KINETICS OF MÜTAROTATIGN OF ALDOSES IN THE PRESENCE OF METALLIC IONS By Nesley Brock Neely A THESIS Submitted to the School of Graduate Studies of Michigan S tate College of A griculture and Applied Science in p a r t i a l fu lfillm e n t of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1922 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. A ■ KINETICS OF >ÎÜTAR0TATI0N OF,ALDOSES IN THE PRESENCE OF metallic ions By Wesley Brock Neely AN ABSTRACT Submitted to tlie School of Graduate Studies of Michigan S tate College of A griculture and Applied Science in p a r t i a l fu lfillm e n t of the requirements fo r the degree of DOCTOR OF PHILOSOPHY Department of Chemistry Year Approved 193’2 O- ■ R eproduced w«h perm ission of the copyright owner. Further reproduction prohibited whhout perm ission. ^ . VJesley Brock Neely THESIS ABSTRACT The m utarotation of aldoses in s a l t solutions was investigated and c a ta ly s is by lithium , beryllium , magnesium, calcium, cupric and f e r r ic ions was observed. C atalytic constants were determined fo r each of these s p e c ie s . Addition of the aforementioned ions to a c eta te buffers caused diminution of the observed ra te constant a t lower concentrations, whereas a t higher concentration augmentation of the constant occurred. This phenomenon is explained by assuming th at the acetates of these ions are incompletely d isso ciated . On th is b asis i t i s possible to t r e a t the lithium acetate system mathematically. matical analyses, A and B were applied. reaction i s bimolecular throughout. allowed. Two d iffe re n t mathe­ In A i t was assumed th a t the In B termolecular processes were Although n eith e r the expression derived in A nor th a t in B permitted exact agreement with the observed ra te constants, b e tte r v a l­ ues for these constants were obtained in the l a t t e r a n a ly s is . From the observation th a t th ird order k in etic s may be applied to the metal ion c a ta ly s is of m utarotation, a mechanism i s presented in which a concerted attack by the metal ion and the nucleophilic reagent appear in the r a te determining s te p . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without nermk^inr, ' ACKNCWLEDGMSNT The author wishes to express h is sincere g ratitu d e to Dr, J . C. Speck, J r . fo r h is i n ­ valuable assistan ce; and to the Graduate Alumni A ssociation fo r th e ir fin a n c ia l aid in the form of a Fellowship . ■»*#r i R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS PAGE HISTORICAL INTRODUCTION.....................-............................................................................................. 1 EXPERIMENTAL PART........................................................................................................................ 5 Chemicals............................................................................................................................................ S o lu tio n s................................................................ Apparatus............................................................................................................................................ Spectral S tudies*..................................................................................................................... Kinetic Method....................................................................................................................... 3’ 5 RESULTS AND DISCUSSION..................................................................................................................... 10 SUjyEiARY................................................................................................................................................................ 36 REFERENCES....................................................................................................................................................... 37 Reproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6 6 6 H I S T O R I C A L IN T R O D U C T IO N & Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. H IS T O R IC A L IN T R O D U C T IO N The phenomenon of m utarotation of reducing sugars occupies an almost unique place in carbohydrate chemistry. Although i t i s of only- minor importance in the synthesis of these substances and has no estab­ lish e d ro le in any metabolic change or other b io lo g ic a l event^ i t s importance in the in v e stig a tio n of homogeneous c a ta ly s is renders i t one of the most s ig n ific a n t of a l l the transform ations associated with carbohydrate substances. M utarotation of a reducing sugar seldom appears to involve a simple change. Notwithstanding t h i s , the -in versio n of the pjrranose form i s probably the c o rre c t mechanism for the m utarotation of glucose as o rd in a rily observed, as well as th a t for many of the other aldoses. Since the development of th is concept has been adequately reviewed e ls e ­ where t h i s intro du ction w ill be lim ited to discussion of the c a ta ly s ts operating in th is type of transform ation. Glucose and i t s d eriv a tiv es have served as the p rin c ip a l substances for in v e s tig a tin g the c a ta ly s is of m utarotation, altliough the f i r s t precise k in e tic analysis of the phenomenon was c a rrie d out on lactose by Hudson ( l ) who observed th a t the re a c tio n i s sub ject to c a ta ly s is by both hydroxyl and hydronium ions and who evaluated c a ta ly tic constants for these species as indicated in h is expression fo r the pseudo constant: k = A + B [HgO^J + C [0H~], where A, B and C are constants a t a given tem perature. Lowry ( 2 ) in in v e stig a tin g the m utarotation of te tram ethyl- glucose in anliydrous pyridine and creso l observed th a t th is re a c tio n is Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. markedly catalyzed by mixtures of these substances and proposed a con­ certed mechanism fo r the c a ta ly s is involving simultaneous attack on the substrate molecule by the acidic creso l and the basic p y rid in e . The c la s s ic a l work of J . N. Brünsted ( 3 ) on the mutarotation of glucose in aqueous so lu tio n g re a tly amplified th a t of Lowry in demonstrating th a t the re a ctio n i s subject to c a ta ly s is by any proton acceptor or donor. I t remains a curious f a c t th a t Bronsted, in h is o rig in a l w ritin g , indicated complete acceptance of the Lowry in te r p r e ta tio n , y et the idea of a concerted c a ta ly s is gradually f e l l into d isre p u te , la rg e ly owing to the f a c t th a t no th ir d order term appears in BrBnsted's r a te expres­ sion. In I 93 U Pederson (U) represented the reactio n as occurring by way of a two step mechanism as shown below: Base catalyzed fa st j-i C H - 0 / + m + ^ A- 0 H0 H slow + HA C % 0 H R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. Aoid catalyzed o + B BH' H0 I slow +B The cu rren t revival o f the concerted mechanism r e s ts p rin c ip a lly on the recent work of Svrnin (5) who in a re in te rp re ta tio n of Bronsted's data showed th a t the m utarotation of glucose does indeed permit inclusion of a th ird order term in the ra te expression, and th a t tiiis term escapes detection because of the magnitude of the water c a ta ly s is . treatment the concerted mechanism was assumed. of the pseudo constant as k = In Si^rain's This led to expression r^ , where N i s any nucleophilic reagent, B any e le c tro p h ilic reagent, and r^ and r^ are the respective r e a c t i v i t i e s of these substances with resp ect to a fixed standard such as w ater. Application of t h i s expression to the mutarota­ tio n of glucose in an acetate buffer and equating B ronsted's experimental c o e ffic ie n ts to the appropriate combinations resu lted in fiv e simultaneous equations which upon solution gave the following expressions k =8 .8 x l0 - ^ + i; .ip c l0 “ ^ [A c 0 -]+ lx l0 2 [0 H " ]+ U x l0 -^ [H 0 A c ]+ 2 .IpclQ-^-K] .2xlO " 2[A cO "] [HOAc] R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. h Tills was exactly equivalent to B ronsted's expression except fo r the presence of the th ir d order term which was too small to be detected experiment a l l y . More re c e n tly Sixain (6) has demonstrated the existence of th ird order k in e tic s for the mutarotation of tetramethylglucose in pyridinecresol mixtures ( th is had not been previously shovm by Loviry) and has observed marked c a ta ly s is of the reactio n by the substances 2-hydroxypyridine and 2-hydroxy-i;-methylquinoline ( 7 ) in which nucleophilic and e le c tro p h ilic centers are combined i-jithin single molecules. Tliis may be regarded in tlie fu tu re as one of the more sig n ific a n t contributions to the general f i e l d o f homogeneous c a ta ly s is as well as to the p a rtic u la r f ie ld of enzyme catal^^^zed reactions . The s ta tu s of the c a ta ly sis of mutarotation a t the beginning of the present work may be summed up as follows; (a) The most p lausible mechanism for c a ta ly s is of the mutarotation of e ith e r glucose or tetramethylglucose involves a concerted attack on the sub strate molecules by nucleophilic and e le c tro p h ilic c e n te r s . These centers may be p a rts of separate molecules^ or io n s, o r may be incorporated within a single sp ecies. (b) Each of the nucleopiiilic c a ta ly sts previously observed i s a proton acceptor (Briînsted base) and each of the e le c tro p h ilic c a ta ly sts is a proton ■donor (BrSnsted a c id ) . Apparently no homogeneous c a ta ly sis by any other species was noted in e a r lie r work. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. EXPÏÏRH4ENTAL PART Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 5 EXPERIMENTAL PART Chemicals The c( -D-glucose used in these experiments was prepared a t the National Bureau of Standards ( l o t number ^ 0 ^ 2 ) . /3 -D-glucose^ D- galactose, D-xylose and L-rhamnose were P fan stieh l Chemical Company p reparations. The -glucose was r e c ry s ta lliz e d by Hudson’s method (8 ), and the galactose was p u rifie d by the Bureau of Standards procedure (9). Beryllium carbonate was a product of C. A. F. Kalilbaum Chemischfabrik. F erric perchlorate was obtained from the G. Frederick Smith Cheraical Company. A ll other reagents used in these experhnents (calcium carbonate^ lithium carbonateJ magnesium carbonate, nickelous chloride, cupric chloride, magnesium chloride, calcium ch lo rid e, sodium hydroxide, potassium hydrogen p h th alate, acetic acid and perchloric acid) were C. P. q u a li ty . Solutions Standard sodium perchlorate solution was prepared by n e u tra liz a tio n of perchloric acid with sodium hydroxide to pH 7.0. The various acetate s a lts were prepared by addition of standard acetic acid to weighed samples of the carbonates. The concentrations of stock solutions of the hydroscopic s a l t s , or those of uncertain composition, were determined by standard a n a ly tic a l procedures. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. Apparatus A Rudolph p olarim eter equipped with a sodiuiTi lamp and a thermo­ s ta te d 1-decim eter tube was used f o r measuring a l l o p tic a l r o ta tio n s . pH determ inations were made w ith a Beckman pH meter equipped with out­ side g lass and calomel e le c tro d e s . A Beckman spectrophotometer (model DU) and 1-cen tim eter Corex c e l l s were employed f o r the s p e c tr a l s tu d ie s . S p e ctra l Studies A 0.2 molar nickelous chloride so lu tio n was prepared and i t s s p e c tra l c h a r a c te r is ti c s determ ined. was observed a t 39$ mu. A maximum in the absorption curve O p tical d en sity readings were made a t four wave­ 3 8 0 , 39$ 5 UlO and 1^20 mu^ on mixtures prepared by adding x lengths m i l l i l i t e r s o f the 0.2 molar nickelous chloride so lu tio n to (lO-x) m i l l i ­ lite rs of 0 .2 molar glucose s o lu tio n . O p tical d e n s itie s were also determined f o r s o lu tio n s of nickelous chloride having the same concentra­ tio n s of nickelous ion as in the glucose mixtures . This i s e s s e n tia lly the method o u tlin e d by Job (lO) fo r the in v e s tig a tio n of complexes by the method of continuous v a r i a t i o n s . K inetic Method The r a te of m utarotation was followed by the change in o p tic a l r o t a ti o n . The r e a c tio n m ixtures were prepared as follow s: An a liq u o t of the app rop riate s a l t solution^ the io n ic stre n g th of which was u su ally R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. adjusted by a d d itio n of sodium p e rc h lo ra te , was cooled to the desired temperature ( e it h e r 18.00 or 18.90°) . This was mixed with a weighed sample of th e ald ose, and, a f t e r so lu tio n of the sugar, i t was d ilu ted to a d e f in ite volunie . so lu tio n of the sugar. The tim er was s ta r te d a t the moment of complete The o p tic a l r o ta tio n was then read a t approxi­ mately one-hundred-second in te r v a ls over a period of tJiree-fourths hour, and the equilibrium r o t a tio n a l value was observed a f t e r twenty-four h ours. constants in these experiments were Values f o r the observed r a te obtained in the usual manner from the following expression: k = + kg = 1 / t log ro -ro o /rt-ro o The r e s u lts of a ty p ic a l v e lo c ity determ ination are shown in Table I and Figure 1 . A ll v e lo c ity data are expressed in decadic logaritlm is, with the second as the u n i t of tim e. Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 8 TABLE I TYPICAL VELOCITY DETERMINATION (M utarotation of 0.5 M aqueous glucose s o lu tio n , pH= 5.8; t= 18.00°.) Seconds Reading 2 8 i |l 305U 9 .5 8 0 9 .5 U 8 9.1:71 9 .3 5 0 9 .2 7 U 9 .1 7 U 9 .0 7 2 8 .9 6 3 8 . BUG 8 .7 3 2 8.651: 8 .U 9 1 8.L 0 7 8 .2 6 1 8 .1 3 7 7 .9 9 5 7 .8 7 6 7 .7 5 2 7 .5 2 0 7 .3 8 3 Equilibrium i f . 760 67 139 207 310 U09 52U 632 751 895 ' 1019 1129 1318 lif53 163 7 181U 20Uit 2211 2hl2 %t - a logCRt - It. 820 U .789 It. 711 it. 590 it .5 ll t It.ltllt it. 312 It. 203 It .0 80 3 .9 7 2 3 .8 9 lt 3 .7 3 1 3 .6L 7 3 .5 0 1 3 .3 7 7 3 .2 3 5 3 .1 1 6 2 .9 9 2 2 .7 6 0 2 .6 2 3 .6 8 3 0 5 .6 8 0 1 5 .6 7 3 1 1 .6 6 1 8 1 .65U 56 .61t It 83 . 63 It68 .6 2 3 5 6 .6 1 0 6 6 .5 9 9 0 1 .590it0 .571 83 .56191: .5Ulti9 .5 2 8 5 3 .5 0 9 8 7 .1:9360 .1:7596 .1:1:091 .1:1880 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 500 1000 1500 TIME 200 0 25 00 3000 (SECONDS) Figure 1. Typical Kinetic Run. M utarotation of O.$M Glucose in a Water S o lu tion , ( t = 18.00° C pH = ^.8) R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. R E SU L T S AND D IS C U S S IO N Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 10 INSULTS AND DISCUSSION Preliminary stu dies of the e ffe c t of m etallic ions on the observed ra te of m utarotation of glucose in aqueous medium showed th a t there was a marked increase in the pseudo f i r s t order r a te c o n sta n t. The observed increase could not be a ttrib u te d to e ith e r a primary or a secondary s a l t effect since 0,2 was the maximum and Bronsted (3) showed th a t strength up to th is value . ionic strength used in these experiments, the reaction was independent of ionic I t must also be concluded th a t the v ariatio n in k i s not due to complexing of glucose by the metal ion fo r i f a complex were formed in appreciable concentration, a s h i f t in the equilibrium ro ta tio n a l readings would have been observed. The absence of such a s h ift in any of the systems studied i s shown in Table I I . Further v e r i f i ­ cation tlxat a complex i s not responsible fo r the e ffe c t was obtained in the experiment where the metal ion concentration was held constant and that of the glucose varied. These re s u lts are indicated in Table I I I . From the f a c t th a t the observed k ’s remained constant, i t i s evident th at a sta b le complex e ith e r i s not formed o r, i f i t i s formed, i s present in in s u ffic ie n t concentration to account for the observed phenomena. Application of the method of continuous v a ria tio n to the nickel glucose system (see Table IV, Figure 2) did indicate the formation of a one to one complex, however, the small change in the o p tic a l density substantiates the previous conclusion th a t the concentration of complex enough to be responsible fo r the increase in k . Reproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. is not large 11 TABLE I I ... COMPARISON OF EQUILIBRIWI ROTATIONAL READINGS IN THE PRESENCE AND ABSENCE OF 14ETALLIC IONS (GLUCOSE = 0.^4) Metal Ion M olarity Equilibrium Reading’'' None - a . 778 Lithium 0 .0 5 0 U.7 6 8 Beryllium 0 .0 5 0 i t . 771 Magnesium 0 .0 5 0 Calcium 0 .0 5 0 it . 778 Copper 0 .0 5 0 i t . 781 Iron 0 .0 U67 i t .765 Nickel 0 .0 5 0 it.7U2 , it.762 These readings represent the average value of several v elo city determ inations. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 12 TABLE I I I EXPERIMENT TO DETEmiNE THE EFFEOT OF VARYING THE GLUCOSE CONCENTRATION ON THE PSEUDO CONSTANT Cation M o larity Ion o .o s ^ Gu++ o .o k M olarity Glucose k X 10° X sec“^ 0 .9 1 .9 2 1 .9 3 1 .9 2 0 .3 0 .9 1-92 1 .9 U 0 .3 o .U Experiments were run in a 0.111 a c e ta te and 0 .1 a c e tic a c id , ( u = 0 .2 , t = 16.90° C) Experiments were run in a water s o lu tio n and the we; ( t = 18.00° C) Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 7} CD ■ D O Û. TABLK IV C g RESULTS Œ CONTimJOUü VACATION STUDY ON THE NICKEL GLUCOSE COMPLEX Q. ■ D CD C /) W o' 3 O ? Ni Voirme" Solution, ml. CD 'iave Length, mu 380 o p tica l D iffe r- Optical Ni++ MixSoln^'" ture** Ni++ Mix­ Soln* t u r e * * D iffe r - 8 T5 (O' 3" i 3 CD TI C 3. 3" CD "O o c a O 3 ■D O 3" CT 1— H CD Q. 3" O "O w w Optical Density, D ifference Ni++ Mix­ S o ln * Optical D iffer- Ni++ tu r e* * S o ln * tu r e 1 .0 7 9 .0 6 8 .0 1 1 .1 0 5 .087 .0 1 8 .0 7 9 .0 6 5 .0 1 4 .0 4 9 .0 4 1 .008 2 .1 6 0 .1 3 3 .0 2 7 .2 1 2 .1 8 1 .0 3 1 .1 5 6 .1 2 6 .0 3 0 .1 0 3 .0 8 3 .0 2 0 3 .2 ) 0 .2 1 2 .0 3 8 .3 2 9 .2 8 4 .0 4 5 ^51 .2 1 0 .0 4 1 .1 6 2 .1 3 2 .0 3 0 h JL8 .2 9 9 .0 4 9 .4 5 9 .3 9 4 .0 6 5 .3 4 9 .2 9 1 .0 5 8 .2 3 0 .19h .036 5 .1 2 9 .3 6 7 .0 6 2 .5 6 0 .4 7 2 .0 7 8 .4 3 4 .3 6 2 .072 .2 8 3 .2 3 6 .01*7 6 .1 8 8 .1 3 9 .0 4 9 .6 4 8 .5 8 5 .0 6 3 .494 .4 3 7 .0 5 7 .3 1 8 .2 5 0 .0 3 8 7 .5 7 8 .0 3 3 .754 .706 .0 4 8 .5 7 5 .5 3 4 .0 4 1 .3 7 9 .3 * .0 2 5 8 .6 5 5 .6 3 0 .0 2 5 .8 5 9 .8 2 9 .030 .660 .6 3 3 .0 2 7 .434 .la s .0 1 6 9 .B ill .8 0 5 .009 1.00 .8 5 0 .0 1 5 .8 1 2 .7 9 7 .0 1 5 .5 4 2 .5 3 3 .0 0 9 CD 3 (/) (/) o' 3 Indicated volume of 0.2 M nickel solu tion made up to fin a l volume o f 10 ml. with water. Indicated volume of 0.2 M nickel solution made up to fin a l volume o f 10 ml. with 0.2 M glucose so lu tio n . 14 .02 .03 . 0-4 Y .05 .06 MV ,07 .0 8 - - 5 X ^80 395 8 Figure 2 . R esults of Continuous V ariation Study .on Nickel Glucose S o lu tio n s. X = m l. o f 0.2M Ni++ so lu tio n made up to 10 ml. Y = (O p tic a l Density of unreacted Nickel) -(O p tic a l D ensity of reacted Nickel) Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 10 IS The e f f e c t of the m etal Ions on to a c a t a l y t i c a c tio n , and i t should be p o ssib le to evaluate c a ta ly tic constants f o r the v ariou s c a tio n s . between U and th e r e f o r e , must he a ttr ib u te d By m aintaining the pH of the medium 6 the pseudo r a te con stant in water s o lu tio n s may be represented by the. follow ing expression: where ko i s th e water ca ta ly sed co n stan t and km i s s ta n t fo r th e p a r t ic u la r m etal io n . the c a ta ly ti c In obtaining c a ta ly tic con­ constants fo r magnesium, calcium and cupric ions in the m utarotation of glucose the re a c tio n was c a r rie d out a t various con cen tratio ns of the ions and the pseudo c o n sta n ts determined. These r e s u l t s are given in Table V. P lo ts of k versus co n cen tratio n are shown in Figure 3. C a ta ly tic c o n stan ts f o r lith iu m , beryllium and f e r r i c ions were evaluated from experiments in p e rc h lo ric acid s o lu tio n by a p p lic a tio n of the expression k = k^ + k^^O [H3O+] in which k i s 4. km again the observed pseudo c o n s ta n t. The c a ta ly tic con­ s ta n t f o r hydro n i urn ion was rechecked with p erc h lo ric acid s o lu tio n s and found to be 2 .U3 x value of 2 . I 4 I X 10“^ 1 0 ( 3) . at 18°C i n close agreement with B rSnsted's ( i n p lo ttin g hydronium ion concentration a g a in st pseudo con stant (Figure U) sto ich io m etric concentrations ox Toerchloric a c id were u_sed f o r the concentrations of hydronium ion) , The r e s u l t s of the v e lo c ity determ inations with these metal ions are given in Table V I. Data f o r magnesium ion obtained in p e rc h lo ric acid are a lso included i n t h i s ta b u la tio n , and i t w ill be noticed th a t the R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 16 TABLE V EFFECT OF CALCIUM MA®IESIUM AM D CUPRIC IONS IN THE tîUTAROTATION OF GLUCOSE IN WATER SOLUTIONS (pH between U and 6, t = 1 8 .00°C ^ Glucose = O . ^ ) Metal Ion C oncentration X 1 Q2 moles k X lO^ sec“^ "^Catalytic Constant x 10'^ Mg** 2.00 U.o o ^ .00 7 .00 .92U .9US .9 7 0 1.0 0 1.72 Ca'^'^ 2 . SO s .00 .9 S 0 1 .12 U.Uo Cu"*"^ 2 .00 2 . SO .9 8 S 1.3S 1.9S 2.2S U.OO s .00 None 11.9 .8 8 0 C a ta ly tic co n stan ts c a lc u la te d from th e slopes in Figure 3. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 17 2 0 K X ro SEC" •9 02 04 M E T A L l OW o =cu ++ 08 MOLARITY 08 Figure 3. R elation of Pseudo Constant (k) to Metal Ion C o ncentratio n . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 18 2 0 KxlO^ 5 SEC’’ 0 •01 •02 03 •0 4 Figure U. R elation of Pseudo Constant (k) C o ncentratio n . •05 •0 6 to Hydrogen Ion R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 19 TABLE VI EFFECT OF FERRIC , MAa'jESIUl'l CALCIUI-'I, BERYLLIUM AND LITHIUM IONS IN PERCHLORIC ACID ÎIEDIÜM IN MUTAROTATION OF GLUCOSE ( t = l8.00°Cj, Glucose = 0 .514) Cation "Li+ Mg'*"* Be++ ^Fe++ M o larity Ion M olarity of [H^J 0.0^00 0.0^00 • 0.100 0.0128 0.0224 0 .0228 0 .0 2 5 0 0 .0 5 0 0 0 .0 5 0 0 0 .0 6 4 0 0 .0 2 7 3 0 .0 2 2 7 0 .0190 0 .0 2 5 0 0 .0 5 0 0 0 .0 5 0 0 0 .0 2 2 3 0 .0 2 2 3 0 .0 2 2 3 0 .0 1 5 5 0 .023 a 0.0640 0.0640 0 .0467 k X 10 4 X sec“^ C a ta ly tic Constant x 10^ 1.21 1.44 1.47 0 .0 2 3 0 2.47 1 .5 8 1 .6 0 1.43 1 .5 1 1 .5 0 3.00 3 .3 0 3 .0 0 1 7 .5 17 .2 1 7 .5 17 .6 1.46 18.0 17 .9 17 .8 2.55 100 2 .6 6 2 .9 0 0 .0640 Catalytic constants calculated from the following expression km = k(observed) - 8.80 x 1 0 - (Metal) 2 ,h3 x 10 ^ (H'*') ~ Catalytic constant calculated from the slope of the line in Figure 5. Reproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 20 a c id ity of th e medium does not a f f e c t the magnitude of i t s c o n s ta n t. F igure 5 shows a p lo t of f e r r i c c a ta ly tic ion concentration a g ain st pseudo co n stan t a t constant hydronium ion concentration (0.06lj.OM) fo r which the slope of the l in e equals the c a ta ly ti c con stant fo r the former s p e c ie s . The c a t a l y t i c co n stan ts fo r a c e ta te ion and a c etic acid were r e ­ checked before attem pting to evaluate the e f f e c t of metal ions on the re a ctio n in an a c e ta te b u f f e r . Since m utarotation i s independent of hydronium io n between pH h and pH 6 the con stants may be determined by varying one species and holding th e other c o n sta n t. s ta n t i s The pseudo con­ given by th e follow ing expression k = ko + k&cCAcCr) + k^^(HOAc) These r e s u l t s are shown in Table VII and Figure 6. The values of h . h ô X 1 0 ^ f o r a c e ta te ion and U.20 x 10“® fo r a c e tic acid agree clo se ly w ith Br8nsted*s values of h , h ^ x 10 ^ and U.O x 10 ® r e ­ s p e c tiv e ly (3) . The e f f e c t of m e ta llic ions on the observed r a te of m utarotation in an a c e ta te b u ffe r in d ic a te d an i n i t i a l decrease in the pseudo con­ s ta n t w ith in c re a sin g m etal ion co n cen tratio n . There was a sim ila r e f f e c t w ith x y lo se, rhamnose and g a la c to se , demonstrating th a t the phenomena was not s p e c if ic fo r the glucose m olecule. constant was observed f o r — glucose as fo r th e The same ra te -isomer in the presence of magnesium io n in d ic a tin g a lack of preference of the cation fo r one stereoisom er over the o th e r , Tables V III, IX, X. These r e s u l t s are tab u la te d in The e f f e c t of lith iu m and magnesium ions i s also Reproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 21 30 2 - 9 __ 2 8 2 6 2-5 001 0 02 003 004 F E R R I C I ON MOLARITY Figure 5. R elation o f • Pseudo Constant (k) to F e rric Ion C oncentration. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 22 TABLE VII EXPERH'ffiîVPS TO DETERMINE THE CATALYTIC CONSTANTS OF ACETATE ION AND ACETIC ACID ON THE l'ÎÜTAROTATION OF GLUCOSE ( t = 18.00°C, = 0 .2 , Glucose = O.^M) M olarity of Acetate 0.100 0 .1 5 0 0.200 0.100 0.100 0.100 M olarity of A cetic Acid k X 10^ X sec ^ Observed k X 10^ X sec C alculated 0.100 0 .100 0.100 1.38 1.61 ■ 1.81 1.37 1.59 1.80 0.100 1 .3 8 0 .150 1.39 0.200 l.h 2 1.37 1.39 i.ia T his was c a lc u la te d from the following expression: k = 8.80 X 10"® + k.20 X 10"® (KOAc) + L.I46 x 10"^ (AcO") R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. —i 23 20 © Ch^COO" 1*0 SÜPf ER MOLARITY" 20 Figure 6. R elatio n of Pseudo Constant (k) to Acetate Ion and Acetic Acid C oncentration. Reproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2h TABLE V III EXPERIMENTS TO DETERMINE THE EFFECT OF METALLIC IONS ON THE MUTAROTATION OF GLUCOSE IN ACETATE BUFFER. ( t = 18.90°C, u = 0 . 2 , HOA = O.IM, AcO“ = O.IM_, Glucose = O.SM) Experiment 5 ,9 ,1 3 ,2 0 ,2 2 Metal Ion M o larity x 10s k X 1 0 sec“^ None 1.52 *12 None 1.52 17 15 16 Mg++ 7 ,8 ,1 0 ,2 3 1 9 ,U2 Ca++ 60 Li+ Uo,55 61 Ul,58 36 35,37 Be** 33,39 Ni** 3 k , 38 None Mg++ ^ 6 6 j 7S 68 6 k ,67 78 63,71 ■ K ^ l.k 7 l.k k l.k 2 1.50 2.50 3.50 5.00 1.36 5.00 l.k k 2.50 5.00 7.50 10 .0 l.k o 2 .50 5 .0 0 1.39 2 .5 0 l.k o 5.00 1.30 2.50 5.00 7.50 10 .0 1.3k 1.37 l.k 2 1 .3 0 1.66 1.79 1.75 1.80 1.67 Reaction run in the absence of sodium p e rc h lo ra te . The remainder of these experiments were run in 0 .214 a c e ta te and 0.2M a c e tic acid ( u = 0 .ii) . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 26 TABLE X EXPERIMENTS TO DETERMINE THE EFFECT OF LITHIUM AND MAGNESIUM IONS ON THE MUTAROTATION OF GLUCOSE ACETATE BUFFER ( t = 18.00OC, u = 0 . 2 , HOAc = 0.]M, AcO" = O.lî-î, Glucose = O Metal Ion L1+ M olarity x 10% k X 10'^ sec“^ 2.00 If .00 S.00 6,00 8.00 10.00 1 .3 h 1.31 1.30 1.31 1.33 1.37 5.00 1.30 None Reproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1.38 27 shown i n Figure 7 . Experiment 12 (Table V U l) was run in the a c e ta te b u ffe r minus the sodium p e rc h lo ra te and c o n s titu te s a v e r i f ic a ti o n of B rcnsted’s observ ation of the absence o f primary and secondary s a l t e ffe c ts . The r e s u l t s o f the e x p e r i m e n t s vrith a c e ta te b u ffe rs in d ic a te th a t a t the lower metal ion concen tratio n a re a c tio n occurs wiiich masks the e f f e c t of th e c a ta ly s is by the m etal io n . A lo g ic a l explanation of such a phenomenon i s t h a t the con centration of one or more o f the c a ta lj-tic species p re se n t i s being e f f e c tiv e ly lowered. This conclusion i s i n d ir e c t accord w ith R. P . B e ll ’s work on the incomplete d is s o c ia ­ tio n of s a l t s ( 1 1 , 1 2 , 13 ) . B e ll p resen ts data f o r the decomposition of n i tramide ( 1 3 ) j s. general base catalyzed r e a c tio n , in the presence of calcium and barium s a l t s of carboxylic a c id s . The observed v e lo c ity c o n stan ts were sm aller in so lu tio n s of the s a l t s o f these b iv a le n t c a tio n s than they were in so lu tio n s of the corresponding sodium s a l t s . In explaining th ese r e s u lt s i t was assumed t h a t the calcium and barium s a l t s are incom pletely d is s o c ia te d , and the re sp e c tiv e d is s o c ia tio n co n stan ts were c a lc u la te d on tiiis b a s is . In any re a c tio n wliich as s u b je c t to c a ta ly s is by both acids and bases the problem of evaluating such d is s o c ia tio n con stants i s more complex. The r a te expression vrill c o n ta in f a c to r s re p re se n tin g the re a c tio n between the t r a n s i ti o n svate and th e o p p o sitely charged species p r e s e n t, and i t d is tin g u is h between in d iv id u a l r e a c tio n s . oecomes d i f f i c u l t to Thus B e ll ’s work, while i t a ffo rd s a reasonable explanation fo r th e observed phenomena, i t does not provide a s a t is f a c to r y method fo r computing the d is s o c ia tio n c o n sta n ts. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 28 f- 9 0 I 80 •60 Mg++ ( t = 18.90° C) 140 130 *2 4 Figure 7. R elatio n of to Pseudo Constant (k) . 6 8 10 and Li^ M olarity in Acetate Buffer Reproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 29 The only case wlilch lends i t s e l f to a reasonable mathematical a n aly sis i s the lith iu m a c e ta te system . The b i - and t r i v a l e n t m e ta llic ion systems involve too many v a ria b le s in the form of c a ta ly tic species (such as [MeAcO]'*’) to be handled q u a n tita tiv e ly . In analyzing the lith iu m a c e ta te system two methods^ A and Bj w ill be d iscu sse d . The assumptions underlying method A are as follow s: 1) Lithium a c e ta te i s incompletely d is s o c ia te d . 2 ) The observed r a te con stant may be expressed as follow s: k = (HOAc) + The d is s o c ia tio n constant k 3 (AcO") + k^ (L i’*') fo r lithium a c e ta te w ill be re p re ­ sented by the follow ing equations: LiAc •:-> (Li^) (AcO") (LiOAc) Let X = the L i’* ’ = + AcO" (l) Ka ^ (2) o rig in a l lithium ion concentration a = the o rig in a l a c e ta te ion concentration y = the amount of undissociated lithium a c e t a t e . Tlierefore = (x -y )(a-y ) y Solving t h i s equation fo r ^ y ie ld s the following: y = a + X + - [(a + X + Kf-j)^ - Uax]^/^ (3) 2 The observed v e lo c ity constant i s k = ko + k l (HOAc) + ks(a-y) S u b s titu tin g equation 3 in to k given by the following: + ks(x-y) (U) k y ie ld s : = ko + ki.(HOAc) + V^kg [ (a-x-Kd>+[ ( a+x+K^j) ^-iiax) i/aka^x-a-Kçj + [(a+x+Kd>^ “ Uax]V^] R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. (5) 30 This gives an expression in which the observed r a te constant i s a function of the metal ion concentration. I f th is fun ction i s in accord with the fa c ts the f i r s t d eriv ativ e should be zero and the second derivative should be greater than zero i f minimum p o in t. equation (5) possesses a Carrying out the required d if f e r e n tia tio n gives the following equations: + 1/2kg r (x-a + K^) L dx2 ■= kg [ ( a + X + [(a+x+K(^) 2 -Uax) x /a ] - Uax) ] 2 [(a + X + j +l/2ka+l/2k3 (x-a+K^)___________ V e ) .( a+x+K^) ^-Uax) - kgCx - a + K^) 2 - iiaxjs/s (7) + ka[(a + X + - ijax] - k^Çx + 2 [(a + X + 2 - Itaxis/a In order th a t d^k dx3 i s th a t; \ 0 (a + X + - a) ^ the necessary and s u f f ic ie n t condition - Uax On expanding th is expression, i t ^ (x - a + i s seen th a t the l e f t side is greater than the rigkit, and the l e f t side of the in eq u ality sign w ill be p o sitiv e i f and X = a^ + + x^ + 2aK^ + 2xK^ ^ 2ax. Substituting a = 0 . 1 0 .0 5 the values th a t these v ariables assume a t the minimum p o in t, in the above expression y ield s ; obviously tru e fo r any value of K^. minimum p o in t. + 0.3K^ + 0.0125 ^ 0.01 which is Therefore, the function does have a To c a lc u la te K(^ the f i r s t d erivativ e in equation (6) is s e t equal to zero , and the values of the v ariables a t the minimum are R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 31 substituted into the expression and is then obtained by approximation. T'nis gives a value of l .i i for the d isso ciation constant of lithium acetate. Employing th is value^ and performing the necessary calculations the calculated ra te constants l i s t e d in Table XI are obtained. In method B, the o rig in a l assumption regarding the dissociation constant fo r lithium acetate w ill be retained^ in addition i t w ill be assumed th a t the c a ta ly sis follows tliird order k in e tic s , assumptionj ^ k may be expressed as follows î =kg + Combining k b 'ith tliis new (KOAc) + ksCAcO') + kgCLi'^) + k a(li^) (AcO") (9) - k^ - ki(HOAc) into one constant K and su b stitu tin g the various algebraic e x p r e s s i o n s fo r the lithium and acetate ions yields the following equation: K = i/sk g [a - X - + [(a + + x)^ - liax]^/^] — + [ (a + + x)^ —Uux] / + k4 Kg [K^ + a + X - [(a + + ^/^kg [ x - a ] (10) + x)^ - Uax]V^l wiiich on d iffe re n tia tio n gives: ( 11) ■ kaKd [ [( a ! K