JOURNAL OF THE AMERICAN CHEMICAL SOCIETY (Registered in U. S. Patent Office)
VOLUME
82
(0Copyright, 1960, by t h e American Chemical Society) NUMBER 15
AUGUST 19, 1960
PHYSICAL AND INORGANIC CHEMISTRY [COSTRIBUTION FROM
THE
DEPARTMENO F CHEMISTRY, UNIVERSITY
OF
WISCONSIN, MADISON, WISCONSIN]
The Kinetics and Mechanism of the Reaction of Cerium(1V) and Chromium(III)1L2 BY
JAMES
YING-PEH T O N G 3 A N D EDWARD L. KING RECEIVEDJANUARY 16, 1960
In acidic aqueous sulfate media, the rate law for the oxidation of chromium(II1) by cerium(1V) has been found to be d[Crvl]/dt = k [Cerv]2[Cr111]/[Ce111].This rate law indicates that the transition state for the reaction contains one cerium 4. A reasonable mechanism atom and one chromium atom with a n average oxidation state for the two metal atoms of consistent with this involves a rate-determining reaction of cerium( I V ) with chromium(IV), the concentration of which is determined in a relatively rapid equilibrium with chromium( 111), cerium(1T') and cerium(II1). T h e empirical rate coefficient k shows an approximately inverse square dependence upon the concentration of bisulfate ion.
+
+
+
The role of the relatively unstable 4 and 5 oxidation states of chromium in oxidation-reduction reactions is of interest. The reaction of the three-equivalent oxidizing agent chromium(V1) and the one-equivalent reducing agent iron(I1) is second order in iron(I1) and is retarded by iron(II1) thus suggesting the one-equivalent reaction step involving iron(I1) and chromium(V) to be rated e t e r m i ~ ~ i n g .Reactions ~ . ~ ~ ~ ~ induced by the reaction of chromium(V1) and various reducing agents demonstrate both chromium(1V) and chromium(V) as possible reaction intermediates.b These relatively unstable oxidation states are also undoubtedly present as reaction intermediates in the reaction of chromium(II1) and the relatively powerful oxidizing agents which are capable of oxidizing chromium(111) in acidic solution. Cerium(1V) is such an oxidizing agent, and although the cerium( IV) -chromium( 111) reaction has been (1) Taken from t h e P h . D . thesis of James Y.-P. Tong, University of Wisconsin, 1953. Presented a t 134th National Meeting of t h e American Chemical Society, Chicago, Ill,, Sept. 1958. (2) This work was supported in part by a grant from t h e U. S. Atomic Energy Commission (Contract AT(l1-1)-64. Project No. 3). (3) Department of Chemistry, Ohio University, Athens, Ohio. (4) (a) C . Benson, J . P h y s . Chcm., 1 , 1, 356 (1903); (b) C . Wagner and W. Preiss, 2. anorg Chcm., 168, 265 (1928); (c) C . Wagner, i b i d . , 168, 279 (1928). ( 6 ) (a) F. H. Westheimer, Chem. Rcvs., 46, 419 (1949); (b) I. M. Kolthoff a n d M. A. Fineman, J . P h y s . Chem., 60, 1383 (1956); (c) W. A. Waters, Quart. Revs., 12, 277 (1958). (6) T h e use of the term three-equivalent oxidizing agent follows the suggestion of 'A'. C. E. Hlgginson and J. W. Marshall (1.Chert. Soc., 447 (1987)); its superiority t o t h e term three-electron oxidizing agent lies in t h e fact t h a t it does not suggest electron transfer a s t h e reaction mechanism.
used in analysis,' the kinetics of this reaction have not been investigated. In the present study, the rate of this reaction 3CeIV
+ Cr"1
= 3CeIII
+ CrVI
has been determined a t 25.0' in aqueous acidic solutions containing sulfate. The rate of reaction is conveniently measurable in such solutions; it is inconveniently high in perchloric acid solution. Sulfate-containing reaction media are not without complexities ; complex ions involving sulfate and cerium(IV),* cerium(II1) and chromium(II1) lo exist. The sulfate complexes of cerium(1V) and cerium(II1) and the outer-sphere complex of sulfate and hexaaquochromium(II1) ion are in rapid equilibrium with their environment. This is not true of the inert chromium(II1) sulfate inner-sphere complexes, which apparently do not form to a significant extent during the course of a kinetic run. The interpretation of kinetic studies in solutions of varying concentrations of cerium(1V) , cerium(II1) and chromium(II1) but constant sulfate ion concentration is not complicated by these sulfate complex ion equilibria. (7) H . H. Willard and P. Young, THISJOURNAL, 61, 139 (1929). ( 8 ) T . J. Hardwicke and E. Robertson, Can. J. Chcm., 29, 828 (1951). (9) T. W. Newton and G. M. Arcand, THIS JOURNAL, T S , 2449 (1953). (10) (a) Outer-sphere complexes, R. E. Connick and M-S. Tsao, Paper KO. 9, Division of Physical and Inorganic Chem., 123rd National A. C. S. RIeeting, Los Angeles, March, 1953. (h) Inner-sphere complexes, reference 1, and N. Fogel and J. M , J. Chow, Paper No. 96, Division of Inorg. Chem., 136th National A. C. S. Meeting, Atlantic City, Sept., 1959.
3805
3806
JAMES YING-PEHTONG AND
EDWARD L. KING
Vol. 82
transferring the mixture to the appropriate spectrophotonieExperimental Details cell. (Cells of 1, 2, 5 and 10 cm. length were used.) Reagents.-Chromium( 111) perchlorate was prepared by ter A Beckman Mode1 DU Spectrophotometer with a thermothe reaction of chromium trioxide with hydrogen peroxide stated cell compartment was used for the absorbancy in perchloric acid solution. Following the reaction, chro- measurements; measured absorbancy values were in the mium(II1) perchlorate was crystallized from solution and range 0.2 t o 0.8.theThe initial absorbancy measurement was then recrystallized from 1 M perchloric acid. generally made 2-4 minutes after mixing; as many as 50 abTwo independent sources of cerium( IV) were used. sorbancy measurements were then made a t 0.5 t o 10 One was reagent grade cerium(1V) perchlorate in 6 M perintervals for a period of 30 to 150 minutes. chloric acid ( G . F. Smith Chemical Company); the other minute The Absorbancy Indices.-The absorbancy values of rewas a cerium( 111)-cerium(1V) solution prepared by the action mixtures have been followed at 492 and 500 m p ; a t electrolytic oxidation of cerium( 111) sulfate in sulfuric acid. these wave only cerium(III), among the reactant Cerium(111) perchlorate was prepared from ( NH4)2Ce- and product lengths, species, is transparent. The absorbancy indices (NOa)&by first converting i t t o a solution of cerium(II1) of cerium(IV), chromium(II1) and chromium(V1) have been chloride in hydrochloric acid, next extracting this solution a t these wave lengths in each of the reaction mewith isopropyl ether to remove any iron which might have determined dia. Outer-sphere complexing of chromium(111) generally been present and then precipitating cerium(II1) chloride itself in the ultraviolet region of the spectrum but by saturation of the solution with h>-dragen chloride. manifests not in the visible region.I2 This was confirmed, a t least apThe cerium( 111) chloride was converted to cerium( 111) proximately; the values of the absorbancy indices of hexaperchlorate by fuming with perchloric acid; if the resulting 0.06 ion at 492 and 500 mp are 3.58 solution showed any coloration due t o the presence of cerium- aquochromium(II1) and 4.21 f 0.07, respectively; the uncertainties listed are ( I V ) , it was reduced with a n equivalent amount of hydrogen the average of the differences between the average value obperoxide. Ceriuni(II1) perchlorate was precipitated from tained for all media and the average values obtained for the solution by chilling. medium. The values of the other relevant absorbancy Ammonium perchlorate solution was prepared by the each are given in Table 11. These absorbancy indices reaction of ammonium hydroxide and perchloric acid. indices were measured on solutions with a five- to ten-fold range of Sodium perchlorate solution was prepared by the reaction of cancentration of the absorbing substance; Beer's law was sodium carbonate and perchloric acid. obeyed in all cases. This, a t first sight, may seem surprising The chemical substances used in the above described prep- since cerium(1V) and chromium(V1) can exist as monoarations as well as all other chemical substances used in this mericboth and dimeric species. I n the case of cerium(IV), the work were of reagent grade quality. dimerization is suppressed by the high concentration of sulDoubly distilled water was used in the preparation of all fate which converts the cerium(1V) very predominantly to solutions; the second distillation was from alkaline per- sulfate (and/or bisulfate) complexes.* I n the case of chromanganate solution using a Barnstead still. mium(VI), the monomer and dimer have approximately The Reaction Media.-The reaction was carried out in equal absorbancy indices (per gram atom of chromium(V1)) media of varying concentration of ammonium ion, hydrogen a t these wave lengths.13 ion, sulfate ion and bisulfate ion. A value of the bisulfate ion acid dissociation equilibrium quotient Q 2 = [H +I [SO4=]/ TABLE I1 [HSOI-] = 0.42 was used in planning the composition of the THE ABSORBANCY INDICES OF CERIUM(IV) A N D CHROMIUM I = 2.35 df." solutions; all solutions have an ionic strength The compositions of the five different reaction media are (VI) IS THE REACTION MEDIA,T = 25.0" given in Table I . The maximum initial concentrations of -Cerium(IV)--Chromium(VI )Medium the reagents not listed in Table I are cerium(Ii.1, 0.023 Ai: 492 500 492 500 for series no. in il mir mp mil ceriumiIII), 0.055 Ai. and chromium(III), 0.042 31. I t was assumed that the presence of these substances did not al82.3 61.1 9.18 1 14.0, ter the medium in the sense that the appropriate activitl57.8 6.39 79.2 2 10.1 coefficients were not changed with a variation in their con81.6 60.6 3 13.34 8.71 centrations. This latter assumption, upon which the deriva(80.5)" (59.4)" 9.11 4 13.9 tion of the reaction orders with respect t o chromium(III), cerium( IV) and cerium(II1) depends, is probably more 79.3 58.1 9.51 5 14.4 nearly correct than is the assumption that Q 2 has the same a Obtained by interpolation value in each of the five media of ionic strength 2.35 ,If. Only the determination of the reaction order with respect t o sulfate Experimental Results ion and hydrogen ion depend upon the assumed constancy The concentration of chromium(VIj, in gram of Qa.
atoms per liter, at a particular time was obtained from the absorbancy reading at that time by the use of an equation derivable from the reaction stoichiometry
TABLE 1 REACTIONMEDIA' . Stoichiometric concentrations
Series
C H C I O ~ C s ~ c ~ o nCmHlizsoa
.
Calculated concentrations [H + I [SOJ-] rHS01-1
1.652 ... 0.464 1 . 3 0 0 . 1 1 0.35 0.522 ... ,800 0 . 2 4 .51 39 ,400 1.06 .ll 29 1 350 0.372 086 22 1 279 599 301 1 06 ;i 1.207 .829 ,200 2 . 0 6 05; 14 '1 A formula in brackets denotes the molar concentration of the indicated species. The quantitl- CXY denotes the stoichiometric molnrity of XY. 1 2 3 4
The Kinetic Runs.-The kinetic runs were conducted by rapidly mixing thermostated stock solutions and then (11) T h e value of 02 at Z = 2 . 3 5 M was ohtained by interpolation of t h e equilibrium quotient values obtained from t h e study of Raman spectra o f ammonium bisulfate solutions: T. F. Young., I, F. Maranville and 11. hl. Smith, C h a p I V of " T h e Structure of Electrolytic Solutions " Edited by W I Hamer. John W i i e y and Sons, Inc., K e w Y o r k , rerv I-urii. 1!l.59 (We art. xrateful t o Professor Vouni: f o r making these d a t a available t < J us in 19.53 1
[CrYI]
=
{ A - Ao)/b(avI -
- 3aiv)
(1)
in which A and A0 are the absorbancy values a t the time under consideration and at zero time, respectively, b is the cell length and UVI, UIII and ~ I are V the absorbancy indices of chromium(VI), chromium(II1) and cerium(IV).14 The value of d [Crvl]/dt is, therefore, directly proportional to drl,:dt. The quantity ( a -~ a111 - 3a1v) was obtained by subtracting numbers of comparable magnitude. It must be admitted, therefore, that the values of the reaction rate obtained were not highly accurate; in the original treatment of the data the values of dA/dt were obtained analytically (12) This has been demonstrated for t h e chromlum(II1)-chloride system; H. S. Gates and E. L. King, THISJ O U R N A L , 80, 5011 (1958). ( 1 3 ) J. E'.-P. Tong and E. L King, ibid., '75, 6180 (1!153). ( 1 4 ) In describing the light ahsurption measurements, the nmiiinclaturr recommendrd i n the Xationa! Rurenu of Standards Letter Circular T,C 837 (1947) is used
Aug. 5 . 1960
3807
KINETICSOF CERIUM(IV) A N D CIIROMIUJI(III) REACTION
a t two to six points in each experiment.' The procedure involved the derivative of the Lagrangian interpolation formula and was applied to seven values of A a t equally spaced time intervals.15 The correlation of the values of dA/dt, with the concentrations indicated that the rate law
was obeyed in each of the reaction media. In this rate law, a symbol in brackets stands for the total concentration of the element in the indicated oxidation state and not the concentration of a particular species. Values of the rate coefficient k were obtained from values of dA/dt by the equation
The empirical rate coefficient defined by rate equation 2 shows an approximate inverse square dependence upon the concentration of bisulfate ion ; the values of the product k[HS04-J2 for the five reaction media are 0.61, 0.74, 0.49, 0.65 and 0.75 mole-' liter-' set.-'. This dependence is, of course, experimentally indistinguishable from one, k a [H+]-2[S04=]-2. The uncertainty in the average value of k obtained in each series is so large and the assumption of a constant value of Q2 is so questionable that there is no point in attempting any more elaborate correlation of the values of k with the composition of the medium.
Discussion
The inverse dependence of the reaction rate upon the concentration of cerium(III), a reaction In the series of experiments in reaction medium product, and the second order dependence upon no. 2, the value of k calculated in this way over a cerium(1V) are the most striking and revealing results of the present study. The retarding action -20-fold variation in [CeIV]/[CeIII] (from -0.2 to -4) varies by 40-5070. Considering that the of cerium(II1) cannot be due to the reverse of the calculated values of k obtained a t a particular value over-all reaction because the form of the rate law of [CelV]/[CelIr] vary by a comparable amount, it is not of the type resulting from such a cause. is clear that the one parameter rate equation is all The particular type of dependence of reaction rate that the present data really warrant. For the ex- upon cerium(II1) suggests that i t is produced periments in this series, there is a faint suggestion in a reaction step which precedes the rate-deterin the data that the denominator might be { [CelIr] mining step. The composition of the transition k' [CeIV]] ; the experiments upon which this state for this rate-determining step, as revealed by CrlIr conclusion depends are ones in which the concen- the form of the rate law (X* = 2 CerV tration of cerium(II1) is known least accurately. - CerlI), contains one cerium atom and one chromium atom, and the average oxidation state It can be stated that k' probably is less than -0.7. Rather than report the values of k calculated of the two metal atoms is +4. A reasonable mechanism for the reaction of the from the values of dA/dt, it seems preferable to report the values obtained from fitting the data to three-equivalent reducing agent chromium(II1) the integrated rate law. The integration of rate and the one-equivalent oxidizing agent cerium(1V) equation 2 by the method of partial fractions yields is the sequence of three one-equivalent reactions
+
+
CeIV + Cr"1
ki
--+ +CeIT' + Cr'V k? ks
Ce'V
+ Cr'V- t- CeT" + Cry kd
ki
CeIV
+ CrV If CeI'r + CrVI ka
which has the form Y = kt
+ YO
(4')
The initial concentrations and the observed values of the absorbancy allow the calculation of both y and yo. All of the data in each run were fit to equation 4' by the method of least squares with yo as a parameter to be evaluated. The values of yo so calculated agreed, with a few exceptions, with the values calculated from the initial composition within a few per cent. The values of k obtained in these calculations, presented in Table 111, differ from those derived from the slopes of A versus time by an average amount of 4.5%. Although the k values are not as accurately known as might be desired, the concentration ranges studied were so large that one has considerable confidence in the form of the rate law. (15) H. E. Salzer, "Table of Coefficients for Obtaining the First Derivative Without Differences," National Bureau of Standards, Applied Mathematics Series (1948).
The observed rate law is consistent with the second of these reactions being the rate-determining step. The concentration of the unstable intermediate chromium(IV), a reactant in this step, is fixed by [CrrV] = kl[CrlI1][Ce1V]/k~[Ce111]16
equilibrium in the first step. The empirical rate coefficient k is, therefore, identified as klk3/k2, and k', which may be barely detectable, is identified as ka/k?. The observed unimportance of the k' term indicates that kZ[CeIT1]> ks [CeIV]. Another consequence of the observed rate law is the inequality kb [CeIV] >> k4 [CeIrl]. That the chromium(IV)-chromium(V) transformation should be the bottleneck in the oxidation of chromium(II1) by cerium(1V) is of interest for, as already mentioned, i t is this same transformation, in reverse, which appears to be the slow step (16) This reversible first step provides a pathway for the cerium(1V)catalyzed exchange of oxygen between hexaaquochromium(II1) ion and water observed by R . A . Plane and H. Taube ( J . P h y a . Chem., S6, 33 (1952)).
3808
JAMES YING-PEH
TONG AND EDWARD L. KING
EXPERIMENTALLY DETERMINED VALUESOF
THE
Vol. 82
TABLEI11 RATECOXSTANTS IN THE SEVERAL REACTION MEDIA
2' = 2 5 i 0.50 concentrations ( X 108 l , / m o l e ) - ~ [Ce'I'] [Crr"]
Extent of reactiou followed
Enp.a, b
--Initial [Ce'vl
1-1 -2 -3 -4d
9.30 4.65 2.79 0.93
6.94 0.033 0.020 0.0066
8.71 8.71 2.18 4.35
5-42 17-63 9-48 8-50
2-1 -2 -3 -4 -5
17.26 17.26 23.32 23.32 23.32 23.32 11.66 23.32 4.65 18.59 18.59 1.86 0.93
2.49 5.94 3.46 3.46 20.73 38.0 1.73 55.3 0,033 27.77 7.04 0.013 .0066
42.6 42.6 21.3 8.52 21.3 42.6 21.3 42.6 8.52 17.04 4.26 8.71 8.71
24-77 21-74 12-44 8-79 11-64 20-55 8-42 14-46 5-41 4-27 18-62 20-60
9.30 4.65 1.86 0.93 0.465
.066 ,033 .013 .0066 ,0033
21.8 21.8 8.71 8.71 4.35
33-63 30-62 22-65 14-63 20-64
4-1 -2 -3d
4.65 2.79 0.93
,033 .020 ,0066
8.71 2.18 4.35
30-75 17-60 16-67
5-1 -2 -3 -4d
12.37 4.65 2.79 0.93 0.465
7.00 0.033 ,020 ,0066 ,0033
8.71 4.35 2.18 4.35 4.35
36-83 3 1-66 26-69 30-76 29-80
(9%)
kc ( X 103 1.-1 mole sec.)
5.5 4.8 5.7 4.0
Av. 5 . 0
-6 7 - 1
-8 -9 -10
-11 -12 -13
18-60
+ 0.6
6.0 5.9 4.6 5.0 4.9 5.8 4.5 5.6 3.8 4.9 5.0 3.7 3.9
Av. 4.9 f.0 . 6 3-1 -24 -3.3 -4 -jd
i .1 4.6 6.6 4.4 6.4
Av. 5 . 8 i 1 15.1 l5,Z 9.9
Av. 13.4 + 2.3
-jd
60 38 48 30 22
.-
Av. 40 & 1 1 a The initial number designates the reaction medium. Measurements made a t 500 mp only unless otherwise noted. The listed uncertainty is the average difference between the average value and the individual values. The temperature uncertainty contributes a n uncertainty of ~ t 6 t7o ~the value of k . Measurements made at 492 mp, e Measurements made a t both wave lengths.
It is also relevant that the X-ray difin the reduction of chromium(V1) by i r ~ n ( I I ) . ~ ,Symons.17 j~ Perhaps it is only a t this step that a change in co- fraction pattern of Ba3(Cr04)? is very similar to ordination number of chromium occurs. The that shown by Ba3(P04)2.18 There is also some evidence supporting the suggestion problem is not, however, as stated by ' C t ' a t e r ~ , ~experimental ~ ". . . . to know when, and how, this removal of that the coordination number of chromium(1V) is oxygen (from Cr04- to give Cr+++) occurs," but six. The similarity of the visible spectra of amrather to know the stage a t which, in the reduction monium vanadium alum, containing hexaaquoof chromium(V1), the coordination number in- vanadium(II1) ion, and vanadium(II1) ion in solucreases; one cannot argue against the existence of tionlg indicates coordination number six for the Cr(OH2)6+3as the form of chrornium(II1) in the latter species, which is isoelectronic with chroacidic non-complexing media. Chromium(IV), like mium(1V). The compounds KzCrFsand K&lnF6 chromium(III), may have coordination number 6, have the same X-ray diffraction pattern; in the and chromium(V), like chromium(VI), may have latter compound, manganese( IV) has six fluoride coordination number 4. The latter possibility is ions around it in an octahedral arrangemenLz0 quite reasonable since manganese(VI), which is iso(17) N. Bailey and M. C. R. Symons, J . Chem. SOL.,203 (1957). (18) J. Kleinberg, J . Chem. E d . , SS, 73 (1986). electronic with chromium(V), has coordination (19) 0. G. Holmes and D. S. IvIcClure. J . Chem. P h y s . , 26, 168G number 4, and direct experimental evidence sup- (1957). porting a tetrahedral configuration for hypochro(20) E. Huss and W. Klemm, Z . anovg. Chein., 262, 2 5 (1950); mate ion CrO4' has been obtained by Bailey and W.Klemm, Angew. Chem., 66, 468 (1964).
Aug. 5, 1960
THERATEOF OXIDATION OF D-GLUCOSE
The inverse dependence of the cerium(1V)chromium(II1) reaction rate upon the concentration of bisulfate ion or upon both the concentration of hydrogen ion and sulfate ion is reasonable. The final products of the reaction are both less cationic and probably less complexed by sulfate
[CONTRIBUTION FROM
THE
DEPARTMENT OF
PHYSICAL
3809
ion than are the reactants. As is generally the case under such circumstances, it is energetically profitable for some of the positive charge and sulfate ions to be lost prior to the formation of the transition-state.21 (21) E. L. King and M. L. Pandow, THISJ O U R N A L , 75,3063 (1x3).
CHEMISTRY, HEBREWUNIVERSITY, JERUSALEM, ISRAEL]
The Influence of Ionic Strength and of Temperature on the Rate of Oxidation of DGlucose by Bromine BY B. PERLMUTTER-HAYMAN AND A. PERSKY RECEIVED JANUARY 11, 1960 The influence of ionic strength on the rate of oxidation of D-glucose by bromine in aqueous solution has been shown t o support the previous assumption t h a t in strongly acid solution molecular bromine reacts with the D-glucose molecule, whereas in moderately acid solution, it reacts with the anion of D-glucose. The energies of activation for the two reactions have been determined. The high value of the rate constant for the reaction between bromine and the D-glucose anion has been shown to be due t o a low energy of activation, the Pz-factors being practically identical.
We have shown recently' that the oxidation of D-glucose in bromine water proceeds vkz molecular bromine and that the p H dependence of the rate of reaction is consistent with the assumption that the anionic form of D-glucose is oxidized much faster than D-ghlCOSe itself. We thought it desirable to substantiate this assumption by further experiments and therefore investigated the influence of ionic strength in somewhat greater detail and also measured the influence of temperature on the reaction rate. Methods The experimental procedure was the same as in our previous work.' The influence of the ionic strength was investigated in solutions containing a mixture of bromine and hypobromous acid. As described in section 4 of our previous paper,' this enables the reaction t o be carried out at very low buffer concentration and therefore a t low ionic strength. We again' achieved the @H by the addition of sulfuric acid and chose the values of PH of 1.5 and 3.03 ( a t an acid concentration corresponding t o a PH markedly higher than 3.03, the buffer-capacity of the acid would become insufficient), The rate equation has been shown' t o be
where c and e are the initial concentrations of bromine and of hypobromous acid, respectively, and x the concentration of the product formed a t timet. At pH 3.03, the second member in the square brackets is negligible; a t pH 1.5 it is small, and no appreciable error is introduced if we assume HOB^/ k B r z to be independent of the ionic strength. The ionic strength was varied by adding the uni-univalent electrolyte sodium nitrate. The influence of temperature was investigated in solutions containing bromine t o which bromide a t an initial concentration of 0.187 iM had been added. Because of the tribromide formed in this mixture (cf. section 2 of our previous paper') the reaction is slowed down sufficiently for kinetic measurements a t temperatures above 0" to be carried out conveniently. The rate constant was calculated from
where K I is the dissociation constant of tribromide (cf. equations 1 and 6 of our previous paper'). The values of pH were 1.57 which again' was achieved by the addition of sulfuric acid, and 4.04 and 4.55 a t which acetate buffers were employed. (1) B. Perlmutter-Hayman and A. Persky, THISJ O U R N A L , 82, 276 (1960).
The temperatures used were 0 and 25" a t pH 1.57 and 0, 9.4 and 25' a t the other two values of pH. The temperature control was 0.08' or better. The values of K 3 employed a t 0 and 25' were 0.051 and 0.0625, as measured by Jones, et At 9.4", we assumed Ks t o be equal t o 0.053. This was obtained from a n interpolation of the log Ka as. l / T plot (Fig. 1, crosses), in which we inserted also the values of Griffith, McKeown and Winn4 a t 16.5 and 21.5". As can be seen from the figure, the various values are not entirely consistent with each other. However, the error introduced into k B r , by a possible error in K Bis not too serious, since ( a ) the temperature dependence of K3 is only slight in comparison with that of the experimental rate constant and ( b ) expression 2 is less sensitive to changes in K 3 than would be an expression directly proportional to K,.
Results and Discussion 1. Influence of Ionic Strength.-At p H 3.03, a pronounced positive salt-effect was observed. This is illustrated by Fig. 2, where log k B r , has been plotted against the square root of the ionic strength (circles). On the basis of the assumption that a t this p H the reaction takes place between bromine and the glucose anion, this can be interpreted a s a typical secondary salt-effect, affecting the degree of dissociation of glucose. At constant pH, the slope in Fig. 2 should be 0.5 provided the Debye Limiting Law is applicable. Our experimental value is about 0.4 a t the lowest concentration amenable to measurement; the difference may well be due to a failure of the Limiting Law a t these concentrations. The slope of course decreases further with increasing ionic strength. On the other hand, a t p H 1.5 the increase of the rate-constant remained within the limit of experimental error when the ionic strength was changed from 0.03 to 0.28 (see Fig. 2, crosses). This is entirely consistent with the assumption of a reaction between two molecules, v k , glucose and bromine. 2. Influence of Temperature.-In Fig. 1, log kBrm has been plotted vs. (l/T). The lines for p H 4.04 and 4.55 are seen to be parallel (half-closed (2) Grinnell Jones aqd M. L. H a r t q a n , Trans. A m . Electrochem. Soc.. 80. 295 11916). (3) &innell Jones and S. BaeckstrSm, THIS JOURNAL, 6 6 , 1517 (1934). (4) R. 0. Griffith, A. McKeown and A. G. Winn, Trans. Faraday Soc., 28. 107 (1932).
