NOTES
Sept., 1963 BRIDGE PROTON-TERMINAL PROTON COUPLING IN DIBORANE
1937
A
B
TMS
TMS
BY DONALD F. GAINES,RILEYSCHAEFFER, AND FRED TEBBE Contribution N o . 114.9 from the Department of Chemistry, Indiana Universaty, Bloomzngton, Indzana Recezved M a y 9. 1965
Early IH n.m.r. spectra of diborane a t 301v2and 401 L1c.p.s. were obtained under conditions such that it was not pos6,ible to achieve high resolution. The bridge proton resonance falls largely underneath the terminal proton resonance lines at these frequencies and only the gross features of the exposed part of the bridge proton resonance lines are observable. Proton spectra of both isotopically normal and 96% loB diborane have been obtained in these laboratories at 60 1fc.p.s. At this frequency the bridge proton group is largely shifted away from the terminal proton peaks, and with good resolution coupling between the bridge and terminal protons can be observed.
c
D
Experimental The samples of diborane for lH and IIB spectra were contained in 5-mm. o.d. Pyrex tubing a t a pressure of about 15 atm.; for 10B spectra the O ' B enriched diborane3 was contained in 15-mm. Pyrex tubing a t a pressure of about 10 atm. The spectra were obtained using a Varian Model 4300B high resolution spectrometer operating at 60, 19.5, and 6.44 Mc.p.s. for 'H, llB, and 'OB, respectively.
Results spectrum of isotopically normal diborane The (Fig. 1A and B) consists of four lines of nearly equal intensity, arising from terminal protons coupled with IlB ( I = 3/2), partially overlapping the seven-lined group (theoretical intensities are 1:2:3:4:3:2:1) that arises from bridge protons coupled with two I1B's. (Chemical shifts and conp!ing constants are listed in Table I.) I n addition the bridge protons are coupled with the four equivalent terminal protons so that each of the seven bridge proton resonances is split into a quintet. Each resonance line arising from terminal protons should be split into a triplet with the coupling constant the same as that observed for the bridge protons. This coupling has not been observed, probably because the much stronger coupling between the boron and the terminal protons, together with the less symmetric field a t the terminal positions, produces sufficient broadening ol the line to mask the proton-proton coupling. The other lines observed in the spectrum result from the coupling of protons with the 20y0 loB in isotopically normal diborane, as previously discussed.] The IH spectrum of 96% loB diborane (Fig. 1C and D) consists of seven equally intense lines arising from terminal protons coupled to loB (I = 3) and a broad upfield group with visible fine structure arising from bridge protons coupled not only with two borons (which produce 13 lines with theoretical intensities of 1:2: 3 :4 : 5 :6 :7 :6 :5 :4 :3 :2 :1) but also with the four terminal protons, whiclh should split each of the 13 lines into a quintet. As the proton-proton coupling constant is about 7 C.P.S.and the IHb--l0B coupling constant determined from the loBspectrum is 15.1 c.P.s., the resulting (1) R. A. Ogg, J Chen. Phys., 22,1933(1954). (2) J. N.Shoolery, Dascusszons Faraday Sac.. 19,215 (1955).
(3) Prepared from CaFPBFa obtained from Oak Ridge National Laboratories.
Fig. 1.-Proton n.m.r. spectra of diboranes: A, isotopically normal diborane; B, isotopically normal diborane, bridge region; C, O ' B diborane; D, O ' B diborane, bridge region.
overlapping composite is complex and would be expected to appear RS a hump with about thirty visible lines. The extraneous downfield peak is due to lrB impurities; the dissymmetry of the 'Hb-lOB hump is probably due to traces of silane as well as to the lLB impurities. The ratio of B-I& coupling constants for *lB and "'B is 3.035, in fair agreement with the value 2.986 for the ratio of gyromagnetic ratios of IlB and lOB.4 TABLE I
-
CHEMICAL SHIFTSAND COUPLING CONSTANTS FOR DIBORANE, P-------BHZ----
-
6 3.95
Isotopically 'Ha normal 1lB5
-17.5
96% 10B
-
lHa
BHH J 46.1 46 rt 2
r--
J 135 rt 2 135rt 2
3.35 44.5rt 1 44.9 1
*
6
f0.53
+0.43& 0 1
H..H J
70
15 7 15.1 rt 0.5
a Chemical shifts are in p.p.m. relative to (CH&Si. I, Chemical shifts are in p.p.m. relative to BF3.0(CzH&. Previous values have been published by: W. D. Phillips, et al., J . Am. Chem SOC.,81, 4496 (1959); T. P. Onak, et al., J . Phys. Chem., 63,1533 (1959); D. Gaines, Inorg.Chem., 2,523 (1963), and ref. 1 and 2.
The only other examples of nuclei coupling through boron are the 'H spectra of dimethylphosphine borane, (CH3)2HPBH3,2 and partially deuterated potassium b~rohydride.~I n dimethylphosphine borane the boron protons are coupled to phosphorus with J = 12 C.P.S. I n partially deuterated potassium borohydride the deuterium-hydrogen coupling constant is 1.7 C.P.S. and the calculated proton-proton coupling constant is (4) J. A. Pople, W. C. Schneider, and H. 5. Bernstein, "High Resolution Nuclear Magnetic Resonance," McGraw-Hill Book Co., Inc., New York, N. Y., 1959,pp. 4 and 480. (6) R. E. Mesmer and W. L. Jolly, J . A m . Cheham. Soe., 84,2039 (1962).
NOTES
1938
10.7 C.P.S. Diborane may be the oiily boron hydride in which proton-proton coupling can be directly observed. In most cases bridge proton-boron interaction is so weak that the coupling produced is not large enough to be resolved; bridge proton-terminal proton coupling likewise would be small and probably unresolvable. Acknowledgment.-This work was supported by the National Science Foundation, Grant G-14595, and by the Army Research Office (Durham), Grant DA ARO(D)-31-124-G99. TEMPERATURE DISTRIBUTIONS I N REACTION VESSELS BY ROBERTG. MORTIMER Department of Chemistry, University of California, L a Jolla, Califo,mia Received May 4, 1968
It has been recognized2 that significant temperature gradients can occur in reaction vessels immersed in constant temperature baths. If convection can be neglected, if concent'ration gradients are small, and if there is only one rate-limiting step in the reaction, the temperature distribut'ioii in a reaction vessel very nearly obeys the eauation3 bT/bt
=
+ CR&/pc
(K/pc)VzT
(1)
Here T is the remperature, t is the time, K is the coefficient of thermal conductivity of the system, @ is the rate of the reaction per unit volume, Q is the heat of reaction (taken as positive if the reaction is exothermic), p is the density, and c is the specific heat of the system. Benson2 has treated the case in which a,Q, p , c, and K may be assumed constant, solving eq. 1 for a spherical reaction vessel. Zatzkis4 has presented a solution to eq. 1 for a spherical vessel imbedded in an infinite medium. He takes the heat evolution inside the sphere to be time-dependent, but if this dependence is replaced by a step-function and the conductivity of the ext'ernal medium is made to approach infinity, the case of Benson is obtained. However, in this limit, the formal solution of Zatzkis does not approach that of Benson, nor does it obey the boundary conditions. Wilson3 has obtained a steady-state solution (setting dT/bt = 0 in eq. 1) for a linear temperature dependence. The solutions for most of his vessel configurations were also obtained by Jakob.5 Wilson assumes &, p , c, and K to be constant, but to have a temperature dependence given by CR =
&7(3
+ Er/RT02)
ture gradient, which for this approximation must of course be much less than the time required for the reaction to reach equilibrium. The purpose of this note is to present a nonsteadystate solution of eq. 1 for the case of Wilson. We solve first for the case of a spherical reaction vessel of radius a and positive &. We assume that E is always positive. The steady-state solution is3 rr, =
(pa
=
(1) Work supported in part by t h e U. S . Atomio Energy Commiesion. (2) 5. W. Benson, J . Chem. Phge., 22,46 (1954). (3) D.J. Wilson, J. Phys. Chem., 62,653 (1958). (4) H.Zatzkis, J. A p p l . Phye., 24, 895 (1953). (5) M. Jakob, Trans. Am. Soc. Mech. Enar., 66, 593 (1943); 70, 25
(
RTo2 a sin y r ___ E sin y a
-
-T)
(3)
where r is the distance from the center of the vessel, and where y2 = /3 = (RoQE/KRTo2.Kote that this solution can be physically meaningful only if y a # n r , since it is otherwise infinite. I n addition, the form of our time-dependent solution will show that only for the region ya < r is it likely that the steady-state solution will actually be approached by a system having a uniform temperature a t the beginning of the reaction, so we restrict our considerations to this region. This means that reaction vessels must be chosen sufficiently small, or reactions with sufficiently low heats of reaction, rates of reaction, or activation energies must be chosen. We seek a solution of the form cp = (pm -
n = l
d,b,(t) sin (nrrla)
(4)
where the d, are independent of time, and where we take bn(0) = 1. Since we must require cp (t = 0) = 0, the d, must be the Fourier coefficients of (pm
(5) Equation 4 is now subst,ituted into eq. 1 and the fact that (p, satisfies the steady-state equation is used. After multiplying by sin (mrrla) and integrating over r from 0 to a, one obtains
(K/pca2)( y 2 a 2- m2n2) b,
(6)
Since bm(0) = 1, this equation has the solution
Thus, for our first case
(2)
which is a linearization of an Arrhenius dependence. Here @tois the rate of the reaction at temperature To (the wall temperature), E is the activation energy, R is the gas constant, and T = T - To. Both of these due i t'o depletion of treatments neglect the change in @ the reactants. In the case of Wilson, t,his is unfortunate, since a steady-state solution gives no information about the time required to establish the tempera-
(1948).
Vol. 67
-
exp
[s pea2
-
(n2~2
y2az)l] sin
(nayla) (8)
We define the establishment time of' the temperature gradient, tl, by b,
=
exp(-tt/tJ
(9)
since b, is the coefficient with the slowest decay. The gradient of course is not attained exponentially, since the other coefficients decay more rapidly, but ti is simi-
