NOTES
2855
relations between the s character (uz)of the CBH bond and 6HBwere found. Attention should be directed to the 6Hp-uz plots for I and I1 being almost parallel, in contrast to that of J P O C(see H -above). ~ The chemical shifts of methyl protons in I1 are downfield on substituting the ethoxy groups by chlorines. It may be of interest to point out that these shifts also correlate with JPOCCH values. For V, however, such a correlation was not observed, probably due to the same reasons discussed earlier.
when the use of conventional methods3 would be difficult. The chief limitations are that one must stay within the bounds of the Debye theory of dilute solutions and of the linearized theory of microwave cavity p e r t ~ r b a t i o n . ~In particular, aqueous reactions are ruled out because of the abnormally high absorption of microwaves by water. The room temperature (22’) liquid phase bromination of benzene with iodine as catalyst was chosen for the present study. C6He,Br2, and Izhave no dipole moments, but CBHsBrand HBr have dipole moments of 1.52 and 0.78 D , respectively.6
Application of Microwave Cavity Perturbation
Experimental Technique
Techniques to a Study of the Kinetics of
The two parameters of a liquid that can be obtained from microwave cavity measurements are the static dielectric constant e, and the loss factor tan 6. A particular cavity resonance is characterized by the resonant frequency fo and the loaded quality factor Q. A liquid placed in a quartz bottle on the axis of the cylindrical cavity introduces a change in both fo and Q. As shown by Dunsmuir and Powles6 and slate^-,^ the first-order perturbation solution takes the form
Reactions in the Liquid Phase
by A. L. Ravimohan Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91109 (Received March 80,1970)
Polar liquids are known to have broad absorption bands in the microwave region which arise from orientation of the molecules with increasing electric field E , followed by relaxation to thermal equilibrium as E falls to zero. The absorption is expressed as the loss factor tan 6, and for a dilute solution of a polar solute in a nonpolar solvent it is given’ by the Debye theory as
where 6 = loss angle, e, = static dielectric constant, dipole moment of solute molecule, c = concentration of solute in moles per cm3, v = frequency of radiation, v0 = 1/2m, where 7 = relaxation time of solute in solution, N = Avogadro’s number, k g = Boltzmann constant, and T = absolute temperature of the solution. For a mixture of solutes, tan 6 is the sum of the loss factors due to the individuaI solutes. Jackson and Powlesz verified eq 1 for solutions of several polar solutes in benzene by measuring resonant frequency shifts and Q factors of cylindrical microwave cavities partially filled with samples of the solution. The proportionality of tan 6 to the concentration of dipole e, for constant values of other variables in (l),suggests a convenient method of following the kinetics of certain classes of liquid reactions. Consider a reaction in which the reactants have no dipole moments but the products have appreciable ~1’s. The time variation of the product concentration, and hence the extent of reaction, can be followed by measuring tan 6 (and e,) of the reaction mixture as a function of time. The method would be fast, accurate, and convenient, as no samples have to be withdrawn for analysis. It is especially suited to the study of the early stages of the reaction,
€,=I+
W O - fa’) fov
where v = dimensionless form-factor depending on cavity geometry, Ro = radius of microwave cavity, RI = inner radius of quartz bottle, RZ = outer radius of quartz bottle, Eb = dielectric constant of bottle material, E, = dielectric constant of the liquid. When RO>> RI, RI II Rz, and Eb E ,
p =
constant
(Q’L - Q
!),/’E,
(4)
The method used for the measurement of fo and Q was a “transmission” method.’ With the circuit of Figure 1, it is possible to obtain a resonance curve in about 20 sec. A faster sweep may be obtained, if necessary, by using an oscilloscope and high-speed photography. fo (1) FV. Gordy, et aE., “Microwave Spectroscopy,” Dover Publications, New York, N. Y., 1966. (2) W. Jackson and J. G. Powles, Trans. Faraday Soc., 42A, 101 (1946). (3) K. J. Laidler, “Chemical Kinetics,” McGraw-Hill, New York, N. Y . , 1965. (4) J. C. Slater, “Microwave Electronics,” Van Nostrand, Princeton, N. J., 1950. (5) N. A . Lange, Ed., “Handbook of Chemistry,” 9th ed, McGrawHill, New York, N. Y . , 1956. (6) R . Dunsmuir and J. G. Powles, Phil. Mag., 37, 747 (1946). (7) E. L. Ginzton, “Microwave Measurements,” McGraw-Hill, New York, N. Y., 1957.
The Journal of Physical Chemistry, Vol. 74, No. 14, 1970
2856
NOTES
SWEEPER
X-Y RECORDER MOSELEY 7 0 0 5 A
KRigLJEBL 5013 PLUG-IN
I
12.5
Y INPUT I mV RANGE MICROWAVE CAVITY
CRYSTAL DETECTOR HP 4 2 0 8
n
II
II 3
I 1 20 d b VARIABLE ARRA ATTENUATOR 4674-20 F
II
J c d
-
&ART, ABSORPTION CELL
FIXED 6 d b ATTENUATOR HP 8 4 9 1 A
Figure 1. Coaxial circuit for automatic plotting of transmission characteristic of microwave cavity with quartz absorption cell. [I~]
and the half-power frequencies fz and fl are determined directly from the calibrated frequency scale. Now Q = fo/(fi - fi). The mode of resonance used was TNIoI~, for which 7 determined empirically from measurements on standard liquids (benzene and m-xylene), was found to be 0.01145. The reaction studied was C6He
4-Brz
5 C6H&
4- HBr
(5)
Since the products are formed in equimolar amounts, a quantity proportional to the common product concentration c can be deduced from (1) and (4)as c=-
+ [(& - ,o&o‘ ) - ;(I
const (EO 212
Eo
I);
-
(6)
where e,o is the dielectric constant and Qo’ is the quality factor at zero time, and the tan 6 of the reaction mixture at zero time has been subtracted out. The reason why QO’is not equal to Q is discussed in the next section. Analytical reagent grade chemicals meeting ACS specifications were used in the work. A known solution of bromine in benzene was prepared and a known weight of iodine dissolved in it. The reaction mixture was poured into the quartz cell which was then closed tightly with a neoprene stopper. Replicated microwave readings were taken at various time intervals, with intermittent shaking of the tube to ensure homogeneity. A test run on the same solution without iodine catalyst revealed that the noncatalytic reaction was negligible under the present conditions. It is believed that the addition reaction is also negligible. Finally, the reaction was stopped after 2.5 hr by pouring the contents into excess KI. Total free halogen was estimated by titration against standard NazS2O3solution using starch as indicator. This titration provided the means for estimating the constant of eq 6 which is necessary as the microwave absorption data determine only a quantity proportional to the product concentration. The Journal of Physical Chemistry, Vol. 7 4 , No. 14, I970
MOLES/LITER
Figure 2. Initial absorption as a function of iodine added,
Discussion of Results The first noteworthy feature about the results is that there is significant absorption even at zero time, since Qo’< Q. This indicates the instantaneous formation of a species with a dipole moment. A survey of the literature reveals that an intermediate of the type I,Brb has been invoked to explain the catalytic action of iodine on the reactionla-” with the most likely form being IBr. Initial absorption data can therefore be used to obtain relative IaBrbconcentrations. Figure 2 shows a plot of this quantity against moles of added iodine. The approximately linear nature of the plot is very high, a indicates that K = [I,Brb]2/[I~]a[Brz]b result in accordance with the findings of Price and Arntzen.lo The high K value means that the I,Brb concentration is not affected appreciably by changes in the Brz concentration. Hence it is a valid procedure to subtract out the initial reading to get the product concentration, as done in eq 6. If it is assumed that a = b = 1, putting [IBr] = [12]/2 in eq 1, along with Sheka’slZvalue of the dipole moment of IBr (1.21 D), yields T = 4 X sec, which is quite reasonable. If measurements are made at other frequencies, it is possible to get both p and T of the intermediate from microwave data, but this was not done here. The existence of a C6H6-Izcomplex with a dipole moment of 0.6 D has been deduced from absorption measurements in the visual range.’s-’6 However, no sig(8) L. Bruner, 2.Phys. Chem., 41, 514 (1902). (9) C. C. Price, J. Amer. Chem. SOC.,58, 2101 (1936). (10) C. C. Price and C. E. Arntaen, ibid., 60, 2835 (1938). (11) P.W.Robertson, el al., J. Chem. Soc., 933 (1949). (12) A. L. McClellan, “Tables of Experimental Dipole Moments,” W. H. Freeman, San Francisco, Calif., 1963. (13) H. A. Benesi and J. H. Hildebrand, J. Amer. Chem. Soc., 71, 2703 (1949). (14) F.Fairbrother, Nature, 160, 87 (1947). (16) R. 9. Mulliken, J. Amer. Chem. Soc., 7 2 , 600 (1950).
CONMUNICATIONS TO THE EDITOR
2857
50 m
0
2!x 4 0 m
c 0 30
z
$ 20 W [L
z’ 8 s
10
Z5
50
75 100 I25 150 REACTION TIME, ItfN
175
Figure 3. P e r cent conversion in substitution reaction as a function of time.
nificant microwave absorption was observed in the present experiments even in saturated solutions of iodine in benzene. This could be either due to the low concentration of the complex or because it has a low vo so that v
