3328
JAMES
H. ESPENSON AND EDWARD L. KING
shown in Fig. 10. These aggregates were obtained by mixing negative and positive sols. The positive sol was prepared by reversing the charge of deionized negative sol u i t h poly-N-isopropyl-4-vinylpyridinium bromide. The experiments made by mixing 400 A negative sol with 200 A. positive sol had shown t h a t this kind of coagulation was not the result of simple interaction between oppositely charged particles, but the result of instant mutual neutralization of opposite charges. If one kind of charge exceeds the other by a small difference, the residual small charge may bring about coagulation of type I11 Owing to imperfect mixing, however, some particles may get practically discharged, while others possessing a small charge of the same kind. for a short period of time during which the discharged particles coagulate rapidly, form compact aggregates of type I , and thus hinder further charge exchange through diffusion of ions. This process is followed by slow coagulation of the primary particles with the compact masses. This is believed to be the case in the formation shown in Fig. 10.
[CONTRIBUTION FROM
THE
Vol. 85
g. Conclusions.-It follows from this discussion that although the current theory of lyophobic colloids has been successful in explaining many aspects of the problem on semiquantitative basis, it fails to account for coagulation satisfactorily under ordinary circumstances. The reason for this failure lies in the fact that the simple picture of coagulation by compression of the double layer, which the theory is mainly concerned with, is frequently complicated. The complications arise from specific adsorbability of ions of both kinds. This conclusion parallels with the recent find~ " Mirnik, et ~ 1 . ~ ~ ings of Glazman, et ~ l . , and The introduction of the Stern correction in some explicit form will be an important refinement of the theory, as remarked by Overbeek (p. 312 of ref. 12). Also, the formulation of the stabilizing effect of the ions introduced (cj. subsection b ) , which appears to be a rate process, is another important and difficult problem to be tackled by the theoretical workers. (39) M. J. H e r a k a n d A I . M i r n i k , Kolloid-Z., 179, 130 (1961); A I M i r n i k , S o l w e , 190, 689 (1961).
DEPARTMENT OF CHEMISTRY, THE USIVERSITY OF WISCOSSIN,MADISOS, WIS.]
Kinetics and Mechanisms of Reactions of Chromium(V1) and Iron(I1) Species in Acidic Solution' BY JAMES H. ESPENSOK~ ASD EDWARD L. KING^ RECEIVED MAY24, 1963 The rates of reaction of chromium( 1.1) with aquoiron( 11) ion and tris-( l,l0-phenanthro1ine)-iron(11) ion have been determined as a function of concentrations of reactants and products. The rate l a w for reaction of k?[HCrOa-]* 1 . I n interpretation aquoiron( 11) ion is - d [ F e z + ,'dt ] = ( [H1' 3 [ F e 2 1' */[ F e 3+I ) 1 k,[HCrOa-] of kinetic d a t a on this reaction, account was taken of interaction of iron(II1) and chromium(\71); spectrophotometric d a t a yield a value Qt6 = [FeCrOa+][H'] /( [ F e 3 + ][HCrOd-] j = 1 . 4 a t 0' in solutions of ionic strength 0.0839 .If. T h e reaction of tris-( l,l0-phenanthroline)-iron(II) ion and chromiurn(1~1)is not retarded by tris(l,l0-phenanthroline)-iron(III)ion. Fewer mechanistic details of this latter reaction are revealed by the kinetic d a t a .
+
Chromiurn(1V) and chromium(V) may be unstable intermediates in reactions of stable + 3 and + G oxidation states of chromium with oxidizing and reducing agents, respectively. Reactions with one-equivalent reagents are particularly informative, and the kinetics of oxidation of c h r o r n i u ~ ~ ~ ( by I I I )cerium(1V) indicate t h a t reaction of cerium(1T.') and chromium(1V) is rate detern ining.l The present study deals with rates of reaction of chromium(V1) with two one-equivalent reducing agents, aquoiron(I1) ion and tris-(1,lo-phenanthro1ine)-iron(I1) ion. T h e first of these reactions HCrOl-
+ XFe** + 7H'
= Cr3+
+ 3Fe3+ f 4H20
(1)
was studied by B e n ~ o nand , ~ her results have been discussed by LfTestheimer.fi The present work done a t 0' using titrimetric and spectrophotometric procedures extends concentration ranges of the earlier work, characterizes the reaction order with respect t o iron(II1) ion more completely, and takes into account the interaction of iron(II1) and chromium(V1) t o form a relatively stable complex ion, FeCr04+. The second of the reactions HCr04-
+ 3Fe(phen)3*+ + 7 H + =
+
Cr3+ 3Fe(phen)13+
+ 4H:O
(2)
the kinetics of which have not been studied previously, ( I ) 'l'aken friim the Ph.1)
Thesis of J a m e s H. Espenson, University T h i i work was supported in part b y t h e United S t a t e s .4tomic Energy Commission (Contract A T i l I - 1 ) - 1 1 0 8 ) (21 Procter a n d G a m b l e Fellow, l'J01-19C,2 (:O 1)elmrtrnrnt of C h e m i s t r y , University of Colorado, Boulder, Colo [ + 1 J Y P l ' o n g and E I.. King, J A m Chein. Soc., 82, 380.5 (1900) ( , T i C . Benson, J P h y s C h e m . , 7 , 1 (1903); 7 , 350 (1903). ( i ; ) F H . Westheimer, Chem. R e o , 46, 419 (1949).
of Wiscimsin, 19fi2
was studied spectrophotometrically a t tempe rature between 0 and 4i)'. Experimental Details and Results Reagents.-At least two independent sources of each reagent except tris-( 1,10-phenanthroline)-iron( 111) ion were used. Doubly distilled water was used in preparation of some solutions; the second distillation was from alkaline permanganate in a Barnstead still. il redistillation of this water from an all-glass still provided another source of water. Reagent grade potassium dichromate was used both without further purification and also after it was recrystallized two or three times from water and dried a t 110'. Perchloric acid solutions were prepared by dilution of 60 and 72:;; reagent grade acids. Lithium perchlorate solutions were prepared either from twice-recrystallized reagent grade material or from material made b y reaction of lithium carbonate and a slight excess of perchloric acid. Lithium perchlorate prepared in the latter way was recrystallized from water. Iron( 111) perchlorate was prepared from both iron( 111) chloride and iron(II1) nitrate by prolonged fuming with perchloric acid. Hydrated iron(II1) perchlorate was crystallized from this medium and once or twice more from 604; perchloric acid. These solids contained appreciable perchloric acid, the concentration of which was determined in each ironf 111) stock solution as the difference between the total normality and the iron( 111) normality. T h e former quantity was determined by titration of the perchloric acid solution resulting from passing an aliquot of stock solution through a column containing cationexchange resin in the hydrogen ion form. Sources o f aquoiron(11) ion used in reaction solutions were irori(I1) sulfate heptahydrate, diammonium iron( 11) disulfate, and iron( 11) perchlorate. Stock solutions of the first two iron( 11) compounds wcrc prepared by dissolving reagent grade solids in dilute ( ( a . 0.01 'If) pcrchloric acid. Iron( 11) perchlorate solutions were prepared by tiissolution of iron wire in m . 0 . 5 .M perchloric acid a t temperatures below 80'. The absence o f irou(I1I) and chloride ion in these solutions was proved by tests with thiocyanate ion and silver ion, respectively. T h e iron( 11) stock solutions were stored under purified nitrogen in bottles equipped with self-sealing rubber disks; aliqnots were removed by hypodermic needle and syringe. hqueouc ~(iliitinnsof tris-( 1,10-phenanthroline)-iron(lI) sulfate
were prepared by appropriate dilution of G. F. Smith 0.025 M solution. Solutions also were prepared with iron( 11) sulfate heptahydrate and a very slight excess of 1,lo-phenanthroline monohydrate which had been recrystallized from a mixture of water and ethanol. D r . S . Sutin of Brookhaven Sational Laboratory generously supplied t h e solid tris-( 1,lO-phenanthroline)-iron( 111) perchlorate? used in these studies. Stock solutions in 9 .Lf perchloric acid were stored in opaque containers a t (-a. 2 . T h e substances used in the above-described preparations as well as all other chemicals used in this work were of reagent grade quality. Solutions were analyzed, if necessary, according t o accepted procedures. Spectrophotometric Experiments.-.Ill spectrophotometric studies were made using a Cary Model 14 recording spectrophotoineter rquipped with a specially constructed 10-cm. quartz cell* having a Liebig-type jacket of ca. 7-ml. volume through which therrnostated water circulated a t -20 rnl./sec. T h e temperature of solutions in the cell was probably constant t o within 0.05'. In spectrophotometric studies of reaction rate, the chart paper was driven a t 5 i n . / m i n . Concentrations were calculated from absorbance values read a t points no more closely spaced than corresponded t o 4-sec. intervals. Spectrophotometric Study of Interaction of Aquoiron(II1) Ion and Chromate Ion.-The Concentration dependence of light absorption of perchloric acid-iron( 111) perchlorate solutions containing potassium dichromate a t low and variable concentration is ciinsistent with occurrence of the reaction Fe3+
+ H C r 0 4 - z FeCr04+ + H +
(3)
Account niust be taken of this equilibrium in formulation of a rate law for the reaction of aquoiron(I1) ion and chromium(I'1). Each series of measurements a t high and constant concentration of iron( 111) perchlorate and perchloric acid and variable concentration of chromium(V1) gave a value of &, which is defined ds = A (log z o l I ) / b A c e with h the cell length and c6 t h e stoichiometric concentration of chroniiuni( \ ' I ) expressed as monomers. Beer's law was obeyed, ? . e . , (i6 is n o t a function of Cg; this is expected since monomeric chromium( \'I ) species predominate a t t h e low concentrations being studied (C6 < 7 X ,l!f).9 T h e dependence of 86 upon the concentration of aquoiron(II1) ion is given by the two-parameter equationlo de - ael a6 - a6 = s - -__ (4) [Fe3+] in which a6 is the molar absorbancy index of hydrogen chromate ion. At an ionic strength of 0.0839 '21 series of experiments were run ' hydrogen ion, a t 1.27 X 10-2, 2.43 X 10-2, and 4.63 X 10-2 h h u t only a t the intermediate acidity was the concentration of iron(II1) varied. It was only a t this acidity, therefore, t h a t values of both I and s were obtained. T h e concentration of aquoiron( I I I ) ion was slightly smaller than the stoichiometric concentration of iron( 111); correction for the acid dissociation of aquoiron(II1) ion was made using QI = [FeOH2+][H']/[Fe3'] = 6.2 X estimated for ionic strength 0.0839 M and 0' from work by Milburn and \-osburgh." The simplest interpretation of conformity t o eq. 4 is the formation of a 1-1 species FeCr04H,' n. If a particular value of n predominates in t h e acidity range studied, and if the absorbancy index of this species shows no medium effect with exchange of 0.034 M hydrogen ion for lithium ion, the value of s, interpreted as (a36 - as) with a36 the absorbancy index of FeCrOlH,,ICn, obtained a t the one acidity may be used t o obtain i' from d a t a a t other acidities. \'slues of Y so obtained are proportional t o the concentration of hydrogen inn, leading t o the conclusion t h a t one hydwgen ion is formed in the complex ion formation reaction. This conclusion is already implied in the balanced chemical eq. 3 . A summary of the derived quantities Q 1 6 = [ H + ] [ F e C r 0 , + ] / [ F e 3 +[]H C r 0 4 - ] = [ H ' ] / Y and (a36 - as) = s is given in Table I . T h e value of Qa6derived from these d a t a is 1.4 f 0.2. T h e maximum extent of formation of this 1-1 complex in the solutions of 0.0243 M hydrogen ion is calculated: [ F e C r O P ] / ([FeCrOl+] jHCrO4-1) = 1.1 X 0.00915/(0.0243 1.4 X 0.00915) = 0.30. T h e fit of the d a t a t o eq. 4 does not prove that a 1-1 complex is the only iron( I 1 I)-chromium(V1) species present in these solutions. Fortuitous combination of absorbancy indices and equilibrium quotient values can disguise the presence of apI
+
+
3329
REACTIONS OF CHROMIUM(VI) AND IRON(II) IN ACID
Nov. ,5, 1963
+
~~~~
(7) S S u t i n a n d B M G o r d o n , J . A m . Chern. Sor , 83, 7 1 (19fil) ( 8 ) T h e spectrophotumeter cells were purchased from t h e American I n s t r u m e n t Co of Silver Spring, M d . (9) J . Y P. T o n g a n d E. I, King, J A m C h e m S o r . , 1 6 , 6180 (19.53) (10) T W. N e w t o n a n d G .\I. A r c a n d , tbirl.. 75, 2449 (19.53); T . W N e w t o n a n d F. B . B a k e r , J . Phys. Chem , 61, 934 119.57) ( 1 1 ) R . hl. Milburn a n d W . C Vosburgh, J . A m C h e m . S o < , 77. 1352 ( 1 9 . 5 ~ ~ )K. hl Milburn. i b i d . , 1 9 , 537 11957)
TABLE I SPECTROPHOTOMETRIC STUDY OF THE REACTION Fer+
+ HCr04t =
0"
X 1 mole-'
10' X [ F e l l ] X 1 mole-]
0 0127
6 00
[Hi]
FeCr042f
I
=
+H+
00839 -21
A mp
10 X ax' X mole I - 1 cm -1
036 1 40 410 1 30 390 1 29 380 1 30 370 0 0243 1 54-9 15 410 3 21 1 53 1 50 390 5 63 1 40 380 6 23 5 86 1 32 370 0 0463 6 21 410 1 52 1 59 390 1 4; 380 1 41) 370 a .4t the two lower acidities, values of the absorbancy index of monomeric chromium(\.I) are 235, 536, 816, and 1130 1 mole-' c m . - ' at 410, 390, 380, and 370 mp, respectively. .It 0.0461 '14 hydrogen ion, the values are appreciably lower, being 215, 508, 791, and 1103 1. mole-' c n - l , respectively. The absorbancy of H.,Cr04 in this sDectral repion is less than t h a t of H C r 0 4 - ( j Y . P Tong and E ' L King,-J A m Chem S O C ,75, 6180 (1953)) preciable amounts of a second species.lZ Despite possible ambiguity, this simplest interpretation of the spectral d a t a in terms of only a 1-1 complex with Q 1 6 = 1.4 has been employed. Using Q 3 6 = 1.4, calculated values of the portion of chromium(1.I) present as iron( 111)-chromate complex range from -8 t o -40% in the solutions in which rates of reaction were measured a t an ionic strength of 0.0839 M . Kinetics of Oxidation of Asuoiron(I1) Ion bv Chromium(VI).This important reaction of analytical chemistry was studied a t concentration coriditioris under which the predominant species of chromium(\.I) were hydrogen chromate ion HCrOd- and iron(III)-chromate complex F e C r 0 4 + ; iron(II1) was present largely as aquoiron( 111) ion, although appreciable amounts of hydroxoiron(II1) ion were also present." Whether chromium(II1) was produced as hesaaquochromium( 111) ion or as dimeric species13 was not investigated in solutions of these c o m p o ~ i t i o n s . ' ~ extent of reaction as a function of time was determined a tT h0 z with both the titrimetric procedure used by Benson6 and a spectrophotometric procedure. Measurements were made on solutions of ionic strength 0.0839 and 0.200 M . Benson's method of measuring the rate of reaction of aquoiron(11) ion and chromium(V1) involved oxidation of iodide ion induced by the iron( 11)-chromium(\'I) reaction.5,6,'5 Under conditions employed in this work, the reaction of iodide ion with either iroti(II1) ion or chromium(V1) is slow. Therefore, the amount of iodine(0) produced when iodide ion is added t o an iron( I1 )-chromium( 1.1) reaction mixture depends upon the amount of iron( 11)-chromium(V1) reaction still t o occur, t h a t is, upon the amount of iron( 11) and chromium(V1) unreacted a t the time of addition of iodide ion. Appropriate calibration experiments were run t o establish t h e relationship between the amount of iodine produced and the amount of iron(I1) and chromium( \ ' I ) present. In calibration experiments, mixtures of iron(I1) ion and iodide ion were added t o solutions containing i r o n ( I I I ) , chromium( ['I), and chromium( 111 ) prepared by prior reduction of chromium(V1) with insufficient iron(I1). Immediately before addition of the iron( I1 ) ion-iodide ion mixture, the concentration of aquoiron(II1) ion was lowered by addition of 1.00 ml. of saturated disodium hydrogen phosphate per 500 ml. of calibration mixture, 500 ml. being the volume of solution used t o obtain each point in experiments a t ionic strength 0.0839 M. Experiments a t ionic strength 0.200 ill were carried out on a tenfold smaller scale. At the moment of addition of the iron(I1) ioniodide ion mixture, a calibration experiment was the same as a kinetic experiment a t the moment of addition of iodide ion. In (121 C. F . Baes, J . P h y s . Chem , 6 0 , 878 (1956). R . F . K r u h . J A m Chem S o < , 1 6 , 4805 (1951) (131 13. A r d m a n d R A P l a n e . %bad , 81, 3197 (19.591. (14) T h e violet color of hexaaquochromium(II1) ion does result. however. if t h e reaction is carried o u t in perchlorate solutions of sufficient concentra tion t h a t t h e c h r o m i u m ( l I 1 ) product is easily vi4ble F u r t h e r , it seems unlikely t h a t t h e pathway for production of d i m e r . n a m e l y , reaction of c h r o m i u m ( I 1 ) a n d c h r o m i u m ( l \ ' ) , could be i m p o r t a n t in this reaction mixture. (15) l a ) R A. G o r t n e r , J P h y s Chem , 1'2, G32 (1908), ib1 C Wagner a n d \V Prei-s, Z a?iorg Chem , 168, 26.5 (19281.
3330
JAMES
H. ESPENSON AND EDWARD L. KING
kinetic experiments, t h e 1.00 ml. of disodium hydrogen phosphate was added with t h e iodide ion.I6 After exactly 2.00 m i n . , t h e acidity was lowered by addition of ammonium hydrogen carbonate, and t h e iodine was titrated with arsenic( 111) solution of known concentration. T h e lowered acidity effectivelJquenches t h e slo\v side reactions of iron( 111) with iodide ion and of chromium(\'I) with iodide ion; it also defines t h e time interval in which induced oxidation of iodide occurs. T h e color of iodine in an immiscible carbon tetrachloride phase was used a s indicator. I t was possible t o determine the iron(I1) ion concentration in reaction mixtures in the t o 10-5 31 range. T h e calibration experiments obviate u s e of an assumed induction factor anti need of correction for iodine-producing side reactions. Titrimetric experitnents a t ionic strength 0.0839 M were run a t nine sets of concentration conditions: f j X 10-5 t o 4 x M chromium(V1) (expressed as m(inorners), 3 X 10-5 t o 6 X 41 irc,n(II), 0.0121 t o 0.0483 .I/ hytlrogen ion, a n d 1.6 x IOF3 tci 6.3 X 10Y3 .\/ i r o n i I I I ) . Xt ionic strength 0.200 .\I, experiments were run a t s i t sets of ctincentratioti conditions: 2.6 X 1 V 4 .If chromium(\'l), 6 x 10-5 t o 1.3 x 10-4 I f iron( I I ) , 0.0842 ,11hydrogen ion, and :3 x 1 0 - 3 t o 2 . 5 x 10-2 ,21 iron(II1). In each set of experiments, the iron(I1) concentration changed greatly, t h e chromium( \'I concentration changed slightly, and the hydrogen ion and iron( 111) concentrations changed almost n o t a t all. At each concentration, 3-7 calibration points were r u n ; t h e results were consistent with a linear dependence of iron( 11 ) concentration upon the concentration of iodine produced in t h e induced reaction. At each concentration, kinetic experiments were r u n with 2 t o 14 different time intervals (average number 6 ) of from 4 sec. t o I O m i n . ; t h e order of ruiining points was random. 'Twenty-six spectrophotometric experiments were run a t an ionic strength of 0.0839 .l1,with measurement being made a t 350, 370, 380, or 390 nip. T h e initial concentration of i r o n ( I I ) , t h e limiting reagent in ztll except two experiments, was 6 . 3 X or 14.8 X IO-5 .1/. T h e initial concentration of chro:16, and t h e initial mium(V1) ranged from 3 . 2 X 1 0 - 5 t o 9 . 6 X concentration of i r o n i I I I ) ranged from 1.6 X t o 9.5 X I f . T h e concentrations of hydrogen ion (0,0127, 0.0243, and 0.O463 .I/) were approxini:ttely the same as in t h e titrimetric experiments. T h e light absorpti
