NOTES
380
'
DETERMINATION OF THE RATE CONSTANT RATIOS I N THREE-STEP COMPETITIVE CONSECUTIVE SECONDORDER REACTIONS BY W. J. SVIRBELY Contribution from the Chemistry Department, University of Maryland, College Park, Mar~Eand Received December 491967
Recently, McMillan described a procedure 'in which the ratio of the rate equations for a twostep competitive consecutive second-order reaction was solved so as to yield the rate constant ratio as an implicit function of any two simultaneous concentrations of components other than that of the reactant common to the two steps. In this paper, we have applied the same analysis to a three step competitive consecutive second-order reaction. The pertinent reactions are illustrated by kl
A+B+C+E
kz
A+C+D+E kr
A + D + F + E
As in the previous case,' we shall only be interested in obtaining our results from a knowledge of the concentrations of components other than A. The rate equations for B, C and D are
Vol. 62
equation 7. If 9 is measured simultaneously, or for any other measured pair ( p , ~ )of experimental concentrations, and from a knowledge of K one may find the value of J which satisfies equation 8. The KJ product would yield the k3/kl ratio. ETHERATES OF LITHIUM BOROHYDRIDE. 111. THE SYSTEM LITHIUM BOROHYDRIDE-DIISOPROPYL ETHER BY JOHNJ. BURNS,S.J.,AND GEORGE W. SCHAEFFER The Department of Chemistry, St. Louis University, S t . Louis. Misaouri Received November 18, 1967
Pressure-composition isotherms a t 0, 10, 15 and 20" for the system lithium borohydridediisopropyl ether have been determined. The data, listed in Table I, are clear evidence for the existence of a single solid etherate in the temperature range examined. The abrupt pressure change a t lithium borohydride mole fraction (nz) of 0.50 denotes a phase transformation between lithium borohydride mono-(diisopropyl etherate) and lithium borohydride and the absence of discontinuities
+
LiBH4.0[CH(CHs)2]2(~) = LiBH4(e) . [(CH&CHI sO(d (1)
at nz = 0.33 and 0.67 shows that neither a bis(diisopropyl etherate) nor an hemi-(diisopropyl etherate) of lithium borohydride exists in the dB _ dt - -kiAB temperature range, 0 to 20°, examined. I n this regard the lithium borohydride-diisopropyl ether = klA(B - KC) (2) system is in distinct contrast to the lithium borohydride-dimethyl ether system in which both a dD = kzA(C - JD) stable bis-(etherate) and hemi-(etherate) are (3) formed.' The present system resembles the lithium respectively, where K = k 2 / k l and J = k3/kt. borohydride-diethyl ether system in not forming a I n terms of the dimensionless parameters stable bis-(etherate), but is distinguished from this latter system in that no hemi-(etherate) is found.2 The heat of dissociation of lithium borohydride The ratios of equation 2 to 1 and of equation 3 to 1 mono-(diisopropyl etherate) into lithium borohybecome dride and the ether, equation 1, was determined from the dissociation pressures a t various temperatures. The data are well represented by the simple linear relation log p m m = 11.274 - 2772.0/T The solution of equation 5 is given by as can be seen by the comparison of Table 11. Values for the various thermodynamic quantities y = k ' - 1 (1 - j3K-I) (7) associated with the dissociation process a t 25" where the constant of integration was determined described by equation 1 are A H d = 12.68 kcal./ by the initial condition that when 6 =: 1, y =O. mole; A F d = 1.24 kcal./mole and A& = 38.4 Substitution of equation 7 into 6 yields an equation e.u. These values may be combined with data which on integration gives for lithium borohydride3 and diisopropyl ether4
(1
- JK)(l
- J)
where the constant of integration was determined by the initial condition that when p = 1! q = 0. As in the case of the two step reaction, for any measured pair (p, 7) of experimental concentrations, one may find the value of K which satisfies (1) W. G. McMillan, J . A m . Chem. SOC.,79, 4838 (1957).
(1) G . W. Schaeffer, T. L. Kolski and D. L. Ekstedt, J . A m . Chem. Soc., 79, 5912 (1957). (2) T. L. Kolski, H. B. Moore, L. E. Roth, K. J. Martin and G. W. Schaeffer, ibid., 80, 549 (1958). (3) AH: = -46.36 kcal./mole: AFf = -30.74 kcal./mole: and Sa = 18.13 e.u. Taken from "Thermodynamic Properties of Boron Compounds at 2 5 O , " National Bureau of Standards, Washington 25, D. C., April. 1954. (4) For diiaopropyl ether the following values were employed: AH: = -69.8 kcal./mole (calculated by a modified Franklin method, c f . G. W. Wheland. "Resonance in Organic Chemistry," John Wiley and Sons, Inc., New York, N. Y., 1955, pp. 94-96): So = 70.4 e a . (G.S. Park and H. M. Huffman, "The Free Energies of Some Organic
March, 1958
NOTES
381
here extended to include ions. For a boron hyTABLE I DATAFOR PRESSURE-COMPOSITION ISOTHERMS AT VARIOUS dride BpHp+,, containing s H bridges, x extra TEMPERATURES FOR THE SYSTEMLITHIUMBOROHYDRIDE- B-H groups, t three-center BBB bonds and y twocenter BB bonds, the equations of balance may be DIISOPROPYL ETHER 8
0.00 10.00 15.00 20.00 Camp., Press., Comp., Press., Camp., Press., Camp., Press. ni mm. nl mm. np mm. nz mm.
0.128 ,143 ,163 ,232 ,295 .366 .464 .485 .496 .502 507 .510 .512 .630 .666 ,906
4 4 . 8 0.128 7 5 . 2 0.143 95.4 0.129 120.5 44.6 .297 7 5 . 2 ,164 9 5 . 4 ,144 119.9 4 4 . 4 .337 7 5 . 0 .298 95.5 .194 119.4 4 4 . 3 .490 7 3 . 6 .339 9 5 . 4 .235 119.5 44.3 .512 36.8 .471 94.5 .299 119.4 44.2 .515 2 9 . 6 .493 9 2 . 4 .373 119.4 43.9 ,634 30.2 ,503 80.0 ,475 119.0 4 3 . 4 ,672 30.3 .513 46.1 .497 113.9 4 3 . 0 ,732 3 1 . 0 .641 44.5 .504 87.0 41.0 ,915 30.8 ,675 4 4 . 5 506 68 0 33.5 ,739 45.4 .517 6 6 . 3 24.2 .923 44.5 , 5 2 2 ' 65.1 16.5 ,645 65.1 13.2 .681 65.0 13.2 ,743 6 6 . 0 13.6 .935 65.2
to allow calculation of the standard heat of formation, standard free energy of formation and absolute entropy a t 25" for lithium borohydride mono(diisopropyl etherate). The values so obtained are: AH: = - 128.9 kcal./mole, AF! = -55.5 kcal./mole and So= 75.6 e.u. TABLE I1 DISSOCIAT:ON PRESSURES OF LiBHn.0 [CH(CH3)2]2 t , "C. 0 10 15 20 pmrn (obsd.) 13.2 30 2 44.5 65.1 pmm(calcd.) 13.2 30.1 44.6 65.0 Experimental The apparatus and techniques are described in the monograph of Sanderson' and in a revious paper.' (a) Materials.-Lithium Rorohydride was purified in the manner previously described. Diisopropyl ether was refluxed over lithium aluminohydride for ten hours, fractionated (67.0-67.4" a t 752 mm.) and introduced into the high vacuum system. The ether was further dried over LiAlHd (20 hours) and LiBH4 (16 hours) and it was then fractionated through traps held a t -78, -112 and -186'. The -112' fraction exhibited a vapor pressure of 155 mm. a t 25". (b) Determination of the Isotherms.-For the measurement of diisopropyl ether quantities, the pressure of the sample was kept a t less than one-half its saturation pressure a t room temperature to minimize deviations from ideal gas behavior. Temperature control was maintained within 0.1 degree by a small constant-temperature water-bath around the sample tube above 0.0" and by a water-crushed ice-bath at 0.0". Compounds," Chemical Catalog Company, New York, N. Y.,1932, P. 169); A F f = -23.5 kcal./mole (calculated from above values); AH(vaporiration) = 7.61 kcal./mole (estimated from vapor pressures of D. R. Stull, Ind. Eno. Chem., 39, 525 (1947)). ( 5 ) R. T. Sanderson, "Vacuum Ivlanipulation of Volatile Comt)ounds," John Wiley and Sons, Inc., New York. N. Y . , 1948.
POSSIBLE BORON HYDRIDE IONS BY WILLIAMN. LIPSCOMB School of Chemistry, University of Minnesota, Minneapolis 14, Minnesota Received November 1 1 , 1967
The present form of the topological theory of boron hydrides by Dickerson and Lipscomb' is
written in a simplified form as follows. The hyx = q. Since drogen atom balance is simply s each boron supplies four orbitals but only three electrons the total number of three-center bonds in the molecule is the same as the number of boron atoms, s t = p . Finally if we consider BH as the bonding unit, each of which then supplies one electron pair, these p pairs are used up as three-center BBB bonds, two-center BB bonds, and in supplying half of each pair to each extra hydrogen, Le., p = t y q/2. It is quite easy to extend these equations to include a description of ions of the type BpHcp+q+c,where c is the charge including its sign. The resulting generalization may be formulated as
+
+
+
s + x = q + c s+t=p+c
An examination of ions based on icosahedral, octahedral and tetrahedral polyhedra and fragments has been made for c = -2, -1, fl and +2. These ions supplement our earlier predictions' for c = 0, and are described by listing the numbers s, t, y and x just preceding the appropriate molecular formula. 1. Ions Similar in Geometrical Structure to Known Hydrides.-The 4450 BloH14-2 ion of Czvsymmetry is the only ion of this type, and is probably the most interesting of all of the ions. Except for a probable contraction of the two 2.0 A B. .B contacts toward a more normal value, the geometry of this ion is probably very similar to that of the well known 4620 B10H14structure. 2. Ions Similar in Electronic Structures to Known Hydrides.-The prediction2 of the B5H9likeions B4H7- and B6Hll+ was based upon analogies of these compounds to C & , , C&- and C7H7+. Equivalent orbital transformations reduce these to 3030 B4Hy- and 5210 B6Hll+ in the present description. 3. Ions Derived from Known Hydrides by Removal of H+ from a BHB Bridge Bond.-These structures satisfy our rules if the electron pair is used to form a B-B bond. It is obvious how a list of these ions can be made from the known and hypothetical neutral hydrides, and hence such a list will not be given here. However the 2013 BaHe- iona is probably either a member of this class or of Class 4. 4. Ions Derived from Known Hydrides by Removal of H+ from a B-H Terminal Bond.-Terminal hydrogens tend to be less negative4 than bridge hydrogens, and might ionize off more readily, although the resulting ion usually does not have as satisfactory a valence structure as the ion produced (1) R. E. Dickerson and W. N. Lipscomb, J . Chem. Phys., 81, 212
-
(1957).
W.N. Lipscomb, J . Chem. Phys., 28, 170 (1958). (3) W.V. Hough, L. J. Edwards and A. D. McElroy. J . Am. Chcm. Ane., 78,fiRR (19.56). (4) W. C. Hamilton, €'roc. Roy. S o c . ( L o n d o n ) , AX%, 395 (1956). (2)
