7250
experimental evidence strongly suggests that at least two of these structures may coexist in the gas. The large number of observed infrared a n d Raman bands can easily be explained if appreciable amounts of VI11 exist. The observed dipole moment can also be accounted for by VIII. Although the electron diffraction experiments cannot give us the hydrogen positions, the recent work may well be correct to the extent that it requires long boron-boron distances, as found here. We also point out that the crystallization of I requires n o hydrogen rearrangements. This is not true of any other structure considered, although the hydrogen rearrangements necessary in 11 and VI11 are minimal. Finally, it is well-known that many metal borohydrides undergo rapid intramolecular hydrogen tautomerism, making the hydrogens equivalent on the nmr
time scale. Although the nmr spectrum of beryllium borohydride has not yet been observed, the three structures I, VIII, a n d I1 provide a convenient and obvious path for such a tautomerism. 26 Acknowledgments. We would like t o thank E. Clementi and the I B M Corporation for generously supplying most of the computer time for this work. We also thank the Office of Naval Research for support of this investigation. (26) As this manuscript was being submitted a similar independent SCF-CI study on beryllium borohydride appeared : R. Ahlrichs, Chem. Phys. Lett., 19, 174 (1973). This study employs a Gaussian basis set and the independent electron pair approximation for correlation corrections. It does not consider structures 111, VI, XI, X, or XI, no configuration interaction results are reported for structure IV or V, and structure IV was not optimized. Our basic conclusions are, however, very similar.
Mechanistic Studies of One- and Two-Equivalent Oxidations of the Mercury( I) Dimer Roger Davies, Brian Kipling, and A. Geoffrey Sykes*
Contribution f r o m the Department of Inorganic and Structural Chemistry, The Unicersity, Leeds L S 2 9JT, England. Received M a y 17, 1973
Kinetic studies on the reactions of mercury(1) dimer with the one-equivalent oxidants F e ( ~ h e n ) ~and ~+ R~(bipy),~'and the two-equivalent oxidant Br03- are described. These and other reactions of the mercury(1) dimer previously reported can be summarized as follows. One-equivalent oxidants usually react by a mechanism (HgI), oxidant (1 e-) HgI HgII and HgI oxidant (1 e-] HgII (fast), with a rate law first order in (Hg')? and oxidant. Two-equivalent oxidants react by a mechanism (HgI)z $ HgO HgIr (fast) and HgG oxidant ( 2 e-) HgII, with a rate law which is first order in both reactants, but which is in addition dependent on [HgIII-l.
Abstract:
+
-
-
+
-
+
D
ifferent reaction sequences are generally observed in redox reactions involving one- and two-equivalent oxidants. As a result a distinction between the two based on differences in stoichiometry, reaction products, and/or rate law is often possible. Wellknown examples are the reactions of one- and twoequivalent oxidants with hydrazine' and with sulfite, where the stoichiometries and products often enable a clearcut distinction to be made. With mercury(1) dimer as reductant a similar distinction is not a t present clearly defined. 4 , 6 Reactions of mercury(1) dimer wiih thallium(III),6 ~ o b a l t ( I I I ) , ~ manganese(III),8 cerium(1V) (in the presence of sulfate9 (1) See, for example, W. C. E. Higginson, Chem. Soc., Spec. Publ., No. 10,95 (1957). ( 2 ) W. C. E. Higginson and J. Marshall, J . Chem. Soc., 447 (1957). (3) A. G. Sykes, Adcan. Inorg. Chem. Radiochem., 10,232 (1967). (4) Reference 3, pp 218-219. (5) M. A. Thompson, J. C. Sullivan, and E. Deutsch, J . Amer. Chem. Soc., 93, 5667 (1971). We note also that no reaction between mercury(1) dimer and neptunium(V1) is observed over cu. 1 hr at 50" with neptunium(V1) concentrations 100 times greater than reported in this paper (personal communication, J. C. Sullivan). (6) A. M. Armstrong, J. Halpern, and W. C. E. Higginson, J. Phys. Chem., 60, 1661 (1956); A. M. Armstrong and J. Halpern, Can. J . Chem., 35,1020(1957). (7) D. R . Rosseinsky and W. C. E. Higginson, J . Chem. SOC.,31 (1960). (8) D. R. Rosseinsky,J. Chem.Soc., 1181 (1963). (9) W. H . McCurdy and G. C. Guilbault, J . Phq's. Chem., 64, 1825 (1960).
+
+
and catalyzed by silver(1) lo a n d hexachloroiridate(II1) "), a n d neptunium(V1I)j have been studied previously. The mechanisms of the reactions of the one-equivalent oxidants tris( 1,lo-phenanthroline)iron(III) and tris(2,2'-bipyridine)ruthenium(III) a n d the two-equivalent oxidant bromate are considered in this paper. The stoichiometries (in equivalents) are the same a n d mercury(I1) is the product in all cases. The rate laws differ, however, and with information from previous studies we feel it is now possible to differentiate between the two types of reactant. Experimental Section Preparation of Solutions of the Mercury(1) Dimer. Stock solutions of the perchlorate salt of (Hgl)z in perchloric acid (cn. 1 M ) were prepared in three different ways. (i) Analar BDH mercury (23.5 g) and 50 ml of water were heated together in a 250-ml beaker, and concentrated nitric acid was added a little at a time to the hot solution until all the mercury dissolved. Nitrogen dioxide was given off. Mercury oxide, HgO, was precipitated by adding Analar anhydrous sodium carbonate. The HgO was dried by suction and then dissolved in 2 M HC104. The mercury( 11) in solution was converted to mercury(1) dimer by shaking with a slight excess of mercury for co, 24 hr.12 (ii) Yellow HgO, May and Baker Labor(10) W. C. E. Higginson, D. R. Rosseinsky, B. Stead, and A. G . Sykes, Discuss.Faraduj Soc., 29,49 (1960). (11) I 7 0 z reaction. Second-order rate constants, k z , are given in Table 11. Variation of the
0 20
Temp. "C
+ 2 R ~ ( b i p y ) ~+ ? + 2Hg" + 2 R ~ ( b i p y ) ~ z +
[(Hgl)zl, [H-I, M
M
0.70 0.70 0.70 0.70 0.70 0.55 0.20
0.10 0. I O 0.08 0.06 0.05
106[Fe104kl, (phen)02+], 1. mol-' [Hg"], M M sec-'
0.01 0.05 0.05
9.62 4.71 9.96 8.74 9.40 4.91 9.75
4.5 5.15 5.05 4.75 4.6 4.9 4.5
45.0 a
2.85 2.75 2.85 2.75 2.55 2.55 2.55 2.00 1.50 1.25 1 .oo 2.85 2.55 2.40 2.40 2.00 2.85 2.00
[Hg"] = 0.05 M .
0.055 0.050 0.05 0.05 0.15 0.lW 0 . 05b 0.05 0.12 0.04 0.05 0.05 0 . 05c 0.20 0.26 0.05 0.05 0.05 [Hg"]
=
0.01 M .
4.55 4.55 5.20 4.15 3.70 2.70 2.04 2.20 2.43 4.35 3.42 3.95 3.92 3.10 3.10 3.85 3.23 3.80 [Hg"]
4.32 4.13 6.8 7.0 7.0 6.7 6.8 7.55 6.8 7.1 6.9 3.13 3.11 3.47 3.56 3.16 6.95 6.65 =
0.05 M .
mercury(1) dimer concentration over a fivefold range was consistent with a first-order dependence o n this reactant. At lower mercury(1) dimer concentrations linear plots were not observed due t o side reactions of R ~ ( b i p y ) , ~ + .Addition of mercury(I1) had no effect on rates, and the rate law is therefore of the same form as also evaluated a t 354 nm at which wavelength the comeq 4. Activation parameters (Table VI) were evaluated plex F e ( ~ h e n absorbs ) ~ ~ ~ most strongly. As far as the by a least-squares treatment (no weighting) from rate mechanism is concerned what is particularly important constants with [(HgI).] = 0.05 M . Runs a t the high is that addition of mercury(I1) (up t o 0.05 M ) clearly mercury(1) dimer concentrations were excluded from has n o effect on k,. The alternative mechanism inthe computation because variations in perchlorate ion volving initial dismutation of mercury(1) dimer gives a n concentration may be relevant. inverse mercury(I1) dependence, which has a proThe Reaction with BrOo-. The stoichiometry was nounced effect on rates (see for example the bromate determined a t 50°, L.I, = 1.0 M (LiClO,), by analyzing study). There is no dependence on [H+] over the reaction solutions, [Br03-] = ca. 4 X M and range 0.2-0.7 M , and results obtained are consistent [(Hg')?] = ca. 0.8 X M , a t varying time intervals. with the rate law Concentrations of bromate were determined iodo-d [ F e ( ~ h e n ) ~ = 2kl[(Hg1)?][Fe( hen)^ 3]' (4) metrically after first removing all metal ions using a cation exchange resin. The concentration of merwhere at 2 5 " , k , = ca. 5.0 X 1. mol-' sec-I. cury(1) dimer was determined at 236 nm ( E 2.77 X lo4 1. mol-' cm-1)*1 after applying corrections for absorThe Reaction with R ~ ( b i p y ) 3 ~ + .Kinetic data obtained using a solid sample believed to be R ~ ( b i p y ) ~ - bance due to bromate and final products. There was no detectable change in stoichiometry over the course ( C ~ O Jwere ) ~ unsatisfactory, and the complex was therefore prepared in situ by cerium(1V) oxidation of Ru(20) A . J. McCafferty, S. F. Mason, and B. J. Norman, J . Cheni. SOC.A , 1428 (1969); J. D. Miller and R. H . Price, h i d . , 1048 (1966); (bipy),+ (see Experimental Section). Solutions of R. R. Miller, W. W. Brandt, and M. Puke, J . A m e r . Chem. SOC.,7 7 , R ~ i ( b i p y ) undergo ~?~ a side reaction at low [HS], and 3178(1955). [H-] values in the range 1.0-2.9 it4 (and a correspond(21) W. C. E.Higginson,J. Chem. SOC.,1438(1951). 0.10 0.10
Joirmul ofihe American Chemical Society
95:22 / October 31, 1973
7253
of the reaction (30-100%) investigated, and a ratio of 2.8 ( 1 0 . 2 ) mol of mercury(1) dimer per mole of bromate is: we feel in accordance with a n overall reaction as in eq 6. A stoichiometry of 3 :1 was assumed in evalu3Hg$
+ Br03- -+ 6Hg11 + Br- + 6 H 2 0
(6)
ating all rate constants below. Absorption changes a t 212 nm were consistent with the formation of HgBrf, E -6 X l o 3 1. mol-' cm-I, as compared with E -400 1. mol-' cm-I for HgZ' (absorption coefficients determined in presence of a n equivalent amount of mercury(1) dimer). Absorbance changes in kinetic runs were monitored at the mercury(1) dimer peak at 236 nm. F o r reactions with high bromate concentrations a correction was applied for absorbance due t o bromate. The reaction was studied over a temperature range of 35-50", I t was assumed that the first stage of the stepwise reduction of bromate Br03- + Br02- + BrO- + Br- is rate determining and that subsequent reactions are fast. Consistent with this it was found in separate experiments that the BrO- --t Br- step is indeed fast. Bromine solutions also react rapidly with mercury(1) dimer under conditions of high [H+], when the extent of formation of hypobromous acid is small. Spectra (200400 nm) recorded during the course of the reaction showed n o evidence for the buildup of intermediates. T h e reaction was slowed down by addition of mercury(II), which suggests a reaction sequence
HgO
+ BrOo-
eHgO + Hgrr HgIr + BrOp- + H 2 0 +PH -
Temp, "C
rH+l, M
35.0
1 .00 1 .OO 0.90 0.80 0.70 0.60 0.40 1 .oo 1 .oo 0.80 0.70 0.60 0.40 1 .oo 1 .00 1 .00 1 .OO 0.90 0.90 0.so 0.80 0.75 0.70 0.65 0.50 0.50 0.40 0.10
(7) (8)
40.0
With a lprge excess of bromate t h i s m i y be written in the form
45.0
_3dx_ - 3k'(a - 3 ~ ) 6x
where k' = k3K[Br03-], a is the initial concentration of mercury(1) dimer. and x is the number of moles of mercury(1) diiner consumed by eq 7 and 8 at time t . O n integratio 1 eq 11 is obtained. Graphs of the left-hand -3x
- a In (a - 3x) = 1.5k't
+ constant
(M)
Table 111. Rate Constants for the Reduction of Bromate Ions by Mercury(1) Dimer, p = 1.O M (LiC104)
The equilibration in eq 7 is known to be rapid,6j22a n d the rate law is therefore as in (9).
dt
[bo;]
Figure 2. The dependence of first-order rate constants k' on bromate ion concentration for the reaction of mercuryil) dimer with bromate (50". p = 1.0 M(LiCI0:). [H+] = 0.8 U . [(Hg')?] = 3.1 X 10-5 M ) .
/>3
__f
6
4
lo3
K
(Hg%
2
0
(11)
45.0
side against t were linear to ca. 70% completion. Bromate concentrations were varied over the range 7 X 10-4-7 X M (Figure 2 ) without any evidence for a [BrO3-I2 dependence as observed by in the bromate oxidation of cerium(III), manganese(II), and neptunium(V). Other values of k3K are listed in Table 111. When mercury(I1) as well as bromate is in large excess eq 12 is obtained on integration, where
50.0
1 .oo
0.90 0.80 0.70 0.60 0.40 0.30
105[(Hg1)J, 10,[ BrOJ-]. M .M 107X ,I
