NOTES
2370
maintains that it shows "that terms of the Drude type do not contribute in any observable measures to the rotatory power in the visible and ultra-violet region of the spectrum. " It ill be first noted that Chandrasekhar's parameters are very close to those in the first line of Table I, for ( A - B ) and L, respectively. The reason for this correspondence is seen with the help of eq. 5 . If one makes first the approximation AB2 = L = Ab2, the denoniinator becomes (Az - L J ) ~ .If one then makes the further approximation that @ A b 2 - BXa2) in the nuinerator is zero, one is left with ( A - B)X2/ (Az - L ) 2 ,which is identically Chandrasekhar's expression. Therefore, contrary to his statement quoted above, he is in fact using the Drude relation, but in a doubly-approximate form. The utility of the expression itself was tested by taking 96 of the shortest wave length points of the Lowry and Coode-Adams data, from 2327 to about 3570 8.)correcting for the infrared contribution, and doing a least-squares fitting to the Lomniel-Chandrasekhar equation. The optimum parameters obtained were 7.2277 and 0.084597. There was an obvious systematic lack of fit to the data and the rootmean-square deviation approached 0.023'. Only 23 of the 96 points showed deviations as small as 0.010', which is alniost the worst deviation with the full Drude expression. The approximations are therefore not good enough to justify using the two-parameter form instead of the full expression. ChandrasekharI2 has placed considerable stress on Kuhn's summation rule14 as a criterion which equations have to meet to be considered valid. Kuhn himself has pointed out that one cannot place much emphasis on this because of the role of potential contributions outside the range of measurement. One can make this more explicit by pointing out that a Drude term a t about 100 p with a numerator parameter equal and opposite in sign to that of the quartz ultraviolet ( A B ) would make a rotatory contribution of less than 0.001" in the region of measurement. One does not know what combination of terms goes into the infrared parameter, -0.1879". I n summary, the rotatory dispersion of quartz is apparently exactly matched by a Drude equation. For the excellent data available from 0.23 to 3.2 p, a match to 10.0037" per nim., root-mean-square deviation, is given by eq. 6 above. The infrared contribution suniniarized in the parameter - 0.1879 is real.
(14) \I7. Kuhn, Z. physik. Chem., B4, 14 (1929).
T h e Journal of Physical Chemistry
The Kinetics of Bromine Exchange between Bromide and Bromoacetate Ions
by F. J. Johnston Department of Chemistry, University of Georgia, Athens, Georgia (Receiz;ed December 83, 1963)
Kinetics of the exchange reactions CH2XCOO-
+ X-
----f
CHzXCOO-
+ X-
for the chloroacetate-chloride1 and iodoacetate-iodide2J systems have been previously described. The corresponding exchanges in the chloro-, * b ~ o m o - , ~ and iodoacetic2zEacid systems have also been studied. This report describes the kinetics of bromine exchange between bromide and bromoacetate ions at 0. I00 ionic strength and compares the results for the different systems. Reaction rates for exchange in this system have been measured from 26.6 to 70.0'. The hydrolysis reaction CH2BrCOO-
+ HOH + CH20HCOO-
+ Br- + H +
occurs simultaneously with the exchange reaction and for this reason experiments were carried out in the presence of sodium acetate to minimize the formation of molecular acid. The extent of the hydrolysis reaction during a given exchange series was small, corresponding always to less than 12y0 decomposition of the bromoacetate. For a system in which exchange occurs and in which one of the exchanging species is being produced a t the expense of the other, the fractional excha1Jge as a function of time is given by17436 d [ln (1 - F)]/dt = W ( a
+ b ) ; [a + p ( 4 I @ - A t ) 3
(1)
F is the fraction of equilibrium exchange a t time t , a and b are initial concentrations of exchanging species, p ( t ) is the extent of chemical change in the system, and R(t) is the exchange rate at time t . For a process first order ~~~~
~
(1) F. J. Johnston, J . Phys. Chem., 6 6 , 1719 (1962). (2) H. van der Stratten and A. H. Aten, J . Am. Chem. SOC.,76, 3798 (1954). (3) R. C. Bond, M.S. Thesis, University of Georgia, 1963. (4) R. -4.Kenney and F. J. Johnston, J . Phys. Chem., 63, 1462 (1959). (5) J. F. Hinton and F. J. Johnson, ibid.,67, 2557 (1963). (6) C. P. Luehr, G. E. Challenger, and B. J. Masters, J . Am. Chem. Soc., 78, 1314 (1956).
NOTES
237 1
Table I : Sumniary of Rate Constants for the Bromide-Rromoacetate Exchange Reaction a t 0.10 Ionic Strength (CHzBr-
(CHs-
coo -)a,
kxi 1. mole-' Bec. -1
M
(Br -1, M
343.1
0.0695 0.0800
0 0205 0 0103
0.0100 1.11 x 10-3 0.0100 1.14 Av. 1.12 X 10-3
333.6
0.0101 0.0400 0.0501 0.0500 0.0700 0.0800
0 0 0 0 0 0
0.0850 0.0200 0.0200 0.0250 0.0100 0,0100 Av.
0.483 0.475 0.475 0.491 0.489 0.483 0.483 X 10-3
0.0600 0.0100 0.0200 0.0100
0.179 0.177 0.178 0.189 0.180
Temp., OK.
323.4
0.0350 0.0500 0.0650 0.0750
0050 0402 0305 0252 0205 0104
0 0036 0 0393 0 0155 0 0152
COO-)o. M
AV.
311.9
299.8
0.0445 0.0497 0.0700 0.0750 0 0800
0 0 0 0 0
0442 0399 0200 0200 0102
0.0552 0.0756
0 0555 0 0256
0.0100 0.0100 0.0100 0.0062 0.0100 Av. ...
... AV.
x
10-3
0.594 X 0.572 0.572 0.602 0.602 0.589 x 10-4 0.152 0.148 0.150 x 10-4
Experimental Sodium bromoacetate was prepared by titration of Eastman White Label broiiioacetic acid. Reagent sodium bromide solutions were labeled with potassium bromide-82 as obtained from Oak Ridge Isotope Sales Department. The sodium acetate added as buffer was reagent grade. Reactions were carried out under conditions of temperature variations of less than 10.05'. Titration with silver nitrate served to follow coiicentration changes in the system and to separate the reactants. _4liquots of the bromoacetate fractions were counted in a scintillation detector system aiid the fraction of equilibrium exchange evaluated froin
F(t)
=
(specific activity of CHzBrCOO-) (specific activity of total Br-)
Counting rates were in every case high enough to allow a comparison of a reacted sample with a stock sample within a time sufficiently short that decay corrections for the 35-hr. bromine were unnecessary. Standard deviations of the net counting rates were less than 1%. Separation induced and background exchange were negligible.
Results and Discussion Bromine Zzchange. Rate constants for exchange, IC, were calculated according to eq. 2 . A summary of the results is given in Table I. The exchange reaction was satisfactorily described by a second-order rate law
Table I1 : Comparison of Exchange Parameters for the Kaloacetate and Haloacetic Acid Systems AH*, oal. male-la
System
AS*, Gal. mole-' deg. -1 a
km
1. mole-' sec. -1
.-10.9 1 1 . 1 1 . 1 x 10-7 23,700 f 350 1 8 , 9 8 0 f 100 --13.4 f 0 . 2 0.92 x 10-4 15,980 =k 380d --14.8 f 1 . 3 0.78 X 15,360" -17 4 CH9C1C00- 4 1 26,080 f 3 0 0 .- 7 . 8 f 0 . 9 0.96 X 5 CHBBrCOO--Br19,7080 f 130 -16.6 i 0 . 4 0.54 X 6 CII,ICO --I - e , g 15,940 f 380' --19.3 i 1 . 2 0 , 7 9 x 10-3 15,3513. -- 20 a Obtained by a least-squares computer programming of k , = kT/hexp[PS*/R] exp[ -- A H ' C / R T ] . The variations listed are standard deviations. The dat,a for syst'ems 1 and 4 were re-evaluated in this fashion. Where deviations are not given, sufficient data were not available to allow such a treatment. Calculated for 298°K. Ref. 4. Ref. 5. e Ref. 2. Ref. 1. ' Ref. 3. The available data for this syslem are for 0.05 ionic strength. 1 2 3
CHzClCOOH-C1-
CHzBrCOOH-BrCHJCOOH-I -
0
~1
with respect to each of the exchanging species, eq. 1 becomes In (I - F )
=
k,(a
+ b)t
(2)
a t all coiicentratioiis aiid temperatures studied. The parameters in the expression k , = kT,'h exp[AS*:R] exp [ - A N * / R T ] were determined by a least-squares computer program for the data at an ionic strength of Volume 68, .Yumber 8 August, 1964
2372
0.100. It was found that AH* = 19,700 i 130 cal. mole-’; the corresponding entropy of activation is A#* = - 16.6 f 0.4cal. mole-’ deg.-l. The variations listed are standard deviations obtained from the same program. Comparison of f h e Different Systems. I n Table I1 are summarized exchange constants for the haloacetic acid-halide and haloacetate-halide systems that have been studied. An essentially linear dependence of the exchange activation enthalpy upon bond strength in the haloacetic acid series has been previously noted.5 The difference in the exchange enthalpies for the chloroacetic acid and chloroacetate systems has been interpreted as due to electrostatic effects.’ (The difference, approximately 2.4 kcal. mole-’, is equivalent to the work done in bringing togetheor two unit charges in water a t 80” to a distance of 2 A. apart.) For the bromide systems, however, the difference is 0.72 kcal. mole-’ and for the iodide systems the enthalpies of activation are experimentally indistinguishable. These results suggest that electrostatic effects are less iniportant in affecting the formation of the traiisition state than, for eyample, the relative degrees of hydration or polarizabilities of the haloacetic acid and haloacetate molecules. Entropies of activation for exchange in the ionic series and in the acid series are in a direction consistent with steric hindrance of the replacement. The reason for the apparently sigiiificaiitly greater negative activation entropy for exchange of chloride with chloroacetic acid than with chloroacetate ion is not obvious.
Acknowledgmenls. Appreciation is expressed to Mr. James Forhon of the computer center for least-squares prograniming and analyses and to RIichael Johnston for assistance with bromine-82 counting. This work was supported by A.E.C. Contract 9T(40-1) 2826.
Association between Silver and Chloride Ions in Aqueous Solution by AI. J. Iiisley, G . D. Parfitt, and A. L. Smith Chemistry Department, C‘niterszty of IVottingham, L’nztersity Park, Nottmgham, England ( R e w a e d February 17, 1964)
I n the course of a conductometric s h d y of the precipitation of silver chloride from aqueous solution, which involved generating chloride ions homogeneously in the presence of silver nitrate, it was necessary to calcu-
T h e Journal of Phvaical Chemistry
NOTES
late the concentrations of silver and chloride ions at any time and for this a knowledge of the formation constants of the various associated species present was required. E istiiig solubility datal seem to show that ion association is significant, IT ith the formation constant for the uncharged species (AgC1) between 10002 and 20003 and appreciable amounts of higher (nioiionuclear) comple ies present in solutions containing a large excess of silver or chloride ions. I n view of the doubt cast on the experimental procedure of some solubility determinations’ and the rather surprising result that silver chloride cannot be considered as a strong electrolyte in aqueous solution, it was considered desirable to verify that the reported formation constants were consistent with conductance measurements. The usual method by u hich conductance data over a range of concentration are analyzed by means, of e.g., the Fuoss equation4 is not readily applicable to an electrolyte as sparingly soluble as silver chloride so that an alternative technique was used which, although not of great precision and unsuitable for detailed investigation of the higher complexes, is sufficiently sensitive to detect association of the order of that reported. This involves the homogeneous generation of chloride ions in an aqueous solution of silver nitrate by the hydrolysis of allyl chloride. The hydrolysis is sufficiently slow, a t suitable concentrations, that an appreciable time elapses before precipitation of silver chloride occurs. During this time the rate of increase of conductance with tinie does riot depart detectably froin linearity if the carbonic acid dissociation is suppressed by keeping the p H to -5. Association of Ag+ and C1- to form a nonconducting species will diiiiinish the rate of increase of conductance relative to that in a control solution identical in every respect except that silver nitrate is replaced by potassium nitrate. Association in the latter, as measured conductometrically, is known to be small.
Experimental Materials. The silver nitrate was Johnson, Matthey, arid Co. Ltd. “Specpure” and the potassium nitrate was A.R. grade. The allyl chloride (British Drug Houses “Laboratory Reagent”) was dried over calcium sulfate and then fractionated, with liberal rejection of the first and last portions, into brown stoppered bottles containing anhydrous calciuiii sulfate. Just prior to (1) E. Berne and I. Leden. Saensk Kern. T i d s k r . , 65, 88 (1953).
(2) I. Leden, ibid.. 64, 249 (1952). (3) ,J. H. Jonte and D. 8. Martin, J . Am. Chem. Soc., 74, 2052 (1952). (4) R.M . Fuoss, ibid., 81, 2659 (1959).
