NOTES
1540 I
I A
1
Vol. 66
Schenck, et al., consisted in determining the equilibrium of the system, R/~o-CH~-I~~-“MO~C.” Unfortunately they used a static system in which considerable thermal segregation of the gases must have occurred. This was evidenced by the fact that their measurements of the C-HZ-CH4 equilibrium by the same method are not in agreement with the presently accepted data for this system. Browning and Emmettll studied the same equilibrium using a dynamic method. Their results lead to an impossibly large entropy change of about 26 e,u. for the reaction 2&Io(s) C(s) = &IozC(s). The observed total pressures of Table I and values of pco,/pco read from the experimental data represented by line D of Fig. 1 yield values for the free energy of formation of “RIo&” shown in Fig. 2 . Here, as before, “illo&” signifies the Mo-rich extremity of the solid solution field including that compositio3. The results in the range 1200-1340°K. are given by
I
GOKCEU
+
T E M P E R A T U R E “K.
energy of formation of MoOz.
Fig. 1.-Free
“Mo2C”; A,Ffo = -11,710 - 1.832’ cal.
1
-14.31
I
I
1200
1220
I
I
I
1240 1260 I280 TEMPERATURE “Ka
1300
1320
1 1343
Fig. %.-Free energy of formation of Mo&.
sidered, only that of Collins9has a slope nearly compatible with the calorimetric value for the entropy. TABLE 1 GASEOUS EQUILIBRIA WITH h ’ f O ~ z - h l O “ ‘ ~ f O & ”
Corrected pressures, mm.-PCO f PCOZ ?IC02/PCO
In the absence of other data on this compound, these figures may be used as roughly valid a t lower temperatures and the heat of formation as approximately -11.7 kcal. Acknowledgments,-The authors wish to thank the National Science Foundation for sponsoring this project, John C. d’Entremont for assistance in constructing and controlling a furnace, and Frank Haynes, without whose sarcasm and wit this work would not have been carried out.
c__-
Temp.,
O R .
1199 1210 1236 1262 1288 1296 1308 132C 1331 1.341
...
64.0- 6 8 . 4 91.9.- 97.6
..
121.8-126.3 I !)5.7-200.1 200.8-308.5
...
342.1-356.8 444.6-452.8 607.0-513.5 610.1-617.1 703.7-708.6
0.393-0.403 .389- .3!)9 ,399.- ,406 .372- .391 .387
...
...
THE DIFFUSIOY OF THIOTiREA IN WL4TER AT 25’ I ~ I)A%ID Y B. LUULIhr,
c. ~TARNER, A N I ) HomR IT. SMITH’
~~OBERT
Department of Physzolog~(and Bzophgszcs and Depnrlment OJ’ Ihorhcrnast r y , h’ea Y o r k Unzverstty School of Medtczne, ew York, N . Y . Receaed January 19, 1982
Interest in the penetration of hiological mcmlraiies by urea and thiourea has led us to search the literature for values of the diffiwion coefficients of The agreenieut among the several sets of dat’a these compounds. Although excellent data are shown in Fig. 1 is fairly good! especially a t the available for urea,2 no comparable information lolver temperat’ures. Our data are represent’ed best appears to have been published for thiourea. by line D, whose slope is based 011 the calorimetric Therefore, the diffusion coefficient of this compound been obtained as a function of concentration entropies. Its equat’ionfor the range 1200-1350°K. has and a comparison has been made with similar data is for urea. This comparison is related t o differences in other properties of these compounds known to Mooz; AFfo = -137,890 40.187’ cal./mole affect diffusion and permeation. On the same basis it’sheat of formation a t 208.15”K. Experimental is - 141.5 kcal./mole. The corresponding caloriDiffusion Measurements.-All measurements nere made metric valuea is - 140.8 kcal./mole. The free energy of formation of “Mo2C” has been on a parallel beam Gouy diffusion apparatus described in a determined by Schenck, Kurzen, and Wesselcocklo preceding publication.“ Design and operation of such and by Browning and Emmett.l’ The method of (1) This investigation was supported in part by the New York Heart
+
(9) B. T. Collins, Sc.D. Thesis, Massachusetts Institute of Tecbnology, Cambridge, Mass., June, 1949. (10) R. Schenck, F. Kurzen, and H. Weaselcook, 2. anorg. albem. Chem., 203, 159 (1932). (11) L. C. Browning a n d P. H. Emmett, J. Am. Chem. Sac., 14,4773 (1952).
Association, the National Science Foundatlon, and PHS Research Grant RG-8987. (2) L. J. Gosting and D. F. Akeley, J. Am. Chem. Soc., 74, 2058 (1982). (3) D. F. Akeley and L. J. Gosting, ibid., 75, 5885 (1953). (4) R. C. Warner, J. Bid. Chem., 230,711 (1957).
August, 11962
:1~ NOTES
equipment has been reviewed recently by Gosting,5 and standard technique was used throughout. Green light from an AH4 meroury lamp was isolated with Wratten 77-A filter, The optical distanoe, b,, was determined for this wave length by measuring the deviation of the slit image resulting from the introduction of a small glass prism at the angle of maximum deviation in the position of the diffusion cell. The optical properties of the prism itself were cletermined independently on two se arate occasions by its manufacturer, the Perkin-Elmer &xorporation, on their Guild-Watts spectrometer. The cell thickness, a, was determined by direct measurement with a traveling microscope. Experiments were performed a t 28.00’ in a thermostat controlled to within =t0.002’. Temperature was determined on a thermometer calibrated against a National Bureau of StandardEi resistance thermometer. Diffusion was carried out in a Tiselius cell with reference windows for Rayleigh optics. After an hour had been allowed for thermal equilibration, a boundary was formed between the more concentrated solution on the bottom and the less concentrated solution on the top. Then the boundary was sharpened through a fine glass capillary siphon for 30 to 60 min. under observation through the Rayleigh system. Time was recorded from the moment when siphoning was discontinued and the capillary withdrawn. From 10 to 15 Gouy photographs were obtained over a period of about 4 hr. in each experiment. Rayleigh photographs were taken during or shortly after completion of boundary sharpening for determination of the total fringe number, J , which was about 150 for the thiourea experiments. The apparent diffusion coefficient, D’, was calculated from fringes 0 to 50 for each Gouy photograph, averaged, and plotted against the reciprocal of the elapsed time. Extrapolation to the y-axis then yielded a corrected value of the diffusion coefficient. The corresponding starting time correction was of the order of 20 sec. Solutions.--Highest purity thiourea from Eastman was recrystallized from reagent grade methyl alcohol and dried to constant weight at 60” in vacuo. Its melting point was 178-179’ with some slight decomposition. Reagent grade urea, similarly recrystallized (melting point 132.5-132.9’) and reagent grade sucrose were used for standard diffusion experiments. All solutions were made up to volume in calibrated glassware with air-saturated distilled water.
1541
0
-
0, @F i 1.38 1.34 1.30
\ m. r6
Q THIOUREA
UREA
0
Eiitrimaiitol
e
t=o.(mny/ac)
I
I
dolo
1.26 !
0
I
0.2 C, moles/l.
0.4
Fig. 1.-Dependence of diffusion coefficient on concentration a t 25’; data for urea taken from work of Gosting and Akeley.*
TABLE I1 DIFFUSIONOF THIOUREA IN WATERAT 25.00’ a, ca C An/AC D,
-
moles/l.
0
I
moles/l.
moleli/l.
l./mod
0.15775 0.07887 2.038 X .07887 .23662 .15775 2.035 X 10-2 .15775 .31549 .23662 2.035 X
cm.*/seo.
1.314 X 1.294 X 1.283 X
y/bC), where Dois the diffusion coefficient at infinite dilution and y is the activity coefficient on the C scale referred to infinite dilution. These points are taken from Gosting and Akeley’s paper on urea and calculated from the thermodynamic data of Redlich, et at., for
Discussion
The first point to be considered is the calibration of the apparatus. As indicated in Table I, diffusion Results coefficients have averaged 0.6% lower than values Optical constants and resulttr from standard reported in the literature for convergent beam diffusion experiments are given in Table I below. equipment. The optical distance, b, which enters Experiments with thiourea are summarized in as a squared term in the calculation of the diffusion Table 11. In these tables, C, and C, are the con- coefficient, is the factor most likely to be involved centrations of the more dilute and more concen- in such a difference. Accordingly, the constants of trated solutions, respectively, in moles per liter; the glass prism used to calibrate the equipment were An/AC is the refractive index increment for X =: redetermined. Substitjutionof the confidence limits 5461 A.; and D is the diffusion coefficient corrected on these values leads to an estimate of b good to by extrapolation to l / t = 0. within 0.05%. It seems unlikely, therefore, that this difference has resulted from an incorrect deterTABLE I mination of the properties of the prism, but no CALIBRATION OF DIFFUSIONEQUIPMEKT Optical constants: a = 2.5065 zk 0.0005 cm.; b = 148.01 other explanation has been forthcoming. Physical constants for urea and thiourea are com=t 0.08 cm. Standard diffusion experiments a t 25.00’ pared below in Table 111. Sucrose Urea Longsworthlo recently has discussed the molecC1, moles/l. 0 0 ular parameters affecting the extrapolated diffuC2,moles/l. (6.043784 0.25018 sion coefficient, Do. To the extent that small moleAn/AC, l./mole 4.895 X 8.594 X cules follow _the Stokes-Einstein relationship, the An/AC, lit. value 4.895 X 10-2(8) 8.602 X 10-3(z) product, DOl.i’/a, is a constant independent of the D,cm.z/sec. 5.140 X 10” 1.365 x nature of the solute. Ig practice, as Longsworth D,lit. value 5.170 X 1.371 X 10-6(2) has shown, values of DoV2’/aincrease linearly with Data from Table I1 are plotted in Fig. 1, together Dofor a variety of simple sugars, amino acids, and with corresponding data for urea from reference 2. other compounds. Also plotted in the same figure are points calculated Among similar substances, an increase in hydrafrom the theoretical equation D = Do(1 C b In tion accompanying an increase in polarity or an in-
+
(5) L. J. Gosting in M. L. Anson, K. Bailey, and J. T. Edsall, ed., “Advances in Protein Chemistry,” Vol. XI, Academic Press, Inc., N e w York,N. Y., 1956, p. 429. (8) J. M. Creeth, J . Phye. Chsm., 62,138(1968).
(7) 0. Redlioh, C. M. Gable, L. T. Beason, and R. W. Millar, J . Am. Chem. Soc., 72,4161 (1950). (8) “International Critical Tables,” Vol. 111, McGraw-Hill Book Co., Ino., New York, N. Y.,1928, p. 111.
1542 T24BLE 111 Urea
Molecular weight
60 06
Vg, cc./mole
44.22
Dipole moment in dioxane, Debye units9 Do, cm.2/spc
n,P2”3
Vol. A6
SOTES
Thiourea
than dipole terms have been neglected. duced dipole moment is written
76.12 53 6* (at 15”)
4.56 4.89 1.382 x 10-6 1.329 48.9 50.3
x
10-6
crease in asymmetry lowers the DO172i21/aproduct. When urea and thiourea are compared on this basis, the increase in partial molar volume of thiourea over urea is paralleled by a decxease in the diffusion coefficient. However, the Do Vz1’’aproduct is larger for thiourea in spite of its lower diffusion coefficient. This difference probably is not significant in terms of differences in hydration or symmetry. The dependence of diffusion coefficient on concentration has been related to the dependence of activity coefficient and viscosity on concentration.ll l 2 As shown in Fig. 1, good agreement is obtained with experimental data for thiourea with the 1 C b In y / b C ) , which mould equation : D = Do( attribute the entire variation in diffusion coefficient to the thermodynamic term, C b In y/bC. Actually, this agreement probably is partly fortuitous in that changes in viscosity of the solution hare been neglected in the equation.
P = a
7 e [4 -
The in-
28]
The second term accounts for the effect of the induced dipole of one halide ion upon the electric field a t the other halide ion. The requirement (dW/dr), = 7 o = 0 allows one to evaluate the term for the repulsion energy.
The additional requirement d2W/dr2 = k , where k is the vibrational force constant for the stretching frequency, allows one to evaluate p directly. However, for the four salts for which k is known,4>5 the p-values range from 0.34 to 0.52. It was decided to evaluate p empirically using a single value, p = 0.27 A., for all of the alkaline earth halides. Certainly a better agreement could be obtained if a slightly different value of p was assigned for each halide ion, but other uncertainties in our calculation would make such a treatment unwarranted a t this time. The polarizabilities used are those calculated by Pauling6 and the internuclear distances have been measured by Akishin and Spiridonov7 by the electron diffraction method.a Their estimated un(9) W. D. Kumler and G. M. Fohlen, J . Am. Chem. Soe., 64, 1944 certainty in r is 0.02 to 0.03 A. (1942). The calculated values for Mi, the binding energy, (10) L. G. Longsworth in T. Shedlovsky, “Electrochemistry in are shown in Table I, along with the recently reBiology and Medicine,” John Wiley and Sons, Inc., New York, N. Y , vised experimental values.8 The agreement is 1955, p. 225. (11) L. Onsager and R. &I. Fuoss, J . Pilus. Chem., 36, 2689 (1932). satisfactory, except for the beryllium halides. In (12) A. R. Gordon, J . Chem. Phys., 5, 522 (1937). this case one might expect a strictly ionic model to be inadequate. The results of both of Cubicciotti’s BIKDIXG ENERGIES OF THE GASEOUS calculations are included for comparison. The major differences between our calculation ALKALIXE EARTH HALIDES1 and the calculation which Cubicciotti found to be BY THONASE. BRACKETT AND ELIZABETH B. BRACKETT unsatisfactory lie in (a) the inclusion of the dipoledipole term in the energy, (b) different values for the Department of Chemistru, Wzlliam Marsh Rzce University, Houston, Texas polarizabilities, (c) different values for the paramReceised January 19, 1962 eter p, and (d) the inclusion of the term p a / 4 r 3 Cubicciotti2 has calculated the binding energies in the calculation of the induced dipole moment. of the gaseous alkaline earth halides, using Ritt- The effect of the dipole terms, (a) and (d), is not ner’s3 method. This calculation, which is based on insignificant, amounting to 60 kcal. in some cases, an ionic model, generally includes a term of the down to 1 or 2 kcal. for others. The choice of polarizabilities deserves some comform A e - r / p for the repulsion energy. The agreement of these calculations with experimental values ment because the values used by Cubicciotti, was not satisfactory. However, Cubicciotti calculated from the indices of refraction of alkali , ~ some 10 t,o 40% smaller than showed that the substitution of an AT-” term for the halide c r y ~ t a l s are those calculated for the free ions by Pauling from repulsion energy gave very good agreement. It seemed worthn-hile to investigate the matter fur- the theory of the quadratic Stark effect. We have ther, as the A e - ? / p form is generally found satis- calculated the energy of the alkaline earth halides using the Tessman, Kahn, and Shockley values factory for expressing repulsion energies. The binding energy for an alkaline earth halide for the polarizabilities. The polarization ternis in molecule, at OOK., assuming a linear, ionic model, the energy are found to be lower, and the parameter p must decrease accordingly. Thus the agreement may be written as with experimental values is about the same, as
+
where a is the polarizability of the halide ion, r is the internuclear distance, and fi the induced dipole moment a t each halide ion. All terms higher (1) This research was supported by the National Aeronautica and Space Administration. (2) D. Cubicoiotti, J . Phys. Chem., 65, 1058 (1961). (a) E,8, Rittner, C h m . Rhua., XP. lOaQ (IQ-51).
(4) A. Buchler and ‘iT7. Klemperer, J . Chem. Phys., 29, 121 (1958). ( 5 ) S.P. Randall, F T. Greene, and J. L. Margrave, J . Phys. Cia~m.,
68,768 (1959). (6) L. Pauling, Proc. Rov. Soc. (London),A i i 4 , 191 (1927). (7)P. A. Akishin and V. P. Spiridonov, Kristallografiya, 2, 475 (1958). (8) L. Brewer, G. R. SomayajuIu, and E. Brackett, Chem. Rev., in press. (9) J. a. Tessman, A. H. Raha, and W. Shnoadeyi Phys. Raw,, P2,890 (106%
