4724
JAMES
[CONTRIBUTION FROM THE WILLIAM
H.
J. BOHNINGAND KARLWEISS
NICHOLS CHEMICAL
VOl. 82
LABORATORY, NEW Y O R K
UNIVERSITY,
NEn'
YORK
53, N. y. 1
The Kinetics of the Oxidation of 3-Mercaptopropionic Acid with Potassium Ferricyanide' BY
JA>IES
J. BOHNING
AND
KARL\YEIES'
RECEIVED FEBRUARY 10, 1960 T h e kinetics of t h e oxidation of 3-mercaptopropionic acid with potassium ferricyanide in aqueous solution have been investigated under a variety of conditions, using a spectrophotometric method. I n the pH range 3.83-4 78, the rate law -d(ferricyanide)/dt = k(ferricyanide)? was found t o apply. The observed rate constant ( k ) was found t o increase with increasing thiol concentration and pH, to decrease with increasing initial ferricyanide ion concentration and with added potassium ferrocyanide, and to be unaffected by added dithiodipropionic acid. These results are discussed in terms of a mechanism in which a n initial reversible electron transfer is followed b y another, irreversible one.
The biologically significant conversion of thiols to disulfides has received much attention. In recent years, kinetic studies of this reaction in homogeneous solution have been made in which potassium persulfate,2s3sodium 2,6-dichlorobenzenenoneindopheno14s5and hydrogen peroxide6 were used as oxidants. These investigations indicated that the mechanism of the oxidation depends upon the nature of the oxidant, and that the transformation of the oxidant to a reactive intermediate may be ratedetermining. The simplest mode of oxidation involves the abstraction of one electron by an oxidizing agent. The present investigation was undertaken in order to obtain kinetic evidence for the occurrence of this electron transfer in the oxidation of thiols in aqueous solution. Potassium ferricyanide was chosen a s oxidant7since it yields a stable reduction product by the gain of a single electron. Further, it was thought that the inert nature of the ferricyanide ion would preclude the formation of complexes with the thiol or disulfide. Orienting experiments showed that reasonable reaction times and freedom for the variation of conditions could be obtained with 3-mercaptopropionic acid (I). The reaction was followed by measuring the decrease in ferricyanide concentration spectrophotometrically. Results The oxidation of I with potassium ferricyanide was first carried out on a larger scale in order to establish the course of the reaction. 3,3'-Dithiodipropionic acid was obtained in 9570 yield; no other organic product could be isolated. The spectra of potassium ferricyanide and potassium ferrocyanide show strong absorption in the ultraviolet r e g i ~ n . ~However, whereas the ferrocyanide has only negligible absorption above 375 m p , the ferricyanide has a strong band at 41s m p (log E 3.01).9 -It this wave length, which was (1) Presented a t t h e 137th National lleeting of the American Chemical Society, Cleveland, Ohio, April 1900 (Abstracts, p . 7 4 - 0 ) . (2) T o whom enquiries should be addressed. (3) R . L. Eager and C . A . Winkler, Cu?i. J . R e s m r c i i , 26B, X i (1948); I. &I. Kolthoff and I . K . lliller, THIS J O U R N A L , 73, S118 (1951). (4) R . E. Basford and 1:. S1. Huennekens, i b i d . , 77, 3879 ( I U 5 5 ) . ( 5 ) C. G. Overberger and P. V. Bonsignore. ibid., 8 0 , 5131 (19,39). (e) I. Pascal and D. S. Tarbell. ibid., 79, 6015 (1957); this reference also cites much of the pertinent literature on t h e kinetics of thiol oxidations. ( 7 ) T h e use of potassium ferricyanide in organic chemistry has recently been reviewed; see B . S. Thyagarajau. C h e m . R P V S .58, . 139 (1958). ( 8 ) J. A. Ibers and S.Davidson, THISJ O U R N A L , 73, 171: (1951). (9) J . Brigando. Bull. SOC. chim. France, 503 (1957), found log c 2.9!1 a t this wave length.
utilized for analytical purposes, solutions of potassium ferricyanide obeyed Beer's law in the concentration range of the kinetic experiments (to 1 X l o p 4 M). Neither Compound I nor dithiodipropionic acid show any absorption in this spectral region. Spectral examination of solutions containing relevant combinations of reactants and products showed no evidence of association or complex formation between these compounds. The spectrum of the ferricyanide-thiol mixture was measured a t an acidity (pH 1.4) a t which disulfide formation is extremely slow.'O The kinetic runs were carried out in sodium acetate-acetic acid buffered solutions using an excess of I. The reaction became extremely rapid as the pH increased, and useful data could only be obtained in the pH 4-5 range. To minimize the effects of spurious oxidation by atmospheric oxygen, all the solutions used were deaerated with nitrogen, and the runs were conducted under a nitrogen atmosphere. Gnder all the conditions examined, the rate of disappearance of potassium ferricyanide ( F ) obeyed a second-order law for the initia 160-9570 of reaction"
- dF/dt
=
kF2
(1)
Typical data are shown in Table I, and in Fig. 1, in which the reciprocal of the potassium ferricyanide concentration is plotted against time. The concentrations were calculated from the optical density a t 415 m p and the molar extinction coefficient a t that wave length. The observed pseudo second-order rate constant ( k ) was found to decrease with increasing initial potassium ferricyanide concentration, and with added potassium ferrocyanide ( F ' ) . The pertinent data are presented in Table 11. The variation of k with initial ferricyanide concentration can apparently be represented by the equation k
=
k'
+ k"/(F)o
(2)
With added potassium ferrocyanide a t constant initial ferricyanide concentration, k was found to vary with the total iron concentration ((F)" (F')o) in accordance with the equation
+
k =
k"' (Fh t (F')n
(3)
(10) T h e spectrum of potassium ferricyanide is unaffected by the addition of strong acid.8 T h e three dissociation constants of HaITe( C S ) Bare those of a strong acid,g and consequently only ferricyanide ions exist in aqueous solution. (11) I n some runs the concentrations of the reactants were such t h a t the concentration of I decreased approximately 105: during t h e course of the reaction. However, taking this variation into account hy using a third-order rate law only introduced a negligible correction term, which did not affect t h e linearity and slope of the plots.
Sept. 5 , 1960
4725
OXIDATION OF 3-hf ERCAPTOPROPIONIC ACID
4
0
4
8
V
16
12
Time, minutes. Fig. 1.-Effect of thiol concentration; ( F h = 9.11 X l O - 5 M ' , p H = 3.83, T = 25.0'. (HRSH)o concentrations: M; 2, 17.9 X l W 4M; 3, 26.9 X lO-'h'; 4, 1, 8.96 X 35.8 X lo-' JI.
These relationships are illustrated in Fig. 2. The slopes (k" and k"') appear to be the same in the presence and absence of added ferrocyanide. Several of the slow, ferrocyanide-retarded reactions were followed for sufficient time to establish that even under these conditions the oxidation proceeds essentially to completion, Dithiodipropionic acid (HRSSRH) was without effect on the rate, even in the presence of additional potassium ferrocyanide (Fig. 3). POTASSICM
TABLE I FERRICYANIDE -3-MERCAPTOPROPIONIC XCID REACTION
IM,pH
(Run 4,Fig. 1) (RSH)o is 35.8 X 25.0' Time, min.
0 2 4 6 8 10 12 14 16
(F),
(F)-II
M X 106
I./mole X 10-4
9.11 5.26 3.92 3.09 2.58 2.14 1.85 1.63 1.45
1.10 1.90
2.55 3.24 3.88 4.67 5.42 6.13 6.91
is 3.83, T is
k . I . mole-' mim-1 X 10-8
4.00 3.63 3.5i 3.48 3.57 3.59 3.59 3.63
+ k"(H+)
Discussion Before consideration of the kinetic results, it is necessary to examine the acid-base relationships of 3-mercaptopropionic acid (I). In contrast to simple thiols bearing only one SH group, I gives rise to TABLE I1 FERRICYANIDE CONCEXTRAT I O N AND OF ADDED POTASSIUM FERROCYANIDE (IZSH)o = 8.75 X 1W4M(Runs 5-9), (RSH)O= 9.32 X 10-4M (Runs 10-14), pH = 4.57, T = 25.0"
EFFECTO F INITIAL
5 6
-
i
The reaction rate increased with increasing p H a t constant initial thiol and potassium ferricyanide concentrations. The dependency of k on the hydrogen ion concentration (Fig. 4) may be expressed by the equation (4)
It can be seen that the plot of l / k vs. (H+) has an apparent negative intercept. This anomaly may in part be due to the change in ionic strength in this
+
series of experiments. The dependency of the rate constant k on the thiol concentration is shown in Fig. 3.
Run
-1v. 3 . 6 3 f 0 . 0 8 X l o 3
1 / k = k~
2 4 6 [(F)o (F')o] -I, 1./mole X lo-&. Fig. 2.-Effect of initial ferricyanide concentration and of added ferrocyanide; for conditions see Table 11: 0, variation of r a t e with added ferrocyanide a t constant initial ferricyanide concentration; 0, variation of rate with initial ferricyanide concentration in the absence of added ferrocyanide. 0
8 9 10 11 12 13 11
M
POTASSIUM
(WO,
x
105
1.89 3.i9 5.69 7.58 9.48 8.35 8.35 8.35 8.35 0.66
(F')o, .M x 10s
k , 1. mol-] m i n . 3 X 10-4
0 0 0 0 0 1.51 4.52 7.53 10.54 63.12
3.16 1.58 1.39 1.19 1.04 0 . ,502 ,429 ,338 288 148
several ionized species. The equilibria involved are shown in Chart 1, which is typical for dibasic acids.12 In this scheme: HRSH = HSCHZCHZCOOH, HRS- = -SCH2CHzCOOH, RSH- = HSCHzCHzCOO-, and RS= = -SCH2CH2COO-. The primed K's represent the individual ionization constants. (12) J . E. Ricci, "Hydrogen Ion Concentration,'' Princeton University Press, Princeton, N. j.,1952, Chapter 6.
4726
JAMES
J. BOHNING AND KARLWEISS
0
I
1
8 13 16 Time, minutes. Fig 3.-Effect of added dithiodipropionic acid ; (HKSH)o = 7.33 X l o w 4;If, pH = 4 57, T = 25.0'; A : no added A, no disulfide. CI, ferrocyanide, (F)o = 1.12 X l O - ' M ; ( H R S S R H ) o = 1.76 X 10-4hf. B: ferrocyanide added, (F')o = 1 2 4 X M, (F)o= 1.33 X loT4X; 0, no disulfide; e,(HRSSRH),, = 1.76 X 10-4M. 4
i)
Fig 5.-Effect
Vol. s2
9 18 27 36 (HKSH)o, X X lo4. of thiol concentration; for conditions see Fig. 1.
HRS- and RS=. From properly defined observed ionization constants of I ( K l and K 2 ) ,it can be shownL2t h a t the concentrations of HRS- and RS= are
and
I 25
d 3
where ht = K"l/K',, and (HRSH)o= (HRSH) 4(HRS-) (RSH-) (RS2). The value of .x cannot be measured. It represents the ratio of the ionization constants of the -COOH and -SH groups. The values of K1 and K2 are 4.6 X and 2.9 X lo-", respectively, a t 20-25' . I 3 Since these values are not very different from those of the ionization and constants of simple carboxylic acids aliphatic thiols (-10-11)j14 the assumption that .Y is equal to the ratio of the observed ionization constants ( K l and K,) appears reasonable. It should be realized that this assumption implies t h a t the sulfhydryl group does not affect the ionization of the carboxylic acid group and vice z'crsa. On this JI sohbasis one can calculate that in a 1 X tion of I the approximate concentrations of the pertinent ionized species are (HIIS-) = 3 X lo-'" J I and (KS=)= 1 X lo-'" J1 a t PH 1.and (HKS-) = S X 1O-'" JI a t PH 5 . and (RS") = 2 x These figures emphasize the extreme rapidity of the elementary processes involved in the oxidation of I . The kinetic data indicate that the rate-determining processes are considerably more complicated than the simple electron transfer envisioned originally. The disappearance of ferricyanide ion according t o a second-order rate law suggests the involvement of a n intermediate, the concentration of which is dependent on the ferricyanide concentration. Although the reaction is apparently not detectibly reversibIe,I5the decrease in rate affected by
+
20
15
X 1 r9!
10
J
0
Fig. 4.--Effcct
5 10 15 ( H + ) , d l X 1iP. of p H : (F)o= 9.41 X 10 Jf; ( H K S H ) o= 7 . ;x ~ 10-4 A I . 7' = 25 oo. CHART1
K 'I
HRSH + HRS-
1 K",
L---t
K '2
+
RS-
J K Z
RSH-
-
The p H dependence of the rate of oxidation of I suggests t h a t only ionized sulfhydryl groups are directly involved in the reaction, i.e., the species
+
(18) E. Larsson, %. o,ior'g. u . ollgern. Chein., 172,373 (1428). (14) D. I,. Yabroff, I i i d . E u ~C.h e m . , 32, 287 (1940). (15) E:ven if the reaction involves an equilibrium, i t s position would
OXIDATION KINETICS OF
Sept. 5, 1960
4727
3-hf ERCAPTOPROPIONIC ACID
Application of the steady state approximation the addition of potassium ferrocyanide provides evidence of the reversibility of one of the rate-de- to the radicals HRS. and RS- involved in steps 7-10 terrnining steps. Dithiodipropionic acid appears leads to the expression for the rate of disappearance not to participate in this process. The most sur- of ferricyanide ion prising result is the observed decrease in k with increasing initial ferricyanide concentration. The I-f erricyanide system bears some resemblance to other oxidation reactions. Thus a second- In this equation, C = total iron concentration = (F)o (F')o,r = k'l/k3, and r' = ktz/k4. Integraorder rate law has been observed to apply to the tion yields an equation in which t is related to the internal oxidation-reduction of ferric ~ y s t e i n a t e ' ~ and ferric thioglycolate.l8 The analogy appears, sum of an (F)-l term and complex logarithmic (F) however, to be superficial since the rates of these terms, the latter being weighted by (1 - r ) and (1 - r') factors. A much simpler expression can be reactions are increased by hydrogen ion and de- obtained by the assumption that r = r'. Since r is creased by the thiols. Waters and Fieset- have the ratio of the specific rates of reduction and oxidafound that the addition of ferrocyanide ion also decreases the rate of oxidation of phenol^'^^^^ by tion of the radical HRS., and r' refers to the correalkaline potassium ferricyanide. On the other sponding processes with RS., this assumption does hand, ferrocyanide ion exerts no significant effect not appear unreasonable. Its adoption leads to in the ferricyanide oxidation of aldehydes, ketones and nitroparaffins.21 Many simple schemes which would explain the which on integration yields second-order dependence on ferricyanide ion concentration, fail to account for the observed varia- 1 - (1 - r ) In F = rC tion of k with the experimental conditions. The sequence of steps presented in eq. 7-12 offers a rearc2 [kl(HRS-) k2(RS-)]t + Constant (15) sonable, semi-quantitative interpretation of the data. We have found that under all conditions plots of ki (F)-I us. t are linear for the major part of the reacHRS- + F HRS. + F' (7) tion. If the proposed scheme applies, this implies that the value of r (and of r') is very close to 1, i.e., kz the spxific rates of oxidation and reduction of the RSF-RSL F' (8) inteiiiiediate radicals are essentially equal. The observed rate constant ( k ) would then be given by
+
-
+
-z
+ + HRS* + F +HRS+ + F' ka RS- + F +RS* + F' ka HRS+ + HRSH HRSSRH + H + ks RS' + HRSH -+-HRSSRH ke
(9)
(10)
k = -2 2:
[(HRS-) + 2ki ( R S ) ] k
(16)
Equation 16 predicts an inverse relationship between k and the total iron concentration, (C). This is obeyed in the presence of added ferrocyanide iron (12) (Fig. 2 ) . In the absence of additional ferrocyanide, the data imply the occurrence of a process which is This scheme is based on a reversible initial elec- independent of C, and which is not predicted by tron transfer of the type proposed by Waters and eq. 16. This discrepancy may be a reflection of F i e ~ e rwhich ~ ~ , is~ followed ~ by another, irreversible, differences in the steady state radical concentrations oxidation step.lg That the ferricyariide-thiol re- under the two sets of conditions, which are not action generates thiyl radicals is evidenced by the taken into account in deriving the rate law. In ability of this system to initiate the polymerization agreement with this point of view is the fact that, a t of olefins.22 Species similar to HRS+ and R S , equal values of C, the rate is greater where the radicorresponding to the oxidation level of a sulfenic cal concentration is expected to be larger, ;.e., in the acid, have previously been suggested as intermedi- absence of added ferrocyanide ion. ates in the oxidation of thiols by Basford and The dependence of k on the total thiol concentraH ~ e n n e k e n s . ~Since sulfenyl halides react rapidly tion is readily derived with the aid of eq. 5 and 6. with thiols and their anions,23i t seems reasonable At constant pH the concentrations of the ions are to assume that steps 11 and 12 are also fast. and (RS=) = given by (HRS-) = CX(HRSH)~ b(HRSH)o, where a and b are constants. Equation probably be highly in favor of the disulfide. Thus for cysteine, the equilibrium constant of the reaction 2 F e + + + RSSR + 2 H + 16 then becomes --f
(11)
+
ZRSH has been found to be 5.3 X 10-24 a t 25",16 (16) N. T a n a k a , I. M.Kolthoff and W. Stricks, THIS J O U R N A L , 77, 2004 (1955). (17) N. T a n a k a , I. bf. Kolthoff and W. Stricks, ibid., 77, 1900 2Fe+++
(1955). (18) D. L. Leussing a n d L. Newman, ibid., 78, 552 (1956); H. Lamfrom a n d S. 0. Nielson, ibid.,79, 1966 (1957). (19) C. G. Haynes, A. H . Turner and W. A. Waters, J . Chcm. Soc., 2823 (1956); this reference cites the earlier literature on this topic. (20) L. F. Fieser, THISJOURNAL, 611,5204 (1930). (21) P. 'F. Speakman and W. A. Waters, J. Chem. Soc., 40 (1955). (22) I. M. Kolthoff and E. J . hleehan, J.Polymer Sci., 11, 71 (1953). (23) N. Kharasch, S . J. Potempa and H. L. Wehrmeister, Chem. Reus., 39, 269 (1946).
The data of Fig. 5 show that k increases with increasing thiol concentration, but somewhat more rapidly a t higher concentrations than is required by eq. 17. As far as the effect of the hydrogen ion concentration is concerned, the application of eq. 16 is not so clear cut. The experimental data (Fig. 4) indicate a linear relationship between ( k ) - l and the hydro-
4728
JAMES
J. BOHNINGAND KARLWEISS
+
gen ion concentration. Thus [(HRS-) (kz/kl) (RS=)]-' should be linearly related to (H+). Incorporating the assumption that x = K1/KZ (1 x), and neglecting the KIKz term,24the application of eq. 5 and 6 yields
+
Obviously, as (H+) is always the same order of magnitude as K1, linearity in (H+) of eq. 18 depends on ks/kl and can only be expected if this ratio is quite small. This might well be the case since electrostatic repulsion is more important in reaction 8 than in reaction 7, and hence kz is probably smaller than k l . The experimental results are certainly not a t variance with a reasonable interpretation of eq. 18, and the conclusion that sulfhydryl anions are the reactive thiol species in the ratedetermining processes. Several variations of the reaction scheme of ey. 7-12 involving the participation of iron-sulfur complexes can be formulated, which lead to similar kinetic expressions. Such paths cannot be ruled out, since the inability to detect these complexes spectroscopically may be due to their law concentration, or other factors. The actual electron transfer is conveniently pictured to proceed ab a cyanidebridged transition state.25 It follows from electrostatic considerations that the transition states of the radical-ferricyanide interactions are more likely to pass into intermediate complexes than the transition states involving sulfhydryl anions. The extremely low radical concentrations would render such complexes undetectible. It is interesting to note that the oxidation of cysteine with potassium nitrosyl disulfonate (,ON(S03K)z)26 in aqueous solution is first order in oxidant.27 I t appears likely that in this system a ratecontrolling electron transfer is followed by the rapid dimerization of the intermediate thiyl radicakz8 Acknowledgments.-We wish to express our sincere thanks to Drs. J. E. Ricci, H. A. Taylor and s. Lipsky for many helpful discussions. Financial assistance from the Arts and Science Research Fund of New York University is gratefully acknowledged. \Ye are also grateful to Evans Chemetics, Inc., for a generous supply of 3-mercaptopropionic acid. Experimental Materials.-3-hIercaptopropionic acid ( E ~ r a n Chenietics, s Inc.) was redistilled several times under reduced pressure. The purified material, b . p . 104' (6 m m . ) (reported2@105107" (4 m m . ) ) , was stored under nitrogen. Potassium ferricyanide (Baker and Adamson, reagent grade) was recrystal(24) K I K is ~ smaller by a factor of about 106 than the other relevant terms in t h e p H range used. ( 2 5 ) Cf. €1. Taube and H. hiyers. THIS J O U R N A L . '76, ?lo:< ( 1 O j 4 ) . (26) Cf. E. Fremy, A?tn. chim. p h y s . , 1 5 , [3], 408 (1843). (27) J . J. Bohning and K . U'eiss, unpublished results. (28) A rate-controlling electron transfer has also been proposed b y G. D. Alien and W. A . Waters, J . Chem. Soc., 1132 (1950), t o account for t h e kinetic features of the oxidation of isobutyraldehyde Kith this oxidizing agent. (29) L. C. Cheney and J . R . Piening, THISJ O L ' R N A L . 67, 731 (l!l45),
VOl. 82
lized several times from hot water. T h e dark-red crystals obtained in this manner were demonstrated t o be free of ferric ion by t h e absence of Prussian Blue formation with ferrous sulfate. Potassium ferrocyanide (Fisher Scientific Co. ) was purified according t o the procedure of Loftfield and Swift.ao T h e pale yellow crystals were stored in t h e dark under nitrogen. Preparative-scale Oxidation of I.--A solution of 3-mercaptopropionic acid (3.0 g.) in 80 ml. of water was added slowly, under nitrogen, t o a stirred solution of potassium ferricyanide (7.0 g . ) in 160 ml. of water. After 2 hours at room temperature, the white precipitate which was formed was filtered (2.0 g., 90%). Recrystallization from ethann: afforded colorless 3,3'-dithiodipropionic acid, m . p . 154 (cor.), reportedal 154'. No other organic products could be isolated. Kinetic Experiments.-For all the spectral work, a Beckman model DK-2 recording spectrophotometer equipped with a Beckman no. 92430 time-drive attachment was used. Special milling of a Beckman no. 92527 temperatureregulated cell holder permitted t o use of a matched pair of 10-cm. quartz cells. Constant temperature (25.00 zt 0.05') was maintidned in the cell holder by t h e circulation of water from an Ultra electronically controlled thermostat circulating bath.32 Preliminary spectral measurements showed t h a t the spectra of the following mixtures were indistinguishable from the spectral sums of their components: solutions 1, 3.56 X M in ferricyanide and 3.14 X 10-5 ,If in ferrocyanide; M in ferricyanide and 1.07 X M in 2, 4.28 X dithiodipropionic acid; 3, 3.48 X 10-5 -44 in ferrocyanide and 3.47 X ;Ifin I ; 4, 3.6 X M i n HCI, 1.93 X ;lf in I. D a t a on ;If in ferricyanide, and 8.69 X the compliance with Beer's law and the extinction coefficient of potassium ferricyanide are given in Table 111.
TABLE 111 EXTIKCTION C O E F P I C I E s l O F POTASSIUM F E R R I C T A S I D E IS
AQGEOGS SOLUTIOS AT 418 mp (I?), -If X lo5 9.43 7.54 5.65 e" 1021 1042 1043 '* A 10-cm. cell was used; a v . 1033 -i. 9 .
3.77 1029
.I11 the solutions were made u p with permanganate-purified, doubly-distilled water.33 Solutions of reactants were always kept in the dark and under nitrogen, but were never stored overnight. The buffer mixtures34were prepared from deaerated stock solutions of 0.2 M sodium acetate and 0.2 M acetic acid, which were stored with a continuous slow stream of moisture-saturated nitrogen bubbling through them. The kinetic measurements were made directly in a IO-cm. quartz cell. For this purpose the wave length of the spectrophotometer was set at 418 mp, and the time-drive unit was put into operation. Buffer solution (20.0 ml.), and sufficient distilled water t o bring the total volume t o 50 ml. after the addition of the reactants, were rapidly delivered into a ground-glass stoppered 125-ml. flask, under a stream of nitrogen. T h e potassium ferricyanide solution was added next and this mixture, as well as the stock solution of I were allowed t o cnme t o temperature equilibrium. T h e time-drive was started imniediatel>- when the solution of I was added. The mixture was briefly swirled, and then rapidly transferred into the absorptiori cell. T h c concentration of ferricyanide ion as a function of time was ohtained directly from the resulting d e n s i t y t i m e plot. Each given run was carried out a t least in duplicate. The PH values, which were detcriniileti will1 a c:tlihratctl Uecktnan mode1 G p€I Inetcr, were found to be identical before and after the reaction. (:10) R. Loftfield and Iibid.. 60, :io83 (1!138). ( 3 1 ) G. G . Stoner and G. Dougherty, tbid., 63,987 (1941). f 3 2 ) Manufactured by Colora. G.m.b.H.. Larch. Germany; plied hy Lux Scientific Instrument Corp.. S e w York, Pi. Y.
(33) Kindly supplied by Dr. S. Lipsky. (:31) I. M. Kolthoff and C. Rosenblum, "Acid-Base T h e hiacmillan Co., New York, N. Y., 1937. p. 230.
SUP-
Indicators,"
