August, 1061
ALKALINEHYDROLYSIS OF DIETHYL MALONATE I N WA4TER-DIOXASF>
surface since they are not easily removed by immersion of the plate in pure solvent. It is therefore conceivable that a point is eventually reached in the progress of our postulated initial two-dimensional adsorption where the subsequently adsorbed polymer molecules may retain a three-dimensional configuration. These molecules may also “crowd” the two-dimensionally adsorbed polymer molecules already on the surface into the three-dimensional configuration. Considerable rearrangement of the polymer segments on the surface is likely t o take place during this crowding stage and maximum adsorption may be reached only slowly. This may account for the adsorption in the plateau region and the subsequent slow rise to the measured “maximum” adsorptions. As the solution concentration was increased beyond 1.15 X mole/l. the plateau region became less well defined. At the concentratioh 1.27 X 10-3 mole/l. a maximum adsorption of about 3.8 X mole/cm.2 is reached within a few seconds (Fig. 2). The initial rates of adsorption a t these concentrations, compared with that a t 1.15 x 10-4 mole/l.: are about 100% higher than that which would be accounted for by the concentration effect alone. It appears that three-dimensional adsorption, now being energetically more favorable, may have set in a t an earlier stage so that a detailed kinetic snalysis is no longer feasible. The existing theories of polymer adsorption7-11 (7) R. Simha. H. I,. Frisch a n d F. R. Eirich, J. Phys. Chem., 67, 584 (1953); also J . Chem. Phye., 81, 365 (1953).
1333
predict isotherms other than the Langmuir type even for the two-dimensional case. Many experimental results can be represented by Langmuir type isotherms12 rather than Simha-Frisch-Eirich isotherms although Frisch pointed out that a clear cut differentiation of the theoretical and the Langmuir type isotherms was often obscured by the scarcity of experimental data for very low concentrations. The present work indicates that the initial stage of the adsorption process can be represented kinetically by an equation of the Langmuir type, when the concentration of the polymer solution is sufficiently low. If our interpretation of the experimental data is correct, the parameter p in the previous theories, defined as the probability that any segment of an adsorbed molecule is in contact with the surface, may very well be a function of the maximum amount adsorbed. This will cause additional complication in comparing experimental data with SFE and GG theories. Acknowledgements.-We wish to express our appreciation to the Directors of Interchemical Corporation for permission to publish this work. We also wish to thank Mr. C. A. Kumins for his constant encouragement and helpful suggestions. (8) H. L. Frisch a n d R. Simha, J. Phys. Chem., 88, 507 (1954); also J . Chem. Phys., 37, 702 (1957). (9) H. L. Friach, J. Phys. Chem.. 69, 633 (1955). (10) R. Simha, J. Polymer Sci., 89, 3 (1958). (11) E. R. Gilliland and E. B. Gutoff, J. Phys. Chem., 64, 407 (1960). (12) See for example, E. Treiber, G. Porod, W. Gierlinger a n d J. Schurr, Makromol. Chem., 9, 241 (1953); R. Perkel, Thesis, Polytechnic Institute of Brooklyn, Brooklyn, New York, 1959.
THE KINETICS OF THE ALKALINE HYDROLYSIS OF DIETHYL MALONATE, DIETHYL SUCCIXATE AND DIETHYL SEBACATE I N WATERDIOXANE MIXTURES BYW. J. SVIRBELY AND AUGUST D. KUCHTA Chemistry Department, University of Maryland, College Park, Md. Received February S, 1961
The kinetics of the alkaline hydrolysis of diethyl malonate, diethyl succinate and dieth 1 sebacate were studied at 25’ in dioxane-water mixtures varying in dielectric constant from 60 to 9. The alkaline hydro$& of diethyl succinate was also studied over a temperature range from 35 to 6” in various dioxane-water mixtures. The effect of an added inert electrolyte was investigated. It was observed that the k l / k z ratio varied from 165 to 1.46 for diethyl malonate, from 7.18 to 1.02 for diethyl succinate and from 2.97 to 1.36 for diethyl sebacate in the range of solvent mixtures used. Thermodynamic activation values have been calculated for both steps of the reaction. It 1s concluded that in the low dielectric media both steps of each reaction are proceeding by essentially the same mechanism. The experimental observations can be explained on the basis of the formation of ion-pairs or aggregates.
Introduction A recent study2 of the alkaline hydrolysis of 1,3,5-tri-(4-carbomethoxyphenyl)-benzene showed that there was a negative primary salt effect on the second and thirid steps of that reaction. That observation is not only a t variance with theory for a reaction between ions of like charge sign but is also a t variance with other observations involving (1) (a) Abstracted from a thesia b y August D. Kuchta t o the Graduate School of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy; (b) presented in part at the New York City Meeting of the American Chemical Society, September, 1960. ( 2 ) W. J. Svirbely and H. E. Weisberg. J . Am. Chem. SOC..81, 257 (1958).
the alkaline hydrolysis of an ester i ~ n . ~Since .~ the study was made in low dielectric constant media (it?., D 9) the existence of ion pairs is quite likely and it was concluded that we may not be dealing with the usual alkaline hydrolysis of an ester ion involving ions of like charge sign. Solubility limitations in dioxane-water media prevented studies being made in solutions of high dielectric constant. To investigate more thoroughly the effect of the medium on the mechanism and the rate constant
-
(3) L. Pekkarinen, Ann. Acad. Sci. Fenn., A l l , 62 (1954). (4) W. J. Svirbely a n d I. Mador, J . Am. Chem. SOC., 7 8 , 5699 (1950).
TT'. J. SVIHBELY AXL) XCGUST D. KUCHTA
1334
ratios of ester hydrolysis, it was decided to study the alkaline hydrolysis of several diesters differing markedly in length. Consequently, the alkaline hydrolysis of diethyl malonate, diethyl succinate and diethyl sebacate were studied at 25' in dioxanewater mixtures varying in dielectric constant from 60 to 9. The alkaline hydrolysis of diethyl succinate also was studied over a temperature range. Materials and Apparatus Dioxane, water, sodium hydroxide solutions and hydrochloric acid solutions were prepared or purified as before.2 The diesters were Eastman best grade. They were distilled under vacuum and a middle cut was taken in each case. The sapopification equivalent of each ester indicated 99.9 f 0.1% purity. The refractive indices were in excellent agreement with those previously reported? The potassium chloride used for salt studies was of analytical reagent grade and was used without further purification. Apparatus.-The apparatus used in this research has been described.% Procedure.-The procedure has been described.2 However, the starting concen+rations of the diester and the sodium hydroxide were adjupted so that equivalent amounts were used (i.e., A0 = 2B0, wnere AOand BOwere the initial concentrations in moles/liter of hydroxide and diester, respectively). At the completion of each run, the density of the solution was determined. This datum was used to transform weight data to volume data. Duplicate runs were made for each environmental condition.
Calculations and Discussion Evaluation of Rate Constants.-The alkaline hydrolysis of the diesters used in this research may be represented by the chemical equations
TABLE I DATAFOR
D
DIETHYLSUCCINATE REACTION I N DIOXANEWATERAT 24.93" = 13.10; Ao = 12.417 X 10-3 mole/l.; Bo = 6.209 X mole/l.; run #31 THE
A
+ C -+kz
D
A X 108 mole/l.
6.00 8.00 10.00 12.00 14.00 16.00 20.00 22.00 24.00
10.244 0.8250 30.00 5.7972 0.4669 9.6263 .7753 32.00 5.5913 ,4503 9.0910 .7321 34.00 5.3854 ,4337 8.6381 .6957 48.00 4.3355 ,3492 8.2264 .6625 50.00 4.2325 ,3409 7.8352 .6310 52.00 4.1296 ,3326 7.1764 .5779 60.00 3.7385 ,3011 6.8265 .5498 70.00 3.3061 ,2663 6.5795 ,5299
mu.
2/20
min.
A X 108
mole/l.
a =
.4/&
TABLE I1 CALCULATIONS OF RATECONSTANTS FOR R U N #31 o s DIETHYL SUCCINATE % Reaction
min.
20 30 40 50 60
6.95 11.72 18.01 26.50 28.90
t,
%Cornpared
ki.
t
ratio
l/K
7
1. mole-' 8ec. - 1
60/20 5.597 1.536 0.2423 5.615 60/30 3.319 1.540 .4087 5.616 60/40 2.160 1.500 .6255 5.594 60/50 1.468 1.500 .9217 5.602 50/20 3.813 1.552 1.355 5.561 50/30 2.261 1.567
-
Av. = 1.533
kp =
+E
Time,
Time,
h
A+B+C+E
Vol. 65
5.598f ADM 0.014
5.598 - = 3,653 1. mole-' sec-1 1.533
TABLE I11
where A, B, C and D represent hydroxyl ion, di7 AS A FUNCTION OF K AND a, ester, monovalent ion of the ester and divalent ion l/K a = 0.8 0.7 0.6 0.5 0.4 of the ester, respectively. Frost and Schwemer6 0 . 0 0.1250 0.2143 0.3333 0.5000 0.7500 have integrated this kinetic system for the special .2701 .3958 .2 ,1710 .5670 .8199 case of stoichiometrically equivalent amounts of .3103 .4529 .6422 .9151 .4 ,1954 the reactants A and B ( i e . , A. = 2Bo) and have .6 ,2103 .3384 .4974 .7074 1.008 prepared tables that enable the evaluation of the ,3598 ,5334 ,7638 1.093 .8 ,2208 rate constants. Table I shows a typical time.2286 ,3767 ,5637 1.0 ,8132 1.171 concentration set of data for run #31. In this ,2346 .3902 ,5891 1.2 .8568 1.243 study, the procedure of Frost and Schwemer6 ,2395 ,4022 ,6122 .8973 1.311 1.4 was used the most frequently in the calculation of .2437 .4121 .6323 ,9343 1.378 1.6 rate constants. Values of cr (defined as A/&) .2471 ,4209 .6503 ,9684 1.441 1.8 for duplicate runs were plotted against time on a TABLE IV large sheet of graph paper. From the resulting smooth curve, the times for fixed percentages of TIMERATIOSAS A FUNCTION OF K completion were determined. Time ratios were 1/K tso/tzo teajtao teo/tra tso/tso tao/tm taoltso then calculated from these times for the various 0.0 6.000 3.500 2.250 1.500 4.000 2.333 percentages of reaction. With the use of the Frost .2 4.795 3.036 2.072 1.446 3.316 2.099 and Schwemer tables and these time ratios, values 4.683 2.949 2.021 1.425 3.287 2.070 .4 of l / K (defined as k , / k t ) were obtained for the 4.793 2.979 2.027 1.425 3.364 2.090 .6 reaction. The average 1/K value was calculated .8 4.950 3.038 2.049 1.431 3.459 2.123 and used to obtain 7 values a t the various selected 1 . 0 5.122 3.109 2.077 1.440 3.557 2.159 values of a. From the definition of 7, (ie., T = 1 . 2 5.298 3.186 2.110 1.451 3.652 2.196 Baklt), values of k, were then calculated. The 1.4 5.474 3.260 2.141 1.461 3.747 2.231 average values of kl and 1/K next were used to 1 . 6 5.654 3.344 2.179 1.475 3.834 2.267 determine kz. Table II summarizes the calcula1.488 3.919 2.301 1 . 8 5.832 3.424 2.216 tions just described for run $431. The T and time Table V summarizes the data a t 24.93'. A , ratio tables of Frost and SchTTemer do not go to 12.64 X 10-3 mole/l. below a value of 1 / K = 2, and so Tables I11 and varied from 12.10 X IV were developed' for values of 1/K from 0 to 2.0. in the various runs. Thus the data in Table V were obtained essentially under the same stoichio( 5 ) C. P. Smyth and W. S. Walls, zbad., 6.9, 527 (1931). met,ric ionic strength conditions as far as the reac(6) A. A . Frost and W. C. Gehwemer, z b z d , 74, 1268 (1952). tants are concerned. (7) B. E.Fry, 31 S.Thesis, University of Maryland, 1959.
August, 1961
ALKALINEHYUHOLYSIS OF DIETHYL X~LOSATE; I N \T-~rm-DIox.~sE TABLE V ESTERS IN
Ester
R.4Tln CONST.4NTS FOR THE HYDROLYSIS O F THE -Without Wt. % D dioxane ki
Diethyl sebacate
Diethyl succinate
42.98 34.26 17.69 13.10 10.71
40.00 50.00 70.00 76.30 80.00
60.79 51.90 49.18 34.26 17.69 13.10 10.71 9.10
20.00 30.00 33.18 50.00 70.00 76.30 80.00 82.75
1.96 1.50 0.843 .736 .783" 10.5 9.06 8.77 7.18 5.71 5.60 5.58 5.80
DIOX.4NE-W.4TER salt----
k?
--ki/kz
0.660 .533 .444 .542 .578"
2.97
1.46 1.34 1.31 1,24 2.19 3.65 3.98 6.69
7.18 G.75 6.68 5.77 2.61 1.53 1.40 1.02
hfEDIA .IT 24.93" KCI addedd ki k?
___-
133.5
---
kilkn
2,82
1.92 1.36 1.36
0.396 10.3
4.76 3.99
60.79 20.00 1IO* 0.666 165* 34.26 50.00 1186 55.76 .473 13.10 76.30 27.7 2.90 9.56 24.5 80.00 10.71 23.2 4.83 4.80 81.72 9.70 19.3 6.88 2.81 82.75 9.10 16.1 11.0 1.4G Computer calculations. Estimated values. Rate constant units are liter mole-1 minute-'. column KCl added was = 0.1454, 0.1464, 0.1472, 0.1463 and 0.1463 mole/l., respectively.
0.401
0.985
2.09
4.91
2.89 3.62
1.65
4.35
5.63
1.10
Diethyl malouate
Reading down the
Table VI summarizes the data over a temperature range in the absence of an inert electrolyte for the diethyl succinate reaction.
the particular run and the value of 1/K corresponding to this particular time ratio was obtained. The kz value for each of these particular runs was obtained from the slope of the straight line produced TABLE VI on making a 1/A us. t plot. The values of 1/A RATECONSTANTS FOR THE DIETHYLSUCCINATE REACTION used in this latter plot included only those Jralues AT DIFFERENT TEMPERATURES existing in the last 45% of the reaction. Through D dioxane m-t. % kl ki kI/kz the use of equation l6 t, oc. 60.79 34.26 13.10 10.71
16.42 46.48 75.22 79.02
19.1 13.9 11.8 12.2
2.83 2.31 6.00 7.38
6.75 6.00 1.97 1.66
24.93
60.79 34.26 13.10 10.71
20.00 50.00 76.30 80.00
10.5 7.18 5.60 5.58
1.46 1.24 3.65 3.98
7.18 5.77 1.53 1.40
14.94
60.79 34.2B 13.10i 10.71
23.45 52.27 77.38 80.92
5.03 3.58 2.66 2.78
0.717 0.633 2.03 2.13
7.02 5.65 1.31 1.31
10.27
10.71
81.34
1.83
1.54
1.19
6.31
60.79 34,26$ 13.10
26.49 54.08 78,14
2.82 1.84 1.32
0.401 0.340 1.22
7.03 5.40 1.08
34.88
The above scheme of calculation of rate constants could not be employed in the case of the diethyl malonate reaction carried out in solvents whose dielectric constant values were 60.79 and 34.26 because the reactions occurred so rapidly that we could not obtain values of the hydroxyl ion concentrations until 40% of the original hydroxide was consumed. As a we were to determine those time ratios which were defined previously in tWms of t 2 0 and t30* Therefore, We plotted the 1/K values against the corresponding as listed in the Frost and Schwemer t60/t60 tables. The resulting straight line Was extrapolated to include the experimental t 6 0 / t 5 0 ratio for
it can be shown that the diester remaining is less than 0.1% when a! = 0.45 and K = 1/120. Thus, it is evident that only the second step of the reaction is significant under such conditions. From the experimental value of lc, and the estimated kl/kz ratio for that run, a value of kl was determined. In the case of the diethyl sebacate reaction carried out in a medium of dielectric constant 10.71, the rate constants were determined using a computer technique.* This was done because the di-ion product precipitated out before t6o could be experimentally determined. Thus only tso/tzo and tS0jt~(t time ratios were available for use with the Frost and Schwemer procedure and in our opinion, two ratios were not enough. Salt Effects.-The stoichiometric ionic strength of this reaction in terms of the reacting species can be expressed by p =
-40
+D
(2)
Equation 2 indicates that as the reaction proceeds, the ionic strength of the solution increases, One would expect this increase in ionic strength to alter the second rate constantsignificantly during the course of the reaction since the second step of the reaction is supposedly between ions. Such changes in k2 should be detectable in using the procedure of Frost and Schwemer. this was not (8) Dlscusslon of this prooedure will be the subject of a later paper. W-e gratefully acknowledge the assistance of J a y Blarier a n d Michael
Rowan on this subject.
W. J. SVIRBELY AND AUGUST D. KUCHTA
1336
the case, it was concluded that changes in ionic strength during the course of the reaction did not cause a significant variation in kz. Similar observations have been made in the p a ~ tfor ~ . reactions ~ betweell ions of like charge sign. It raises the question of the necessity of swamping the "ionic strength effect" in such reactions of changing ionic strength through the use of inert electrolyte. In light of the above, it is not necessary. It is actually undesirable since it may lead to other complications. To demonstrate this latter point, salt studies using KC1 as an inert electrolyte were made under a number of environmental conditions. The mean stoichiometric ionic strength of each of the reaction mixtures was about 0.16 with the added salt and 0.013 without any added salt. Table T' includes these results on which we shall comment shortly. Thermodynamic Activation Terms.-Activation energies and the Arrhenius frequency factors (log A ) for the succinate reaction in isodielectric media were calculated through use of the least squares method applied to the linear form of the Arrhenius equntioii, namely log k = log A
E - 2.303RT ___
(3)
D
60.79
11,580 11,750 18,490 AF1* ( c a l . / m t r l ~ ~ ) 19,(iGO A S - * e.U. -25.22 A&* e.u. -28.49 log A, 9.4860 lug A * 8.7804
34.26
13.10
10.71
12,070 11,47G 18,710 19,750 -24.25 -29.77 9.7062 8.5015
13,110 0,500 18,860 10,110 -21.24 -33.95 10.3639 7.5869
13,140 10,950 18,860 19,060 -21.08 -29.17 10.4001 8.6311
3
4
Fig. l.-log
TABLE VI1 ACTIVATION E N E R G I E S AND RELATEDQUANTITIES( A T 24.93") FOR THE DIETHYL SUCCIXATE REACTION El (cal./mole) E? (cnl./mole) Mi*(cnl.,'mole)
;I 2
The results arc listed in Table VII. The free
Q
-
w
5
6 7 10O/D.
8
0
1
0
K z's. 100/D at 24.03'.
0.4
0.2 0
energy and the entropy of activation a t 24.93' v w e calculated by means of the equationsg
Vol. 65
-0.2 -0.4
(4)
1 ';.--./ ,
,,,, ~
,...---
,//,
, : 1 log1 Kz , , I;
0
'I
-0.6 2
Some of the results are summarized in Table VII. Discussion.-The variation of log kl and log kz with decrease in the dielectric constant is strikingly shown in Fig. 1and Fig. 2. While in high dielectric media there is a marked difference between the values of kl and k2 for each diester reaction, this difference disappears in low dielectric media. It is apparent that the k l / k z ratio is approaching unity. One concludes that the mechanisms of both steps of the reaction are becoming more nearly alike as the dioxane content of the medium is increased. If one plots log IC against D, one will observe that with the exception of the first step of the malonate reaction, there is evidence of linearity over two distinct dielectric ranges, with a change in slope occurring a t a dielectric value of about (9) S. Glasstone, K.J. Laidler a n d H. Eyring, "The Theory of Rate Processes." JlcOraw-Hill Book Co., Ino., New York, N. Y.. 1941, p. 19.5,
Fig. 2.-log
4
6 S l00lD.
1
0
K u s . 100/D at various temperatures for the alkaline hydrolysis of diethyl succinate.
25. Based on conductance measurements, lo evidence has been presented that ion-pairing occurs in media where the dielectric constant is equal to or lower than 30. This value of 30 would correspond to a value of 100/0 equal to 3.33. Reference to Fig. 1 shows that a t a 1OO/D value of 3 to 4,each of the log ICz curves is going through a minimum. This could be the point a t which ion-pair formation becomes important and the second step of each reaction is changing from an ion-ion reaction in media of high dielectric constant to one involving ion-pairs in media of lower dielectric constant. On going to still lower dielectric media, the formation of ion pairs or large ion clusters for both steps of (10) A. L. Jacobson and J. B. Hyne, J . A m . Chem. Soc.. 82, 2418 (1960).
August, 1901
HEATOF FORMATION OF MOLYBDENUM HEXAFLUORIDE
the reaction would be accentuated. Thus both steps of each diester reaction would be to a large extent between more similar aggregates, leading to values of the rate constants approaching each other. It should also be noted that while at high dielectrics the values of kz decrease with a decrease in dielectric constant in accordance to theory for a reaction between ions of like sign yet a t values of dielectric constant lower than 25, values of kz increase with further decrease in dielectric constant. In terms of the theory this latter observation implies that we are no longer dealing with a reaction between ions of like sign. Reference to Table V shows that on the addition of the same stoichiometric amount of an inert electrolyte, the kl/kz ratios decreased in all cases from the values obtained in the absence of the inert electrolyte. However, the magnitude and the direction of the salt effect depend on the medium, the reaction step and the diester or monoester ion involved. In the same medium of D = 13.1 for all three diester reactions, there was a negative salt effect on the first step of the reaction, its magnitude being proportionately larger, the larger the diester. However, in the same medium, the salt effect on the second step of the reaction was negative, zero and positive for the sebacate monoester, succinate monoester and malonate monoester reactions, respectively. Considering the fact that the basic differlence in the three diesters is size, thus leading to various distances between the attached ester groups, we believe that this structural difference makes a difference in the extent and nature of the ion-pairs or aggregates formed with the ions of the added electrolyte and is reflected in the nature of the observed salt effect. In the high dielectric media, D = 60.79, the second step of the succinate reaction showed a positive salt effect, an observation in accordance with theory for a reaction between ions of like charge sign.
1337
A comparison of calculated free energies of activation shows that the free energies of activation of the two steps in each of the diester reactions approach each other as the dielectric constant of the medium is lowered. If one accepts the argument that the free energy of activation is a measure of the coulombic interaction in the formation of the activated complex, again one must conclude that the two steps of the reaction become more nearly alike as the dielectric constant is lowered. Thus it is evident that our results can be explained by ion-association. The extent and the nature of the ion aggregates formed would depend on the reactants and the dielectric constant of the medium. It would also be affected by the presence of an added inert electrolyte. It is not expected that the activation energies would be nearly the same for both steps of the reaction a t any one dielectric constant unless we are dealing with the same kind of aggregates in both steps. Having obtained constancy in the activation energy for any step in two different media implies that we are now dealing with the same kind of aggregates in the two media. Several of the kl/kz ratios were used to calculate “T” by means of Ingold’s equation,” namely k1 = 2ed/DrkT kn
While acceptable values of Y ’ are obtained in high dielectric media (D = 60.79) the results are meaningless in low dielectric media. The effect of the media on the kl/k2 ratios clearly demonstrates the inadequacy of Ingold’s equation as a general equation. Acknowledgment.-We wish to express our appreciation to E. I. du Pont de Nemours and Company for the du Pont Fellowship held by A. Kuchta from 1959-1960. (11) C. K. Ingold, J . Chem. SOC.,1375 (1930).
FLUORISE BOMB CALORIMETRY. 11. THE HEAT OF FORMATION OF MOLYBDENUM HEXAFLUORIDE’ BYJACKL. SETTLE, HAROLD M. FEDERAND WARDN. HUBBARD Chemical Enginewing Division,Argonne National Laboratory, Argonne, Illinois Received February 8 , 1961
The heat of formation of molybdenum hexafluoride was measured by direct combination of its elements in a bomb calorimeter. AHf“at 25’ of molybdenum hexafluoride gas was found to be -372.36 f 0.22 kcal. mole-’.
Introduction This Laboratory has undertaken to obtain precise thermochemical data for refractory substances such as the borides, carbides, nitrides and silicides of the transition metals, the rare earth metals, uranium and thorium. Typical of the substances to be studied are the borides and silicides of molybdenum which have recently achieved technological importance. Because of the difficulty of obtaining well-defined products by combustion of these substauces in oxygen, or by solution or (1) This work was performed under the auspices of the U. 6. Atomic Energy Commission.
synthesis reactions, an alternative technique, namely, combustion in fluorine has been proposed2 for calorimetry. To determine the desired heats of formation by fluorine combustion calorimetry, however, it is necessary to have available the heats of formation of R!IoF6, BFa and SiF,. The heat of formation of BF, has recently been determined3 with an estimated over-all uncertainty (2) E. Greenberg, J. L. Settle, H. M. Feder and W. N. Hubbard, J . Phys. Chem., 66, 1168 (1961). (3) 9. Wise, W. N. Hubbard, H. M. Feder and J . L. Margrave, “Fluorine Bomb Calorimetry: 111. The Heat of Formation of Boron Trifluoride.” to be published.
