Kinetics of Osmium-Catalyzed Reaction between Cerium(lV) and Arsenic(ll1) in Sulfuric Acid Medium Robert L. Habig,' H a r r y L. Pardue, and J a m e s B. Worthington Department of Chemistry, Purdue Unicersity, Lafayette, Ind. The oxidation-reduction reaction between Ce(lV) and As(l1l) as catalyzed by Os(VIII) has been studied in 2M sulfuric acid. The reaction is first-order in Os(VIII) over a wide concentration range. The Ce(lV) and As(l1l) dependencies are complex and depend upon the relative ratios of these two species. A reaction mechanism and resulting rate law which satisfy the experimental results are reported. Arsenic(ll1) reduces Os(VIII) to Os(VI) and Os(lV) by two-electron steps. The resulting Os(1V) and Os(V1) are reoxidized to Os(V1II) by Ce(lV) in one-electron steps. Specific rate constants are estimated for each step and rate expressions which accurately predict reaction rate over a wide range of conditions are computed.
THE OXIDATION-REDUCTION REACTION between Ce(1V) and As(II1) is catalyzed by iodine ( I ) , osmium ( 2 ) , and ruthenium (3, 4 ) . The iodine-catalyzed reaction is widely used in the determination of iodine a t the trace level in biological materials. However, from a kinetic or mechanistic point of view, none of these reactions is well understood. Sandell and coworkers ( 2 , 3, 4 ) have reported kinetic information on the osmium- and ruthenium-catalyzed reaction. In the range of solution conditions investigated by them, it was reported that the osmium-catalyzed reaction is dependent upon the Os(VII1) and As(II1) concentration but independent of the Ce(IV), Ce(III), and As(V) concentrations; the ruthenium-catalyzed reaction is'dependent upon the Ru (VIII) and Ce(1V) concentrations but independent of the As(III), As(V), and Ce(II1) concentrations. Our interest in these reactions stemmed from a desire to exploit these differences in kinetic behavior to obtain Selectivity for the determination of osmium and ruthenium in mixtures of the two without prior separation. According to the abovementioned observations, any change in reaction rate resulting from a change in As(II1) concentration would depend only upon the osmium concentration; any change resulting from a change in Ce(1V) concentration would be indicative of the ruthenium concentration. Rates measured under different solution conditions could be used to compute individual concentrations of osmium and ruthenium, thus providing selectivity without time-consuming separations. Upon initiation of the work with the osmium-catalyzed reaction, it was noted that our observations differed significantly from those reported earlier ( 2 ) . The form of the rate expression reported is correct over only a limited range of As(II1) concentration. Rates predicted by their expression and reported experimentally are four orders of magnitude larger than any observed by us for similar conditions. In addition, 1 Present address, Duke University Medical Center, Department of Biochemistry. Durham, N. C.
(1) E. B. Sandell and I. M. Kolthoff, J . Am. Chern. SOC.,56, 1426 (1934). (2) R . D. Sauerbrunn and E. B. Sandell, Mikroclrim. A r f a , 1953, p. 22. (3) C. Surasiti and E. B. Sandell, Anal. Chim. Acta, 22, 261 (1960). (4) C. Surasiti and E. B. Sandell, J . Phys. Chem., 63,890 (1959).
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a real and rather complex dependence on Ce(1V) concentration was observed by us. Therefore, it was necessary to carry out a more thorough investigation of the kinetics of these reactions before attempting to utilize kinetic differences for analytical purposes. This report contains results of a study of the osmium-catalyzed reaction in 2 M sulfuric acid, interpreted in terms of the most probable pathway, and values for specific rate constants for the individual steps. Results of this study are compared critically with those obtained by other workers ( 2 ) . REAGENTS
All reagents are reagent grade or better, unless otherwise specified. They are prepared in deionized water from a mixedresin ion exchange column and stored in glass bottles. Primary standard grade As203was weighed on an analytical balance to prepare the stock As(II1) solution. The powder was dissolved in NaOH, then neutralized with HCIOI and diluted to volume with deionized water. Dilutions of this stock solution, 0.0625M, were made with volumetric glassware and diluted with the appropriate acid. The stock Ce(IV) solution, 0.125M, was prepared by dissolving (NH,),Ce(SOr)., .2H20 (G. F. Smith Chemical c o . , Columbus, Ohio) in 2 M H2S04 and was standardized by titration with the previously prepared As(II1) solution in the presence of Os04. Ferroin indicator was used for end point detection. The osmium solutions were prepared by dilution from a stock solution of 1.54 mg per ml in 2 M H2S04(or HCIOJ. The stock solution was prepared by dissolving 1 gram of OsOa (Engelhard Industries, Inc., Newark, N. J.) in 500 ml of acid. This solution was standardized by liberation of iodine from excess KI and subsequent titration with thiosulfate to an amperometric end point. Dilutions of a 100-ppm Os solution (prepared from the stock above) were made regularly before each series of experiments. INSTRUMENTATION
A modified (3, transistor-stabilized Spectronic 20 colorimeter (Bausch & Lomb, Inc., Rochester, N. Y . ) was used to make the measurements. The phototube current was taken directly to the summing point of a chopper-stabilized, solidstate, operational amplifier (SP65A, George A. Philbrick Researches, Dedham, Mass.). The output was stable to about 0 . 2 z T (O.OOO8 A) for several hours. The circuit in Figure 1 is used to convert the phototube current to a voltage proportional to absorbance. Operational amplifiers OA2, OA3, and OA4 are Philbrick P65AU solid-state amplifiers mounted on a Model MP Philbrick chassis with a self-contained power supply. The transistors in the feedback loops of OA2 and OA3 are housed in the same unit (Philbrick PLlP logarithmic transconductor) to reduce temperature effects. The output of OA4 is given by the following equation:
(5) H. L. Pardue and R. L. Habig, Anal. Chim. Acfu, in press.
--.
c
To Recorder
IK
1 Figure 1. Photometer circuit O.l/lf
kT where RI = 1.0 K , RP = 3.9 K , Eo = 2.303yand il and iz are the input currents to OA2 and OA3, respectively. When the output is recorded with time, a decreasing potential is produced for decreasing absorbance in the cell. PROCEDURE
The reagents are handled with tuberculin-type hypodermic syringes, fitted with Teflon needles (KF 18 TF, Hamilton Co., Inc., Whittier, Calif.). The full-scale rarige and chart speed of the recorder are coordinated with the wavelength and Ce(IV) concentration range to produce response curves which are easily interpreted. The initial rate is determined by measuring the initial slope of the response curves and using experimentally determined calibration factors to convert voltage change to concentration. Rate dependency upon the various parameters was determined by observing changes in the initial rate as a function of the parameter of interest, other variables being held constant. RESULTS
All results reported here were obtained in 2M sulfuric acid at 25°C unless stated otherwise. All experimental points are averages of a minimum of three runs each and most have been duplicated over extended periods of time varying from
weeks to months. These data exhibited relative standard deviations between -5 and 10%. Data showing the dependence upon total osmium added are represented in Figure 2. The dependencey on Ce(1V) and As(II1) concentrations are shown in Figures 3 through 6. Experimental data are represented by circles, triangles, and squares. The solid and dashed lines represent computed values of reaction rate using rate laws discussed later. In every case data points from different solution conditions are normalized and plotted on the same scale. In many cases, the changes in absorbance with time were very small. Consider the data in Figure 3 as a case in point. The rate of 1.O x 10-6 mole per liter-second corresponds to an absorbance change of about 2 X lo-' absorbance unit per second. Rate constants obtained from the two sets of experimental data in this figure differ by about 7 %. Figures 3 and 5 represent dependency upon Ce(IV) and As(II1) at very small ratios of [Ce(IV)]/[As(III)] and [As("/ [Ce(IV)], respectively. These dependencies are observed to be linear functions of concentration. Figures 4 and 6 represent dependencies upon Ce(IV) and As(II1) at ratios of [Ce(IV)]/ [As(III)] nearer unity. There are pertinent points to observe from these data. The As(II1) dependency is first-order at low ratios of [As(III)]/[Ce(IV)] and drops off gradually to zeroorder as this ratio increases. The Ce(IV) dependence is first-
b Figure 2. Rate dependency upon total Os(VII1) added
Osmium Concentration ( M o l e s / L i t e r
x I O')
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On standing, a dark precipitate settles from the mixture. The latter is thought to be a colloidal suspension of hydrated OsOz -Le., Os(IV) (6)-and the former an unstable form of Os(V1). 2.0 If the supernatant is made basic, the yellow Os(VII1) color appears. If two equivalents of As(II1) are mixed with one equivalent of Os(VIII), the resulting black solution contains twice as much Os(IV) as the solution from the previous experiment (determined by turbidimetric measurements). No Os (VIII) was found in the supernatant of this solution. If an [As(IUll : 1.0 x IO-* Os(VII1) solution, equivalent to those in the previous experiments, is made basic (yellow), it can be titrated with As(II1) to Os(V1) (pink). When this pink solution is acidified, a blackRate + 2 ,Los(m)3; , , 5 8 ,o-7 purple suspension is again obtained. This suspension is half as concentrated as one formed by complete As(II1) reduction I I I I I . 1.0 2.0 3.0 4.0 5.0 6.0 to Os(IV), and the supernatant again shows the presence of Os(VII1). R a t i o ( [ C e ( I P ) I / [ A s ( U I ) ] x 10') If either Os(IV) or Os(V1) obtained by reduction of Os(VII1) Figure 3. Rate dependency upon Ce(IV) at small ratios of [ W W I by As(III) is diluted and used as the catalyst in the redox to [.4s(III)] reaction, the reaction rate is identical to that observed for an equivalent amount of Os(VII1). Several pertinent conclusions can be drawn from these oborder at low ratios of [Ce(IV)]/[As(III)]and breaks off sharply servations. Arsenic(II1) is capable of rapidly reducing Os to a narrow region of zero-order as the ratio increases and then (VIII) to both Os(V1) and Os(1V). There is no evidence that passes through a region of negative dependency to zero delower oxidation states of osmium are produced. Cerium(1V) pendency as the ratio is increased further. can oxidize both Os(IV) and Os(V1) to a catalytically active These data demonstrate two limiting conditions, one in oxidation state. It is concluded further that Os(V1) in acid which Ce(1V) is in excess and one in which As(II1) is in excess. solution disproportionates rapidly to Os(IV) and Os(VII1). The variation of rate with total osmium added was investigated However, this disproportionation should have little effect on at each limit. In each case the Os dependency is first-order the catalytic reaction, as it is mzny times more probable that for a concentration range from 2.0 X 10-9 to 2.0 x 10-7 M . an Os(V1) species, if produced, will react with either Ce(IV) The data in Figure 2 represent the situation when As(II1) is in or As(II1) present at the millimolar level than with another excess. Os(V1) present at the submicromolar concentration range. The reaction rate was measured under these limiting conditions for Ce(II1) and As(V) concentrations up to 0.0125M. DISCUSSION Neither species affected the reaction rate. The effect of ionic strength on the reaction was studied beIn arriving at a probable pathway for the reaction, the tween 0.2 and 2.0 by adding NaCIOa to solutions which were principal facts which must be considered and accounted for 0.2M in H2S04. Variations of ionic strength in this range proare the Ce(IV), As(III), and Os(VII1) rate dependencies as well duced no effect on the reaction rate. as the lack of dependence upon Ce(II1) and As(V) and the fact In an attempt to determine the possible oxidation states of that any oxidation state of osmium between IV and VIII, Os involved in the catalysis, several experiments were perinclusive, can be produced. The Os(VII1) dependency is unformed with macro amounts (millimolar solutions) of OS complicated, being first-order throughout the hundredfold (VIII). If equivalent solutions of Os(VII1) and As(II1) in 2M H2S04are mixed rapidly, a rust-colored solution results, which ( 6 ) R. Cover and L. Meites, J . Am. Chem. Soc., 83,4706 (1961). rapidly undergoes transformation into a black-purple solution. 2.4
1
I
A
B
As(IU)
n
a 2.5x10-* 4 A 2 . 5 ~ 1 0 - 5~
2 . 5 ~ l O - 6~
0.4 I 1
Figure 4. Rate dependency upon Ce(1V) at large ratios of [Ce(IV)Jto [As(III)] 602
ANALYTICAL CHEMISTRY
1.0
1
I
3.0 4.0 5.0 Ratio (tCe(IP)l/IAs(tU)'l)
2.0
I
6.0
' I
7.0
8,0
concentration range studied. The As(lI1) dependency changes gradually from first-order to zero-order as the [As(III)]/ [Ce(IV)] ratio is increased. The Ce(1V) dependency is more complex, exhibiting a sharp rise to a maximum which preceeds the zero-order region. There are at least three possible pathways which must be considered. The! simplest and initially most attractive possibility is a cycle represented by Reactions 1, 2, and 3.
+ Os(VII1) Ce(IV) + Os(V1) Ce(IV) + Os(VI1) As(1II)
ki +
kz +
La
+ Os(V1) Ce(II1) + Os(VI1) Ce(II1) + Os(VII1) As(V)
+ Os(V1) Ce(IV) + Os(1V) Ce(&V) + OsW)
k4 -+
ks
kc -*
+ Os(1V) Ce(II1) + Osw) Ce(II1) + Os(V1) As(V)
--E!
I
8
/
1.0-
x
0
; 0.8, L
V
c .-
-1 0.6-
\
-n V
0
(1)
f 0.4-
[Os(pm)],= 3.16 x10”
-
4
tce(mi =
Y
(2)
0.2;
IO-’
5.0
Rote i 5
cce(mc)~ = 1.0
I I
x
t
1.0
(3)
o r a similar cycle involving the IV, V, and VI oxidation states of osmium as represented in Equations 4,5, and 6. All equations are written a s irreversible reactions, since neither Ce(II1) As(II1)
I
I
Ratio ( t A s ( I I I ) l /
2.0 tCe(I!Z)l
4.0
3.0 X
10‘)
SigUre’5. Rate dependency upon As(II1) at small ratios of
EAs(ur>lto [CecIV)l
(4)
+ kdCe(WI[Os(VII)l
(5)
(6)
nor As(V) affected the reaction rate. Applying steady-state approximations to Reactions 1 to 3 yields the rate expression given in Equation 7,
where [0slT, represents the total osmium added. (A similar expression applies for Reactions 4 to 6.) While this expression adequately accounts for the osmium dependency, it fails to account for both the Ce(1V) and As(II1) dependencies on two counts. First, any value of kl, k2, and k B which will satisfy the As(I11) dependency gives a much too gradual rise in the Ce(JV) dependency curve. Alternatively, any value of these constants which satisfies the sharp rise in the Ce(IV) curve gives a much too gradual rise in the As(II1) dependency curve. Second, this expression cannot account for the maximum in the Ce(IV) dependency. Therefore this simple type pathway must be discounted. Another possible pathway involving the As(IV) species as an intermediate was considered. This possibility could not be discounted as completely as those mentioned above. However, as we found no evidence to support this possibility, and as the reaction sequence outlined below satisfies all experimental observations completely, the As(IV) species was discounted as an intermediate. While neither cbf the reaction sequences (1 to 3 or 4 to 6) given above will satisfy the experimental observations when taken alone, it is possible that a combination of the two will be sufficient. Chemically, this is feasible, since as reported above As(II1) is capable of reducing Os(VII1) to Os(V1) and Os(IV) and the reaction rate is independent of whether the osmium is added in the IV, VI, or VI11 oxidation state. Furthermore, the negative slope in the Ce(IV) dependency curve suggests competing reactions such as would be involved in this sequence. The rate expression is easily derived for this sequence. The reaction rate is measured as the decrease of [Ce(IV)] with time, The rate is given by:
kz[Ce(IV)l[0~(VI)l
The total Os added, (OS18 = [OS(VIII)I
(8)
OS]^, is represented by:
+ [OS(VII)l + ~Os(V1)l+ [OSW)I + [OS(IV)I
(9)
It is assumed that no other oxidation states of Os are present. If the steady-state approximation is now applied to each of the Os species, and the individual concentrations are expressed in terms of [Os(VIII)], Equation 9 becomes:
When Equations 8 and 10 are combined and simplified, the following rate expression is obtained:
v =
+ +
A[Ce(IV)][As(~I)][Os~~k4[As(III)] k2[Ce(IV)J (11) B[Ce(lV)12 -I- C[Ce(IV)][As(III)] D[As(III)]*
where
A = 2kik3k~k6
B
= kzkksk6
+ k3) k:krkr(k~+ k6)
C = kikskdk,
D
=
If [ce(IV)] >> [As(III)], Equation 11 reduces to v
and if [ce(IV)]
Z~~[AS(III)][OS~]
(12)
k5)were obtained from the first-order portions of the rate-dependence curves, and the rest were picked to be in the same range. The program used gave both estimated values for the rate constants and predicted rates. Best values for the rate constants (in liters per mole-second) are kl = 3.9 X lo4, kz = 8.1 X lo4, k 3 = 8.1 X lo4, k4 = 2.5 X lo5, k5 = 1.2 x 105, and kg = 7.6 X lo5. Predicted rates are plotted as the solid curves in Figures 2 to 6. Close agreement between experimental and predicted rate is observed. Clearly then, the reaction sequence from which this rate expression was derived adequately fits these experimental observations. Furthermore, the reported rate expression and constants adequately predict the observed rate in the 2M HSS04 medium. Unfortunately, none of these constants, except kl, is unique, as other combinations will also satisfy the experimental observations. In this case the actual values obtained except for kl and to a lesser extent k5 depend upon the initial guesses made. An explicit value for kl can be obtained from the slope of the first-order region in Figure 5. The experimental value is kl = 4.0 x l o 4 liters per mole-second. Similarly, the magnitude of the quantity k5k6/(k5 k6) is determined from Figure 3 to be 1.05 x 105 liters per mole-second. Clearly it is not possible to separate k 5 and k6 from these data. The above treatment has assumed that all reactions in the sequence proceed at approximately the same rates. However, the odd-numbered oxidation states of osmium especially Os(V) and Os(VI1) are not stable in solution. In the macrolevel experiments reported in this work, no evidence of the presence of appreciable concentrations of these odd-numbered oxidation states was observed. Therefore it may be reasonable to assume that steps 3 and 6 in the above sequence are much faster than the other steps. Substituting k3 >> kzand k 6 >> k5,
+
Equation 11 reduces to:
where
E
=
Zki'k,'
F
=
ky'X-5'
G
kl'k5'
H
= kl'k4'
and where k,' is used to differentiate these constants from those obtained using Equation 11. When [Ce(IV)] >> [As(III)], Equation 14 reduces to: v
=
2kl'[A~(II1)][0~,]
(15)
When [Ce(IV)] ]?
= -__-___
+
(171
The expression obtained by substituting kl', k?', k4', and kb', into Equation 14 is: u =
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ANALYTICAL CHEMISTRY
8.4 X 104[Ce(IV)l[As(III)][Osl, { 4.0[Ce(IV)] -_ + 12.6[As(III)]I 4.2[Ce(IV)Jz 4.2[Ce(IV)] [As(III)] + S.O[AS(~II)]~
+
(1 8)
Both these expressions satisfy the experimental observations over a wide range of conditions. It is desirable to compare these results to those reported by Sauerbrunn and Sandell (2). Equations 17 and 18 were utilized to compute results for the conditions reported by these authors. Ratios of theii reported rates to the computed rates were evaluated. The average value of these ratios for the As(II1) dependency data is 1.01 x l o 4 with a range of 0.89 X l o 4to 1.09 X lo4. The data differ by a factor of lo‘. It is interesting to note the absolute values of their reported rates relative to the concentration levels-for example, for [Os(VIII)], = 5.26 X [Ce(IV)] = 1.00 X lO-3M, and [As(III)] = 5.0 X 10-4M they report a rate of 0.172 mole per liter-minute. Cleairly the reaction would approach completion in a fraction o f a second if this rate were correct. As these authors did riot use fast measurement techniques, and indeed report measurements made over periods of several minutes, such a reaction would have been complete before the measurement was begun. Therefore, it would appear that the reported rates are too high to have been measured by the techniques used by them. They report some raw data in their Table 11-namely, the time required for the transmittance to increase to 40% with initial Ce(1V) and ,4s(III) concentrations of 0.02M and variable amounts of Os(VII1). The molar absorptivity of Ce(1V) at 340 mg in 1M ]-GO4is about 5 X lo3. Therefore, the Ce(IV) concentration has decreased from 0.02M to 8.0 X 10“M during the reported measurement interval. As is noted in Figure 4 of this report, the reaction approaches a first-order dependence on Ce(lV) at a [Ce(IV)]/[As(IV)]ratio of unity or less as was the case in their work. Evaluation of the pseudofirst-order rate constant at 20 ppb osmium (approximately lO-’M) and using this to compute the initial reaction rate gives mole per liter second, which is of the a value of 1.6 x same order of magnitude as observed in this work. Therefore, it appears that a factor of lo4has been omitted in reporting the results of this earlier work. This conclusion is supported by the results of Surasiti and Sandell (3). The data in Figure 2 of this report indicate that mole for mole ruthenium is about five times more active as a catalyst than osrnium. Using their rate expression and Ru = 5.26 X lo-$’,[Ce(JV)] = 1.0 X and [As(IV)J = 5 x 10-4 a rate of 2 x 10-6 mole per liter-second is computed. Assuming VVnu = 5 Vo,the estimated value for Vo, under these conditions is 4 x 10-7 mole per liter-second. The computer value using Equation 11 or 14 is 3 X lo-’ mole per litersecond, representing reasonable agreement considering the assumptions involved.
CONCLUSIONS
The pathway proposed reveals that there are two cycles in which the osmium can operate: a cycle involving Reactions 1, 2, and 3 and one involving Reactions 4, 5, and 6. When the Ce(IV)/As(III) ratio is small, the rate-determining step will be Reaction 5 and the osmium will be operating in the lower oxidation-state cycle. As the [Ce(IV)] is increased, at constant [As(III)], Reaction 2 starts to compete with Reaction 4 for the Os(V1). At this point some of the osmium will be forced into the “upper” oxidation-state cycle. When a significant amount of osmium is oxidized to Os(VIII), the ratedetermining step will begin to shift to Reaction l , which is slower than Reaction 5 , and the observed reaction rate will decrease. When the Ce(1V) is made very large, Reaction 1 will be the sole rate-determining step and the Ce(IV) dependence will be zero-order. This qualitatively explains the shape of the curves in Figure 2. A similar argument can be- presented to describe chemically the expected shape of the curves in Figure 3. When the As(1II) is small, Reaction 1 will be the rate-determining step. As the As(II1) is increased, Reaction 4 will begin to reduce some of the Os(V1) to Os(1V). When a significant amount of Os is in the Os(1V) state, the lower oxidation-state cycle will affect the catalysis. Since the rate-determining step in the lower cycle is Reaction 5 , the As(II1) dependence will drop off to zero-order. In this report we have been concerned primarily with the probable reaction mechanism and the resulting rate expression in 2.OM H2S04at 25” C. There are complex dependencies upon both acid and bisulfate. This is to be expected, because of the existence of a variety of complexes between Ce(1V) and sulfate (7). These dependencies and their effect on the rate expression are being studied in detail and will be the subject of a future report. ACKNOWLEDGMENT
Appreciation is expressed to F. R. Duke for valuable discussions concerning the interpretation of this work. RECEIVED for review January 16,1967. Accepted February 13, 1967. Investigation supported in part by a David Ross XR Grant from Purdue Research Foundation and in part by the Air Force Office of Scientific Research. ~
~~
~
(7) T. J . Hardwick and E. Robertson, CUH.J . Ch~m., 29, 828 (1951)
V3.-39, NO. 6, M A Y 1967
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