THEEXPLOSIVE OXIDATIONOF DIBORANE
May, 1956
638
barrier hindering internal rotation in CH3CF3. the wireribbon method here described gives Since potential barriers are calculated from small accurate heat capacity values which can be used differences between two experimental quantities, directly with spectroscopic data to verify the the possible error is always large, 200 cal./mole assignments of fundamental vibrational frequencies for a 0.02 cal./mole/deg. error in the torsional and to estimate potential barriers hindering component of the heat capacity; and thus our internal rotation. value agrees well with those calculated by others: Acknowledgments.-The authors wish to ac3290 cal./mole by Nielsen, Claassen and Smith,lS knowledge the financial support of the Purdue 3450 cal./mole by Russell, Golding and Y ~ s t ’ ~Research Foundation and The Proctor and Gamble and 3250 cal./mole by Thompson and Temple.la Company in the form of fellowships, and to thank The results of this investigation have shown that H. Susi, Chemistry Department, Purdue University, for the purified sample of l,l,l-trifluoroeth(19) H. Russell, D. R. V. Golding and D. M. Yost, J . Am. Chem. ane. SOC.,66, 16 (1944).
THE EXPLOSIVE OXIDATION OF DIBORANE BY WALTERROTHAND WALTERH. BAUER Walker Laboratory, Rensselaer Polytechnic Institute, Troy, New York Received November 11, 1055
Studies on the oxidation of diborane a t the second pressure explosion limit have been extended. The effects of the addition of varying amounts of Nz,Het A and Hz to the stoichiometric mixture have been investigated. The results are shown to sup ort a reaction mechanism involving bimolecular chain branching and trimolecular chain breaking. The gases, Nz, He an$ A are shown to act as third bodies in excellent agreement with thew behavior predicted by collision theory. The B z H+ ~ BsH, HZoccurs to a small extent, and that results of hydrogen addition indicate that the reaction BHs there is a competition between the reactions 0 B z H + ~ BH20H BHs and 0 HZ+OH H for the removal of oxygen atoms.
+
+
+
++
+
The pressure’s2 and compositiona explosion means for testing the validity of the trimolecular limits have been studied for mixtures of diborane chain breaking postulate. For example, the effect and oxygen. A mechanism for the reaction a t the on the second limit explosion temperature of adding second pressure explosion limit was proposed. varying amounts of inert gases to a mixture whose ~ O P remains constant permits a calculaThis work represents an extension of the experi- ~ B . ~ H ~ / ratio mental studies a t the second pressure explosion tion of relative efficiencies of the inert constituents limit and provides additional support for the as third bodies in chain breaking. These efficiencies may then be compared with those calcusuggested mechanism. The mechanism proposed2for the second pressure lated from collision theory. limit explosion involves bimolecular chain branchExperimental ing and trimolecular chain breaking reactions. Nitrogen.-Matheson prepurified nitrogen (99.9% purity) Steady-state assumptions permitted the simplified was allowed to flow slowly through a series of two liquid nitrogen cooled traps and directly to a glass storage vessel. limit expression
The initial storage pressure was about one atmosphere. Helium.-Airco reagent helium in a 1-liter Pyrex breakto be derived. Here (M) is the total concentra- seal vessel a t one atm. was used without further purification. Mass s ectrometric analysis by the manufacturer indicated tion a t the second limit and f~ are mole fractions. the fofowing impurities: oxygen, 0.001, nitrogen and/or kl is the rate constant for the reaction carbon monoxide, 0.015, argon, 0.001, carbon dioxide, 0.001, and hydrocarbons, 0.005 mole per cent. BHs 0 2 --t BHzOH 0 (1) Argon.-Arco reagent argon in a 1-liter Pyrex break-seal vessel at one atm. was used without further purification. k i , is ~ the rate constant for the reaction Mass spectrometric analysis by the manufacturer indicated BHs 0 2 M +HBOz 2H M (2) the following impurities: hydrogen, 0.004, nitrogen and/or and is dependent on the nature of the third body, M. carbon monoxide, 0.004,oxygen, 0.002, and hydrocarbons, mole per cent. Equation (a) may be expanded and rearranged to 0.005 Hydrogen .-Matheson electrolytic hydrogen was passed give through a De Oxo filter to remove oxygen and then through a series of two liquid nitrogen cooled traps and directly to a fE~,HdfOi ~2,02/kZIB2H.3 h , M / h , B & .fM/fOp glass storage vessel. The initial storage pressure was one = CTdjo, exp (-AE/RTa) (b) atm . Diborane and oxygen were prepared and purified as preM represents any third body except BzHe or 02.viously described.* A E = E1 - E2,the difference between the activaMixtures were prepared on a pressure basis. Detailed tion energies of reactions (1) and (2). C is a con- description of the apparatus and the heatin method for stant and T2 is the second limit temperature, both determining explosion limits have been reportef previously.2 only alteration in the procedure waa in the method for a t constant pressure. This equation provides a The cleaning vessels when the solid coating of reaction products (1) F. P. Price, J . A m . Chem. Soc.. 71, 5361 (1950). became too heavy. Previously these had been treated with (2) W.Roth and W. H. Bauer, “Fifth Symposium on Combustion,’’ methyl alcohol, hot cleaning solution, distilled water and Reinhold Publ. Corp., New York, N. Y. steam. In this work, it was found equally effective to flame (3) A. J. Whatley and R. N. Pease, J. A m . Chem. Soc., 7 6 , 1997 the vessels during evacuation in order to remove coatings. (1954). Treatment of vessels in this manner caused a small shift in (M) = 2kl/%,MfM
+ + +
+
(a)
+ + +
+
+
WALTERROTHAND WALTERH. BAUER
640
+
the second limit for the pure stoichiometric mixture, BZH6 302. Therefore, the effect of inert gas addition was determined by comparison with the result for BZH6 $309 in a flame treated vessel. Explosion limit temperatures at constant pressure were compared rather than explosion limit pressures at constant temperature for reasons previously discussed.* The constant pressure chosen was 23 mm. It represented a point 302 about midway between on the second limit for BZH6 the first and third limits. Since only explosion limit temperatures at 23 mm. were significant, entire limit curves were not determined. Instead, linear interpolation of several points around 23 mm. was used to give the required value. In view of the steepness of the limits, linear interpolation could not have resulted in errors greater than f0.5’.
.+
Vol. 60
bodies in the chain breaking reaction,’ Le., h,H,,/ k a , ~ ,= 1. It is interesting to compare this with the relative third body efficiencies calculated from collision theory. Thus, Tolman4 derived an expression for the termolecular collision frequency from which it can be shown that
Subscripts 1 and 2 refer to BzHa and 02, respectively. Subscripts 3 and 4 refer to He and Nz, respectively. u is the mean of molecular diameters and I-C is the reduced mass. Substitution of a Results range of molecular diameters calculated from Second limit explosion temperatures for stoichio- viscosities and lists in several different tables and a metric mixtures of diborane-oxygen containing molecular diameter for .B*Hs estimated from its approximately 5, 10 and 20y0 of Nz, He, A and Hz liquid density gives a range for Z H ~ / Z from N ~ 0.97 were determined a t a pressure of 23 mm. Results to 1.05. This is in agreement with the experiare given in Table I. Results for NZand He were mentally determined value of kZSHe/k2.N2. Equation (b) may be applied to the results obTABLEI tained from argon addition experiments. If E EFFECTOF ADDED GASES ON SECOND LIMITEXPLOSION is assumed equal to zero and TZ/fo, is plotted TEMPERATURE OF B9Hs + 302 against fdfo,, the straight line shown in Fig. 1 is Mo!e Explosi.on obtained. Here, the slope, S, is equal to C’(~Z,A/ fraction temp. Gas added at 23 ~ z , B , H @and ) the intercept, I,is equal to C’ [(fB2Ha/fOr) mm. added gas (~z,O,/kz,B,H,)]. Therefore 171 A 0
+
Hz
0.058 0.116 0.214 0 0.055 0.101 0,198
165 158 161 171 164 160
(kz,A/kmzHa)
=
+
(s/l)(f~~~s/f~s) (ks,odkz,Bd
It was found previously2 that E 6 2 kcal./mole. The assumption that it is equal to zero, however, does not significantly affect the ratio ( S / I ) . I t
~HJ also was shown previously that ( ~ Z , O ~ / ~ Z , B h 1.50. Therefore, since ( ~ B ~ H J ~ Owas J always 0.33 177 k z , a / k z , B s a s 2 1.83(5/1) (d) constant within experimental error. These gases Using the method of least squares, the best straight could therefore be considered to have no significant line of Fig. 1 has a slope equal to 407 and an intereffect on the second explosion limit. Argon and cept equal to 586. Thus, kZ,A/k2,BsH6 2 1.27. hydrogen, however, clearly exert a significant A somewhat simpler treatment of the results from Nz addition is possible since this had no significant effect on the limit. effect on the second limit explosion temperature, Discussion The equivalence of behavior of He and NZ If equation (b) is multiplied by fopand then differindicates that they are equally effective as third entiated with respect to fos and the condition dT,/dfo, = 0 applied, the equation
dfem I @os
kz.02
kzlB2Hs
+-kz
NI dfN0 X~ z , B , H @ dfo,
=
+
is obtained. Further, if the conditions fJ+ fo, 4- fN, = 1 andfB2H8/fo2= 1/3 are applied, it is , B 1.38. ~ H ~ The minimum found that ~ z , N ~ / ~ ~ h values k2,A/k2,B2He = 1.27 and ~ z N ~ / ~ ~=, 1.38 B ~ are H ~ for the condition A E = 0. If these are compared, it is found that kZ,A/k2,N2 = 0.92. This ratio is clearly independent of the actual value of A E . Application of equation (e) to this case gives a range of ZA/ZN~ from 0.88 to 0.92 in excellent agreement with the experimental value. The agreement with collision theory constitutes strong evidence in favor of trimolecular chain breaking in the second limit explosive reaction of 1 I I I I BzHs and 02.The existence of a second pressure 0 0.1 0.2 03 04 limit in branched chain explosions has necessitated fdfG8 the assumption that chain breaking reactions are of Fig. 1.-The effect of mixture composition on a function of the second explosion limit temperature at a pressure of a higher molecularity than chain branching reactions.6 If the former are trimolecular, therefore, 23 mm. the latter must be bi- or unimolecular. Uni(4) R. C. Tolman, “Statistical Mechanics with Applications to Physics and Chemistry,” A.S.C. Monograph, Chemical Catalog CO.. New York, 1827, pp. 248, 327.
(5) B. Lewis and G. von Elbe, “Combustion, Flames and Explosions of Gases,” Academic Press, New York, N. Y., 1951, p. 29-30.
A MODELFOR CROSS-LINKED POLYELECTROLYTES
May, 1956
molecular branching is inconceivable for the system under discussion in view of the pressures and the chemistry involved. Chain branching is thus probably bimolecular as was proposed.2 Addition of Hz up to a mole fraction of 0.10 caused a decrease in explosion temperature. However, for a hydrogen mole fraction of 0.20, the explosion temperature increased. These results are explained by assuming that Hz at relatively low concentration inhibits the reaction BHs
+ BZHB+BaHi + Ha
(3)
This reaction may normally remove the chain carrier, BH3, to a small extent. Inhibition of reaction2 would result in the observed decrease in explosion temperature. At higher Hz concentration, oxygen atoms may be removed in the well known reaction O
+ Ha --+
OH
+H
(4)
followed by
641
+ Hz +HzO + H + + M + HOa + M
OH
H
(5)
(6)
0 2
This would result in the increased explosion limit temperature which was observed when hydrogen concentration was increased sufficiently. It appears, therefore, that reaction (4)and 0
+ BzHa +BHZOH + BHa
(7)
compete for the removal of 0-atoms when the system contains hydrogen. Further, the validity of the foregoing would indicate that reaction (3) is not entirely negligible at the second explosion limit as was previously assumed. Indeed, the increasing importance of reaction (3) as the B2He concentration increases may explain the corresponding change in the slope of the second limit as (B2He)/(02) is increased.2
A MODEL FOR CROSS-LINKED POLYELECTROLYTES1 BY LEONL A Z A R EBENSON , ~ ~ R. SUNDHEIM~~ AND HARRY P. GREGOR Contribution from the Department of Chemistry of the Polytechnic Institute of Brooklyn, New York, and the Department of Chemistry, Washington Square College, New York University, New York Received November 16, 1066
The swelling behavior of cross-linked polyelectrolytes is treated from the oint of view of a non-ideal membrane equilibrium. I n addition to osmotic effects and restraints provided by the cross-lids the effect of the charge of the network on the swelling equilibrium is taken into account. Numerical results are obtained for typical values of parameters of the system.
Introduction Experimental studies of the swelling behavior of cross-linked polyelectrolytes such as ion-exchange resins immersed in salt solutions of varying concentrations indicate that these systems may be considered as a charged polymeric network and an internal solution consisting of interstitial water, counter-ions and diffusible electrolyte in equilibrium across a thermodynamic phase boundary with the ambient s ~ l u t i o n . The ~ behavior is best described by plotting the swollen volume of one gram of dry resin, vel and the apparent mean , the mobile (rational) activity coefficient, f i ~ of ions in the internal solution as functions of the external electrolytic concentration. This apparent activity coefficient is obtained indirectly from concentration measurements, according to the following defined relationship, in which corrections arising from differences in standard states or osmotic-pressure are omitted. where X ) and Xi- are the mole fractions of the cations and anions in the internal (i) solution, (1) Based on a diasertation submitted by Leon Laeare in June, 1954, to the Graduate Faculty of the Polytechnic Institute of Brooklyn in partial fulfillment of the requirements for the degree of Doctor of Philoaophy i n Chemiatry. (2) (a) Chemical Construction Corporation, New York, N. Y. (b) New York University, New York, N. Y. (3) H. P. Gregor, F. Gutoff and J. I. Bregman, J . Colloid Sci., 6 , 245 (1951). (4) f*& is a calcd. quantity, not strictly thermodynamic in nature.
including counter-ions, but not fixed charges, while Xo* = (XO,XO_)'/zis the mole fraction of the ions in the ambient solution ( O ) . The calculated relationships, which for any given resin differ somewhat for different salts, show the general behavior of Figs. la and lb. The strong variation of and its very low value for low external concentrations should be particularly noted. Deviations from ideality in the usual Debye-Huckel sense cannot account for"this behavior. Thermodynamic Treatment For simplicity, it is assumed that the diffusible salt is a 1-1 electrolyte, that the ionized groups fixed to the polymeric network are univalent and that all mobile ions of the same sign are identical. We confine our analysis to that quantity of swollen I
I X;
.
L
x;
.
Fig. 1.-(a left) Swelling and deswelling of ion exchange resins of high and low cross-linka e. Generalized curves based on data of Gregor, et al. (ref 3). ( b right)-Mean internal activity coefficients of ions absorbed in ion exchange resins of high and low cross-linkage as functions of the salt activity in the external solution. Generalized curves based on data of Gregor, et al.
