AND ETHANE AT %'"7"K. BY THERMAL CONDUCTIVITY BY J. 0. HALFIORD AND GEORGE A. MILLER Department of Chemistry, University of Michigan, Ann Arbor, .Michigan Received M a y 1 1 , 1967
Limiting low pressure gaseous heat capacities are measured with a band-wire type thermal conductivity celI and a Knudsen pressure gage. The spectroscopic heat capacities of nitrogen and methane and the accurately known heat capacity of The Knudsen gage provides some extenethane are reproduced a t 279'K. within the estimated uncertainty of =!=l.O%. sion of the scope of the thermal conductivity heat capacity method to compounds of higher molecular weight and lower volatility and yields measurements which should be substantially independent of adsorption and gas imperfection errors. 0.13 cal./deg. mole, agrees accurately with an earlier thermal conductivity result. The A new Ct for ethanol, 12.90 new C$ for methanol, 8.14 f 0.08, is 3% below an earlier result by Eucken and Franck and 2% below a recent well supported value calculated from incomplete spectroscopic d a h
It has been demonstratedl that the thermal conductivity method can be used to measure the limiting low pressure heat capacities (C:) of the simpler vapors and permanent gases with useful accuracy. Precise spectroscopic heat capacities have been reproduced within about i= 1.0%, in some cases a t temperatures well below 200°K. The measurement is conducted a t a pressure of the order of low3mni., which must be accurately measured. In the more accurate applications of the method the pressure has been determined either with a McLeod gage or by a pipetting procedure, that is, by compressing to or expanding from a measurable pressure within the ordinary manometric range. Such measurements are limited to materials having high enough vapor pressures somewhere within the reasonable working temperature range. The thermal conductivity, however, can be measured for less volatile species for which the usual pressure measurement involving attenuation or compression is impractical. It is evident that a sufficiently accurate gage designed for direct measurement of tQe pressure in the conductivity cell could extend the scope of the heat capacity method. As the molecular weight increases the suitable pressures decrease. Consequently, the range of molecular species for which heat capacity (1) For examples and earlier references, see: (a) W. N . Vanderkooi a n d T. D e Vries, Tilts JOURNAL, 60, 636 (1956); (1)) A. Eucken a n d E. U. Franck. Z. Eleklrochem.. 63, 195 (19.18); (c) C.B. Kistirtkowsky, J. R. Lacher and F. Stitt, J . Chem. P h y s . , 7 , 289 (1939).
measurements are feasible will increase with the precision of the pressure gage. The Knudsen gage, which is designed to measure pressures in the range suitable for heat capacity determination, offers the possibility of some extension of the scope of the method. A Knudsen gage has therefore been constructed and calibrated, with argon and nitrogen, against a MCLeod gage of high sensitivity. I n the calibration, the maximum deviation was less than 2.0%, the mean deviation about 1.0%. With the Knudsen gage and a band-wire conductivity cell of the Eucken-Krome2 type, the spectroscopic heat capacities of nitrogen and methane and the accurately known heat capacity of ethane have been obtained at 279"K., relative to argon, within f 1.0%. Measurenients at lower temperatures, which may be needed when an internal rotation barrier is to be estimated, will be attempted a t a later date. Optimum accuracy in a rotation barrier will be realized only in a most favorable temperature range, which may be quite low. In addition, heat capacities a t two well spaced temperatures are required in order to support a choice between two barrier values calculable at each temperature from a heat capacity increment above R / 2 . New measurements are reported here for methanol and ethanol, chosen as compounds which may be appreciably adsorbed, even at the low pressures used. With these compounds it is more difficult (2) A. Eucken and H. lironie, 2. physlk. Chem., B46, 175 (1940).
Nov., 1957
Low PRESSURE GASEOUS HEATCAPACITIES
to judge the accuracy of the results, since the true heat capacities are not known with dependable precision, Both the theory and the experience with nitrogen, methane and ethane indicate that the Knudsen gage should give reliable pressures. Gas imperfection must be negligible at the pressures below 10 p , but adsorption might cause the accommodation coeffic,ient to increase with increasing pressure. This increase, however, should be accompanied by a decrease in the effective pressure whkh would eliminate any trend i n the calculated heat capacity with the pressure. Such trends in the pressure and the accommodation coefficient were observed, for the most part within the estimated uncertainty, but they were not reproducible between runs and they left smaller residual trends in the heat capacity which were also not reproducible. Larger deviations occurred near the ends of the working pressure range where it, was most difficult to locate correct,ly the smooth curves through the data from which the heat capacity was c,alculated. At the lowest pressures, deviations due to lower precision of the dat'a could occur. Consequently, alt'hough the data on the alcohols are a little more variable than those of the other test gases, it still appears very probable that the average of the mean heat capacities from the individual runs is within 1.0% of the correct CP,. While the new result for ethanol at 279°K. agrees closely with the earlier thermal conductivity heat capacity of Eucken and Franck, the new met,hanol value, 8.14 f 0.08 cal./deg. mole, is 3y0lower than their C;, 8.38 f 0.08, which could be high because of gas imperfection. With the potential barrier to internal rotation precisely known,3 but with tlhe normal frequencies still uncertain, only a range of probable values can be calculated from spectroscopic data for comparison. The frequencies chosen by Noether4 lead to 8.13 for Cg at 279", while t'hose of Plyler,6or the nearly equivalent frequencies of Ivash, Li and Pitzer6 lead to Ct = 8.28 to 8.30. The frequencies used by Eucken and Franck,lb or those of Borden and Barker,7 yield 8.21 for CO, a.t 279". From incomplete spectroscopic evidence, therefore, C; = 8.21 f 0.09. The new methanol heat capacity reported here agrees closely with Noether's frequency assignment and appears to exclude the frequencies proposed by Plyler and by Ivash, Li and Pit,zer, who, however, have supported t'heir choice by a rather convincing argument. I t is evident that sufficiently precise thermal conductivity heat capacity data can clarify the met,haiiol frequency problem. It appears best, homever, to defer any firm decision about the frequencies until more data have been collected, possibly with improved experimental procedures. The new methanol heat capac,ity can be used with each proposed frequency assignment to illustrate the accuracy with which the internal rotation (3) E. V. Ivash a n d D. M. Dennison, J . Chem. PhUs., 21, 1804 (1953). (4) H. D. Noether, ibid.,10, 693 (1942). (5) E. K. Plyler, J : Research N a f l . Bur. Standards, 48, 281 (1952). (6) E. V. Ivash, J. C . >I. Li and R. 8. Pitzer, J . Chem. P h y s . , 23, 1814 (1955). (7) A. Borden and E. F. Balker, ibid., 6, 553 (1938).
1537
barrier can be estimated from heat capacity data. The estimates are : with Noether's frequencies, 1110 f 190 cal./mole; with the Borden-Barker frequencies, 915 f 180; with the Plyler frequencies, 770 f 170. From data of comparable accuracy at lower temperatures the uncertainty in the methanol bnrrier would be greater. For other molecules, the most favorable temperature can be much lower, and the uncertainty is likely to be greater than for methanol. From their methanol heat capacity, Eucken and Franck have estimated an internal rotation barrier of 1800 cal./mole. It is not clear how they obtained this estimate. From their CO, at 280", with their chosen frequencies, the indicated barrier range is about 1600 f 300. Their measurement at 200", 7.46 f 0.11, yields approximately 1000 & 400. Since these ranges overlap near 1400 cal./ mole, this appears to be the most supportable barrier estimate from their data. The uncertainty of barrier values derived from thermal data of normally achieved precision is unfort8unately large. Refinement of the thermal conductivity heat capacity method for the purpose of improving the barrier accuracy is now under consideration. Although, as illustrated in the above estimates, uncertainty in the normal frequencies will continue to undermine the accuracy of barrier determinations, it is fortunate that an inaccurate barrier derived with a particular frequency assignment can be used with the same frequencies to calculate thermodynamic properties of useful accuracy over a wide temperature range. The new C:, for ethanol, 12.90 f 0.13, agrees closely with the result reported by Eucken and Franck, 12.85 f 0.10. Their estimate of the barrier to hydroxyl group rotation is 1000 cal./mole. From the data they have extracted the sum of the heat capacity contributions of the two internal rotations. They assume that the rotations are substantially independent and obtain the hydroxyl increment from the sum by subtracting the methyl contribut,ion based upon an assumed barrier of 3000 cal./mole. The hydroxyl barrier is then taken from the tables as the barrier for the equivalent symmetrical rotator. I n this evaluation, the most likely source of serious error is the frequency assignment. Since, at 280°, the heat capacity is not very sensitive to the methyl group barrier, an error in the assumed methyl barrier will produce only a relatively small uncertainty in the estimate for the hydroxyl group. If the frequency assignment is correct, the hydroxyl barrier obtained should not be in error by much more than 300 cal./mole, with the major part of the error due to the uncertainty of the experimental heat capacity. For calculations with ethanol, it is probably best to assume that the barrier height for the hydroxyl rotation, that is, for the equivalent symmetrical rotation, is the same as the methanol barrier, 1071 cal./mole. Experimental Conductivity Cell.-The cell followed closely in essential dimensions the design of Eucken and Krome. F o r easy dismounting for adjustment or repair, the band and wire were attached to a framework supported by a brass rod which could be exposed by detaching the surrounding con-
1538
J. 0. HALFORD AND GEORGE A. MILLER
tainer at a ground glass joint near the top of the assembly. Since experiments with a modified design are now in progress, further details will be given for a later design which is deemed most suitable for general use. Knudsen Gage.-The over-all design of Klumb and Schwarz8 was used to provide minimum sensitivity t o vibration along with simplicity and adequate accuracy. A hollow cylindrical vane system consisted of 10 equally spaced platinum vanes each mounted a t 45" t o a radius. The vane system was suspended by means of a tungsten wire over a heater finger and inside a 25 mm. glass envelope. The gage was fitted with a magnetic damping device and with an aluminum mirror attached to facilitate optical observation of the torsional displacement. In operation a constant temperature difference was maintained between the heater surface and the outer glass envelope surface. With low pressure and long mean free path, the vane system is subjected under these conditions to a torsional displacement nearly proportional to the pressure which, except for accommodation effects, is in theory independent of the molecular species. The lower part of the gage, including the vane system, was immersed in a water-bath a t room temperature, and the heating current was adjusted to maintain a constant difference of 48" between the bath and a point on the heater casing, as determined with a copper-constantan thermocouple. The Knudsen gage was calibrated against the McLeod gage, with argon and nitrogen, for pressures from 0.3 to 1.5 M of mercury. The gage was first adjusted to zero in high vacuum with the damping magnet activated but with the heater turned off. The heater was then turned on and adjusted. After 5 minutes, if the deflection was not more than 0.2 mm. (pressure about 5 X mm.), the vacuum was taken to be adequate. Under these conditions the McLeod gage always read less than mm., indicating the presence of condensable vapors. For the calibration, the vacuum reading of the Knudsen gage was adjusted to zero, so that, like the McLeod gage, it would read only the pressure due to non-condensable vapors. Increments of about 0.3 p of argon or nitrogen were introduced through a pipet system. Five minutes after each addition the deflection was recorded and the pressure was measured with the McLeod gage. The deflection was nearly proportional to the pressure. Calibrations with argon and nitrogen agreed closely, but deflections with hydrogen at corresponding pressures were about 5% lower. It is concluded that for gases with high acconimodation relative to argon, that is, with relative accon~modation coefficientsabove about 0.8, the gage is independent of the molecular species. For hydrogen, however, which has a very low accommodation coefficient, the calibration with argon and nitrogen is somewhat inaccurate. The calibration was re-checked a t intervals during periods when the gage was used frequently. Some trouble occurred with swinging vibrations of the vane system when the larger deflections were maintained for more than 15 minutes. To eliminate these vibrations, the heater was turned off for one hour while the pressure was above one micron. McLeod Gage.-A gage as designed by RosenbergP with large volume and small capillary bore, was made to order by Eck and Krebs Glassblowing Company under the guidance of Professor Rosenberg. To minimize sticking of mercury in the capillaries, the inner surfaces had been conditioned by grinding. Suitable linear and squared type scales had been provided with the gage, along with a graph of mg. of mercury per mm. of capillary against the distance from the sealed end. The ratio of volume per mm. A of bore to the cut-off volume was about 2.5 X small correction for the difference in capillary depression of the two capillary bores was determined in two independent ways with good agreement. Because of the large weight of mercury in the gage, the bulb and reservoir were supported by imbedding them in plaster of Paris. The lowest pressures, about 0.3 M , were measured within 0.5%. Heat Capacity Determination .-The band acquired cons t s i t electrical DroDerties after it had been annealed in vacuo for 15 minbtes a t a dull orange heat (without the wire (8) 11. Klurnb and H. Sohwarz, Z. Plrysik, 122, 418 (1944). (Q) P. Rosenberg, Rev. S c i . I n s t . , 10, 131 (1939).
Vol. Gl
suspended alongside). The wire, however, was satisfactory without annealing. A drift in wire resistance obtained with the first assembly was eliminated by re-mounting the wire and re-setting the potential leads. With the cell i n t,he ice-bath, band and wire c,urrent,swere turned on and the cell was allowed to stand for three hours. The currents were then adjusted with the aid of standard resistors in series. Band and wire standard resistances were, respectively, 1.0 ohm and 125 ohms, and the corresponding potentials, E! and E:, were maintained a t 80.000 and 15.8 f 0.1 mv. in all experimental runs. Thc vacuum was checked to be sure that the pressure, measured with the Knudsen gage, was less than 5 X 10-6 mm. Resistances of band and wire were then measured for comparison with their usual vacuum values. Since, from one run to another, these limiting resistances showed small shifts presumably due to differences in the pressure of the so-called vacuum and possibly to other causes, such as small variations in the bath temperature, they were redetermined immediately before and after each run, and the average value so determined was used in the interpretation of the run. Five minutes after the introduction of a pipetful of argon into the cell, the resistances of band and wire were recorded and the pressure was determined with the McLeod gage. This procedure was repeated with five or six further successive increments of argon, covering the range from 0.4 to 2.8 p . The band and wire currents were held constant throughout the run. The system was evacuated a t the end of the run and the procedure was repeated a t least once. After the last run the limiting resistances in vacuo were measured again. The same procedure, with the range of pressures appropriately adjusted, was followed with the other gases studied, except that the pressures of ethane and the alcohols were obtained with the Knudsen gage. With the alcohols i t was necessary because of adsorption to wait about 45 minutes until a steady pressure was obtained. Experimental pressures were, for argon, less than 3 p , for nitrogen, less than 2 p , for ethane and the alcohols, less than 1.2 p . The data of Vanderkooi and De Vries indicate that theee pressures should be low enough to ensure the linear dependence of conduct,ivity on the pressure which IS necessary for the heat capacity determination. At each pressure, including the vacuum limit), the potential drop, Eb or E,, across band or wire a t constant known current, was measured to determine the resistance. The potent,ials, rather than the corresponding resistances or temperatures, were used in the interpretation of the data.
Interpretation of Data ; Results When the filament (band) current is constant, the filament assumes a temperature which is a function, for each gas, of the pressure alone. For two gases, extraneous energy losses are the same for the same filament temperature, and the energy transported by the gas molecules from filament to mall, that is, the quantity paChi-'/x is the same for both gases. The pressure is represented by p and a, C and M are, reepectively, the accommodation coefficient, the heat capacity factor and the molecular weight. As a result, for the two gases, with the same band current and potential drop cz = C,(;o,/;o,)(a,/cuz)(Mz/M1)'I2 (1) With the wire current also constant, according to Eucken and Krome, the ratio of accommodation COefficients is the ratio of net wire temperatures, or of the equivalent net mire potentials, E, - E,(p = 0 ) . Adequacy of their interpretation is supported by the accuracy obtained here with nitrogen, methane and ethane. For each gas, smooth curves are drawn through the data expressing the band and wire potentials as functions of the pressure a t constant band and wire currents. Equation 1 is valid when the band PO-
I I
SOLUBILITY OF SILICA IN SOLUTIONS OF ELECTROLYTES
Nov., 1957
1539
TABLE I HEATCAPACITY OF GASESAT 279’K., RELATIVE TO ARGON,BY THERMAL CONDUCTIVITY Mean a J a A
Mean P A / P .
A Nt CHI C2H6 CHaOH
CzHbOH
1,000
1,000 1.603 2.484 3.125 2.668 2 . 66:3 2,670 2.658 3.417
0.884 ,851 ,970 1.037 1.047 1.036 1.036 1.044
tential drop is the same for both gases. A band potential in the working range is chosen, and the corresponding pressures are taken from the curves and used to find the net wire potentials or the ratio of accommodation coefficients. Consequently, C2 is expressed in terms of C1, in effect, as a function of either of the pressures. With completely accurate theory and data, the ratio C2/Cl obtained in this may would be independent of the pressure. In practice, however, since the smooth curves are arbitrarily located and the accuracy of the data decreases at lower pressures, trends in the heat capacity ratio with the pressure are obtained. The results given below are averages over the major part of the working pressure range. Averages taken from the data over shorter ranges immediately above the median pressure do not differ significantly from the broader averages. The heat capacity is related to the factor C by the equation
c = (4/3)C, + c,,= c: + R / 2
(2)
which takes account, according to Knudsen’O and Smoluchowsky,lLof the larger fraction of the energy transported by the faster molecules. Ct is the translational heat capacity and Ci, is the sum (IO) b4. Knudsen, A n n . Physzk, 84, 593 (1911). (11) M .Smoluchowsky, zb7d.. SS, 983 (1911).
e:,
cal./deg. mole
2.98 5.04 f 0.05 6.36 i0.06 10.12 f O . 1 0 8.17 8.06 Mean 8.18 8 . 1 4 i 0 . 0 8 8.14 12.90 f 0 . 1 3
Spectroscopic (or other) C,?
2.98 4.99 6.39 10.0012.13 8.21 i 0.09 (8.38 f 0 . 0 8 )
(12.85 f 0.10)
for rotation and the internal degrees of freedom. This equation assumes that, in any limited range of velocities, the distribution in rotational and internal energies is normal for the mean effective temperature. The adequacy of eq. 2 is supported by the results obtained with argon, nitrogen, methane and ethane. The accommodation coefficient is defined as a! = (T, T O ) / ( T b - To) where T b and T o are the known band and wall temperatures and Tm is the effective mean temperature of the molecules leaving the band. The average heat capacities, C& relative to argon, are summarized in Table I. For the gas indicated in the first column, the second and third columns show the mean pressure and accommodation coefficient ratios at equal conductivity, relative to argon, the fourth gives the experimental heat capacity, and the last column shows spectroscopic or earlier experimental heat capacities for comparison. The Darenthesized heat capacities were measured a t 280°K. by Eucken and- Franck. The ethane value, actually experimental, is for practical purposes the equivalent of a spectroscopic result. The “spectroscopic” range given for inethanol has been .explained in an earlier paragraph.
-
(12) A. Eucken and A. Parts, 2. physik. Chem., BaO, 184 (1933). (13) G. B. Kistiakowsky and W. W. Rice, J . Cliem. Phya., 1 , 281 (1939).
THE SOLUBILITY OF SILICA I N SOLUTIONS OF ELECTROLYTES BY S. A. GREENBERG AND E. W. PRICE Seton Hall University, Sozith Orange, New Jersey Received May BO, I967
The solubility of colloidal silica in solutions of electrolytes and in alkaline solutions was examined. The solubility of n dK1 the first ionization constant of silica was explained on the basis of two equilibrium constants: ( 1 ) K = a ~ ~ s i o ~ . ?(2) silicic acid. The pK1( -log K I )values a t 25 and 35’ were evaluated from solubility and pH measurements and are 9.77 j~ 0.05 and 9.70 0.05, respectively. The concentrations of silicic acid H4SiOcand the silicate ion HsSiOl- are not markedly affected by ionic strengths up to 0.1 normal in elect’rolyt’econcentration. In solutions with concentrations of salts one normal and above, the solubility decreases.
*
Introduction The solubility of silica in aqueous solutions has been studied as a function of temperature,I-4 of (1) For discussion aee R. K.Iler, “The Colloid Chemistry of Silica a n d t h e Silicates,” Cornel1 University Press, Ithaca, N. Y., 1955. (2) G. B. Alexander, W. M. Heston and R. ti. Iler, THIS JOURNAL, 58, 453 (1954). (3) 9. A. Greenberg, i b i d . , 61, 196 (1957). (4) Ii.Goto, ibid.,60, 1007 (196G).
sodium hydroxide concentration2J-7 and of calcium hydroxide concentration.*~9 Alexander, Hes(5) S. W. Sprauer and D. W. Pearce, ibid., 44, 909 (1940). (6) €3. Seidell and W. F. Linke, “Solubilities of Inorganic and Organic Compounds,” Supplement t o 3rd Ed., D. Van Nostrand Co., New York, N. Y.,1952. (7) I
