KOTES
Feb., 1961
entropy at 100°K. given by Frank and C l ~ s i u s ’ ~ and the data in Table IV from the relation rn
Si = Si(100”K.)
+ J$ dT 100
The entropy of the saturated vapor S, was calculated from the saturated liquid and the heat of vaporization data obtained both calorimetrically and from vapor pressure data (Table VI).
s, = 81 + AH, -gi-
TABLE VI1 T.
OK.
(3)
(4)
The results are summarized in Table VII. Two values for S, are given. The super script “c” refers to the entropy calculated from equation 4 using the calorimetric heats of vaporization (Table VI, column 2). The super script “vp” refers to the entropy calculated from heats of vaporization derived from the vapor pressure data (Table VI column 3 ) . In order t,o check the self-consistancy and accuracy of the various experiments, the entropy of methane in the ideal gas state So has been calculated and compared with those obtained from statistical calculations. The ideal gas entropy has been calculated from the expression
so = sg + R In p - (8, - Si) (5) The term R In p was computed from the data in Table I1 and the last term, the difference between
real and ideal gas entropy, from A. P. I. tables.3 The results are shown in columns 6 and 7 of Table VII. So(cal.) and So(v. p.) mere calculated from Sgcand Spv.p.,respectively. In the last column of Table VI1 the statistical entropy of methane is given. It can he seen that these entropies are in excellent agreement with those calculated from the
365
100 105 110 111.42 115 120 125 130 135 140 145 150 155 160 163 170 175 180 185 190
Si,
e.u. 17.43“ 18.07 18.68 18.79 19.27 19.85 20.42 20.97 21 51 22.04 22.56 23.08 23.59 24.11 24.62 25.16 25.71 26.32 27.07 28.42
S,,. e.u. 37.73 37.09 36.53 36.35 36.03 35.58 35.19 34.82 34 48 34.17 33.87 33.59 33.31 33.05 32.76 32.46 32.13 31.6G 31.09 29.32
-(SFSi),
SBv,~.,
e.u.
.. . ...
36.62 36.39 36.04 35.54 35.14 34.76 34.40 34.11 33.81 33.56 33.29 33.02 32.69 32.38 32.04 31.58 31.08 29.40
e.u. 0.09 .12 .17 .19 .22 .28 .34 .40 .49 .59 .68 .78 .93 1.08 1.24 1.42 1.68 1.89 2.30 2.92
so
(cal.), e.u. 35.71 36.07 36.48 36.54 36.80 37.14 37.47 37.77 38.10 38.42 38.71 38.99 39.30 39.60 39.86 40.11 40.39 40.46 40.63 39.79
so
SQ
(v.P.), (Stat), e.u. e.u. 35.72 . 36.10 ... 36.48 36.57 36.59 36.58 36 8 3 36.81 3 7 . 1 0 37.17 37 I49 37.42 37.80 37.71 38.02 38.10 38.39 38.36 38.67 38.68 38.94 38.96 39.28 39.20 39.46 39.57 39.79 39.71 4 0 . 0 3 39.95 40.30 40.18 40.38 40.40 40.62 40.62 40.83 39.87
. .
a Entropy of liquid methane at 100°K. = 17.43 cal. deg.-l mole-1 from Frank and C ~ U S ~ U S . ~ ~
experimental data except for the last point (190’ IC.). This is probably due to the large uncertainty in the extrapolation of the heat of vaporization from 185°K. to the critical temperature. Acknowledgement.-One of the authors (P.H.) is indebted to the “Institut pour L’Encouragement de la Researche Scientifique dans 1’Industrie et 1’Agriculture’’ for a grant which permitted his visit to the Cryogenic Laboratory, to the du Pont Chemical Co. which in part supported the research and to Dr. L. Deffet, Director of the “Institut Belge des Hautes Pressions” for the arrangements which made the visit possible. We would also like to thank Dr. P. K. Walsh and Ah-. A. Brooke for their help and advice during the experimental investigations.
NOTES IONIC STRENGTH EFFECT IN THE
more reasonably consider for the several a-chlorotoluenes differences in the localization of charge in the (somewhat different) transition states,’ with REhCTIOhT resultant differenccs in the degree of solvation. BY RICHARD FUCHS AND ALEXNISBET Another viewpoint would consider differences in Department of Chemistry, The University of Texas, Austin 12, Texas the degree of thiosulfate-carbon bond formation in the transition states for the various a-chloroReceaued July I, I960 toluenes, with concomitant variations in the Changes in solvent composition and dielectric amount of deformation of the thiosulfate solvation constant (D)affect unequally the rates of reaction required to attain these configurations. of a-chloro-p-nitro-, a-p-dichloro-, a-chloro- and a- shell It is usually stated2 that ion-neutral molecule chloro-p-isopropy1tr)luene with sodium thiosulfate, reactions proceed relatively rapidly in solvents of The relative rates (or Hammett p constant) are in low This is not confirmed by dielectric most solvent mixtures a logarithmic function of work with theconstant. a-chlorotoluene-thiosulfate system 1,’D.I The solvent must not, therefore, be acting in 40% ~ a t e r - 6 0 7 ~ organic solvent mixtures,‘ solely by affecting the activity coeffcient of the atis definitely contradicted by work involving tacking species, thiosulfate ion, for this would lead and butyrolactcne-water mixtures of varying composito uniform rate changes for all the a-chloro- t i ~ n . ~ toluenes as the solvent was varied. One might
THIOSULFATE-~-CHLOROTOLUENES
(1) R. Fuchs and A. Nisbct, J . Am. Chem. SOC.,81, 2371 (1959).
(2) K. J. Laidler and H. Eyring, A n n . N . Y. Acnd. Sci.. 39, 303 (1940); subsequent citations are numerous.
1.4
8
SULFATE (s208-)b
’
1.2
?i
0.06 .04 .02 ,008 ,004 ,002 ,0008
’
+ 1.0
e M
3
-
0.8
0.6
0.4
TABLEI ~-CHLOROTOLUENES WITH THIOAT VARIOUSIOXIC STRENGTHS
RATEsQ OF REACTION OF
*
~
(P-H)
(p-i-Pr)
In 60% acetone 3.85 4.43 4.71 5.58 5.90 7.28 6.76 8.85 7.89 9.74 8.01 10.8
..
..
(p-NO3)
.. 11.9 15.1 18.7 30.7 23.3 25.2
In 60% dioxane 0.04 3.63 4.03 10.9 .02 4.42 5.08 13.7 .008 5.22 6.03 16.8 .004 6.25 6.76 18.8 .002 6.30 6.89 21.3 .0008 .. 7.82 .. Second-order rate constants a t 30’; k X 10-3 1. mole-’ sec.-l. All values are averages of two or more determinations. b Contains added potassium acetate as a buffer; total ionic strength 0.192, 0.128, 0.640, 0.0256, 0.128, 0,00640 and 0.00256, respectively. (RCl) approximately 60% of (&03=‘). For a description of the method of measurement and the purification of reagents, see ref. 1. Q
~~
0.0
0.2 0.3 0.4 0.5 v‘ionic strength. Fig. 1.-Effect of ionic strength on the rates of reaction of a-chlorot oluenes with thiosulfate: (1) p-NOz in acetone; (2) p-;zIC)z in dioxane; ( 3 ) p-isopropyl in acetone; (4) p-H in acetone; (5) p-isopropyl in dioxane; (6) p-H in dioxane. 0.1
It is, therefore, of interest to determine for the same reacting systems whether an “anomalous” ionic strength (p) effect accompanies the unexpected solvent effect. Agreement on an “expected” ionic strength effect is not complete. Qualitatively, an increase in p might be expected, as would an increase in solvent dielectric constant, to inhibit slightly the rate of a bimolecular ion-neutral molecule reaxtion. Other considerations afforded predictions of no ionic strength effect, or a dependence of rate on the first power of the p.4 The present work contradicts these predictions; the rate constants are logarithmically dependent on dp. Thus the rate constants are directly proportional to the activity coefficient of sodium thiosulfate as calculated from the Debye-Huckel limiting law The satisfactory experimental agreement (Fig. I and Table I) up to ionic strengths greater than 0.1 is particularly surprising, for the solvents wed (60% dioxane-40% water, D = 25, and 605% ncetone-400j, water, D = 45.5) should encourage deviations from the Debye-Huckel equation a t even lower ionic strengths than does water. It has been suggested4 previously that rates are dependent on the product of the charges of the reacting species and &, which, for an uncharged re:tctant, predicts k independent of p. Two causes of failure of this relationship are deviations from the Debye-Huckel equation, and the influence of p on the activity coefficients of neutral moleculcs (see below). The presence of inert salts in the reacting systems produced a variety of effects on the rates. The additions of vsrious amounts of sodium perchlorate not only depressed rates of reaction, but did so be(3) Unpublished studies in this Laboratory. (4) For references, see A . 4 . Frost and R . G . Pearson, “Kinetics and Rfcchanism,” .John W i l e j and Sons, Inc.. New York, N. T.,1953, Ch. 7
low that of solutions of the same ionic strength made up only of sodium thiosulfate (Table 11). The addition of assorted inert salts (to p = 0.1) increased the rate slightly (tetramethylammonium chloride), decreased the rate slightly (sodium perchlorate and nitrate, lithium perchlorate), or decreased the rate strongly (calcium perchlorate and chloride, magnesium perchloratme) (Table 11). No quantitative rationalization of this behavior is offered, but qualitatively it is to be expected that the highly charged Mg++ and Ca++ ions enhance ion-pair formation (compared with Na+) with thiosulfate ion (and depress the activity coefficient of thiosulfate ion), and that the large, diffusely charged tetramethylammonium ion should have the opposite effecte5 Slight differences in slope (Fig. 1) which appear for the several a-chlorotoluenes show no systematic trends. Eveii if these be attributed to variations in the influence of p on the different transition states, this must be a niinvr consideration compared wit’h other fact,ors, perhaps, the influence on the activity coefficients of thiosulfate. Figure 1 also reveals that the slope is virtually independent of the solvent dielectric constant, whereas the Debye( 5 ) (a) Similar rate accelerations have been report,ed. See, for example, S. Winstein, L. G. Savednff a n d S. Smith, Tetrahedron Letters, No. Y, 24 (19601, for a n acceleration of chloiide ion displacement by added tetrabutylammonium perchlorate; J. D. Reinheinier, W. F. Kieffer, S. W. Frey, J. C. Cochran and E. W.Barr, J. A m . Chem. Sac., 80, 164 (lY58), for a n acceleration of the reaction of methoxide ion with 2,4-dinitrochlorobenzene by added potassium salts. (b) Evidence for ion-pair formation in sodium thiosulfate has been reported J. R. Bevan and C. B. Monk, J . Chem. Soc., 1392, 1396 (1956), and earlier publications. These authors found that the rate of reaction of sodium thiosulfate with 1-bromopropane is directly proportional t,o the fraction of sodium thiosulfate dissociated (assuming ion-pairs unreactive). and not otherwise dependent on the ionic strength and the nature of the cation present (except as these factors affect the degree of dissociation). (c) Highly apecifie salt effects have previously been relmrted. See, for example, ref. 5a, and F. A . Long, W.F. McDevit a n d F. B. Dunkle. J . Phi@. CoEloid Chem.. 55, 813,820 (1051).
Feb., 1961
367
SOTES
Huckel theory predicts a considerable difference for D = 25 vs. D = 45.5. The lack of correlation with theory is hardly unexpected in the light of previous work' in which absolutely no relationship was found to exist between the rate of the achlorotoluene-thiosulfate reaction and dielectric constant of the solvent. The rates in 60% dioxane and in 60% acetone (Table I) differ only by about lo%, which cert,ainly does not reflect the "predicted" variation with D. Both solvent mixtures contain 40% water, and it may well be that tjhe bulk dielectric constants are not reflected in large differences in the degree of ion solvation, in solvated-ion radii, and in distance of closest approach, because of a tendency of water to be present in the solvation shell at a higher concentration than in the bulk solution. Another route by which p may affect the reaction rates is through an influence on the activity coefficient of the neutral m ~ l e c u l e . In ~ ~the ~ acid hydrolysis of butyrolactone the effect of added salts on the rate parallels the effect on the independently determined activity coefficient of butyroThis relationship is between the logarithm of t,he activity coefficient and p,7 rather than p 1 / 2as mas observed in the present work. TABLE I1 RATEO F R E A C T I O N O F LY-CHLOROTOLUENE WITH THIOSULFATE IN 60% ACE TOKE'.^
(2700") has been investigated in the very dilute range (coverages of less than about 10% of the monolayer). The precision apparatus employed in this study is described elsewhere.2 The experiments consist of measurements of the apparent volume of the sample bulb containing the solid. V.
Salt
hIolar concn.
lo3
1. mole-1 see.-'
?r'aC1O4
0,010 6.21 ,025 5.55 .10 4.05 .20 3.08 1.0 1.80 Ca (C104)? 0.033 3.03 Mg(ClO4)n ,033 2.98 CaCl? .033 2.73 LiCIOi .10 4.63 NaNOa .10 4.27 (CH3)aNCl .10 7.74 5 Initial (SzOs-) = 0.008 M ,(RCl) = 0.005 M . Second-order rate constants at 30'; k X I O 3 1. mole-' see.-'. All values are average of two more determinations.
Acknowledgment.-This work was supported by National Science Foundation Grant NSF-G10033, arid by The University of Texas Research Institute Grant 934-Srf. (6) We arc indebted to Dr. F. A . Long for suggesting this possibility. (7) For an expression in which the logarithm of the activity coefficient of a molecule or of tho rate constant is a linear function of p see ref. 4,p . 140.
THE IXTERSCTION OF Hz, Dz, CH, ASD CDd WITH GRAPHITIZED CA4RRO?J RLA4CK'
nbRT/P
(1)
TABLE I APPAREKTVOLUMEAT ZERO PRES~CRE
90,057 97.122 104,156 109.903 117.049 124.128 131.069 138.128
Hz-D? 1.9388 1.7999 1,7164 1.6707 1.6339 1.6088 1.5906 1 .5774
1.9523 1.8073 1,7242 1,6742 1 ,6362 1.6098 1.5917
Temp.. OK.
V. (CHn), ml./g.
Va (CDd,
E F F E C T OF ADDED SALTS ON THE
k X
=
where nb is the number of moles of gas inside the bulb, R is the gas constant, T the Kelvin temperature and P the pressure. Yalues for the apparent volume extrapolated to zero pressure are presented in Table I .
224.118 230,203 234.982 242,278 250.486 263,276 277.219 287.283 297,153
CHA-CD4 1.9425 1.8829 1,8441 1,7976 1,7532 1.7052 1.6643 1.6458 1,6276
1.5i83 rnl./g.
1.9277 I .8737 1,8330 1.7886 1.7471 1.6998 1.6622 1,6441
The gases employed in this investigation m-ere as follows: assayed reagent grade hydrogen obtained from Air Reduction Sales Company; cylinder deuterium from Stuart Oxygen Company; cylinder methane from the Phillips Petroleum Company; flask tetradeuteriomethane from Merck and Company, Ltd. The CD, (minimum isotopic purity 99%) and Hz were used without further purification. The DP,which was reported to be better than 99.5y0 p y e , was passed through a charcoal-filled trap a t liquid nitrogen temperature prior to use. This procedure may cause a shift of the ortho-para equilibrium; but a t least, no uncertainty in the interaction energy due to such B shift appears in the experimental results. The CH, was distilled several times, with intermittent pumping, between nitrogen and oxygen temperatures. The CHa was analyzed mass spectrometrically in this Laboratory and was found to contain traces of nitrogen (0.03%) and oxygen (0.005%). The CD, was tested for the presence of light gases (e.g., H I or DP) by condensing the gas a t nitrogen temperature and measuring the vapor pressure on a McLeod gauge, then pumping off the gas phase and remeasuring the vapor pressure. No difference in pressure could be detected.
The data have been analyzed in terms of a virial
BYG. CONSTABARIS, J. R. SAYS,JR.,.4ND G. D. HALSEY, JR. coefficients treatment.3j4 The apparent volume Department of Chemistry, University of Washinoton, Seattle 6 , Washington Received July 6 , 1960
The adsorption of the isotopic pairs H2-D2 and CH4-CD4 on the graphitized carbon black P33 (1) This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command.
extrapolated to zero pressure is related to the molecular configuration integral for gas-surface interaction, BAS,through the equation (2) G. Constabaris, J. H. Singleton and G. D. Halaey, Jr., J . Phys. Chem., 6S, 1350 (1959). (3) W. A. Steele and G. D. Halsey. Jr., J . Chem. Phys., 2 2 , 979 (1954). (4) W. A. Steels and G. D. Halsey, Jr., J . Phys. Chem., 69, 57 (1955).
