4380
K. MOEDRITZER, L.
fact that lVIoser, et al., used defatted material. In the case of the relaxation frequency, our result refers to a 7 g/dl solution, whereas the previous value was obtained by extrapolating the dielectric parameters to infinite dilution; precise agreement is therefore not to be expected. With regard to the high-frequency decrement, Moser, et al., quote 0.60 as compared with our 0.35, which is probably due to our use of the Cole-Cole function (rather than two Debye functions) as the best representation of the p dispersion. However, there would still appear to be some unresolved difference present which must await further work for explanation; experimentally the region around 10 MHz is one of the most difficult to investigate. For the y dispersion it was found that the results were not consistent with a single relaxation time ( i e . , 01 = 0 ) as has been suggested by Buchanan, et u Z . , ~ but were more compatible with a small distribution with 01 = 0.02. A large degree of overlap between the 6 and y dispersion is also indicated. The results clearly confirm the existence of the 6 dispersion and are compatible with the suggestion that it is due to the rotation of the bound water. However, it has been pointed out previously by Schwana that the polar side chains could also relax in this frequency region, and the present measurements cannot be taken to disprove this. Although at the beginning of this re-
c. D. GROENWEGHE, AND J. R. VAN WAZER
search it had been hoped that it would be possible to account unambiguously for the 6 dispersion in molecular terms, this has not been proved to be the case. Measurements on very pure proteins of known structure will have to be carried out to illuminate the situation further, and future progress will also depend on some theoretical advancement being made on the question of the appropriate mixture formula. Acknowledgments. The authors wish to thank Professor C. B. Allsopp of Guy’s Hospital Medical School and Professor H. P. Schwan of the Vniversity of Pennsylvania for providing the facilities which enable the experimental work to be carried out. Acknowledgment is also due to Dr. W. L. G. Gent and Mr. F. A. Huthwaite for valuable discussions and technical assistance, respectively. We are also indebted to Mr. G. Pugh of the Borough Polytechnic for advice in connection with the use of the computer. This work formed part of a research program leading to the Ph.D. degree of the University of London for s.E. K., and it is a pleasure to thank the Science Research Council for a research studentship. We also thank the Central Research Fund of London University and the Science Research Council for equipment grants, and we acknowledge the support by Grants NSFGB-855, NIHHE-01253, and KONR-551-(52).
Multicomponent Equilibria in Exchange of Substituents between the Dimethylsilicon and Dimethylgermanium Moieties by Kurt Moedritzer, Leo C. D. Groenweghe, and John R. Van Wazer Central Research Department, Monsanto Company, St. Louis,Missouri
63166
(Received February 6,1968)
Scrambling equilibria of the substituents C1, Br, and I (system I) and C1, Br, I, and OGH6 (system 11)between the dimethylsilicon and dimethylgermanium moieties have been studied by quantitative proton nuclear magnetic resonance spectroscopy. The experimental data have been evaluated in terms of sets of the minimum number of equilibrium constants, which in turn have been used to compute theoretical equilibrium distributions. As a result of preferential affinities for silicon us. germanium, certain species do not appear at equilibrium. Although a few studies by various authors deal with redistribution equilibria involving the exchange of more than two different kinds of substituents on a given central moiety, we believe that there has not been a report prior to this one of the situation where more than two kinds of substituents were scrambled between more The Journal of Physical Chemistry
than one kind of polyfunctional moiety. The work reported herein was undertaken as part of a broad study of equilibrium-controlled structural chemistry, and it demonstrates the fact that reactions involving as many as 20 different product species may be treated quantitatively. The goal of the broad study is to be able to
EXCHANGE OF SUBSTITUENTS BETWEEN
THE
4381
(CH3)2SiAND (CH3)2GeMOIETIES
handle in detail any equilibrium-controlled situation on either an a priori or an a posteriori basis. This paper presents part of the mathematics needed for the quantitative treatment and gives experimental data which will be used in a future theoretical summation aimed at establishing the basis for a priori predictions. Previous studies of simple redistribution' equilibria in systems based on either dimethylsilicon or dimethylgermanium as well as competition studies of the exchange of pairs of substituent^^+^ between dimethylsilicon and dimethylgermanium moieties prompted the present investigation of the competition equilibria involving three and four different kinds of substituents between these two moieties. The reason for selecting dimethylsilicon and dimethylgermanium as the central moieties in this work lies in the availability from previous studies of pertinent equilibrium constants which are required for the calculations presented in this paper and which due to inherent reasons could not be determined from the experimental data described herein.
I'
lA
lB
IJ
jL
TMS
Figure 1. Proton nmr spectra of equilibrated samples: top spectrum, experiment 1 of Table 11; bottom spectrum, experiment 1 of Table 111. The lettering of the peaks refers to the assignments in Tables I1 and 111.
Computer Program. The following discusses the computer logic used to obtain the equilibrium composition of systems in which several substituents undergo exchange between one or more different central moieties. It is possible to write a more efficient program using the presently available convergence techniques. The case Experimental Part of four kinds of monofunctional substituents reorganizStarting Materials. The dimethyldihalogermane~~ ing on two kinds of polyfunctional central moieties is deand dimethyldibromo~ilane~ were prepared according scribed in detail. The logic for other systems (includto methods of the literature. Dimethyldiphenoxying the exchange of several substituents on a single germane was made from dimethyldibromogermane, central moiety) may readily be derived therefrom. phenol, and triethylamine in benzene (bp 135" a t 0.6 Let Q and M be the two different central moieties on mm) . Dimethyldichlorosilane was purchased from which the substituents T, X, Y, and Z exchange sites. Alfa Inorganics, Inc., Beverly, Mass., and was redisdenote the concenLet, furthermore, 92,5&,Z and mi31tk,z tilled before use. tration of the compounds &T&YkZz and MTiZjYkZz, Sample Preparation and Data Acquisition. For the respectively. I n the case of the compounds &T,X,YkZz, first system studied in this paper (system I) the sami j k 1 = v, and in the case of the compounds ples were prepared by sealing various proportions of MT,XIYkZ,, i 4-j 4- k 1 = p , where v and p are the four of the five components, (CH&SiC12, (CH3),SiBr2, number of exchangeable sites on the Q and M moieties, (CH3)2GeC12,(CH&GeBr2, and (CH3)2Ge121 in 5 mm respectively. Furthermore, let the stoichiometry be 0.d. nmr tubes and heating at 120". As seen from the defined by nmr patterns obtained in 1-day intervals, equilibrium Ri = [Xl/(lQl [MI) (1) was attained in 5.5 days at this temperature. The final equilibrium data were obtained after having held the [MI) R2 = [Yl/([QI (2) samples for 14.5 days a t this temperature. Samples of Ra = [ZI/([Ql D4I> (3) the second system of this paper (system 11) were studied in a similar manner. They were prepared from RI = [&I/([&] [MI) (4) various proportions of the four components, (CH3)2SiC12, (CH3)28iBrz,(CH3)2GeI~, and (CH3)zGe(OCBH~)2. The equilibrium constants used are of the form corresponding to the formation of a compound from two Equilibrium was reached in less than 9 days a t 120°, other ones each containing all but one of the substituwith the final equilibrium data having been measured ents of that compound. Such reactions are exempliafter 17.5 days a t this temperature. fied by reactions 5 and 6 Quantitative equilibrium data were obtained from the electronically integrated peak areas of the methyl protons of the dimethylsilicon or dimethylgermanium (1) K.Moedritrer, Adwan. Organometal. Chem., 6 , 171 (1968). moieties of the respective compounds a t equilibrium (2) K.Moedritrer and J. R. Van Warer, J. Inorg. Nucl. Chem., 28, using a Varian A-60 spectrometer. Typical nmr spec957 (1966). (3) J. R. Van Warer, K. Moedritrer, and L. C. D. Groenweghe, tra are shown in Figure 1, from which it can be seen J . Organometal. Chem., 5 , 420 (1966). that, in spite of the complicated nature of the spectral (4) K. Moedritrer, ibid., 6 , 282 (1966). patterns, the individual resonances are well resolved. (6) K. Moedritzer and J. R. Van Wazer, ibkl., 6 , 242 (1966). Weighted-average equilibrium constantse were cal(6) L. C. D. Groenweghe, J. R. Van Warer, and A. W. Dickinson, culated using a computer program for the IBM 7044. Anal. Chem., 36, 303 (1964).
+ + +
+
+ + + +
Volume 78, Number 18 December 1068
K. MOEDRITZER, L. C. D. GROENWEGHE, AND J. R. VANWAZER
4382
k&TtXjYk+i whereifj
+ iQT&&+i
+ k + Z = vand
kMTtXfYk+Z
+
(k
+ 1)QTiXjYkZz
(5)
(k
+ l)MTtXjYkZi
(6)
+ lMTiXjZk+l
+ +
whereif j k 1 = p. The equilibrium constants for these reactions are represented as QKt,j,k,land MKt,j,k,t,respectively. (This notation does not specify exactly from which two components the formation occurs except when two of the subscripts in the equilibrium constant equal zero in which case the reagents are the two pertinent endmember compounds, i.e., Q compounds having one of the set i,j , k, 1 being equal to v or M compounds where one of the set equals p ) . Equilibrium constants between compounds containing different central moieties are chosen to have the form KI = m, ,o ,o,oyqo ,”,o ,o’
(7)
mo,,,O,OYqV,O,O,OC(
(9)
The iterative computer procedure consists of a FibonaccianTr8search method on the natural logarithm of the ratios of the end-member molecules, 71 = q 0 , ~ , 0 , 0 / Q ~ , o , o , o ; 7 2 = q o , o , v , ~ / q v , o , o , o ; and 7 3 = qo,o,o,v/qv,o,o,o, which are allowed to vary between -88 and +88 to accommodate the IBM 7044 computer overflow limitations. The first Fibonaccian value in this range is taken for In r l , In r2, and In r3, from which the ratios of the corresponding end members containing the other central moiety, M, are obtained m, ,o ,o ,o
V
. .
The remaining ratios of end members may readily be calculated; e.g.
eter RI = [Q]/([Q] [MI) by adjusting the starting values of qv,o,o,o and m,,o,o,o. Then the calculated values of R1, Rz, and R3 represented by RlO,RsO,and RaO,respectively, may be obtained. When RaOturns out to be larger or smaller than R3,In r 3 is increased or decreased, respectively, to the next Fibonaccian value in the series, and all concentrations involving the substituent 2 are reevaluated to obtain a new R30, which process is repeated until a satisfactory agreement between R3 and R30 is obtained. Then In r2 is altered in a similar fashion to adjust for R2, and the search on In 7 3 is started all over again. When R2 and Ra are satisfactorily close to Rz0and RsO,In 71 is adjusted and In r2and In r 3are searched as above, which isrepeated until all three composition parameters, RP, Rzo,and RsO, reach the desired values a t which time an acceptable solution has been obtained. Although it has not been proven that this procedure should always lead to the proper solution, Le., that RlO,R2, and R30 each vary monotonically with rl, r2, and r3,respectively, the program has never failed to do so in the many cases tested. The constant
may be defined from the constants of the form
by the relationship k ‘Kt,j,lc.l
=
1-1
II ‘K‘i,j,m,lc+i-m m=l
II QK‘l,j,k+m,l-m
--L(
1 -9n)
wmZ
m=l
(15)
Using the usual experimental data, the primed constants may be calculated with much higher accuracy than the unprimed ones, and the unprimed constants calculated therefrom thus have a smaller experimental error. Therefore, the first step in the computer program is to apply eq 15.
Results and Conclusions
Setting qv,o,o.o = m,,o,o,o = 1, qo,.,O,o and mo,u,o,oare calculated from r1 and 71’) respectively, and the compounds with two different substituents are obtained as exemplified for q i , j , o , o where i j = v
Three-Substituent Xystem. Scrambling involving three kinds of monofunctional substituents on a single difunctional central moiety results9 at equilibrium in the presence of no more than six compounds, three containing two like substituents and three containing two different substituents. A quantitative description of all equilibria for the central moiety being (CH&Ge
The concentrations of all the other compounds can be calculated in a similar fashion. All concentrations are normalized to sum to unity and to satisfy the param-
(7) R. E. Billman and S. E. Deyfrus, “Applied Dynamic Programming,” Princeton University Press, Princeton, N. J., 1962, p 152. (8) J. Kiefer, Proc. Amer. Math. Soc., 4, 502 (1953). (9) K. Moedritzer, and J. R. Van Wazer, submitted for publication in J . Chem. Soc.
- In In qo,u,o,o --
r1
- In
qo,o,v,o
r2
(11)
+
The Journal of Physical Chemistry
EXCHANGE OF E~UBSTITUENTS
BETWEEN THE
(CH&Si
AND
(CH&Ge MOIETIES
4383 ~~
Table I : Equilibrium Constants" Q
-
System I* (CHa)zSi Q = (CHa)zGe
(at 1209
(Et
0.31i0.02 (0 40)d (0.45)6
0.20i0.01 0.58 i 0.05 0.31 i 0.02
I
... ...
*..
...
System I (at l2Oo)
(2.9 x 10-4)' (5.0 X loa)'
KI = [MezSiBr2][MezGeCl~] /[MezSiCl~][MezGeBr~] KII = [Me~SiBrz][MezGeIz]/ [MezSiIz][MezGeBrzl KIII = [Me~SilBrz] [MenGe(OPh)z]/[MezSi(OPh)zI[Me~GeBrzl
350)
...
7 -
Q
System IIc Q = (CHa)zGe (at 3 5 O ) (at 120°) = (CHdaSi
0.30i0.02 (0. 40)d (0.45)' 0.11 i 0.01 0.16i0.04 (0.12)8
0.29i0.07 (0.67)" 0.33 i 0.02 (0.24)' (0.15)' (1.33)'
System I1 (at 1 2 0 9
(2.9 (5.0
x x
10-418
103)"
(6.6 X
Weighted-average values and their standard errors. The constants with the corresponding standard errors given were determined from the experimental equilibrium data; the others listed in parentheses are literature values which were used in the computer calculaDealing with the exchange of C1, Br, I, and tions. a Dealing with the exchange of C1, Br, and I between (CH&Si and (CH&Ge. From a study of the equilibrium in the exchange of C1, Br, OPh between (CH3)zSiand (CH&Ge. Reference 1. ' Reference 2. I, and OPh on (CH&Ge. Estimated. Unpublished results.
'
and the substituents C1, Br, and I is given by the three equilibrium constants of the form of K1, K2, and K3 in Table I. I n addition to these, equilibria involving compounds having the same set of exchangeable substituents but a central moiety different from the first one will be controlled by a similar set of three constants. Thus for the second central moiety, (CH&Si, and the same set of exchangeable substituents, an additional set of constants of the form of K1, K2, and K3 are needed for quantitative characterization of all equilibria involving only this moiety. The sorting of exchangeable substituents between two kinds of central moieties generally is expressed in terms of intersystem equilibrium constants involving pairs of exchangeable substituents. Since there are three different kinds of exchangeable substituents in the present system, one could write three intersystem equilibrium constants dealing with the sorting of C1 os. Br, Br vs. I, and C1 vs. I between the two central moieties. However, two such constants of the form of KI and KII in Table I are sufficient, since the third constant involving the sorting of C1 11s. I may be calculated from the former two. Thus the 12 possible different compounds expected at equilibrium are determined by a total of 8 equilibrium constants. The experimental data in Table I1 show, however, that of these 12 expected species, only 9 are seen at equilibrium in the mixtures studied. The absence of (CH3)&iL, (CH&SiBrI, and (CH&SiClI at equilibrium is a result of the nonrandomness of the intersystem equilibrium constants KI and KII in Table I-a situation which favors a distribution of the low atomic weight halogens on silicon and of the high atomic weight halogens on germanium. To some extent, this depends also on the over-all composition.
Owing to the absence at equilibrium of certain species, reliable values for all eight equilibrium constants could not be determined. As seen in Table I, these are K Band K 8 for the silicon part of the equilibria and the intersystem constants K I and KII. Therefore, when utilizing the computer program for the calculation of the theoretical equilibrium-distribution data corresponding to the experimental composition parameters R1,Rz, R3, and RI from the minimum-number set of equilibrium constants, the values for K Zand K3 (for the silicon part) and K I and KII were obtained from previous separate studies.lP2 These values are listed in parentheses in Table I. Good agreement is observed in Table I1 for the experimental and theoretical equilibrium concentrations as well as for all of the R values calculated from the ingredients of the mixture and as obtained from the experimental data based on the assignments of Table 11. The observed proton n m r chemical shifts of the compounds seen at equilibrium are also listed in Table 11. The six experiments shown in this table correspond to different proportions of the reagents, with the resulting stoichiometry for each experiment being defined by composition parameters (mole ratios) given at the bottom of the table. Four-Substituent Sgstem. A similar treatment of the scrambling equilibria of the four exchangeable substituents C1, Br, I, and OC6H6 on the dimethylgermanium moiety leads to a maximum of four species containing like substituents and six species containing mixed substituents with the equilibria in this system determined by the six equilibrium constants of the form of K1 to K6 in Table I. Analogously, the presence of dimethylsilicon moieties in the equilibria gives the ten corresponding silicon compounds, which are determined Volume 78, Number 19 December 1988
K. MOEDRITZER, L. C. D. GROENWEGHE, AND J. R. VAN WAZER
4384
Table 11: Experimental and Calculated Equilibrium Data a t 120’ (in Mole Percentages) for the System Involving the Exchange of C1, Br, and I on the (CH&Si and (CHs)ZGe Moieties Signal
Chemical shifta
A B C
-1.85 -1.63 -1.48
D E
-1.44 -1.30
F
-1.17
G I
-1.06 -0.91 -0.76
J
-
...
...
...
Composition parameter
RI [Cl]/([Si] + [Gel) RZE [Br]/([Si] [Gel) R3 EZ
RIG
+ [L]/([Si] + [Gel) [Si]/([Si] + [Gel)
3
2
1
3.3b(3.4)” 9.6(9.3) 12.3(12.5) 22.8(22.7) 7.4(6.6) 0.9(0.4) , . . (0.0) . . , (0.0) 13.6(14.4) 17.9(17.3) 1.2(0.8) 20.8(20.1) . . . (0.0) . . , (0.6) . . . (0.0) 8.7(7.4)
(CHdzGeL (CH&GeBrI (CH&GeClI (CHdzSiIz (CHdzGeBrz (CHa)zGeBrCl (CH&SiBrI (CH&GeCh (CH&SiCII (CHa)zSiBrz (CHa)zSiBrCl (CHa)zSiClz
. . . (0.1) , . , (0.0)
1.9(1.4) 32.1(34.2)
. . , (1.0)
9.9(9.2) 22.2(22.1) 15.7 (16.7)
4
9.8(10.0) 15.5(16.8) 6.6(5.5) . . . (0.0) 8.2(8.9) 8.4(7.7) , , . (0.0) 3.4(1.8) . . , (0.2) 0.1(0.1) 4.5(3.1) 43.7(46.0)
--------1
--
Experiment no.
7-
Assignment
5
5.3(5.9) 10.0(10.1) 11.2(10.8)
. . . (0.0) 4.5(5.5) 16.1(15.6) . . . (0.0) 12.9(11.7)
. . (0.1) . . . (0.0) *
9.2(9.0) 15.6(15.9) 7.7(6.9) . . . (0.0) 8.2(8.7) 10.3(10.1) . . . (0.0) 4.2(3.0)
. . (0.1) . . , (0.0) *
1.2(0.8) 38.9(39.5)
3.0(2.3) 41.7(44.0)
1.113d(1.117)e 0.576(0.557) 0.62@(0.622)6 0.991(1.018) 0.259d(0.263)80.433(0.429) 0.357d(0.340y 0.496(0.478)
3
l.lZO(1.137) 0.456(0.449) 0.424(0.417) 0.494(0.483)
2.8(2.7) 9.6(9.4) 10.7(10.2)
. . . (0.0)
10.1 (10.2) 30.1 (29.3)
. . . (0.0)
22.7(22.1)
. . . (0.0) , . . (0.0)
0.3(0.3) 13.8(15.7)
--
Experiment ----.on 2
6
4
1.297(1.321) 0.376(0.363) 0.327(0.316) 0.404(0.401)
5
1.134(1.128) 0.457(0.453) 0.409(0.417) 0.464(0.447)
6
1.155(1.141) 0.595(0.602) 0.251(0.259) 0.161(0.141)
a I n parts per million relative to internal tetramethylsilane as measured in experiment 3. From the nmr peak areas. Calculated from the constants for system I in Table I and for R values calculated from the ingredients. From the ingredients of the mixture. Calculated from the experimental nmr data.
by another set of six equilibrium constants of the form of KI-KB for silicon. Relating the sorting of the four exchangeable substituents between dimethylsilicon and dimethylgermanium are six intersystem constants, one for each different pair of substituents. Of these, however, only three are independent ones, from which the other three may be calculated. We selected the constants represented by K I , K I I ,and KIIIin Table I as the three independent ones. Thus a t equilibrium in this system, there may be as many as 20 different species, the relative concentrations of which are determined by the 15 equilibrium constants of Table I. Again, only 5 of the 15 equilibrium constants in Table I (system 11) could be determined from the experimental data in Table 111, owing to the high degree of nonrandomness in the sorting of substituents between dimethylsilicon and dimethylgermanium. Therefore, the theoretical mole percentage concentrations listed in parentheses in Table 111 were calculated using previously determined values for the required additional ten equilibrium constants which could not be obtained from the present experimental data. Also for this system at equilibrium, good agreement between experimental and calculated concentrations is observed. As seen from the experimental data in Table 111, the distribution of the substituents between the silicon and germanium moieties is similar to the first system discussed in this paper. The low atomic weight halogens favor the dimethylsilicon moieties at equilibrium, and the high atomic weight halogens favor the dimethylgermanium moieties, with the phenoxyl groups favoring The Journal of Physical Chemistry
the dimethylsilicon moiety. As a result of this preference, species containing Si-I bonds do not appear a t equilibrium, e.g., (CH3)&3i12, (CHJ zSiBrI, (CH,) 2SiC11, and (CH&SiI (OCaHs). Similarly, compounds having Ge-0 bonds are not favored at equilibrium, e.g., (CHd 2Ge (OC6H6)2, (CHd zGeCl (OCsHd, (CHdzGeBr(OCeHs), and (CH3)2GeI(OC6HG).Also (CH&GeC12 a t equilibrium appears in only small amounts.
Discussion The rates of equilibration for analogous germanium compounds generally are much faster than for silicon compounds. This means that during the equilibration process the germanium species in the systems described in this paper are at equilibrium at all times. The ratedetermining steps are substitutions on silicon, processes which have been found previously to be quite slow, particularly the reactions involving phenoxyl groups. Therefore, it appears that of the equilibrium constants in Table I the ones involving germanium moieties only correspond to the temperature of the nmr probe, since upon quenching of the samples to room temperature, the germanium species will attain the equilibrium corresponding to that temperature. The transfer of substituents from germanium to silicon and vice versa generally has been found to be relatively slow at room temperature. l1 This means that, upon quenching and (10) K.,Moedritzer and J. R. Van Wazer, J . Inorg. Nucl. Chem., 29, 1571 (1967). (11) K.Moedritzer and J. R. Van Wazer,Inorg. Chem., 5,647(1986).
EXCHANGE OF I~UBSTITUENTS
BETWEEN THE
(CH&Si
AND
(CH&Ge MOIETIES
4385
Table 111: Experimental and Calculated Equilibrium Data (in Mole Percentages) for the System Involving the Exchange of C1, Br, I, and ocSH6 on the (CH8)zSi and (CH&Ge Moieties Signal
Chemioal shift0,
1
2
3
4
5
15.6b(15.8)o 19.8 (18.7) . . . (0.0) 0 . 9 (0.5) 8 . 4 (7.3) . . . (0.1) O.S(O.5)'
10.4(10.9) 13.5 (12.6) . . . (0.0) 0 . 3 (0.2) 5 . 7 (4.8) . . . (0.3) 1- 4 (0.2) . . . (0.0)
24.3 (23.5) 18.5 (16.5) . . . (0.0) 0.3(0.1) 4 . 7 (3.8) . . . (0.6) 1.o (0.1) . . . (0.0)
25.1 (24.0) 22.8(21.5) . . . (0.0) 4.4(3.5) 7 . 0 (6.4) . . . (0.0) 3 . 2 (2.7) . . . (0.0) 0 . 4 (0.3) . . . (0.0) . . . (0.2) . . . (0.0) 0 . 8 (0.1) . . . (0.0) . . . (0.8) 4 . 4 (5.9) 1 . 3 (1.4)
8 . 5 (8.8) 1 4 . 3 (14.0)
A B
-1.79 - 1.Ei7
c D
-1.43 -1.38
E
-1.25
F
-1.11
G H
- 1.02
2 . 1 (2.6)
. . . (0.0) . . . (0.2)
8.1 (8.1)
-0.90
I J K
-0.87 - 0. '72 -0.168
L M
-0.63 -0.31
10.1 (10.5) 13.5 (12.7) 6 . 5 (7.4) . , . (0.0) 19.0 (20.1) 3.2 (3.3)
23.3 (22.5) 19.5(18.8) 6 . 1 (7.0) . . . (0.0) 1 2 . 0 (13.0) 0.8 (1.0)
...
. . . (0.0) . . . (0.0) . . . (0.2) . . . (0.0)
...
... ...
...
+
RI 3 [C1]/([13i] [Gel) RZ= [Brl /([Si1 [Gel ) R3 5 [Il/([SiI [Gel) R 4 3 [OCeHs]/([Si] [Gel) RI s [Si]/([Esi] [Gel)
+
. . . (0.0) . . . (0.2)
. . . (0.0) . . . (0.5) . . . (0.0)
10.5(11.4) . . . (0.0) . . . (0.4) 15.2 (15.6) 7 . 2 (6.4) 8 . 7 (10.2) , . . (0.0) 8 . 3 (9.4) l.l(l.4) no .-----
_-____------------Experiment
Composition parameter
+ +
. . . (0.0) . . . (0.4) . . . (0.0)
+
. . . (0.0)
6.0(4.9) 7.8(7.5)
. . : (0.0)
8.7(6.8)
. . . (0.0)
2 . 6 (1.8) . . . (0.0) . . . (0.3)
. . . (0.0) 0 . 5 (0.2) ... (0.0) . . . (0.8) 11.0 (12.4 0 . 3 (0.9) . . . (0.0) 30.8 (32.6 9.4(9.0)
. . . (0.0)
21.3 (23.4) 9 . 4 (9.7)
~.
-----------_
1
2
3
4
6
0.572d(0.578)" 0.572d (0.582y 0 . 512d (0.519)' 0.344d(0.319)" 0. 572d (0.544)"
0.741 (0.760) 0.684 (0.719) 0,355 (0.346) 0.221 (0.197) 0.712 (0.698)
0.387 (0.392) 0.733 (0.738) 0.652 (0.674) 0.229(0.192) 0.560 (0.510)
0.431 (0.393) 0.394 (0.413) 0.730 (0.774) 0.445 (0.422) 0.412 (0.364)
0.737 (0.732) 0.378 (0.389) 0.365 (0,373) 0.521 (0.504) 0.557 (0.515)
'
I n parts per million relative to internal tetramethylsilane as measured in experiment 3. From the nmr peak areas. Calculated From the ingredients of the mixture. from the constants for system I1 in Table I and from R values calculated from the ingredients. Calculated from the experimental nmr data.
immediately obtaining the nmr spectra, the equilibria with regard to the distribution of the substituents between silicon and germanium will correspond to the temperature at which the samples were held for equilibration, which in the present case is 120'. Since equilibration of these substituents on silicon at room temperature in the absence of catalysts' does not proceed at all, the equilibria between the silicon species also represent the situation at 120". The results reported here exemplify the usual situation12 in which the values of an equilibrium constant (for a substituent-exchange reaction in a set of reactions in which all chemical species are accounted for) are seen to vary by only a small amount with environmental changes, while nmr chemical shifts may show appreciable variations. Thus not only do the values of a given constant not change appreciably in the various experiments listed in Table I1 and 111, but also, as shown in Table I, there is no distinguishable difference between values of the same constant measured in the two different systems istudied here. Moreover, the results obtained here agree with va1uesl3of the same equilibrium constant as measured in the exchange of only two kinds of substituents on a single kind of polyfunctional moiety.
From a quantum-mechanical viewpoint, l4 it is not surprising that there are noticeable changes in the nmr chemical shifts with variation in molecular environment, while equilibrium constants for substituent exchange are virtually unaffected. Since hydrogen nmr shifts are mainly attributable to the paramagnetic terms, the predominant operator for this property involves the expectation value of l/r. Since the hydrogen atoms are positioned in the outer regions of the molecule, this slowly declining (l/r) function is expected to be affected by neighboring molecules. On the other hand, the energy changes induced by atom or group (12) See K. Moedritaer, Advan. Organometal. Chem., 6, 171 (1968), and J. R. Van Wazer and K. Moedritaer, Anoew. Chem. Int. Ed., 5 , 341 (1966), for reviews. (13) I n ref 2, it is shown that, for Q = (CHa)zSi a t 120°, K 1 = 0.31 0.03, and for Q = (CHa)nGe a t 35', K I = 0.30 =k 0.02, K z = 0.67 f 0.07, and Ka = 0.35 =IC 0.01. K. Moedritaer and J. R. Van Waaer, Inorg. Chem., 7, 2105 (1968), have also shown that for Q = (CH8)zSi at 150°, K4 = 0.16 =k 0.01 and K5 = 0.14 i. 0.01. K. M o ~ dritzer and J. R. Van Wazer, J . Organometal. Chem., 13, 145 (1968), have shown that, for exchange of the appropriate monofunctional s u b stituenta between the CHaGe6 and (CH3)2Ge< moieties, K 5 = 0.24 rt 0.01 and K E = 1.61 =k 0.05, for Q = (CHa)nGe a t 350. (14) Ab initio calculations are now being interpreted in our laboratories to elucidate both of the matters touched upon in the reference paragraph.
*
Volume 7.8, Number 13 December 1968
4386
T. B. JOYNER
substitutions to the most part come from quite deep within the molecule so that they are little perturbed by the presence of neighboring molecules. The equilibrium constants in Table I make up one complete minimum-number set of the constants required for the complete mathematical determination of all equilibria in these systems. Of course, any other set of constants which satisfies the conditions of totally determining all equilibria in these systems may be chosen. From any such properly chosen set of constants, any other equilibrium not expressed specifically by that set may be calculated from it. From the three intersystem equilibrium constants KI, KII, and K I I ~the , following additional intersystem constants have been calculated KIV = [(CH3)2SiLI[(CH&Ge(OPh)21 [(CH&Si(OPh)z1 [(CH&GeI2 1
-
KIII - = 1.3 X KII
KI
lo-* (18)
KII
Whereas KIV and KV have not been measured previously, KVIhas been found in a separate study2to have avalueof 1.2 X Another example for these kinds of calculations is the equilibrium constant for the reaction of eq 19 (CHJZSiBrz
KVII
+ (CH&GeCl(OPh) (CH3)zSiBrCl + (CH&GeBr(OPh)
[(CH3)zSiBrCI][(CH&GeBr(OPh) ] [(CHdzSiBrzI [(CHa)zGeCI(OPh)] d G e ~ 4 / s i ~ 1 G e ~= 5 ~1.3 I
(16)
(19)
-
x
io2
(20)
The value of KVIIshows that the equilibrium of eq 19 lies well to the right.
Kv = [(CH3)2SiC121[ ( C H ~ ) Z G ~ ( O P-~ ) Z I [(CH3)2Si(OPh)z1[(CH3)2GeC121 KIII = 2.3 X
KI = 5.8 X
(17)
Acknowledgment. We wish to thank Raymond E. Miller for valuable experimental assistance.
The Thermal Decomposition of Solid Hexaamminecobalt (111) Azide. The Cobalt(I1) Reaction by T. B. Joyner Chemistry Division, Naval Weapon8 Center, China Lake, California 93666 (Received February 19, 1968)
The rates of decomposition of solid hexaamminecobalt(II1) azide to cobalt(I1) complexes have been measured, and the kinetic parameters have been determined. Under low ammonia pressures an apparent activation energy of ca. 46 kcal/mol is close to the values obtained for the analogous reactions of azidopentaamminecobalt(II1) azide and cis- and tram-diazidotetraamminecobalt(II1) azide, suggesting a reaction mechanism common throughout the series. Under higher ammonia pressures (50-200 torr), the hexaammine is unique in showing a lower apparent activation energy of ca. 32 kcal/mol. This may indicate a reaction path unavailable to the substituted compounds.
Introduction The ability of solid hexaamminecobalt(II1) azide to decompose to either CON or cobalt(I1) has been established, and the rather complicated relationship between the reactions has been qualitatively discussed.' This paper considers the kinetics of the cobalt(I1) reaction. The COWreaction, with its interesting induction period, The Jourwl of Phyaical Chemistry
will be dealt with separately. The cobalt(I1) reaction [CO("36
I (Nd3 + Co(NHa)z(N&
(1)
+ 43"
+ 1.5N-z
(1)
T.B. Joyner and F. H. Verhoek, Inorg. Chem., 2 , 334 (1963).
