(1728) Yagodin, G. A, Chekmarev, A. M., “Extraction,” pp. 141-53, Gosatoniiadat, Moscow, 1962. (1729) Yajima, S., Sibiiga, M., Yoehiyuki, K., J . At. Energg. SOC., J a p a n 4, 361 (1962). (1730) Yakabe. H. M..Dimitroff. J. M.. h u g , E. P., J . Assoc.‘Ofic. Agr. Chemists 45, 775 (1962). 731) Yaltkaya, E., Smturk, S., RILEM, Bull. Intern. (-&on Testing Res. Lab. Mater. Struct. (S.S.) No. 15, 110 (1962). 732) Yamada, S., Yamamoto, H., N i p pon Genshiryoku Gakicaishi 4,607( 1962). 733) Yamaeata. N.. Iwashima. K.. Koshu EiGiin’ Keiikyu Hokoku 10; 135 (1961); Nucl. Sci. Abstr. 17, 12206 (1963). 734) Yamashita, T , Kitamura, S., Amano, Y., Nat. Tech. Rept. ( J a p a n ) 8, No. 5, 436 ( 1 962). 735) Yamashita, M , Watanabe, H., S i p p o n Genshiryoku Gakkaishi 4, 588 i19fi2). ( I i 3 6 ) Yang, Y., H u a Hsueh Tung Pao, Yo. 5, 7(1961); Nzicl. Sci. -4hstr. 16, 31569 (1962). (1737) Yashchenko, M. L., Ovichinni-
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Nucl.
(1741) Yoshioka, T., Inouye, T., l’roceedings of 5th Japan Conference on Radioisotopes, Tokyo, May 21-23, 1963. Japan Atomic Industrial Forum, Inc., Tokyo, 1963. (1742) Yokoyarna, Y., Mabuchi, H., Shoji, H., Saito, N., Bull. Chem. SOC. J a p a n 36, 352 (1963). (1743) Young, R. J., Khorana, H. G., J . Am. Chem. Soc. 85, 245 (1963). (1744) Zaborenko, K. B., Alian, A,, “Apparatus for Continuous Extraction of Radioactive Isotopes with Automatic, Recording of Activity,” Zavod. Lab. 28, 1380 (1962). (1745) Zaduban, M., Jaderna Energte 9, No. 4, 114 (1963). (1746) Zakharievskii, M. S., Li, Y., Vestnik Leningr. Univ., No. 16, Ser. Fiz. i Khzm, No. 3, 131 (1962); ,l.’ucl. Sci. Ahstr. 17, 4549 (1963). (1747) Zaitseva, N. G., Chou, M. L., Radiokhimiya 4, 738 (1962). (1748) Zaitsev, V. A,, Grivkova, A . I.,
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Kinetic Aspects of Analytical Chemistry G a r r y A. Rechnitz, Department o f Chemistry, University o f Pennsylvania, Philadelphia 4, P a .
T
HIS REVIEW covees the pertinent literature through December 1963, with particular emphasis being given to work done in the 1:mt two or three years. Much progress has been made in recent years toward the generalization of kinetic models suitable for the classification of reactions according to their mechanistic properties (SO). Cnfortunately, such generalizations are still, a t best, semiquantitative in nature and can be applied only with caution even to idealized systems. The analytical chemist is forced to deal with real systems and is, therefore, largely dependent on experimental results gained by the study of individual reactions under practical conditions. A striking example of this situation exists in the case of he solution reactions of cerium(1V). Such reactions, which might be espected to proceed through relatively simple mechanisms because a one-electron rate step should be favored, actually are so enormously complicated by complesation steps, solvent effects, and reactions of intermediate species that i t has not been possible to write general mech-
anism for cerium(1V) oxidations. The work of Muhammad and Rao (65, 66), for example, seems to indicate that the osidation of methanol by cerium(1V) in perchloric acid media involves the formation of a 1 to 1 intermediate complex (with formation constant of 6.67) prior to the osidation-reduction step, while the identical reaction in sulfuric acid solutions gives no indication of such complex formation. The ohidation of oxalic acid by cerium(1V) in sulfate media has been studied by Rechnita and El-Tantawy (77, 7 8 ) , who found conclusive evidence for complex formation between sulfatocerium(1V) and osalate prior to the rate step. The effect of sulfate concentration on the rate of the over-all reaction was shown to result from the displacement of the complex formation equilibrium by sulfate or bisulfate, while the rate of the oxidation-reduction step itself is entirely independent of sulfate concentration. I n addition to classifying the mechanism of the cerium(1V)-osalate standardization reaction, the kinetic information obtained was also useful in explaining discrepancies in the stoichi-
ometry of other cerium(1V) osidation reactions carried out in the presence of oxalic acid. As in the study of the cerium(1V)osalate reaction (77, 7 8 ) , many authors have found it necessary to postulate free radical intermediates in order to esplain the esperimentally observed stoichiometry of the rate-determining steps in reactions where cerium(1V) interacts with species requiring two electrons for osidation. An important paper by Saffir and Taube (83) on the osidation of captive osalate gave strong indication that cerium(1V) acts to estract one electron a t a time. Similar conclusions were reached by Agrawal and Kapobr ( 2 ) in their polarographic study of the cerium(1V)-thiocyanate reaction, which appears to involve the intermediate formation of a thiocyanate free radical, and by Ramasnamy, Venkatarhalapathy, and I‘dupa (76) for the osidation of p-tolualdehyde by cerium(1V). Furt,her evidence favoring the formation of free radical intermediates in such stepwise reactions is given by Fronaeus and Ostman (SS), who concerned themselves with the VOL. 36, NO. 5 , APRIL 1964
s
453
R
reverse reaction-Le., the oxidation of cerium(II1). Using persulfate as the osidizing agent, the formation of cerium ( W ) was accompanied by the production of sulfate radical ions. Reactions of cerium(1V) with one-equivd e n t reducing agents also present something of a paradox. On the one hand, there are the studies of Dulz and Sutin (28) who, for reactions with iron (11) complexes, found that the free energies of activation of the complexes could be related to their standard free energy changes and that rate constants increase with increasing sulfuric acid concentration. King and Pandow (48),on the other hand, showed that the oxidation of bromide by cerium(1V) proceeds through at least two active intermediate complexes containing one and two bromide species, respectively, and that the rate of the reaction is retarded bv increasing sulfate concentration. Duke and Borchers (27) support a similar mechanism for the oxidation of chloride by cerium(1V). Because of the dimeric nature of mercury(I), its oxidation by cerium(IV), as studied by McCurdy and Guilbault (54, represents a unique opportunity to test the proposed mechanistic models for cerium(1V) reactions. McCurdy and Guilbault present evidence that the cerium(1V)-mercury(1) reaction indeed proceeds in two distinct steps with the breaking of the mercury-mercury bond, resulting from the oxidation of half the dimer, being rate-determining. The remaining mercury(1) fragment can then react rapidly with additional cerium(1V). A somewhat analogous situation is encountered in the cerium(1V) oxidation of thallium(1) which, according to Dorfman and Gryder (as), proceeds through the following mechanism in 6.18Fnitric acid: K
2Ce(IV) e [Ce(IV)] [Ce(IV)I2 Ce(II1)
+
Ce( IV) Tl(1)
K’ Ce(1V) 8 [Ce(IV) Ce(III)] 1
+ OH + OH
3
Ce( 111)
TI(I1)
+ OH
+ OH-
5
Tl(1)
+ Ce(1T’) e6 Tl(I1) + Ce(II1)
TI(II)
+ Ce(Iv) -ITI(III) . + Ce(II1)
suggesting that both direct electron transfer and radical intermediate paths may be simultaneously. involved in the over-all reaction. Yet a third alternative is presented by the cerium(1V)-manganese(I1) electron transfer reaction, studied by Aspray, Rosseinsky, and Sham (6)) which 454 R *
ANALYTICAL CHEMISTRY
involves an actual equilibrium of the type Mn(II1) Ce(1V) Mn(I1) Ce(II1)
+
+
for which equilibrium constants have been evaluated. Recent work on this reaction in sulfuric acid media by Rechnitz and El-Tantawy (79) has shown the important role of the solvent in determining not only the rate but even the net direction of this reaction. Free radical intermediates have also beeu proposed for the reduction of permanganate by cyanide ion in strongly basic media (32). In less alkaline media (pH about 12) the rate of the reaction is first-order with respect to cyanide and permanganate but independent of hydroxyl ion concentration. The thiocyanate-hydrogen peroxide reaction, studied by Csanyi and Horvath (25), is extremely complicated despite the deceptively simple rate law first-order with respect to the reactants and in hydrogen ion. The mechanism probably consists of a preequilibrium step forming a 1 to 1 complex of the reactants whose decomposition by interaction with hydrogen ions represents the rate-determining step. On the basis of oxygen exchange data, the initial decomposition product appears to be the thiocyanate free radical which rapidly hydrolyzes to sulfoxylic acid. Data gathered by Karraker (47) on the reduction of iron (111) by sulfurous acid in perchlorate media support the view that this reaction also proceeds through the formation of a bisulfite-free radical formed by the decomposition of a n unstable complex of the reactants. The bisulfite free radical reacts some 30 times faster with oxygen than with iron(III), resulting in nonstoichiometric results when the reaction is carried out in the presence of oxygen. Reactions of cobalt(II1) often proceed through bridged intermediates. In his study of the reduction of cobalt(II1) complexes by iron(II), for example, Sykes (91) was able to show that the mechanism involves the formation of a single bridged intermediate containing both cobalt(II1) and cobalt(I1). 10dide, thiosulfate, vanadium(V), and tin(I1) act through a mechanism similar to that of iron(II), while sulfite and nitrite reduce cobalt(II1) via a different route. According to hdamson and Gonick (1) the osidation of cobaltEDTA complexes by ferricyanide involves two successive steps-Le., the formation of a bridged intermediate and its dissociation to the final products. The intermediate species, it is suggested, contains EDTA functioning as a pentadentate ligand. Kopple and Miller (50) were able to show that the mechanism of the reduction of carboxylatotetrammine cobalt(II1) perchlorates by chromium(I1) also involves the for-
mation of a bridged intermediate. The two-step mechanism for the osidation of formatopentaammine cobalt (111) by permanganate recently proposed by Candlin and Halpern (19), however, features the formation of manganate and C o g + as intermediates. The oxidation of chromium(II1) by hydrogen peroxide, studied by Baloga and Earley ( 7 ) ,also seems to involve bridged intermediates, as does the more complicated reduction of chromium(V1) by iron(I1) (29).
A number of other reactions are of interest to analytical chemists. The decomposition of silver(I1) in water, for example, presents the main obstacle to the use of this strong oxidizing agent for analytical purposes. A recent kinetic study by Kirwin et al. (49) has shown that the rate of this decomposition in perchloric acid solutions can be retarded by silver(1). The complete rate law for this reaction is -d[MII)I
=
dt
~[MII)I2 [H+I
where IC = 0.14 X-l sec.-l a t 25’ C. with [Ag(I)] = 0.25.U in 6 X HC104, suggesting the disproportionation step BAg(I1)
Ag(1)
+ Ag(II1)
Unpublished experiments at higher perchlorate concentration (81) have given optical evidence of the formation of silver(I1) perchlorate complexes, as well. Disproportionation mechanisms are common to many oxidation-reduction reactions of analytical interest. I t was suggested by Bergh and Haight (9), on the basis of product analysis, that the reduction of molybdenum(V1) by tin(I1) in hydrochloric acid media consists of a two-step mechanism with the formation and subsequent disproportionation of molybdenum(1V) according to Mo(V1)
+ Sn(I1)
-
Sn(1V)
2Mo(IV) -.* Mo(5’)
+ Mo(1V)
+ Mo(II1)
Similarly, Hall and Markin (44) were able to show that the reduction of americium(V) involves possible disproportionation steps. A detailed kinetic study of the same reaction, recently reported by Coleman (ZOO), indicates that a t least two modes of disproportionation are operative, depending, in part, on the nature and concentration of the acidic electrolyte. Gordon and Taube (35) have reported that the exchange reaction between UOz+’ and water in perchloric acid is catalyzed by uranium(V), which disproportionates by a second-order process. The two-term rate law established for the vanadium(II1)-neptunium(V) reaction by hppelman and Sullivan (4) is interpreted as arising from the disproportionation of one of the prod-
ucts, neptunium(ITr), to regenerate neptunium(V) and yield neptunium (111). According ,o Higginson and Sykes (467, the oxidation of vanadium (111) by iron(II1) in perchloric acid proceeds via two routes, one of which involves the regeneration of vanadium (111) through the di!qwoportionation of the initial product, vrtnadium(IV), 21’(17’) + Y(’{)
+ Y(II1)
Fortunately for the analytical chemist, a large number of reactions obey relatively simple kinetics and can be assigned fairly straightforward mechanisms. The reduction of vanadium (V) by iron(I1) (:?5), for euample, follows mixed second-order kinetics a t constant acidity and probably proceeds through an activated complex composed of the original reactants. The plutonium(1V)-vanadium (111)reaction studied by Rabideai and Kline (75) obeys similar kinetic:, in perchloric acid media and does not seem to involve bridging groups. The interesting work of Peterson and Duke (74) on the ferricinium-tin(I1) reaction, which is mixed second-order iii the reactants but of complex order with respect to chloride ion, indicates that the favored reaction path involves chloro complexes of both reactanty, with five chloride ions in the activated complex, probably because chloride is necessary to reduce the free energy of the tin(II1) intermediate formed. Relatively stable binuclear intermediates have been obqerved by h’ewton and Baker (67) for the oyidation of chromium(I1) by uranium(V1) using a competitive reaction technique. The evidence for binuclertr tin(I1) species in the reduction of rhenium(V), as propoced by Banerje~,and Mohan (8), is unfortunately less convincing. Woods, Kolthoff, iind Meehan (92, 93) have recently undertaken the task of elucidating the mechanism of the induced oxidation of’ arsenic(II1) by the iron(I1)-persulfate reaction. The most important features of this complex reaction system are i,he apparent formation of arsenic(1’i) as an intermediate, a free radicsl chain reaction sequence, and the recognition of the fact that different mechanisms are operative in the presc:nce and absence of oxygen. CATALYTIC REACTIONS
Catalyzed reactions are of particular analytical interest from several viewpoints: Reactions too slow i,o be analytically useful may, in some ca:,es, be accelerated in the presence of a catalyst. Chemical reactants can sometimes be separated by the use of a selective catalyst. The rates of catalyzed chemical reac-
tions may be employed to determine the concentration of catalytic species. The determination of catalyst concentrations by reaction rate measurements may, in fact, be one of the most sensitive analytical detection methods yet devised. Michalski and Wtorkowska (64) report the detection of lo-” to gram per ml. of thiosulfate, with a standard deviation of less than lo%, by its effect on the rate of the iodine-azide reaction as followed amperometrically using a rotating electrode. Similarly, Bognar and Jellinek (24) were able to determine as little as 0.002 pg. of cobalt(I1) with an accuracy of *lo% by measuring the rate of the reaction between diphenylcarbazone and hydrogen peroxide in the presence of iron. Bognar and Sarosi (16) also detected as little as 0.001 pg. of osmium tetroxide a t a dilut’ion limit of 1 to lo9 by its effect on the oxidation of 3,3‘dimethylnaphthidine by chlorate, while Babkin (6) followed the rat,e of the manganese-catalyzed permanganate-oxalate reaction to determine concentrations of manganese in the 0.01- to 0.6-mg. range (chromium and iron interfere). Instead of making true rate measurements, which require fairly stringent observations, many workers have preferred to determine catalyst concentrations by measuring the accumulation of products or disappearance of reactants after a given time interval, or, in cases where the catalytic material i s consumed, carry out measurements only after the reaction has gone t.o apparent cornpletion. Lakin and Thompson (52), for example, showed that metallic gold is formed in proportion to the amount of tellurium present during the induced precipitation of gold from an acidic solut,ion of auric chloride, cupric chloride, and hypophosphorous acid. A measurable reaction takes place with as little as 10-9 gram of tellurium in 50 ml. of solution containing 1 mg. of gold. Similarly, the reduction of tellurate to tellurium metal by stannous chloride is rheniumcatalyzed and was used by Simon and Grimaldi (89) to determine rhenium in amounts as l o a as 2 x 10-’0 gram. Bontschev (17) was able to determine 0.1 t’o 8 pg. of vanadium as catalyst, in the oxidation of p-phenetidine citrate by chlorate in the presence of phenol as an activator. In a later paper (18), the same author identified vanadium(V) as the active cahlytic species. Bognar and Sarosi ( I 5 ) have examined t’he osmium tetroxide-catalyzed reactions of hydrogen peroxide with hydroxinone, orcinol, and 1,3-dihydroxynaphthalene by measuring color formation after a specified time interval to determine as little as 0.001 fig. of osmium(VII1) per 5 ml. of reaction mixture. Interference due to ot,her
heavy metals can be effectively masked by complexone(II1). A somewhat different approach was taken by Guilbault and McCurdy ($6, 37, 53), who employed silver(1) and/or manganese(I1) to speed u p the oxidation, by cerium(IV), of mercury(I), phosphite, hypophosphite, glycerol, erythritol, pentaerythritol, and 8-quinolinol in the precise (+0.3y0)determination of these materials. The unexpectedly effective action of the mixed silver(1)-manganese(I1) catalyst remains yet to be explained. I h h t and Srivastava (11) achieved similar precision in the determination of persulfate by t,he copper(I1)-catalyzed thiosulfatepersulfate reaction using an excess of thiosulfate and back-titrating. Most of the “catalytic” analyses depend upon the establishment of a simple proportionality bet’ween effective catalyst concentration and reaction rat,e (usually pseudo-first-order). This is not always the case, as is shown in the work of Fernandez, Sobel, and #Jacobs (31) on the periodate oxidation of leucomalachite green in the presence of manganese as catalyst. Here, a detailed kinetic study showed the nonlinear relationship between manganese concentration and reaction rate to be the result of a subsequent reaction which destroys the dye material. I t may safely be stated that the versatility and effectiveness of catalytic methods could be greatly extended if more detailed and reliable information concerning the effect of experimental variables were available. Ideally, this implies, complete kinetic st’udies aimed a t t’heelucidation of catalytic cycles and over-all mechanisms should be carried out in each case, a t least until sufficient data are available to permit generalization. It seems, however, that there is lit’tlecommunication between workers in the basic areas of reaction kinetics and those interested in the analytical exploitation of rate techniques. The experiments of Gupta and Ghosh, for example, on the reduction of persulfate by manganese(I1) (38), arsenic(II1) (39),and oxalate (40) in the presence of silver(1) as catalyst have shown that the reaction rate in each case is firstorder in persulfate concentration but independent of the concentration of the reducing agent. .4lkali metal cations and common solvent anions have an appreciable effect upon the reactiou rate-information which is surely needed if these reactions are to serve as the basis for versatile analytical methods. A more ambitious study has been undertaken by Csanyi and cokorkers in their investigations of the induced decomposition of hydrogen peroxide (24) and persulfate (62), respectively. The induced decomposition of hydrogen peroxide when oxidized by one-equivVOL. 36, N O . 5, APRIL 1964
455 R
alent reagents such as cerium(1V) and permanganate was found to be proportional to the hydrogen peroxide concentration with a limiting induction factor of 7 . 5 . The authors found a large number of ions which accelerate or inhibit the decomposition and were able to elucidate the actual catalytic cycle for the most effective catalyst, osmium tetroxide, in both acid and alkaline media. I n the system persulfate-hydrogen peroxide-cerium(1V) or permanganate (22) the induced disappearance of persulfate could be traced to the formation of HOz radicals via the primary reactions between hydrogen peroside and one-equivalent osidizing agent. Copper(I1) catalyzes the rate of the process without changing the characteristics of the induced reaction. Haight and coworkers have studied the molybdenum-catalyzed reduction of hydroxylamine (41) and nitrate (42, 43) by tin(I1). The over-all kinetics of these reactions are exceedingly complex and yield empirical rate expressions with fractional concentration dependences. I n the reduction of nitrate both the rate expression and extent of reduction depend on the nature of the (acidic) solvent. I n all cases, however, the authors propose molybdenum(1V) as the active catalytic species. In a study of the molybdenum-catalyzed reduction of perchlorate, on the other hand, Rechnitz and Laitinen (80) identified a molybdenum(V) dimer as the active catalyst on the basis of kinetic, optical, and electrochemical evidence. il particularly fine analytical kinetic study of the induced air oxidation of antimony(II1) accompanying the primary reaction between this reducing agent and bromate has been reported by Bishop, Ottaway, and Short (10). After an induction period, the rate of the primary reaction is first-order with respect to bromate and bromide, secondorder in hydrogen ion concentration, and independent of antimony(II1) concentration. The results are of much analytical significance, showing, in particular, over what p H range the reaction will be stoichiometric for a given set of experimental cimditions.
ANALYSIS BY REACTION RATES
In the past few years chemical analysis utilizing reaction rates has gained considerable popularity. Two basic approaches may be distinguished: analysis by means of direct reaction rate measurements and use of differential reaction rate measurements in multicomponent systems. The application of reaction rate methods to chemical analysis is, in itself, not a new approach and finds its basis, in fact, entirely in classical kinetics. So called “theoreb 456 R
e
ANALYTICAL CHEMISTRY
ical” papers consist largely of mathematical restatements of well known rate expressions into forms which are explicit in concentration terms or are convenient for graphical analysis. An excellent comprehensive ieview of the theoretical and practical aspects of reaction rate methods has recently been given by Mark, Papa, and Reilley (63). A t’ypical example of the direct use of reaction rate measurements in chemical analysis is given by the work of Malmstadt and Pardue (&?), who followed the rate of the enzyme-catalyzed conversion of glucose to hydrogen peroxide by an automatic potentiometric method based upon the further reaction of the product with iodide present in the system. Using the initial reaction rates, glucose could be determined in the 5- to 500-p.p.m. range. The identical reaction was also followed spect’rophotometrically by Malmstadt and Hadjiioannou (55) [see also Blaedel and Hicks (I$?)]. Furt,her work by hlalmstadt and Hadjiioannou has dealt with the automatic optical determination of alcohol by a reaction rate method (66) and the determination of a-amino acids by a similar technique (57). The alcohol is oxidized in the presence of enzyme and diphosphopyridine nucleotide, producing the reduced form of the nucleotide whose appearance is followed optically. The concentration of alcohol can then be calculated from t’he initial reaction rate. I n the second paper (67) the determination of nine different a-amino acids in the 4- to 50-p.p.m. range with a relative error of less than Zoj, is described. More recently, Pardue (71) has rest,udied once again the enzymecatalyzed glucose decomposition, using a rotating platinum electrode for amperometric rate measurements and, with Shepherd (73), devised a rapid automatic rate method for the det’ermination of cystine with a relative error of about 1% in the 0.25- to 25-p.p.m. range. The automatic device designed by Pardue (72) for the measurement’ of reaction rate curve slopes is also notewort’hy. Krivis and Supp (51) have used the pseudo-first-order reaction of ketosteroids with semicarbazone for analytical purposes. The course of the reaction is followed polarographically and the steroid concentration calculated from log current us. time curves. Zak and Baginski (94) determined labile iodine in organic compounds by its effect on the rate of the iodide-catalyzed cerium(1V)-arsenic(II1) reaction. .in optical flow met’hod was used to study reaction variables. I n a more fundamental study, Manni and Sinsheimer (59) used reaction rate measurements to elucidate the structure of hydrosyketones and determined mixtures of these ketones on the basis of their interact,ion with blue tetrazolium. Fi-
nally, Schenk (84) determined carbonyl derivatives by means of acid-catalyzed acetylation. In this study conditions were chosen so that the rate of acetylation is rapid compared to the rate of the competing hydrolysis reaction. The analysis of multicomponent mixtures via differential reaction rate measurements gained much impetus by the work of Siggia and Hanna, who applied this technique to the determination of mixtures of organic compounds having the same functional group. Thus, these authors were able to determine (86) mixtures of alcohols, aldehydes, and ketones, respectively, using a second-order differential rate method effective in distinguishing even between isomeric primary and seconda r y alcohols. Later, the same authors (45)were able to analyze mixtures of several types of amines by differences in their rates of reaction with isothiocyanate to form thiourea. More recently, Siggia and his coworkers have used the differential rate technique in the determination of unsaturated compounds (87) by second-order bromination or pseudo-first-order hydrogenation, diazonium compounds (88) by first-order decomposition in the presence of cuprous chloride, and mixtures of nitrogen-containing compounds by a modified micro-Dumas method ( I S ) . To minimize interfering side reactions, Schmalz and Geiseler (85) used a simultaneous rate method to follow the reaction between “benzoperacids” and olefins, while Sully and Williams (90) used the interaction of peracids and hydrogen peroxide with iodide to determine these substances by differential rate techniques. The latter study is made possible by the fact that the rates of equilibration b e h e e n peracids and hydrogen peroside are negligible in the p H 3 t,o 5 range employed. Garmon and Reilley (34) have proposed a method of proportional equations applicable to the solution of differential rate data for first-order or pseudo-first-order processes. In a later paper, Reilley and Papa (82) also demonst’rated a method useful for second-order processes, provided the reactants are initially present in equal concentrations. The method was applied to the determination of mixtures of 2- and ]-butanol. In addition, Papa, Mark, and Reilley (69) used a variety of differential rate t’echniques to analyze mixtures of fructose and glucose by reaction with acidic ammonium molybdate. The determination of carbonyl mixtures by reaction with hydroxylamine hydrochloride and/ or semicarbazide hydrochloride via continuous recording of conductance further served t o illustrate the pseudofirst-order method of measuring fractional lifetimes (10).
MISCELLANEOUS
.-l number of other ingenious applications of kinetic principles to analj.tical 1)rot)lems halie been reported. Aikens and Reilley ( 3 ) , for example, used a type of kinetic masking to 1)revcnt undehirable side reactions in the reduction of thromium(V1) by bisulfite. The authors carried out this rcduvtion in the presence of a slight excesb of E:IlTh whici served to chelate the labile possible i ntermediates4.e.) chromiuni(V) or (IV). Cover and lfeites (21) have proposed a method of studying first-order processes (such as ligand exchange) by producing or removing a reactant at constant rate by means of titration or coulometric generation. A t,heoretical treatment, showing how rate and equilibrium constants may be deduced from the resulting titration curve, i,j given. Finally, Margerum and coworkers (60, 61, 62, 68) have devised a new technique for the study of coordination kinetics based upon the use of cation exchange resins as metal ion buffers to control rates of coordination reaction$; by giving a low but constant concentration of metal ions. At present,, this technique is limited to negatively charged complexes of moderate stability and to rate constants not exceeding those of particle diffusion limits. LITERATURE CITED
(1) Adamson, A. W., ‘Gonick, E., Inorg. Cheni. 2, 129 (1963). (2) Agrawal, D. P., Kapoor, R. C., J . Prakt. Chem. 20,81 (1963).
( 3 ) Aikens, I). A,, Reilley, C. N., ANAL. CHEM.34, 1707 (1962). (4)
Applernan, E: H., !iullivan, J. C., J .
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