45 16
A.
n.BRITTAND ~ V K L I A MhT. 1-m-
s::
Vol
[CONTRIBUTION F R O X \NASHISGTON vXIVERSITY, S A I X T L O U I S , h f I S S O C R I ]
Rate of the Manganate-Permanganate Exchange by Pulsed Nuclear Magnetic Resonance BY A . D. BRITTAND W'ILI,IAM M. YENI~I RECEIVEDJVLV 13, 1961 The electron-exchange between M n 0 . - and hln0,- is investigated by measurements of relaxation times T , and Tr, using spin-echo techniques. The results are in agreement with the results of isotopic-tmcer techniques :LS to the value of the rate constant k and the kinetic order of the exchange.
The electron-exchange between MnOs= and (pink) to iMn04- (green) was obsexved and filtration of the suspensjon through asbestos mats. Solutions IInOa- has been measured by Sheppard and tlrahl resulting of NanMnOa tagged with lvInE4 were prepared by air oxidawith the isotopic-tracer technique.2 The reaction tion of tagged MnOz in a molten Pl-aOH flux, dissolution of was found to follow second order kinetics and t o the cooled melt in water and removal of the excess MnOz by be first order with respect to either Mn04= or filtration through asbestos mats. Concentrations of either M n O r . The rate was found to increase with in- S a h l n O l or NasMnOd were determined by reaction with Fe( ~ Y H ~ ) P ( S O < ) ~ .and ~ H ~titration O of the excess creasing electrolyte concentration and to depend excess with standardized KMnQ. All other reagents were comon the specific cations present. mercial chemicals of analytical grade. Procedure.-Solutions for pulsed n.m.r. studies were preElectron-exchange reactions may be studied also by the techniques of nuclear magnetic reso- pared a t 0" in the dark by accurate dilution of aliquots of concentrated stock solutions. Immediately prior to the nance (n.m.r.) and electron spin resonance (e.s.r.). pulsed n.m.r. measurements, the solutions were either The e.s.r. spectrum of hInOd= has been investigated ultracentrifuged at 20,000 r.p.m. for one hour or filtered but was found to be unresolvable in liquid s o l ~ t i o n . ~through 450 mu millipore filters. Aliquots of the solutions were diluted accurately and the The continuous-wave n.1n.r. spectrum of Mn04- concentrations in the resulting solutions spectrophotoshows a singlet absorption peak. Since one metrically determined by their absorption at 564 and 615 singlet absorption peak is observed, the system is mu. Concentrations were obtained from formulas derived suitable for study by pulsed n.rn.r. as well as from the respective extinction coefficients, under the a$continuous-wave (c.-w.) n.rn.r. The measurement sumption of additive optical densities. of relaxation times by pulsed n.m.r. has certain = 1.37 X 103 [MnO,-] + 1.15 X lo3 [MnO:-] (1) experimental advantages over the line-broadening technique of c.-w. n.rn.r. X o corrections for Us:j = 2.0 x 102 [hfn04-] 1.50 X l o 3 [Mn04-l (2) radio frequency power saturation and overmodulation are necessary, as the r.f. oscillator is not in operation during the period of measurement. Magnetic field inhomogeneities, which may broaden absorption peaks by the c.-w. n.rI1.r. method, have no effect on the pulsed n.m.r. measurements (ill D X = meawrecf optical density a t wave length A the absence of appreciable diffusion). Lastly, Speclrophotonietrically determined concentrations were the pulsed n.m.r. technique measures T I far more with the total oxidizing capacity of many soluaccurately and conveniently than does the c.-w. cpmpared tions. Measured and calculated total oxidizing capacities n .m .r. technique. agreed to =I= 2 to 3Ye, on the average, for more than 50 TI and TZwere measured by the pulsed n.m.r. solutions; the maximum discrepancy was 6%. T?was evaluated by a sequence of one 90"pulse, followed technique for a series of l I n 0 4 = and I\InOdseries of 180" pulses. T I was evaluated b y a 180mixtures of accurately known composition. Re- -:,190' apulse sequence. The t w o techniques have been rlelationships between relaxation time and compo- ~ c r i b e d . ~ sition enabled the evaluation of the rate constant k . Independent variation of either the Mn04Results and Discussion concentration or the l1nO4=concentration afforded The results of the experiment are listed in Table information as to the kinetics of the exchange. I . The rate constant k was evaluated graphically Experimental
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Materials.-Concentrated solutions of NaMnOc were prepared by dissolving C.P. NaMnOc.3H20 and filtering through asbestos mats. Concentrated solutions of SazMnOl were prepared by boiling solutions of concentrated NaMnOd in 5 f NaOH until a complete conversion of MnOl(1) (a) Taken in part from a thesis submitted by A. D. Britt in partial fulfillment of the requirements for the degree of Master of Arts a t Washington University, June 1961. This work was supported by research grants from t h e Sational Science Foundation and t h e Otiice of Scientific Research, United States Air Force. (b) Ohio Oil Fellow 1959-1960. ( 2 ) 1. C. Sheppard and A . C. \Vahl, J . A m Citem. Soc.. 79, 1020 (1957). ( 3 ) S. I. Weissman, private communication. T h e e.s.r. spectrum nf SlnOl' in mixed crystals has been obtained by A. Carrington, D. J. E. Ingram, K. A. K. Lott, D. S . Schonland and >I, C . R.Symons, Proc. Roy. SOL.( L o n d o n ) , 8254, 101 (1900).
1 1.06 (except the neutral solution)
TABLE
Temperature
= Oo, p =
Concentration in gram irms !liter OHIInOaM11Ol-
0 554 ,547 53 1 ,519 .343 228 234 226
0 4.3 x 1.86 X 3.30 x 4.88 X 8.3 x '7.46 X 5.82 x
10-7
10-3
lo-*
10-3
lo-? 10-2
0.30 .30 .30 .30 .68 68
.os
xd+
Characteristic time in msec. so,- T~ 'r2
0.577 0 1.00 0 063 047 1.00 1, 00 ,033 ,017 1.00 1 .oo ,063 1.00 047 1.00 ,017
. . 56 46
sa
4;
22 17 17 13 12 39 . . 22 . . 12 . .
(4) H Y. Carr and E , 11. Putcell. P h r s . Reo , 9 4 , GRO ( l Y j 4 )
100
._
;
..
80
-
60
I
5 F 40
LEGEND:
0 = 0.54M MnO; D = 0 . 2 3 M MnO; 20
0 I0
0
20
1
1
30
40
0, 50
60
0
('> T2
= m
('TZ > + k [MnO,'] i
(T2),= (TI), (experimentally) (&)m
( T2),
(Tz),
= constant
+ k [MnO,-]
TZvalue in the presence of electronexchange = measured TI value in t h e presence of electronexchange = measured T , value a t zero Mn04- concentration = measured
[Mn04'] = concentration of Mn04- in g. ions/liter k = rate constant of the Mn04- - MnOl- electronexchange
Sheppard and Wahl obtained a value of k = 1.70 x IO3 sec.-l for a similar system using the isotopic-tracer technique. A repetition of their experiment was performed a t MnO4= concentrations higher by a factor of 50 and Mn04concentrations higher by a factor of 10. The value of k = 1.70 X l o 3 M-l set.-' was obtained a t these higher concentrations, confirming the applicability of the second order rate equation (R = k [h!In04-][llnO4=]) over a large range of X n O b and hfn0,- concentrations. On the basis of an approximate calculation of the errors involved in the pulsed n.m.r. measurements, the standard deviation of the rate constant k is k 20%. An error calculation for the isotopictracer experiments gives a standard deviation of 13%. the rate constant k of
*
k,,, = (1 23 k 0 25) X 108 i1f-I sec. -l k , - t = (1.70 zk 0.22) x l o 3 M-1 sec.-l
1
30
Fig 2.-T*
data.
(Figs. 1and 2 ) by the relationships
1
20
[MnO,']
[MnOt] x IO'
Fig. L-Tl
IO
x
-
40
50
to'
data.
Conclusion.-It was not possible to make measurements on a system both by the n.m.r. technique and by the isotopic-tracer method. Solutions which were dilute enough to be studied by isotopic-exchange gave undetectable resonance signals. However, it was possible to compare similar systems in which the temperature, type and concentration of positive ion and the ionic strength were the same, although the Mn04- concentration differed by a factor of 200-500 and the l f n 0 4 = concentration by a factor of 20-50. The comparison of the results obtained by the two techniques then involves the assumption that the second-order rate law applies over the large variation in reactant concentrations. The experimental results tend to validate this assumption in two ways. First, an increase by a factor of 50 in total reactant concentration (Mn04Mn04=)in the low concentration range caused no change in the rate constant k as measured by isotopic-exchange. Secondly, in the high concentration range, the first-order dependence of the reciprocal of T I or T Zon the L!In04= concentration, together with lack of dependence on the k h 0 4 concentration, offers strong indication that the rate is first-order with respect to -Mn04- and to lZ/n04=. The values of the rate constant k obtained by the two methods are different by about 309;b, which is about the experimental uncertainty. Therefore, the conclusion is drawn that, within the experimental uncertainty of ~ - 3 0 %the ~ specific rates measured by the n.m.r. and isotopic-tracer method are the same. Acknowledgments.-The authors wish to acknowledge the assistance of Professors Arthur C. Xahl, Richard E. Norberg and S.I. JVeissman.
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