Kinetic Studies of Fast Bromination Reactions with a Constant Current Generator and Amperometric Indicator System GEORGE O ' D O M and QUINTUS FERNANDO Department of Chemistry, University of Arizona, Tucson, Ariz. A commercially available constant current source and recording polarograph were used to measure the kinetics of several bromination reactions in aqueous solutions. The effect of varying the rate of bromine generation, rate of stirring, and concentration of reactants, on the rate constants was determined and the maximum value of a second order rate constant that could b e measured with this instrumentation was established. A detailed rate study on the monobromination of tyrosine, 3-(p-hydroxyphenyl) alanine, showed that the reaction was first order with respect to tyrosine and to bromine. Molecular bromine was found to b e the only brominating species a t pH values less than 2.0. The zwitter ion and protonated forms of tyrosine were found to monobrominate at approximately the same rate; the second order specific rate constant for the monobromination of tyrosine was 2.5 X lO4M-I set.-' at 25' C.
0
THE MANY METHODS that are available for the study of the kinetics of fast reactions in solution, little attention seems to have been paid to the method in which one of the reactants is added electrolytically to the reaction mixture a t a constant rate (5). Examples of such studies that have been reported are hydrolysis or bromination reactions in which hydrogen ions, hydroxide ions, or bromine were generated electrolytically (with 100% current efficiency) in aqueous media containing the reactant species (6, 7 , 1 3 , 14). Rate constants for these reactions were obtained by achieving a steady state (14,or by analyzing the indicator response vs. time curves (12). As part of a systematic study of the rates of halogenation of phenolic compounds, the kinetics (of bromination of several model compounds have been investigated by a coulometric technique in which constant current pulses were used (11, 12). I n this work a commercially available constant current source and a recording polarograph have been used to investigate the kinetics of several fast bromination reactions in aqueous solutions and to F
establish the magnitude of second order rate constants that can be determined a t the maximum and minimum rate a t which bromine can be generated with this instrumentation. The bromination of tyrosine was selected for a detailed kinetic study because this reaction, although far too rapid to be investigated by the usual methods, has a second order rate constant that is well below the upper limit that can be determined with the instrumentation used. EXPERIMENTAL
Reagents. The following compounds were of reagent grade purity and used without further purification: perchloric acid, sodium bromide, 50dium nitrate, acetone, allyl alcohol, d,Z-o-tyrosine, and 3,5-dibromotyrosine, Chromatographically pure I-tyrosine and paper chromatographically homogeneous d-tyrosine were obtained from Mann Research Laboratories. m-Nitrophenol was resublimed before use. Apparatus. The electrolysis cell consisted of a 100-ml. central compartment which was connected by means of two side-arms to tu-o electrode vessels. Medium porosity sintered glass disks and agar plugs, saturated with sodium nitrate, separated the two electrode vessels from the central compartment which contained a platinum foil (6.5 sq. cm.) generating electrode and a rotating platinum microelectrode, rotated a t a constant speed of 600 r.p.m. by means of a Sargent Synchronous rotator. The solution in the central compartment was stirred continuously by a magnetic stirrer whose speed could be varied between 525 r.p.m. and 900 r.p.m. The speed of the stirrer was measured with a General Radio Company Strobotac. One of the electrode vessels connected to the central compartment was a saturated calomel electrode, which, together with the rotating platinum microelectrode formed the amperometric indicator system. A Sargent Model XV polarograph provided the recorder and the polarizing voltage for the amperometric circuit. The second electrode vessel, connected to the central compartment, contained a solution of O.1M perchloric acid in which was immersed 40 sq. cm. of silver foil which formed the auxiliary electrode of the generating system. The two
generator electrodes were connected t o a constant current supply. I n this work a Sargent Coulometric Current Source Model IV was used to supply a constant current of 4.825 ma. Calibration of this constant current source was carried out by measurement of the potential drop across a standard resistor with a Minneapolis-Honeywell Model 2730 potentiometer. The recorder in the amperometric circuit was calibrated with respect to the amount of bromine generated by the constant current source. Bromine was generated in an acid solution of sodium bromide for a short period of time and the recorder response followed a t a sensitivity of 1 pa. full scale. The recorder deflected rapidly and then leveled off. More bromine was then generated and the recorder response followed. This sequence was repeated several times until full scale deflection was obtained. A plot of the amount of bromine generated us. recorder deflection gave a straight line of constant slope over a range of bromide ion concentrations from 0 . 2 X to 1.OM and over-all acid concentrations used in these experiments. Blank experiments as described above were made before each series of kinetic experiments and the constancy of the slope of the calibration plot was verified. Current-Time Curves. dliquots of standard solutions of sodium bromide, perchloric acid, and the compound t o be brominated were introduced into the central compartment of the electrolysis cell. The magnetic stirrer, the rotating platinum microelectrode, and the amperometric current recorder were switched on. When the current-time curve had leveled off, (usually within several seconds), the constant current supply was switched on, and the currenttime curve recorded. The current in such a curve is proportional to the sum of the concentrations of unreacted bromine and tribromide ions and the time is proportional t o the total amount of bromine generated. Figure 1 shows a typical current-time curve, A . I n the initial portion of this curve the rate of generation of bromine is greater than its rate of reaction. I n the relatively flat portion of the curve the rate of reaction is equal to the rate of bromine generation, and in the rising portion of the curve the rate of bromine generation is much greater than the reaction rate. The calculation of reVOL. 37, NO. 7, JUNE 1965
* 893
IP0
the damping switch in position 2 in the Sargent Model XV polarograph, no appreciable error of this type was incurred.
tI
RESULTS
60
120
180
240
300
Sconds
Figure 1.
Typical current-time curves
action rates and rate constants from current-time curves whose slopes gradually increased between 10 and 80% reaction, has been previously described (11). If the slope of the current-time curve is similar to that of the blank B, the bromination reaction is too slow t o be followed by this method. In such an instance the rate of reaction can be increased by increasing the concentration of the reactants. Usable currenttime curves can also be obtained by decreasing the rate of bromine generation. If the reaction is so slow that either of these methods fails to give satisfactory current-time curves, it is more convenient in such cases to use a titrimetric method of following the reaction. If the slope of the current-time curve is similar t o that of C, a typical amperometric titration curve, the bromination reaction is too rapid and cannot be studied by this method. The rate of reaction can however be slowed down to a certain extent by decreasing the concentrations of the reactants. For example, since molecular bromine is the brominating species in most bromination reactions, its concentration in solution can be reduced by increasing the concentration of bromide ions. Satisfactory current-time curves for such fast reactions can also be obtained by increasing the rate of bromine generation. With the equipment described in this study, an upper limit is set on the rate of bromine generation since i t is not possible to use a current greater than 20 ma. If the damped circuit of the Sargent Model XV polarograph was used t o record the current-time curves, circuit equilibrium was not obtained throughout the course of an experiment since the recorder deflection lagged behind that which would have been obtained with the undamped circuit. This effect was more prominent in regions where the current was changing rapidly rather than in the relatively flat portions of the current-time curves. For this reason the concentrations of reactants, in this study, were so chosen that in the 20 to 50% reaction region the currenttime curve was relatively flat. With 894
ANALYTICAL CHEMISTRY
One of the objectives of this work was to establish the magnitude of second order rate constants for bromination reactions that could be determined with the Sargent Coulometric Current Source and the amperometric indicator system. The kinetics of bromination of acetone and m-nitrophenol was investigated in this work a t the lowest current setting of the coulometer ( 5 ma.) since Bell and coworkers have shown that these reactions are relatively slow bromination reactions (3, 4). Currentrtime curves for the bromination of acetone are shown in Figure 2. When the concentration of the acetone is increased to about 0.130M, a steady state is reached. Although the kinetics of bromination of acetone was not studied in detail, especially since the rate of enolization of acetone is a complicating factor, the order of magnitude of the rate constants reported by Bell and Davis for this reaction was confirmed (3). A typical current-time curve for the bromination of m-nitrophenol is shown in Figure 3. During the first 60 seconds of the reaction, the rate of bromination is slower than the rate of bromine generation. After about 90 seconds the rate of bromination increased to a value greater than the rate of generation of bromine. Calculated values of the rate constants, hobs from Equation 1, were found to increase as the reaction proceeded toward completion.
60
120
180
240
300
Seconds
Figure 2. Current-time curves for bromination of acetone in 0.1M NaBr and 0.1M HClOl A. 6.5 X 10-2M acetone B. 8.6 X 10-ZM acetone C. 9.8 X 10%i acetone D. 0.13M acetone
a , , , , , 60
I20
180
240
300
Seconds
Figure 3. Current-time curve for bromination of 1.16 X 10-3M mnitrophenol in 0.1 2M NaBr and 0.056M
HC104 where [XI represents the analytical concentration of m-nitrophenol. Bell and Spencer found that this compound is readily dibrominated (4). The acid strengthening effect of the monobromo substituent on the phenolic group results in an increase in the concentration of the reactive monobromo anionic species, thereby facilitating the introduction of a second bromine atom. The shape of the curve shown in Figure 3 can be explained on this basis. A value of /coba calculated for the monobromination reaction was 115 1. mo1e-I sec.-l which compares reasonably well with the value of 100 1. mole-1 set.-' reported by Bell and Spencer (4) for k o b s , measured under the same conditions. The latter value of k,bs was corrected for the dibromination reaction that undoubtedly occurs, by means of an experimentally measured value of the rate constant (which was not reported) for the bromination of the monobromo compound whereas the former value was not correct in this manner. Although it was found possible to measure, conveniently and reproducibly, second order rate constants from 10 to about 100 1. mole-I sec.-l, by this technique, the utility of the method would lie in its ability to give rate constants for much faster reactions. Accurate kinetic data could not be obtained for the bromination of allyl alcohol because the current-time curves obtained even with a current setting of 20 ma. resembled a typical amperometric titration curve (Figure I). The value of k o b s reported for this bromination reaction is lo5 1. mole-' sec.-l (W), which is therefore an upper limit for second order rate constants which can be determined by this method. A detailed study of a bromination reaction with a ten times smaller value of k&s was carried out to illustrate the kind of results that could be obtained by this method. The kinetics of monobromination of tyrosine was investigated in acid
solutions. The current-time curves obtained, resembled curve A in Figure 1, and a typical set of data that can be obtained from such a curve is shown in Table I. The sum of the bromine and tribromide ion concentrations was determined from the calibration curve described above and the concentration of free bromine present in solution could be calculated since the value of the formation constant of the tribromide ion is known (8, 16). The concentration of bromine that had reacted was obtained from Equation 2.
Table 1.
Kinetic Data for Bromination of Tyrosine
Initial concentration of tyrosine = 127.56 X 10-GM Initial concentration of NaBr = 0.64M Initial concentration of HClO4 = 0.34M [BrzI ([Brzl X 106M Bs-1) [Brt] [Tyrosine] x 106M x 107M x 106M X 104M electrogenerated unreacted unreacted reacted unreacted 21.58 105.98 0.92 0.77 22.50 29.00 98.56 0.84 30.00 1.00 36.40 91.16 1.10 0.92 37.50 83.72 0.97 43.84 1.16 45.00 76.31 1.05 51.25 52.50 1.25 58.65 68.91 1.13 60.00 1.35 66.00 61.56 1.50 1.26 67.50 54.23 1.40 73.33 75.00 1.67
+
Time 90 120 150 180 210 240 270 300
The concentration of free tyrosine in solution was then calculated by subtracting [Br2Ireacted from the initial tyrosine concentration. The reaction rate, -d [Brz]/dt, was determined a t a number of time intervals by measurement of the tangent a t any point on the current-time curve, by means of a glassrod technique (9, IO). From the constant value of the rate constant obtained by assuming a reaction which is first order with respect to tyrosine &nd to bromine, it was concluded from the examination of about seventy sets of data that the reaction has an over-all order of two. The rate of stirring with the magnetic stirrer could be varied from 525 r.p.m. to 900 r.p.m. Values of k o b s were determined for a solution which contained tyrosine (1.16 X 10-4M),sodium bromide (0.5M), and perchloric acid (O.lM), when the rate of stirring was 525 r.p.m. and 900 r.p.m. The value of k o b s a t 525 r.p.m. was 2.15 X lo3 1. mole-I set.-' and a t 900 r.p.m. was 2.06 X 103 1. mole-I sec-l. Therefore the rate of stirring seems to have little effect on rate constants which have an order of magnitude of l o 3 1. mole-I sec.-l OH OH
Table II.
Effect of [Br-] on Rate of Bromination of Tyrosine
Ionic strength held constant by addition of NaK03 kabs [Br-I [Hi1 p M-' SeC.-' kabs (1 f K[Br-]) M 2.2 x 104 0.25 1.0 3.4 x 103 0.32 2.3 x 104 0.25 1.0 2.9 x 103 0.40 1.0 2.3 x 103 2.1 x 104 0.25 0.48 1.0 2.3 x 103 2.4 x 104 0.25 0.56 1.0 2.1 x 103 2.5 x 104 0.25 0.64 1.0 1.8 x 103 2.6 x 104 0.24 0.80
Ctnoaine
x lO6M 124.68 124.68 124.68 124.68 124.68 122.40
Table 111.
Effect of pH on Bromination of /-Tyrosine" k
[FI
Bh-1
Ctvrosine
X 10BM
0
127.56 127.56 127.56 127.56 127.56 127.56 127.56 127.56 Ionic strength kept
0.64 0.77 0.89 0.92 0.96 0.96 0.96 0.96 constant by the
I
predominate with the resultant formation of only a small amount of the monobromotyrosine. In this work, a hydrogen ion concentration of 0.4M to 0.002M was used in order to study the monobroOH
I
CH
H3N+'
\coo-
H3N+'
\Coo
-
/ \
H ~ N + COO-
Tyrosine
(4)
o-Tyrosine
Br
The bromination of tyrosine gives the 3-bromo derivative first and the 3,5dibromo compound is formed subsequently (Equation 3) (16). Unless the brominations are carried out in acid solutions, the dibromination reaction together with an oxidation reaction
x 10-4 M-l see.-' 2.5 2.9 2.7 3.1 2.6 3.0 3.2 5.9
/J
0.34 1.0 0.223 1.0 0.113 1.0 0,068 1.0 0,045 1.0 1.0 0.023 0,0045 1.0 1.0 0.0023 addition of NaBr
(3) CH
k X M-l set.-' 2.4 2.4 2.6 2.4 2.4 2.4 2.1 1.9
mination of tyrosine. The specific rate constants for the monobromination reaction (Table I) show a significant decrease after about 50% of the tyrosine is brominated. This decrease may be attributed partly to errors caused by current damping. No attempt was
therefore made to utilize the rate data beyond the 50% reaction region. Below about 20% reaction, the amount of unreacted bromine and tribromide ion present in solution is too small to give reliable measurements. Under these experimental conditions, only Brz and Br3- need be considered as active brominating agents. A plot of values of k o b s (1 K [Br-1) vs. [Br-] (Table 11) gave a straight line of zero slope from which it can be concluded, that within the limitations of the experimental method, Br3- is not an active brominating agent. The value of K , the formation constant of the tribromide ion that was used in these calculations was 17; k o b s is the second order rate constant in the rate Equation 1 where [SI represents the total concentration of tyrosine, in the protonated, neutral and zwitter ion forms. The effect of p H on the rate of bromination of both tyrosine and otyrosine is shown in Tables I11 and IV. With both compounds the rate constant shows little change below a pH of 2, but above this p H the rate constant increases rapidly.
+
VOL. 37, NO. 7, JUNE 1965
895
Table IV.
Effect of pH on Bromination of o-Tyrosine
Pr-I M 0.72
Ctyrosine
X 106M
78. AS 78.69 78.69 78.69 78.69 78 69
O . 76 ._
0.80 0.80 0.80
0.80
~
rg1
0.113 __ n c -.n -58 0.023 0.0069 0.0046 0.0023
P
i n 1.0 1.0 1.0 1.0
1.0
k x 10-5 M-’ sec. -1 1.4
1.5
1.5 2.0 3.3 4.9
molecule has little effect on the electron availability in position ortho and para to the phenolic groups in tyrosine and o-tyrosine. This is substantiated by the value determined for the second order rate constant for the monobromination of phenol (2 x lo51. mole-1 sec.-l) (11) which is identical with that obtained for o-tyrosine. LITERATURE CITED
Tyrosine is present mainly as the protonated form and the zwitter ion form a t p H vaIues less than 2. When K [Br-]).(l values of hobs (1 K , i [ H + ] )are plotted against K./[H+], the slope gives the second order rate constant for the reaction of the zwitter ion with bromine and the intercept the second order rate constant for the reaction of the protonated form of tyrosine with bromine. The rate constant obtained from the slope of the straight line is 2.6 x lo4 and that from the intercept, 3 X lo4. It can therefore be concluded that both protonated and zwitter ion forms of tyrosine react a t about the same rate with bromine. The value of K,, the first acid dissociation constant of the protonated form of tyrosine that was used in these calculations was 10-2.2(1). Insufficient data were obtained on the manner in which the rate constants increased above p H 2. It is, therefore, not possible to explain this increased rate of reaction on a quantitative basis, although there can be little doubt that the dibromination as well as the oxidation reactions are contributory factors.
+
+
This is supported by the observation that 3,5-dibromotyrosine is not oxidized by bromine below p H 2.5 but that its rate of oxidation above pH 3.0 is comparable with the observed bromination rates. The rates of bromination of d-tyrosine and o-tyrosine were also investigated. As expected, the rate of bromination of &tyrosine was the same as that of 1-tyrosine: the observed second order rate constant for the bromination of o-tyrosine was 1.5 x lo51. mole-1 set.-' which is about ten times greater than that obtained for tyrosine. In phenol, bromination in para position occurs more readily than bromination in the ortho position. Consequently the introduction of a bromine atom is expected to take place more readily in the position para to the phenolic group in o-tyrosine (Equation 4) than in the position ortho to the phenolic group in tyrosine. Since the zwitter ion and protonated forms of both tyrosine and o-tyrosine were found to brominate a t about the same rate, the effect of introducing a positive charge in the side-chain of the tyrosine
(1) Albert, A., Biochem. J . 1952, 690. (2) Bell, R. P., Atkinson, J. R., J . Chem. SOC.1963, 3200. (3) Bell, R. P., Davis, G. G., Ibid., 1964,
902. (4) Bell, R. P., Spencer, T., Ibid., 1959, 1156. (5) Caldin, E. F., “Fast Reactions in Solution,” Wiley, New York, 1964. (6) Dubois, J. E., Elektrochem. 64, 143 (1960). (7) Farrington, S., Sawyer, D. T., J . Am. Chem. SOC.78, 5536 (1956). (8) Griffith, R., RlcKlown, M., Winn, H., Trans. Faraday SOC.28, 101 (1932). (9) Hoare, J., J . Chem. Educ. 38, 570 (1961). (10) Hockandel, C. J., Ibid., 39, 299 (1962). (11) Kozak, G. S., Fernando, Q., Anal. Chim. Acta 26, 541 (1962). (12) Kozak, G. S., Fernando, Q., J . Phys. Chem. 67,811 (1963). (13) Kozak, G. S., Fernando, Q., Freiser, H., ANAL. CHEM.36, 296 (1964). (14) Pearson, R. G., Piette, L. H., J . Am. Chem. SOC.76, 3087 (1964). (15) Scaife, D. B., Tyrrell, H. J. V., J . Chem. SOC.1958, 386. (16) Yagi, Y., hlichel, R., Rocke, J., Ann. Pharm. France 11, 30 (1963). RECEIVEDfor review January 8, 1965. Accepted March 23, 1965. The authors are grateful to the National Institutes of Health for financial assistance.
Spectrophotometric Determination of Lactulose with Methylamine SUSUMU ADACHI laboratory o f Animal Products Technology, College o f Agriculfure, Tohoku Universify, Sendai, Japan
b The violet-reddish color obtained on addition of methylamine to a lactulose solution in the presence of sodium hydroxide was used for the qualitative and quantitative determination of lactulose. By working at the optimum conditions established in this report, 2 to 8 mg. of lactulose can be determined. The absorptivity of the colored solutions at 540 mp is constant at lactulose concentrations from 0.4 to 1.6 mg. per ml. For direct spectrophotometric observation dark solutions may be diluted with water to 2 to 5 volumes without loss of linearity. Interference by lactose, maltose, and other aldoses i s overcome by hypoiodite 896
ANALYTICAL CHEMISTRY
oxidation and desalting with ion exchange resins; the presence of small amounts of ketohexoses and sucrose can be tolerated.
C
effort has been devoted to developing suitable methods for the routine quantitative determination of laCtUlOSe(4-O-P-D-galaCtOpyranosyl-D-fructose) in preparations containing lactose and other sugars. Unfortunately, the published chemical methods are time-consuming or are susceptible to serious errors caused by interference by the contaminants. A colorimetric method for the estiONSIDERABLE
mation of lactulose, first proposed by Adachi ( S ) , is based upon the color reaction of ketoses with cystein-carbazole in concentrated sulfuric acid. It was necesary to separate lactulose from the other ketoses present in the sample. The only available method (16) which gives a quantitative measure of lactulose involves quantitative paper chromatography, and would be tedious if many samples had to be analyzed. Verhoog reported recently on the polarographic reduction of lactulose (16). The use of the polarographic method has been complicated by the fact that heated milk or heated lactose solutions contain substances which affect the wave height
