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 =: 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
