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
?r'aC1O4
hIolar concn.
0,010 ,025 .10 .20 1.0
lo3
1. mole-1 see.-'
6.21 5.55 4.05 3.08 1.80 3.03 2.98 2.73 4.63 4.27 7.74
Ca (C104)? 0.033 Mg(ClO4)n ,033 CaCl? .033 LiCIOi .10 NaNOa .10 (CH3)aNCl .10 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 coeffi-
cient of a molecule or of tho rate constant is a linear function of see ref. 4,p . 140.
p
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., HI 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).
NOTES
368
90 057
a/
0 0
0
0
0 0
0
\
0
Q '\ I
_-_---.
i
C5
0
___
, ,
5
25
20 V*
__30 _ _ ~--~35 45 40
m1/gm
Fig. 1.-Experimental values of the excess volume as a function of pressure: Hz and Dn on P33 (2700'). 70
Cxcess
Volume Y S
60-
Pressui8
} P3317'00~1
CH4
Go
v, ,
mllqm
Fig. 2.-Experimental values of the excess volume as a function of pressure: CH4and CD, on P33 (2700').
vo - v,,,= v, = Bas
(2)
Vgeqis found from the helium dead space volume at the ice point and BAS,which is equal to the experimental excess volume V,, is defined as BAS J Y S ~ O [exp(-ei&T) - 11 d V (3) where ais is the interaction energy of a single gas system with the surface, in a given volume element dV. No quantum mechanical correction to the classical configuration integral has been made for a reason explained below. We have investigated four models for the interaction potential €is: an inverse cube attraction coupled with a hard-sphere repulsion (3 - m), and three Lennard-Jones type functions (3-9,3-12 and 4-10).6 These four models all yield equations of the form BAdAso = f(EiB* /kT) (4) where A is the area of the solid adsorbent, so is the apparent distance between the gas system and the surface at zero net interaction energy, and em* is the maximum energy of gas-surface interaction. In Figs. 1 and 2 the pressure is plotted against experimental values of V , for the H2-D2 and CH4-CD4 pairs, respectively. These volume data, extrapolated to zero pressure, were fitted t o the curves generated by each of the four equations of the type (4) to determine the best-fit values of the two parameters As0 and €is* for each potential ( 5 ) For a discussion of these potential functions see: J. R. Gams, Jr., G. Constabaria and G. D. Hahoy, Jr., J . Phye. Chsm., 64, lG89 (1960).
VOl. 65
model. The details of the calculations and a discussion of the limits of error to be expected in the values of the parameters obtained are given in ref. 5. The gas-surface attractive potential may be identified with the London forces attraction of two isolated s y ~ t e m s . Then, ~ ~ ~ from the experimental ei* and any one of several formulas which have been proposed for the constant of proportionality in the London expression,6 a value for so can be calculated, and an apparent area of the adsorbent emerges. Areas determined through the use of two such formulas, those of Kirkwood and MUller*J and of Londons are reported here (as AKMand AL). These represent the lower and upper limits, respectively, of areas found by the five formulas discussed in a previous publicati~n.~ In the case of the H2-Dz pair, Dz shows the anticipated higher interaction energy and lower area (Table 11). Freemane found for this same isotopic pair adsorbed on the low ash sugar charcoal SU-60 these values of interaction energies when the data were analyzed in terms of the classical configuration integral using a 3-9 otential law: Hz, 1866 cal./ mole; Dz, 1914 cal/.!mole. The percentage difference found by Freeman is slightly higher than the present results indicate. The Va data can be converted into the usual terms of volume adsorbed at STP (ref. 5 , eq. 8), and conventional adsorption isotherms then can be plotted. The isosteric heats of adsorption at zero coverage obtained in this manner are 1293 and 1337 cal./mole for Hz and Dz, respectively. Pace and Siebert'o have obtained low temperature calorimetric heats of adsorption of parahydrogen and orthodeuterium on Graphon. The difference in their values at low coverage (e LZ 0.2) compares favorably with that found in our isosteric heat values. The CH4-CD4results are surprising in that CH4 is found to yield a higher energy of interaction with the surface than does CD4 (Table 11). The isotherms of both gases were found to be quite reproducible on outgassing the system overnight and introducing a fresh charge of gas. Illustrative of this are the following pairs of values for the apparent volumes at zero pressure in ml./g. of adsorbent for CHa and CD, at 235"K., each value representing a different gas dose: CH4, 1.8444 and 1.8437; CD4, 1.8333 and 1.8327. The isosteric heats of adsorption at zero coverage are found to be 3032 cal./mole for CHd and 3005 cal./mole for CD4. The rather large inversion in interaction energies with the methane pair is reflected in sizable differences in areas computed from the data. As can be seen from Table 11, these differences amount to more than 1 ms2/g.in some cases, or almost 10%. The area differences in the case of the hydrogen pair are commensurate with the small differences in interaction energies. It is clear from Figs. 1 and 2 that there is no possibility to explain this effect with the methanes (6) J. G. Kirkwood, Z.Physik, 33, 57 (1932). (7) A. Muller, Proc. Roy. SOC.(London), A164, 024 (1036). (8)H.Margenau, R m Modern Phys., 11, 1 (1939). (9) M. P. Freeman, J . Phys. Chem., 64,32 (1960). (10) E. 1,. Paoe and A. R. Siebert, ibid., 63, 1398 (1959).
Feb., 1961
369
NOTES
TABLE I1 INTERACTION ENERGIES AND AREASFOR VARIOUS POTENTIAL MODELS K = 2 ~ ~ v ~ ( b v / d c ) ~ v/ isX the ~ ~ refractive N~; index AKM,
*is*,
Model
cal./mole
3-9 3-12 3- m 4-10
1141 1145 1298 1097
3-9 3-12 3- m 4-10
1151 1155 1306 1109
3-0 3-12 3- m 4-10
2947 2955 3297 2846
AL.
m.*/g.
m.a/g.
13.50 14.52 19.69 13.12
17.45 18.80 25.54 15.93
13.20 14.34 19.45 12.81
17.12 18.54 25.22 15.53
7.57 8.19 11.99 7.85
12.96 13.99 20.50 11.74
Ht
D 2
CHI
of the solution, XO the wave length in vacuo of the light used, N A Avogadro’s number, P the osmotic pressure, p the depolarization ratio, i.e., the ratio of the horizontally polarized to the vertically polarized light a t 90” with unpolarized incident light. Hill2 and Stigter3J have pointed out recently that eq. 1 is not quite correct. The calculated deviations are for sucrose solutions, however, within the accuracy obtainable with light scattering instruments. We will therefore use eq. 1in this Note. The following remarks can be made in connection with these data. 1. Maron and Lou as well as Stigter deduce from measurements at 90” that the total turbidity of the solute is T’
= (16~/3)Rgo
This r’ differs, however, slightly from the real turbidity T as shown by Cabannes5 and restated by 3-9 2881 8.24 14.13 several authors.6 This is due to the fact that the 3-12 2889 8.91 15.20 form of the depolarization factor (6 6 p ) / ( 6 - 7 p ) 3227 12.97 22.15 3- m changes with the angle of observation and can 4-10 2846 8.59 12.87 therefore not be considered constant during the in terms of the mass effect on the vibrational energy integration over all angles as is necessary to oblevels. It also appears that even though the Hz-D2 tain r from Rw. The real turbidity T is experiments could be fitted to such a theory there is the strong probability that there is a second effect here, too. We surmise that the effect is a rotational one; for the same factor of change in the moment The numerical differences between T and T’ are of inertia, the relative mass change on going from usually small for solutions, but can be appreciable for liquids. It seems advisable to keep this difCH4 t o CD, is much smaller than for the pair ference in mind and to report light scattering H2-Dz. The results of Armstrong, Brickwedde measurements in terms of Reo rather than T’, aland Scott“ for the vapor pressures of the pure though both, of course,, yield exactly the same methanes should be mentioned here. Between the melting point and the critical point, the heavier dP/& (or osmotic coefficient in Hill’s formulation). 2. Various authors7have introduced orientation species is found to have the higher vapor pressure. We intend to extend this work to other isotopic correlation in gases, liquids and solutions. Benoit and spin-isomer species and other surfaces in the and Stockmayer have theoretically deduced that this type of ordering would be impossible to detect future. in gases and probably obscured by internal field (11) G. T. Armstrong, F. G . Brickwcdde and R. B. Scott, J . Redifficulties in liquids. However, considering the search Natl. Bur. Standards. 66, 39 (1955). case of non-in teracting rigid rod-like molecules in solution, these authors estimate that orientation correlation may amount t o 12% of the second virial, LIGHT SCATTERING BY AQUEOUS which in this model is due solely to the finite size of the molecules. Since Stigter4 has shown that SUCROSE SOLUTIONS in the case of sucrose there is a definite attractive BY W. PRINS potential between sucrose molecules, the orientaCeZluZose Research Institute, State Uniueraity College of Forestrv, tion correlation may well be appreciably enhanced Syracuse, New York above the amount estimated by Benoit and StockReceived J d y IS, 1060 mayer. It seems interesting, therefore, to calculate In recent years the light scattering of aqueous this effect from Maron and Lou’s data. Using the sucrose solutions has received considerable atten- notation developed by Prins and Prins,’ we have tion, due to the fact that these solutions form con(2) T. L. Hill, J . Chem. Phys., S O , 93 (1959). venient primary standards for the calibration of (3) D.Stigter, J . Phys. Chem., 64, 114 (1960). (4) D . Stigter, ibid., 64, 118 (1960). light scattering photometers. Maron and Lou’ ( 5 ) J. Cabannes, “La Diffusion Moleculaire de la Lumidre,” have measured the Rayleigh ratios, &, due t o Paris, 1929, p. 33. solute scattering for concentrations up to c = 0.6 (6) W. H. Stockmayer quoted in W. B. Dandliker and J. Kraut, g./ml. and found correspondence within a few per J . Chem. Phys., 28, 1544 (1955); J. A. Prina and W. Prins, Physica, cent. with the measured osmotic pressures accord- aa, 576 (1956). (7) M. Goldstein and E. R. Illichalik, J . A p p l . Phys., 86, 1450 ing to the well known formula (1955); H. Benoit and W. H. Stockmayer. J . Phus. Rad., 17, 17 CDa
+
(1) S. H. Maron and R. L. 11. Lou, J . Phys. Chem.. 59, 231 (1955).
(1956); J. A. Prins and W. Prins, Phyaica, 23, 253 (1957).
