KOTES
4391
suggest that the difficulty of reduction should increase in the order of increasing size of the ortho halogen substituent, the order of the reduction potentials is reversed and a "positive ortho effect'' is observed. However, if the effect of the rate of the irreversible loss of halide ion upon the location of the reduction potenital is taken into oonsideration,g the expected order for the standard reduction potential is obtained (Ella = -1.12 V and A o , ~ = r -100 mV). Thus, while steric interaction increases with increasing size of the orthosubstituted halogen, this also facilitates the loss of halide ion. The anodic shift caused by the enhanced rate of halide elimination more than compensates for the cathodic shift that would normally accompany increased steric interaction. Although our present equipment does not permit the direct determination of rate constants in excess of 500 sec-l, a lower limit of 8 X lo4 sec-' can be estimated for the elimination of iodide ion from o-iodonitrobenzene anion radical if one assumes 1 hat
1
3
1 A o , ~ rml d IEl,,(o-iodonitrobenzene)l 2 IE l/a(o-bromonitrobenzene)I
The results above clearly show that twisting of the nitro group from the plane of the benzene ring enhances the rate of loss of halide ion. As expected, the substitution of alkyl groups adjacent to the halogen also assists elimination of halide ion. I n the case of the alkyl-substituted 4-bromonitrobenzenes, the rate of bromide loss increases with increasing si5e of the substituent in the 3 positionb r v , H = 1.20 A, SeC-'; I^v,min,CHs = 1.72 A, IC = 8.5 X IO-' k =4 X sec-'; and ~ ~ , ~ , ~ , =~ -2.44 - h &, ~ ~k ~=l 3.1 sec-1.8 A similar order in rate of halide loss is observed in the 3-bromo-4-alkylnitrobenzenes (compare compounds 14 and 15). Substitution of a methyl group in the 3 position of 4-iodonitrobenzene increases the rate of iodide loss by a factor of 1.5. The similar addition of a methyl group to the 4 position of 3-iodonitrobenzene is more effective, causing an eightfold enhancement in the rate constant. Experimental Section Rate constants for the elimination of halide ion from halogenated nitrobenzene anion radicals were determined by a chronoamperometric technique. Details of the experimental procedure and of the instrumentation have been described previously. All studies were made at 23 f 0.5' in purified dimethylformamide. T'he supporting electrolyte for the iodonitrobenzenes was 0.1 F tetraethylammonium iodide; the remaining halogenated and alkyl-substituted nitrobenzenes were studied in 0.1 F tetraethylammonium perchlorate. The rate constants for the elimination of bromide ion from anion radicals of bromonitrobenzenes were unaffected by change of the anion of tetraeth] hmmonium salt from perchlorate to bromide.
Compounds 1-8, 11-13, 18, 22, and 23 were commercially available samples. Of these compounds, 2 was sublimed and 11-13 were purified further by repeated recrystallizations. 4-Bromo-2,6-dimethylnitrobenzene was prepared by nitration of 3,j-dimethylacetanilide,1° followed by deacylation, diazotization with HBr and NaNOz, and reaction of the diazonium salt with CuzBrz. Recrystallization from ethanol and subsequent sublimation gave a low yield of the desired product (mp 63-64'), 2,6-Dimethyl-4-iodonitrobenzene was prepared analogously using KI to convert the diazonium salt into the iodide (mp 59--61", decomposing with light). Compounds 14 and 16 were prepared by diazotization of the corresponding amines with 48% HBr and SaSOz. Treatment of the resulting salts with an HBr solution of CuzBrz gave solid products which were washed with NaOH and HzO and recrystallized from ethanol (mp compound 14, 77-77.5"; mp compound 16, 78.5-79.5"). 3Bromo-4-t-butylnitrobenzene was prepared by nitration of t-butylbenzene," followed by brominationlZ of the 4-nitro-t-butylbenzene to give 15 (mp 93-94'). Compound 17 was prepared from compound 15 by reduction with Fe and HCI, the product subsequently being deaminated with HC1, NaN02, and H3P02.13 The resulting o-bromo-t-butylbenzene was then nitrated according to the procedure described in the 1 i t e r a t ~ r e . l ~
Acknowledgments. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work (Grant P R F No. 1123-G1) and to the Kansas State University Bureau of General Research. (10) K. Ibbotson and J. Kenner, J . Chem. Soc., 1260 (1923). (11) D. Craig, J . Amer. Chem. floc., 57, 195 (1935). (12) M. H. Klouwen and H. Boelens, Rec. Trav. Chim., Pays-Bas, 79, 1022 (1960). (13) M. Crawford and F. H. C. Stewart, J . Chem. Soc., 4443 (1952). (14) P. B. D. de la Mare and J. T. Harvey, ibid., 131 (1957).
T h e Kinetics of t h e Hydrolysis of t h e Dichromate Ion.
V.
General Acid Catalysis
by R. Baharad, Berta Perlmutter-Hayman, and Michael A. Wolff Department of Physical Chemistry, Hebrew University, Jerusalem, Israel (Receiued Julu 28, 1969)
The hydrolysis of the dichromate ion
+ H20
CrZOT2-
2HCr04-
(11
(1) Department of Chemistry, Brandeis University, Waltham, Mass.
Volume 78, Number 12 December 1969
4392
NOTES
is known to be catalyzed by bases and by nucleophiles,Z13 and the laws governing this catalysis have been discussed.2 The reaction is also acid-catalyzed, and the catalytic constant k~ + has been determined.4r5 In order to get some insight into the mechanism of the acid catalysis, we considered it desirable to determine whether this catalysis is general or specific. Because of the high value of k ~ - the , hydrogen ion makes the dominant contribution to the observed reaction rate, unless its concentration is very low. In buffer solution, this concentration is given by the expression K,[HA]/ [A-] (where K , is the dissociation constant of the general acid HA). We see that when the acid is fairly strong, we may have to use impracticably high concentrations of A- in order to suppress the contribution of H + sufficiently for general acid catalysis to make itself felt. On the other hand, when the acid is very weak, its anion has a high catalytic constant2and its contribution to the observed rate is apt to obscure any catalytic effect which the acid may have. We compromised on acetic acid and chloroacetic acid, employing a ratio of salt to acid 1in the second.
Procedure ( a ) Experiinental Technique. We used the same experimental procedures as those described earlier,2 except that in the rapid mixing technique6 we used a Hamilton 725 LL syringe equipped with a bayonet socket. This socket prevents the needle from coming loose under pressure. Therefore, a finer needle than previously can be used (Luer 21 HL instead of 19 HL). This increases the linear velocity of the injected liquid, and hence the efficiency of mixing. The recorder was employed when the half-times were >3.5 sec; for shorter , 0.17) we used an oscilloscope.0 half-times (3.5 > T ~ /> For experiments at pH 7, the wavelength was 370 mp; in acid solution it was 385 mp. The dichromate concentration was -3.3 X M. The temperature was 25". ( b ) Methods of Calculation. For the reversible reaction we are dealing with we can again4 define an observed pseudo-first-order rate constant kobsd by kobsd
=
d In (Of - D,) - d In (x, - xt) dt dt
+
The Journal of Physical Chemistry
+
Results ( a ) Acetic Acid. We carried out two series of experiments, both at [Naf] = 0.2 M, kept constant by the addition of sodium nitrate. In the first series, the ratio of salt to acid was 0.175 and the pH was 4.0, whereas in the second the ratio was 0.40 and the pH 4.36. The highest acid concentration employed was 0.855 and 0.50 M , respectively. Taking the value of K1 at our ionic concentration8 as K I = 2.5 X M, we obtain from eq 2, k o b s d l k ~ 1 . 0 9 at [Na+] = 0.2 M, i.e., the back reaction contributes -9% to the observed rate. In Figure 1 we plotted k against acetate concentration, a t the two values of pH. For the sake of comparison, we also present the influence of acetate in the absence of acid, at pH 7, taken from our previous papera4 Straight lines are seen to be obtained, their slopes increasing significantly with increasing relative acid concentration. Quantitatively, the slopes are equal to kCHuCOO-1 ( ~ C H ~ C O O - 1CCHsCOOH/ 0.4) and ( ~ C H ~ C O O - kCH8COOH/0.175), respectively. 1.92, we obtain, ~ C H ~ C O O H= 1.06 Using4 ~ C H ~ C O O = M-'sec-'. The intercepts at zero acid concentration are due to the contributions of water and of hydrogen ion. Taking* k H z O = 0.03 sec-I, we obtain k ~ c+z 1.05 X lo4M-' sec-' at [Na+] = 0.2. (b) Chloroacetate. The catalytic constant of the chloroacetate ion is not reported in the literature, and therefore had to be determined. We carried out the measurement in the presence of [Na+] = 1 M , in order to be able to apply chloroacetate in large excess over chloroacetic acid (see section (c)). The sodium ion concentration was again regulated by the addition of sodium nitrate. The pH was 7, achieved by phosphate M . As buffer at a total phosphate concentration of a result of 3 experiments at chloroacetate concentrations
+
+
(1)
where D ,and D, are the optical densities at time t, and at the end of the reaction, respectively, and the z's are the corresponding amounts of dichromate hydrolyzed, measured in moles per liter. From this we calculate k ) the pseudo-first-order rate constant of the forward reaction, using an approximate expression employed earlier (eq 3 of ref 4). In the present case, where the concentration of Cr042- is negligibly small, and the ratio P [HCrO4-]/( [HCr04-] [Cr04-2])equals unity, that expression takes the form kobsd/k = 1 4(1 ,5x, 0.5xo)/K1 (2)
+
where KI is the equilibrium constant of reaction I, and xo the value of x at zero time.7 The rate constant k thus obtained is composed of ~ H ~ othe , contribution of the "spontaneous" reaction, and the sum of the various catalytic constants k H t , k ~ - and , HA, each multiplied by the appropriate catalyst concentration.
(2) B. Perlmutter-Hayman and M. A. Wolff, J . Phys. Chem., 71, 1416 (1967), where earlier literature is quoted. (3) Y. Egosy and A. Loewenstein, J . Magnetic Resonance, 1, 494 (1 969). (4) B. Vlmutter-Hayman, J. Phys. Chem., 69, 1736 (1965),where earlier literature is quoted. (5) J. A. Jackson and H . Taube, ibid.,69,1844 (1965). (6) B. Perlmutter-Hayman and M. A. Wolff, Israel J. Chem., 3, 155 (1965). (7) The use of eq 2, instead of the exact equation d In (z, - zt)/dt = k[l 4(z, zt)/Kr] (eq2 of ref 4),is justifiedprovided thecontribution of the back reaction is small and no great error is introduced by replacing (r, zt) by its mean value, thus treating kobsd as a true constant during any given run. (8) B. Perlmutter-Hayman and Y. Weissmann, Israel J. Chem., 6, 17 (1968).
+
+
+
4393
NOTES between 0.24 to 0.32 M we obtained ~ C H ~ E O O = - Q.28 M - l sec-' (See also Figure 2, lower line, where IC is plotted against [CHzCICOO-].) (c) Chloyoacetic Acid. The value of ~ C H ~ C ~ C O was OH determined in a solution where the ratio salt to acid was 8: 1, and the concentration of the acid varied from 0.024 to 0.118 M. The pH was 3.8, and the sodium ion concentration was again kept constant at 1 M by the
addition of sodium nitrate. Taking the value of K , a t M we obtain this ionic strength8 as K, = 1.8 X from eq 2, IcOb,/k N 1.12 at [Na+] = 1.0 M. I n Figure 2 we plotted k against [CHzCICOO-] (upper line). The slope of the straight line obtained is equal to (kCHzCICOOkcH2clcoo~/8.1). From this we obtain kCH2C1COOII = 20 M-' sec-l. Furthermore, assumingg 1 ~ N ~ 0.06 ~ 0 sec-' we obtain from the intercept, k ~ N+ 0.55 X lo4M-'sec-' a t [?Ja+] = 1.0 1%'.
+
Discussion ( a ) Comparison with Previous Results. In our previous paperj4 in addition to the experiments at pH 7 from which ~ C H ~ C O Ohad been calculated, we also reported results at lower pH. The fact that the contribution of acetic acid had remained undetected does however not contradict the present findings. At pII > 5.5, the contribution of the acid to the observed rate is
