Mushtaq Ahmad and Jan Hamer Tulane University N e w Orleans, Louisiana
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Pseudo First-Order-Second-Order Kinetics Experiment
I
An illustration of the Guggenheim method
Aromatic nitroso compounds lend themselves well to spectrophotometry ( I ) , but only in recent years ha.s this property been exploited to study the kinetics of some of the characteristic reactions of the nitroso group (8-4). In the experiment described in this paper the rate of one of the typical reactions of the aromatic nitroso group is determined spectrophotometrically employing the Guggenheim method (5). The experiment may be done in one 2-hr Iaboratory period, or in two 2-hr periods if calculation of the energy of activation is desired. Hamer. Ahmad. and Hollidav (4 " ,., renorted the kinetics 'of the reaction between p-bromonitrosobenzene and 2,3-dimethyl-1,3-butadiene.The reaction is an interesting example of the Diels-Alder reaction of heteroatomic compounds. The reaction is first
order with respect to the nitroso compound and to the conjugated diene: The change of concentration of the nitroso compound may be followed in the visible region at 720 mu, a region where both the conjugated diene and the reaction product are transparent. A recording Beckman DB spectrophotometer mas employed.
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Dilute solutions of p-hromonitrosobenzene follow Beer's law. Also, the reaction between p-bromonitrosobenzene and 2,3dimethyl-1,3-butadienebecomes a pseudo first-order reaction when a large (fifty-fold
and up) excess of one of the reactants is present in the reaction mixture. In this experiment, a fifty-fold excess of the conjugated diene is employed. The Gnggenheim method (6) was employed for the determination of the rate constant at Z°C. This method may be used for the determination of the rate constant of a first order reaction if the concentration of the reactant can be determined directly, but the initial and infinite reaction times are not known. The Guggenheim method is based on the following considerations. If time 11, t2, t3, etc., and 11 A, & A, ts A, etc., are selected, where A is constant increment, the following equations hold true.
+
+
+
where At and A,' are the absorbancies a t tl and 11 respectively. From equations (1) and (2) we find: (A, - A,') kt,
graph of log b(a - x)/ a(b - z) versus t a t 2 5 T are shown in Figures 1and 2. If p-bromonitrosobenzene is not available commercially, it can be prepared in the laboratory by Bamberger's method (6) which consists of a variation of the procedure described in "Organic Syntheses" (7) for the preparation of nitrosobenzene by the reduction of nitrobenzene.
=
(Ao - A=) e-k" (1 - e - k A )
+ In(A, - A,') = In (A, - A,) ( 1 - e - k A ) kt, + In(Al - A,') = constant
+A (3)
(4) (5)
A plot of -In(A,
- A,') versus time has a slope k. Since the reaction is a pseudo first order, it is then necessary t o divide the rate constant by the molarity of 2,3-dimethyl-1,3-butadiene to obtain the true second order rate constant. I n order to achieve accuracy, the time interval A should be two or three times as great as the half life period of the reaction. If standardization curves of optical density1 versus concentration are prepared, the familiar second order rate equation can be used.
Stock solutions of the reactants are prepared by dissolving 0.465 g of pbromonitrosobenzene in 25 ml of dichloromethane (0.100 M), and 10.264 g of 2,3dimethyl-1,3-butadiene in 25 rnl of dichloromethane (5.00 M) respectively. The solutions are kept in the constant temperature bath for 30 min. At Z°C, equal volumes of 0.100 M p-bromonitrosobenzene and 5.00 M conjugated diene solutions are mixed in the cell. The reaction is recorded for about an hour a t 720 mp, using dichloromethane as a reference. Optical densities1 are calculated at certain time intervals from the graph of transmittance versus time. At 25'C, it is convenient to dilute stock solutions: p-bromonitrososbenzene to 0.05 M and 2,3dimethyl-1, 3-butadiene to 0.20 M. A similar procedure is followed by plotting known concentrations of p b r e monitrosobenzene versus optical densities. Concentrations at various optical densities are calculated from the standard graph. The rate of reaction is obtained graphically by plotting log b(a - s)/a(b - x) versus time; k (Z°C) = 1.10 X 10-3, k (25°C) = 7.60 X 10WS 1 mole-' sec-' (4) Energy of activation is then calculated from the values for k a t 2 and 25°C; E* = 12.46 kcal mole-'. The Guggenheim plot a t Z°C and 1 The conversion of transmittance to optical density may be found in tables, e.g., p. 3023, "Handbook of Chemistry and Physics," 42nd ed.
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Figure 1.
Guggenheim plot at 2'C.
Figure 2. Rote of reaction of p-bmmonitrorobenzene m d 2.3-dirnethyl1.3-butadiene o t 2S°C.
p-Bromonitrobenzene (11.5 g) is dissolved in a mixture of ethanol (100 ml) and water (15 ml). Calcium chloride (0.50 g) and zinc dust (10 g) are added to the solution which is heated to the boiling point. The mixture is then filtered in a Buchner funnel. The cooled filtrate is treated with a solution of iron(II1) chloride (18.5 g) dissolved in 600 ml of ice water. p-Bromonitrosobenzene precipitates and is collected by filtration. I t is purified by steam distillation and recrystallization from ethanol. Yield, 3.70 g (35%); mp, 97OC. Literature Cited
B. G., A N D LC-ETTKE, W., Quart. Re". (London), (1) GOWENLOCK, 12,321 (1958). Y., AND TAGAKI, Y., J. Am. Chem. Soe., 80, 3591 (2) OGATA, (1958). K. M., LAUEO,C. G., AND EDWARDS, J. O., (3) IBNE-RASA, J. Am. Chem. Soc., 85,1165 (1963). R. E., J . Org. (4) HAMER,J., AHMAD, M., AND HOLLIDAY, Chem., 28, 3034 (1963). E. A., Phil Mag., 2,538 (1926). (5) GUGGENHEIM, E., chm.Bey., 28,1222 (1895). (6) BAMBERGER, (7) "Organic Syntheses," eoll. vol. 111, New York, John Wiley and Sons, Inc., 1955, p. 668.
