2662
VICTORK. LA MERAND MILDRED E.
distinguishable from those given by our polymerization hypothesis; whether any explanation based on intermolecular forces, but not assuming compound formation, will do this becomes doubtful when we remember (see Fig. 1) that AE becomes constant long before “infinite dilution” is reached. It is not (claimed, finally, that a concentration treatment of amalgams is generally preferable to a treatment in terms of activities. The latter quantities are always valuable since they stand, by definition, in simple relation to the free energies of the amalgams, and thus bridge the gap be-
[CONTRIBUTION FROM THE
VOl. 57
m N E R
tween the thermodynamic functions for an amalgam and its stoichiometric composition. But when amalgams become experimentally indistinguishable from ideal solutions in the manner of Fig. 1, then it seems desirable to try a concentration treatment also, in order to determine whether the deviations from ideality at the higher concentration cannot be quantitatively accounted for by assuming polymerization of the solute; for we may discover in this way what molecular species actually exist in these amalgams. SCHENECTADY, N. Y.
DEPARTMENT OF CHEMISTRY,
RECEIVED OCTOBER 1, 1935
COLUMBIA UNIVERSITY]
The Energies and Entropies of Activation of the Reaction between Bromoacetate and Thiosulfate Ions1 BY VICTORK. LA MER AND MILDREDE. KAMNER The f i s t term of B represents the increase in entropy due to the temperature dependence of Eactfor the process, inactive molecules -+ active molecules, and hence has been called2 the entropy of activation. Further experimental evidence for the temperature dependence of B and Eaetfor a d log k / d T = EaCt/2.3RTz (1) and the action constant B = log Q in the in- zero type reaction will appear in another papers3 The present paper will deal primarily with tegrated form, namely the temperature dependence of the kinetic salt k = e-Eact/RT (2) effect in a reaction between ions of the same sign log k = B - Eact/2.3RT (3) Eactrepre,sents the average energy of those to ascertain in how far interionic attraction inmolecules which react minus the average energy of fluences Eact and B. The bromoacetate-thioSz03” + all the molecules in the system, all quantities sulfate ion reaction BrCH2COOB; was selected for the experibeing defined per mole. La Mer2 has shown as a SzO&!HL!OO’ consequence of this definition of EaOt,due to mental study since it is almost unique among ionic reactions for the absence of side reactions and Tolman, that the high precision with which the velocity constant can be d e t e r m i ~ ~ e d . ~ determines the frequency with which the actiAccordingly, the experiments were designed to vated molecules react. In the special case where test the behavior of E and B for (a) change of Eactremains independent of T a t all tempera- temperature at constant concentration of retures, the integration constant in (4) equals log actants; (b) change of ionic strength (BronstedZo. In the case of unimolecular reactions Zo Debye effect) for the same temperature interval; is the frequeincy of breaking the reactive bond in (c) the effect of substituting high valence cations the activated molecule, whereas in a true bi- like La+++ for the lower valence ions Ba++ and molecular reaction Zo equals the collision fre- Naf at the same ionic strength, and (d) the influquency a t unit concentrations. The dimension ence of dielectric constant produced by the addiof B is time-’. tion of non-electrolytes.6 (1) A preliminary report of these data was given in THIS JOURNAL, The Limiting Law for EBCtand B.-Equation 66, 1739 (1933). A more complete report was read at the St. Peters-
In the theory of chemical kinetics there are two important quantities which determine the specific rate constant k, namely, the energy of activation Eact,defined through the differential form of the well-known Arrhenius equation
+
burg, Florida, meeting of the Society in March, 1934. (2) La Mer, J. Chrm. P h y r . , t , 289 ( 1 9 W ; THISJOURNAL, 66, 1789 (1833).
+
(3) V.K. La Mer and M. L. Miller, ibrd , 67, 2674 (1985,. (4) La Mer and Fessenden, ibid., 64, 2351 (1932). ( 6 ) La Mer and Kamner. i b i d . , 67, 2669 (1936).
ENERGIES AND ENTROPIES OF ACTIVATION OF
Dec., 1935
(1) and the Bronsted equation log k = log ko log f ~ f ~yields / f ~
+
= -&et [z;X= E$t -k Axact
(ZA
+
ZB)l
+
(5)
when we recall that = -RT2 b Inf/bT. The superscript zero refers to the standard state of infinite dilution. = €1 - Ho is the relative partial molal heat content, so that Azact may be called the heat of dilution for the activation B 7 3 X. process A Similarly by using eq. (4))B can be decomposed into the components.
+
+
+ (6) + ASaot/2.3R
B = B o [ S x - (SA = log: Zo S k / 2 . 3 R
+
SB)]
AS/2.3R is the increase in entropy of activation arising from interionic attraction. When the thermodynamic operators = -bF/bT and = @’/T)/b(l/T) are applied to the Debye-Huckel limiting law
F, K
= -N(EZ)~K/~D =
(7)
C(DTV)-‘/r
one obtains on substituting Wyman’s valuess of b In D / b In T = -1.371 for water a t 25’) that
zi = pi [3 / z bb--Il nn DT + 2-1ahv bl n T + 3/21
(8)
-
Si = Fi/T = E/T[-1.52]
It is important to emphasize that in the limit for high dilutions, the reversible heat of dilution (-Tsi) is almost exactly three times greater, but ofiposite in sign to the irrarersible heat of dilution ( B i ) . Now pJ2.3RT = log f, = -0.506Zi2 fi (10) and Z Z 2= (2, $. Z B ) ~hence , AEaCt/2.3RT= 0 . 5 1 Z n Z ~fi ASaOt/2.3R= 1.52 ZAZBg i j
(11) (12)
The Bronsted-De bye equation, accordingly, can be written log k = [log Zo S;,,/2.3R f 1.52 ZAZB
