3863
KINETICSOF PERMANGANATE OXIDATION OF IODIDE ION
Kinetic Studies of Permanganate Oxidation Reactions.
I.
Reaction with Iodide Ion
by Louis J. Kirschenbaum and John R. Sutter Department of Chemistry, Howard University, Washington, D . C . (Received June 10, 1966)
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The reaction of 8 H + Rln04- 51- -t 6 / ~ 1 ~Mn2+ 4H20 has been studied in acidic media using phosphate buffers. At 35” and at ionic strength I = 0.9 M over the pH range 3 to 6 the reaction follows the rate expression -d(Mn04-)/dt
=
(MnO,-)(I-) (kz
+ k3a~+)
In the pH 5 region, kz = 51.2 I./mole sec and kl = 1.70 X lo71.2/mole2sec. The activation parameters for the second-order path at AH* = 1.30 kcal and AS* = -45.8 eu, while those for the third-order path are 3.77 kcal and -14.4 eu, respectively. Mechanisms for the two paths involving the formation of a (RIIn0J)2- complex prior to the rate-determining step are consistent with the data.
Introduction The reaction between the permanganate ion and iodide ion affords an opportunity to study kinetically the five-equivalent reduction of permanganate. It should be noted that the formation of either iodine or HOI as a product of a step in which manganate would be produced as a reduction product of permanganate would constitute a barrier to the progress of the reaction. The 1 - 4 2 couple has a potential’ approximately equal to that of the fi4n04--Mn042- couple, and the I--HOI reaction is thermodynamically forbidden. In spite of these factors, the reaction is extremely rapid. The formation of Mn(V) and HOI in a two-equivalent reduction is thermodynamically favorable. Experimental Section Reagent grade chemicals were used in all cases. Initially, they were recrystallized several times from water before kinetic use; results showed no difference in the experimental rate constant before and after recrystallization, and further runs were made without purification. Water was freshly distilled from a Barnstead still. Potassium iodide solutions were made up by weight while the potassium permanganate solutions were standardized spectrophotometrically at 520 mp where E = 2184 M-I cm-’. The stock solution of permanganate used in the Beer’s law experiments was
standardized against standard arsenious trioxide by titration. Verification that the reaction proceeded quantitatively to manganous ion and iodide (I3-), exclusively, under the conditions of the experiment ( K I ~=- 720) was accomplished in two ways. First, the amount of 13- produced in the reaction was observed spectrophotometrically at the end of the reaction,2 and secondly, experiments were performed in such a way that the amount of 13- produced could be titrated with standard thiosulfate. In both experiments the amount of I,formed in the reaction agreed very well with the amount calculated from permanganate present initially. The rate of the reaction was determined by following the disappearance of permanganate at 520 mp spectrophotometrically, using a specially adapted Beckman DU. In all reactions the iodide ion concentration was maintained constant by having it in large (from 40- to 100-fold) excess. Thus the kinetic disappearance of permanganate was pseudo-first order throughout the course of the reaction, as determined from the plots of
(1) W.M.Latimer, “Oxidation Potentials,” 2nd ed, Prentice-Hall. Inc., New York, N. Y., 1952. All thermodynamic estimates taken from this source. (2) A. D.Awtrey and R. E. Connick, J . Am. Chem. SOC.,7 3 , 1842 (1951).
Volume 70, Number 18 December 1066
LOUISJ. KIRSCHENBAUM AND JOHN R. SUTTER
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3864
log ( A , - A ) , the difference in the absorbance at infinite time and at time t. The order of the reaction with respect to permanganate and iodide was determined by this technique to be first order in each. The results are summarized in Table I. I n certain runs the reaction was followed through five half-lives to ensure a noncomplicated reaction scheme independent of products. The phosphate buffers were made up by weight to the approximate desired pH, using K2HPO4 and KH2PO,. These solutions were used to make up the stock solutions of the reactants. I n this way the solutions were made up to the same ionic strength and pH prior to mixing. The ionic strength was calculated in the usual fashion and was held constant in all reactions at I = 0.933 by keeping the total concentration of salts fixed. The buffers thus functioned to hold both pH and ionic strength constant. I n the low p H range, the buffers were made from KH2P04 to which small amounts of H Z 0 4were added to adjust the pH. ~
Table I: Rate Dependence on Mn04- and I- a [&hOa-],
[I-1,
moles,%
moles/l. x 102
Run
x
la lb 2a 2b 3a 3b 4a 4b 5a 5b 5c 6a 7a 7b 8a 8b 9a
8.22 8.22 8.50 8.50 3.40 3.40 3.28 3.28 1.86 1.86 1.86 1.92 15.3 15.3 2.88 2.88 2.88
105
3.49 3.49 2.57 2.57 1.29 1.29 1.74 1.74 0.872 0.872 0.872 0. €43 6.97 6.97 0.697 0.697 6.97
kz' = k/l-, k,
1. mole-'
8ec-1
aec - 1
1.98 2.08 1.52 1.50 0.737 0.740 1.01 1.08 0.518 0.535 0.556 0.410 4.06 4.28 0.400 0.399 4.10
56.7 59.6 59.1 58.4 57.1 57.4 58.0 62.1 59.4 61.4 63.8 63.8 58.2 61.4 57.4 57.2 58.8
59.3 i 1 . 8
t = 34.92'; Z = 0.933 A f ; h 5200 A; 2-cmcell; engnoa- = 2184 M-l em-1; pH 6.13.
The pH of the reactant solutions was measured before and after individual runs, using a Netrohm E-300 p~ meter which was standardized at the temperature of the reaction mixtures against standard buffers of known temperature dependence. In Order to the Of &? rapid reaction! a rapid mixing device was utilized. The permanganate The Journal of Phgsical Chemistry
solution was diluted to the desired initial concentration and ionic strength with phosphate buffer of the proper pH. A calibrated volume (3 ml) was pipetted into a special water-jacketed quartz cell of 2-cm path length.3 The solution in this was thermostated by flowing water, and the temperature was regulated to .t0.05' or better. Five-tenths of a milliliter (calibrated) of the iodide solution, made up to the same ionic strength and pH as the permanganate solution was taken up with a %nil hypodermic syringe equipped with an 18-gauge needle. The iodide ion concentration was adjusted so that the iodide concentration after mixing the two solutions would be in the proper excess necessary for the isolation technique. The syringe was housed in a thermostated brass cylinder which also served to hold it in a vertical position on top of the DU cell compartment, with the needle dipping into the permanganate solution. The syringe plunger was fitted with a tight compression spring4 which, when released, rapidly mixed the two solutions by forcing one into the other. In a separate series of experiments, the mixing time was determined using hydrochloric acid and sodium hydroxide solutions of equivalent composition, and observing the disappearance of the phenolphthalein color. The mixing time for complete color disappearance was approximately 30 msec. The change in absorbance during the kinetic runs was followed by taking the signal from the anode of an IP28 photomultiplier and leading it into a Type D Tektronix differential amplifier and Model 532 oscilloscope. The triggering of the oscilloscope was made to coincide with the mixing of the solution by coupling the release arm of the spring on the rapid mixing device to a microswitch and the external trigger input of the oscilloscope. The resultant change in absorbance was photographed with a Tektronix C-12 Polaroid oscilloscope camera. The film was read under a microscope equipped with a movable Vernier stage. The data so obtained were plotted in order to determine the rate law.
Results and Discussion Dependence on hydrogen ion activity mas determined in the pH range 6.2 to 3.2 (Table 11). A plot of the observed second-order rate constant, kz' us. U H C is linear in the high pH region (pH 5-6) showing a twopart rate law of the form rate = (Mn04-)(I-) { kz where the term in braces is
+ k3uH+]
h',the observed second-
(3) Constructed by Optical Cell Co., Brentwood, Md. (4) Design by R. G. Thompson and G. Gordon, University of Mary-
land, private communication, The reader may refer $0 R. Thompson and G. Gordon, J . S C ~Instr., . 41, 480 (1964).
KJNETICSOF PERMANGANATE OXIDATION OF IODIDE ION
order rate constant. Values of the slope and intercept 1.70 X are consistent with a value of lc2‘ = 51.2 107aHA. It is to be noted that this equation gives values for k3 in the pH 3 region that are higher than those observed experimentally. However, a plot of log (kz’- kz) vs. pH is linear over the entire pH 3 to pH 6 range, with a slope of -0.94, indicating that the two-part rate law is probably maintained throughout, but that the “long” extrapolation is responsible for the lack of agreement in the numbers. Examination of the last three entries of Table I1 lends support that the two-part rate law is being obeyed throughout the entire pH range studied. Here, although the p H spread is admittedly not large, the values of kZ’/aH+ = k3 result in a rate constant of 9.66 f 0.2 X lo6 (l./mole)2 sec-I, showing a simple first-order dependence on a H + , in agreement with the expected behavior of the two-part rate law on going to low pH. It is apparent that the errors in the rate constants determined in the pH 5-6 region, although reasonable, will not allow a proper extrapolation to the pH 3 region without including values from the intermediate pH 4 region, which are inaccessible in a system using phosphate buffers. The dependence of rate on temperature was determined at both a pH of 3.3 and of 5.49 (Tables I11 and IV). A plot of log (kz’/T) us. 1/T at the low pH gives a straight line and a calculated AH* and AS* of 3.77 kcal and -14.42 eu, respectively. In these calcula-
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Table I1 : Dependence of Rate on pH
PH
6.13 5.86 5.46 5.16 3.40 3.34 3.18
59.3 79.1 104.8 177.0 3.77 X loa 4.38 X lo3 6 . 5 8 X IOa
x lo8,
[I-1
k?‘, I./mole seea
[KHIPO~I, [KsHPOdI, M M
0. 133b 0.626 0.780 0.833 0.930 0.930 0.930
0. 533b 0.102 0.0587 0.033 d
... ...
M C
8.66 8.66 8.72 4.33 4.33 4.33
All rate constants are the average of two to four runs. These are approximate values that were adjusted to correspond to I = 0.933. ‘See Table I. d Small amount of Hap04 added to adjust pH. All runs at t = 34.92”, I = 0.933.
tions k2‘/aat was taken equal to k3, and no correction was made for the small contribution to k3 from the rate constant k2 of the nonprotonated path in this low pH region. A plot of log (k2’/T)vs. 1/T at the high pH value yields a curved line which is expected, due to the sizable contribution from k,. These kz values were corrected
3865
Table 111: Temperature Dependence at Low pH” ks = (kz’/aH+)
PH
I./mole Bec
x 10-6, (l./mole)a aec -1
3.46 3.44 3.38 3.33 3.34
1.61 2.14 2.62 3.56 4.38
4.63 5.89 6.28 7.59 9.59
kz’ X 10-4, t, OC
6.40 15.16 18.95 25.20 34.92
[I-]
=
M ; [Mn04-]
4.33 X
=
M; I
2.47 X
=
0.933.
Table IV : Temperature Dependence at High pH Correction t,
to
DC
PH
6.40 15.16 19.40 23.90 34.92 45.00
5.52 5.48 5.49 5.49 5.46 5.40
ka X 10-8’
ke‘
68.1 77.6 82.5 88.3 105.3 130.1
4.63 5.89 6.54 7.35 9.59 12.10
(ks X
k2’ UH+)
13.9 19.5 21.2 23.8 33.3 48.2
kz
54.2 58.1 61.3 64.5 72.0 81.9
From Table I11 by extrapolation or interpolation.
by subtracting k 3 a ~from + the kz‘, giving a value of kz at each temperature. These data plot linearly to give AH* and AS* of 1.3 kcal and -45.85 eu, respectively. The treatment of the data in this fashion is justified even though a given set of parameters lcz and k, will not span the entire pH range because of the argument presented above. Once the form of the rate law has been shown to be obeyed over this range, the subtraction of the experimental product IC,UH+ from kz’, even though they are of comparable magnitude at high pH, will yield values of kz without appreciable loss of precision. Since the AH is quite low for both the protonated and nonprotonated paths, the formation of an intermediate complex is i n d i ~ a t e d . ~This seems more likely than the formation of 01- through the rupture or partial rupture of an A h - 0 bond in a single step, and even more likely than the formation of either I or I + species in solution. The energy necessary to form such species in solution is in excess of 1 ev.6 I n the hydrogen ion independent step of the two-part rate law, the mechanism
*
(5) J. P. Hunt, “Metal Ions in Aqueous Solution,” W. A. Benjamin, Inc., New York, N. Y., 1963, p 114. (6) Z. Simon, Can. J . Chem., 38, 2373 (1960).
Volume 7’0, Number 19 December 1866
3866
LOUISJ. KIRSCHENBAUM AND JOHN R. SUTTER
MnOo-
+ I-
K
(03MnOI)2-
+
( 0 3 ~ h O I ) 2 - HOH k_ KO1
(rapid, K) (I)
+ HMnOd2-
H+
(rate determining)
(11)
is consistent with the observed kinetics. The observed AH * o ~ s dbeing the sum of the AHo for the complex formation step and the AH*II of the rate-determining step. The HOI formed would be rapidly reduced HOI
+ Haof + 21-
41 3 -
+ 2H20
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(rapid and complex) with HMn02- present to further the reaction. The formation of this hypomanganate species and transfer of oxygen is in keeping with arguments put forth by Carrington and Symond and by Stewart and van der Lindens in the permanganate-cyanide reaction. The (Mn041)2- complex is to be considered a derivative of hypomanganate with the character of the kinetic intermediates (01-) (htn04)2- being fairly well established prior to the rate-determining step. The hydrogen ion dependent path parallels the above mechanism
+
+ I- )J(03r\lInOI)2- (rapid, K ) (03MnOI)2- + H30+ k_ HOI + H&n04Mn04-
(rate determining)
+ MnO4-
= HMn04
(k = 5.6 X
mation of the HMnOr species may be important to the kinetics, it would be kinetically indistinguishable from the above mechanism. Five runs were made at 34.92O and pH 6.18 with various permanganate-iodide concentrations, and in addition, at ionic strength I = 0.0933. The observed second-order rate constant, kt', at this ionic strength was 18.6 d= 0.7 I./mole sec. No attempt was made to correlate the increase in rate with increasing ionic strength in terms of the Br@nsted-Bjerrum equation. The increase in A S in comparing the nonprotonated and protonated paths (with activation entropies of -45.8 and -14.4 eu, respectively) reflects the release of water molecules by the proton during the formation of the transition state. Assuming three water molecules released per proton, a value of -10 eu per water molecule is obtained for this entropy. Acknowledgment. The authors acknowledge partial support of this work through a grant from the donors of the Petroleum Research Fund, administered by the American Chemical Society. L. J. K. acknowledges support under a National Science Foundation Undergraduate Summer Research Program grant.
*
(111)
In this case, the change from second to third order with decrease in pH is seen in terms of a competition between HzO and HaO+ as an electrophile. Under the conditions of our experiments in the low
The Journal of Physical Chentiatw
pH range, permanganate is present almost exclusively in the nonprotonated form, e.g. and although the for-
(7) A. Carrington and M. C. R. Symons, Chem. Rev., 63,443 (1963).
(8) R. Stewart and R. van der Linden, Can. J. Chem., 38, 2237 (1960). (9) N.Bailey, A. Carrington, T. A. K. Lott, and M. C. R. Symons, J. Chem. floc., 290 (1960).
