June, 1963
THERMODYNAMIC AND P H Y S I C A L P R O P E R T I E S O F
where KI is the equilibrium constant for reaction 1. The form of (8) will be unchanged should one consider that reactions 2 and 3 occur in a single step as was suggested with the formaldehyde-dimedone reaction.6 From (6) and (8) hobs
=
Kih(H +) (H+)/K.1-1
(9)
The constant term in (9) will depend on the reaction system and a best value can be obtained using experimental values for the second-order rate constant at a known hydrogen ion concentration (as shown in Tables VI and VIII). If the value of kl in (7) is 0.92, thien a t pH less than about 4.0, the agreement between observed and calculated values of the second-order rate constant is approximate (Tables VI and VIII). .Above pH 4.0, the rate of increase in the calculated value of the secondorder rate constant with increase in pH is greater than that found experimentally, as might be expected from the postulated change in the rate-determining step. It is noteworthy that similar relationships were obtained by Jencks in accounting for tlhe rates of reaction of hydroxylamine with acetone and with furfural as a function of pH.12 The vertical displacement of the experimental rate curves above the theoretical curve a t pH less than about 4.0 suggests that some reaction occurs between dimedone and aromatic aldehydes in this region. Further, such reaction is catalyzed by hydrogen ions (Table X). The increased reactivity of aromatic aldehydes compared with formaldehyde in this region of low pH may be due ts the formation of ions of the type + Ar.CHOH which participate in the rate-dete.rmining step. However, all attempts to detect the existence of such ions under these conditions were unsuacessf ul. Such ions are commonly proposed to account inter alia
BERYLLIUM COMPOUNDS
1191
for the polarographic reduction of aldehydes, which is strongly dependent) on the pH of the supporting electrolyte.' Arrhenius Parameters.-The value of the A-factor of the Arrhenius equation has been found not to be constant for this sequence of reactions. In the majority of cases, as the value of the Arrhenius energy of activation increases, the value of A increases thereby showing- that the over-all reaction mechanism is complex. The electronic influence of the substituent group on the reactivity of the aldehyde may be shown by comparing the free energy of activation for these reactions with the ease of reduction of the aldehyde a t the dropping mercury cathode in acid buffer solutions. Relevant data are recorded in Table XI. TABLE XI Aldehyde substituent
A F * , kcal. a t 25' - E l / z sv. a t 26' p-HO 17 21 1.116 p-MeO 16 61 I . 07" p-Ale 16 01 1 020 0-HO 16.46 1 050 m-BO 15 34 1 008 15.14 1 000 H p-c1 15.10 0 952 o-Me0 14 88 960 0-c1 14 76 .868 a M7ith the exception of the reduction of p-methoxybenxaldehyde which was carried out in aqueous buffer a t pH 1.81,14 all reductions were carried out in 607, alcoholic buffers at pH 1.73.16
Acknowledgments.-Grateful acknowledgment is made to the Central Research Fund of the University of London for a girant toward the cost of apparatus, and to Imperial Chemical Industries Ltd., for a grant toward the cost of materials. (14) F. Santavy, ref. 7. (15) E. Gergely and T. Iredale, ref. 7.
THE THERM0DYNAM:IC AND PHYSICAL PROPERTIES OF BERYLLIUM COMPOUNDS. 111. HEAT OF FORMATION ASD EITTROPY OF BeF2(g)l B Y hfICHAEL
A.
GREENBAUM,
M. LOUISARIN, AND MILTONFARBER
Thermodynamics Section, Rocket Power, Inc., Pasadena, Calif. Eeceived October 22, 1962
+
+
The reaction BeO(s) 2HF(g) 4 BeFz(g) HzO(g) has been employed to yield values for AHf298 and S02ss of BeFz(g). The experimentallly determined values for A H , and ASr for the above reactions over the temperature range 943-1243'K. are 20.5 & 1.7 kcal. and 6.0 & 0.3 cal./deg./mole, respectively. From these values and available thermodynamic data on all the species of interest, the second-law valuers for AHf2g8 and SO298 of BeFg(g) were found to be -191.3 & 2.0 kcal./mole and 52.4 f 0.3 cal./deg./mole, respectively. The third-law AHfigS for BeFz(g) was determined to be -191.2 3: 0.4 kcal./mole.
I. Introduction A direct experimental determination of the heat of formation and entropy of BeF2(g) has not been previously reported. A value of -184.5 kcal./mole for AHf298 has been reported12however, based upon an experimental determination of the heat of forma,tion of BeF2(s) by means of solution thermochemistry of Be0
in aqueous H F and a measured heat of vaporization of BeFz.a The entropy of BeFz(g) has been calculated by Stull, et u Z . , ~ using the spectroscopic data (first two vibrational levels, symmetric stretching mode and bending mode) of Buchler and Klemperer4 and the bond length data of Akishin and Spiridoiiov.6 Because of the uncertainty in all the data involved in
(1) This research was supported by the Air Research and Development Command of the United States Air Force. (2) JANAF ThermoohemirLal Tables, USAF Contract No. AI' 33(616)6149, Advanced Research Projects Agency, Weshington 26, D. C., Sept. 1961.
(3) (a) V. P. Kolesov, hl. M. Popov, and S. M. Skuratov, Z h . Neorg. Khim., 4, 1233 (19.59); (ti) K. A. Sense and R. W. Stone, J . Phys. Chem.. 62, 453 (1958). (4) A. Buchler and W. Klemperer, J . Chem. Phys., 29, 121 (1958). (5) P. A. Akishin and V. P. Spiridonov, Kristallografiya, 2, 476 (1967).
1192
M. A. GREENBAUM, M. L. ARIN, AND M. FARBER
the derivations of the available thermodynamic data for BeFz(g) (a new experimental value for the heat of vaporization of BeFz has recently been reported6), new determinations of the heat of formation and entropy of BeFz(g) mere carried out by measuring the equilibrium constants of the reaction Based on the available thermodynamic data on all the speciesinvolved, it appeared that good equilibrium measurements could be carried out in the range of 12001700'K. It was found, however, that good equilibrium data could be obtained a t considerably lower temperatures. The measurements were carried out in the 9431243'R. range. 11. Experimental The procedure used to determine the heat and entropy of formation of BeFz(g)was to pass gaseous H F through an effusion cell made of high purity BeO, the entire apparatus being under vacuum. Measurements of the weight loss of the Be0 tube coupled with the measurement of the amount of H F used provides a ready method of calculating the requisite equilibrium constants. This procedure was employed recently by Farber' for the measurements of thermodynamic properties of BOF.* To ensure molecular flow conditions, reactions were carried out under a good vacuum with pressures in the range of l o + to 10-8 atm. Hydrogen fluoride was generated by heating sodium bifluoride under vacuum a t temperatures between 100 and 200". The NaHFz generator and 0.25 in. tubing leading into the furnace which held the Be0 cell were constructed of copper. Since the H F and copper in this part of the apparatus were never heated above 150°, there was no problem of H F attack on the copper. The part of the apparatus which connected the Be0 effusion cell to the copper tubing of the HF generator was constructed of either graphite (a 1-in. inside diameter tube with graphite reducing fittings a t each end) or high purity nickel (0.25-in. tubing soldered to the copper tubing a t one end and holding a nickel adapter a t the other). Runs were made using both materials a t most temperatures to ensure that HF was not reacting with either material and that the products of the HF-Be0 reaction (BeF2, HzO) likewise did not react with either material. The Be0 effusion cell employed was a 0.5-in. 0.d. tube, 2 in. in length with a 1-mm. effusion orifice located about 0.5 in. from the closed end of the tube. The tube of 99+% purity Be0 was obtained from the Brush Beryllium Company. It was necessary to ensure that the entire apparatus from H F generator to Be0 cell was gas tight. Any leakage of H F along the system would result in erroneously low equilibrium constants. Any reactim of the HF with any of the materials, other than the Be0 would, again, result in low K values. Further, any reaction of either the BeFz or HzO produced from the BeO-HF reaction, with materials of the cell before escaping through the effusion orifice would result in high K values. With these considerations in mind, i t was necessary to use two different methods of attaching the Be0 cell to the carbon and nickel tubes. When a graphite tube was used to connect the copper tubing of the H F generator to the Be0 cell, a graphite adapter was used for the latter. This adapter held the Be0 cell around the outside, i.e., the Be0 cell fitted into a graphite holder rather than having the graphite fit inside the Be0 cell. When the reverse procedure was tried, it was found that the HzOformed during the HF-Be0 reactions very rapidly reacted with the graphite to yield high equilibrium constants. It was necessary t o replace the graphite adapter frequently because of gradual loosening of the Be0 cell from continued removal and insertion in the adapter. This would result in a combination of H F leakage and reaction of the outside surface of the Be0 cell with leaking H F , coupled with reaction of the formed HzO with the adjacent carbon. However, when the graphite adapters were replaced after 5-6 runs, no such problems were encountered. With the nickel connecting tube i t was necessary to insert the ( G ) M. A. Greenbaurn, J. N. Foster, M. L.Srin, and AT. Farber, J. Phys. Chem., 61, 30 (1963). (7) M. Farber, J . Chem. Phys., 36, 1101 (1962). (8) M. Farber and J. Blauer, Trans. F w a d a y Soc., 58, 2090 (1962).
Vol. 67
nickel adapter inside the Be0 cell rather than the reverse procedure, because of differences in the coefficients of expansion of Be0 and Ni. By making the Ni finger slightly smaller than the inside diameter of the Be0 cell, allowance for the differential thermal expansions could be made. It was not necessary to ensure a gas-tight fit in this case as any H F vapors which might tend to escape from around the Ni finger would, of necessity, be forced to escape back along more than half the length of the Be0 cell and would thus still have an opportunity t o react. It should be pointed out that the necessity for a connecting tube between the copper tubing of the HF generator and the Be0 cell existed because of the nature of the furnace used to heat the Be0 cell. The furnace was a standard automatically controlled Leco tube furnace. The length of the tubes in this furnace are 18 in. with a significant temperature gradient along this length. It thus was necessary to place the Be0 tube in the center section of the furnace to ensure maximum temperature. Insertions of copper tubing into the hot reaction of the furnace would have resulted in reaction with the HF. The experimental procedure consisted of weighing the Be0 effusion cell, attaching it to the adapter, connecting tube and H F generator, and inserting the Be0 cell, adapter and connecting tube into the large Ni tube in the furnace. A weighed sample of NaHFz contained in a graphite cell was placed in the copper cell and the bottom sealed with a copper, flanged gasket. The system was evacuated through two copper traps cooled in liquid nitrogen until the requisite to 10-6 atm, pressure had been reached. The NaHFz cell was then heated to the desired temperature by means of a heating tape wound around the outside and connected to a powerstat. After an experiment the XaHFg cell was cooled in water and the apparatus disassembled. Weighing of the NaHFz cell and beryllia tube resulted in the necessary weight loss information from which the equilibrium constants were calculated. Runs were made a t six different temperatures over the range 943-1243°K. Temperatures were checked frequently during the actual runs by means of a thermocouple inserted in a well in the cell. At least three runs were made at each temperature, a total of 27 being made in all. The actual temperature inside the Be0 cell was determined for each setting on the furnace control by inserting a calibrated chromel-alumel thermocouple inside the cell and obtaining a graph of the temperature us. time curve by means of a Leeads and Northrup automatic recorder-controller. Calibrations were made a t frequent intervals to ensure no fluctuations in the furnace. To ensure that no NaF was being lost under the conditions employed to generate H F from NaHF2, a sample of pure KaF was heated under vacuum in the H F generator to a temperature 100' higher than was ueed in any of the actual runs. Sfter two hours time, the longest ever employed for a run, no loss in weight of the NaF was detected. In addition, heating sample of NaHFz to a high temperature for a prolonged period of time under vacuum resulted in the loss of the theoretical amount of H F and never any more, also indicating no loss of NaF under the experimental conditions.
111. Discussion of Results The experimentally determined quantities in the investigation of the heat of formation of BeFz(g) mere weight loss of €IF (from a sample of TJaHF2) and weight loss of BeO. From these values it was necessary to determine the equilibrium constant, K , which in turn would lead to values of AHfZg8 and So. The equilibrium expression for the reaction BeO(s)
4- 2HF(g)
= BeFdg)
+ HzO(g)
(1)
is
K =
P H s 0 PBeFz
P'HF
(2)
In the molecular flow regime, the pressures of the various components are given by the Rnudsen equation. Thus the pressures of interest are defined as
THERMODYNAMIC AND PHYSICAL PROPERTIES OF BERYLLIUM COMPOUNDS
June, 1963
I
PHF!
=
nHF d 2 T 1 & l 7 1 & f H F-
(5)
iAt
where n = moles; k = Boltzmann constant; T = temperature; M = molecular weight; A = area, of effusion orifice; t -- time; and N = Avogadro's number. Rewriting eq. 3, 4, and 5 and equating moles of HzO(g) and BeFz(g) formed to moles of BeO(E;) lost leads to
nHF =
PHFA = nHF* d 2~ ~ N T ~ M H F
2rlBeO
(8)
where nHF* is the number of moles of HF lost from the NaHF2. Substituting eq. 6, 7, and 8 into the equilibrium expression, equation 2, leads to -
(n B e O d % k l v T l ~ ~ ,nBeo ~ , )d(2 a k N T M ~-, o \
which reduces to eq. 10
The reaction of BeO(s) with HF(g) was studied over the temperature range 943-1243OK. At these temperatures it was assumed that (a) the BeFz formed from the reaction was all gaseous, and (b) that the HzO formed in the reaction did not react with the Be0 effusion cell. Previous work6 on the heat of vaporization of BeFz demonstrated that at the temperatures and pressures employed in the present investigation any BeFz formed would be gaseous and exist only as a monomer. Physical inspection of the apparatus after all runs never gave any indication of condensed BeFz in or around the Be0 cell. -4s a further check on the formation of BeFx(g) from the BeO-HF reaction, as opposed to formation of a condensed phase of BeF2, the effect of H F partial pressure on the equilibrium constant was studied in detail a t 1073O:K. The reaction as shown in equation I is pressure independent. If any significant amount of BeFz(s,l)is formed the K values should show a marked pressure dependence. h series of 7 runs was made a t 1073"K., where the H F partial pressure was varied by a factor of more than 10. The calculated K values were found to be independent of pressure within experimental error. A sixfold variation in H F pressure a t 1003OK. likewise showed no effect on the calculated K values and a 2.5-fold variation j i i HF pressure a t the lowest temperatures studied, 94.3OK., also failed to demonstrate any pressure dependence of K . The possibility of reaction of the HzO formed during
1193
the reaction with the Be0 was considered because of reported reactions of HzO and Be0 in the l i t e r a t ~ r e . ~ - l ~ These reports stated that significant weight losses occurred from the passage of HzO(g) over BeO(s) a t ternperatures as low as 1473'K. Although this temperature was 230' higher than any used in the present studies, it mas considered necessary to eliminate the possibility of any such reaction occurring a t the highest temperatures used. Using the identical experimental apparatus employed in the BeO-HF runs, 2 g. of gaseous HaO was passed through the Be0 effusion cell at, 1243OK. Weighing of the Be0 cell after reaction indicated that within the experimental error (h0.5 mg.) no reaction occurs between HzO(g) and BeO(s) a t the highest temperatures employed in the current investigation. To ensure that none of the materials of the experi-. mental apparatus were reacting with either the H F or with the HzO and BeFzproduced from the reaction, two entirely different set-ups were used, one made of graphite and the other of nickel. If reactions were occurring between the gaseous species and the tube materials, then the ca,lculated K values would be different when carbon and nickel were used at the samr: temperature. The formation of NiFz and N O by reaction of Xi with BeFz, HF, and HzO was considered in the temperature range of the investigation. The reaction of HzO and Ni a t temperatures up to l l O O o has been reported not to occur.ll Theoretically, employing data in the literaturejZthe reaction of H F and Ni a t temperatures as high as 1 2 5 O o K . is unlikely. Weighings of the nickel holder prior to and after each determination indicated a negligible reaction with the H F gas a t the experimental temperatures. This is in agreement with the results of Farber, Darnell, and Ehrenberg12and Myers and Delong.l:' The reaction of BeFz(g) with Ni was previously found not to occur.6 (These same studies indicated that graphite did not react with gaseous BeF, in this temperature range.) However, both experimentally and theoretically the reaction of water vapor and graphite does take place in this temperature range. Therefore, as explained in the Experimental section, it was necessary to minimize the possible reaction of 1320 with C. A gas-tight fit of the Be0 cell in the graphite holder was necessary to prevent any H F escaping along the outside of the Be0 cell. If this occurred, the reaction of HzO formed with the carbon would take place yielding high values for the equilibrium constant. When reactions were carried out using both the Xi and C systems, the resulting K values were the same within experimental error at both the highest and lo\\& temperatures. Weight of the Ki holder before and after several runs indicated no significant reaction was occurring between the Ni and any of the species present. To ascertain whether YaF was evaporating from the NaHF, a sample of reagent grade KaF was heated to the highest temperature t o which the sodium bifluoride mais subjected with no apparent weight (9) L. I. Grossweiner and R. L. Seifert, J . Am. Chem. S o c . , 74, 2701 (1952). (10) W. A. Yound, U. S. Atomic Energy Commission Report No. NAA. SR-4446,March 15, 1960. (11) M. Farber, J. Electrochem. Soc., 106, 761 (1959). (12) M. Farber, A. J. Darnell, and D. Ehrenberg, abid., 102, 446 (1955). (13) W. R. Myers and W. B. Delong, Chem. Eng. Progr., 4 4 , 5 , 859 (1948).
SIDNEY W. BENSOSASD CHARLES S. COPELASD
1194
loss. Under the conditions of these experiments NaF will react with beryllium oxide. The values for K as calculated from the experimental data are listed in Table I. A plot of log K vs. 1 / T TABLE I
wt.
wt.
of HF lost,
w.
of Be0 lost, mg.
943 943 943
308.8 399.3 164.7
1003 1003 1003
K X 108
AF Reaction, kcal./ mole
AHfBeFe
7.9 10.9 4.3
0.61 0.69 0.63
13.9 13.6 13.8
-192.6 -192.9 -192.7
534.5 86.9 251.2
16.2 2.8 7.7
0.99 0.97 0.87
13.8 13.8 14.0
-192.5 -192.5 -192.3
1073 1073 1073 1073 1073 1073 1073
1368.3 465.7 842.5 130.6 561.6 146.5 855.3
61.9 22.7 36.0 5.1 28.7 7.0 43.4
1.90 2.21 1.71 1.42 2.41 2.12 2.41
13.4 13.0 13.6 14.0 12.9 13.1 12.9
-192.6 -193.0 -192.4 -192.0 -193.1 -192.9 -193.2
1133 1133 1133 1133 1133
464.6 267.7 124.5 277.2 114.6
33.8 17.7 6.7 16.6 6.8
4.87 4.07 2.69 3.31 3.28
12.0 12.4 13.3 12.9 12.9
-193.7 -193.3 -192.4 -192.8 -192.8
1188 1188 1188 1188
91.6 87.2 200.4 164.2
8.2 6.8 14.0 12.9
7.47 5.65 4.56 5.74
11.6 12.2 12.7 12.2
-193.8 -193.2 -192.7 -193.2
1243 1243 1243 1243 1243
134.7 59.6 194.4 274.7 114.4
12.0 5.6 16.9 25.2 10.2
7.37 8.21 6.68 7.89 7.38
12.1 11.9 12.4 12.0 12.1
-193.1 -193.3 -192.8 -193.2 -193.1
Temp., OK.
Vol. 67
yields a least squares slope of 20.5 f 1.7 kcal., corresponding to the AH, over khe temperature range. Using the available thermodynamic data for all species involved2 and extrapolating to 298OK., a value for the AHfisS of BeF2(g) of -191.3 f 2.0 kcal./mole is obtained. The corresponding third law value is -191.2 f 0.4 kcal./mole. From a plot of AF, vs. T the AS, of 6.0 =k 0.3 cal./deg./mole is obtained over the reaction temperature range by means of a least squares analysis. Using the available entropy data2for BeO(s), HF(g), and HzO(g), a value of 52.4 f 0.3 cal./deg./mole of BeFz(g). This compares is obtained for the Sozg8 with a theoretical value of 52.3 cal./deg./mole calculated from spectroscopic data.4~5 A calculation of the Sofor BeFz(g) a t llOO°K., using the experimental AS, and the thermodynamic values for the other species a t this temperature, leads to a value of 67.5 cal./deg./ mole compared to 66.9 reported in the JANAF Tables2 The AH298 and SO298 of BeF2(g) reported here represent the first experimentally determined values of these thermodynamic properties. Since the thermodynamic values of HzO(g), HF(g), and BeO(s) are considered to be of a high order of reliability a t this time, the thermodynamic values for BeFz(g) reported here based on experimental measurements of a reaction involving only these species should be considered established. Employing the latest value for the heat of sublimalead to a value of aption6 the data of Kolesov, et proximately - 188 kcal./mole for AHf of BeFz(g). The remaining discrepancy between this work and that of Kolesov may be due in part to the extensive polymerization of HF(g) at room temperature, since Kolesov’s did not take this polymerization into account in employing a value of the heat of solution of gaseous H F monomer to form HF(aq).
THE PARTIAL MOLAR VOLUMES OF IOSSl BY SIDNEY
w.BENSONAXD
CHARLES
8. C O P E L A N D
Che nistry Department, University of Southern Calzfornia, Los Angeles 7 , Caltfornia Received Oclober 51,1Q66w
It is shown that the recent successes of Mukerjee in correlating partial molar volumes of ions with the continuum model of Born can be understood in terms of an isomorphic replacement of water molecules in a simple cubic lattice by ions whose sixes range from smaller to not too much larger than HZO. The anomalously large values of the intrinsic volumes are then shown to be accounted for very closely by the void volume of the ion in such a lattice. This lends strong support to Mukerjee’s suggestion that ion volumes should be monotonic functions of crystal radius, independent of the sign of the charge. A simple free volume model is used to show that the radius of an ion in either a solid or a solution should be the same to within 0.02 A. of its “hard sphere” radius. The effects of temperature on partial molar volume are discussed briefly. Finally it is pointed out that the dipole-dipole repulsions between solvation shell molecules prevent the large ions such as Cs+, C1-, Br-, I-, etc., from having very large coordination numbers.
Introduction The partial molar volumes of salts a t infinite dilution can be obtained from precise density measurements on salt solutions and must be additive in the individual partial molar volumes of the ions, P i o . However, as with all such ionic quantities there is no direct experimental method of making a separation of the sum of the Vio into the separate Vio and one is forced to other criteria if such separations are to be made. Any theory of the 7e should of course predict the individual values (1) This work has been supported by a grant from the Office of Naval Research,
and should be tested by direct comparison with experimental values, an apparently circular dilemma. Recently Mukerjee2 has argued that for spherically symmetrical ions such as the alkali metal cations and the halide anions, the partial molar volume should be a smooth monotonic function of the ionic radius quite independent of the sign of the ionic charge. This would seem to be an inescapable argument if the solvent molecule, H20, were also spherically symmetrical. Unfortunately, such is not the case and in fact a number of authors have made quite strong arguments3 in favor of (2) P. Mukerjee, J . Phys. Chem., 65, 740, 744 (1961).
