April, 1935
NOTES
699
columns of this table shows that while B is ap- should be used as a standard temperature for the proximately constant (within 30%) and shows no comparison of viscosities. regular dependence on molecular symmetry, The writer is indebted to Professor Hans Erlenl/Tf 1/Tb varies over a four-fold range and meyer for advice and help on this note. shows a definite increase with decreasing sym- ANSTALT PUR ANORGANISCHE CHEMIE JANUARY 9, 1935 metry. In other words the increase of r with de- BASEL,SWITZERLAND RECEIVED creasing molecular symmetry can be largely attributed to changes in 1/Tf - 1/Tb. In the An Explanation of Hysteresis in the Hydration case of the parafEins (Table 11) B increases reguand Dehydration of Gels larly with the increase in the number of carbon BY JAMES W. MCBAIN atoms, as has been pointed out by DunnJ6while l/Tf - l/Tb decreases on changing from a It is well known that hysteresis in the hydration hydrocarbon containing an odd number of carbon and dehydration of porous gels at moderately high atoms to one containing an even number of relative humidities is connected with the filling carbon atoms and increases on proceeding to the and emptying of pores with liquid.’ next (odd) hydrocarbon. This is evident from Such hysteresis sometimes persists even after 1/Tb are rigorous evacuation in the attempts to eliminate Fig. 1 in which log r, B and 1/Tf plotted against the number of carbon atoms in other impurities.2 An explanation is usually the molecule. The alternation in r, pointed out sought in terms of “friction in the contact angle” by Miss Waller, can thus be traced to an alterna- or the familiar “Jamin effect.” tion in l/Tf - 1/Tb which is due to the well It is the purpose of this note to present an known alternation in the melting points. alternative mechanism, suggested in discussion with the class on Sorption at Stanford University. Figure l a gives in well-known fashion an illustration of the fact that capillary condensation occurs (4 in wettable pores of sufticiently small radius and relatively high humidities in accordance with the formula of Lord Kelvin3 as used by Anderson’ In p / p , = -2m/rRT - 6.0 X 10’ where p is the pressure a t concave surface, ps is the pressure of saturated vapors of liquid in bulk a t that temperature, Q is the surface tension, v is the volume of 1 gram mole of condensed liquid, r the - 5.0X 10* radius of the capillary, R the gas constant, T the absolute temperature, and In represents the B natural logarithm to the base e. I The applicability of the formula depends upon 4.0 X lo* the liquid and is generally restricted to pores of radius from about 20 A. up to visible dimensions. 2 Figure l b gives a diagram of a lecture experi/ I I 1 ment we have used to show two possible positions 5 6 7 8 9 1 0 1 1 of true stable reversible equilibrium, where a Number of carbon atoms. stoppered bell jar has a narrow capillary passing Fig. 1.-Logr. 0 ; ( l / T - l / T ) , A; B, 0. through the stopper. Either the capillary is From these calculations it appears that the filled to the same height as in Fig. la, the bell jar (1) McBain, “The Sorption of Gases and Vapours by Solids,” correlation between values of r and molecular George Routledge and Sons, Ltd., London, 1932; Zsigmondy, 2. symmetry is due, in a large part a t least, to the anorg. Chcm., 71,356 (1911); “Kolloidchernie,” 0.Spamer, Leipzig, Aufl., Bd. 11, p. 76,1927; Zsigmondy, Bachmann and Stevenson, dependence of the melting point on molecular 26$*anurg. Chcm. 75, 189(1012); Anderson 2. physik. Chem., 88, 212 symmetry, which does not involve viscosity. It (1914). (2) Lambert and Clark, PYOC.Roy. SOC.(London), 8132, 507 is doubtful, therefore, whether the melting point
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I
I
( 5 ) Dunn, Truns. Furaduy Soc.. 22,401 (1926).
(1929); Foster, ibid., Al47, 128 (1934). (3) Thomaon, Phil. Mag., [4]49,448(1871).
700
NOTES
VOl. 57
likewise remaining full up to this point (liquid largest orifice leading to any particular cavity and shown by oblique lines in the diagram) ,or, alterna- since this principle holds for every enlargement in tively, the meniscus is even more stably placed at each of the numerous pores, the curve representing a very slightly greater height inside the bell jar the amount of liquid retained during dehydration than outside, both the capillary and most of the will lie above that for progressive hydration and bell jar thus being empty (this position is drawn this hysteresis will be due to the mechanism here pictured. in solid black). It might be thought that in the lecture experiment, Fig. lb, the liquid in the stoppered bell jar should break and fall away. However, it is well known that a great reduction in pressure is required to initiate the formation of a bubble in a mass of liquid. Hence the liquid under slight hydrostatic tension is forever stable. If through chance a very minute bubble be- ~ i 2. ~ . gan to form in any particular spot, where in accordance with Maxwell’s distribution law of a. b. thermal vibrations a group of adjacent molecules Fig. 1. simultaneously acquired a sufficiently high kinetic The interstices in a gel may be extremely ir- energy, the ultramicroscopic or even microscopic regular in every respect, since they are built up bubble would be immediately crushed and elimifrom the juxtaposition of myriads of ultramicrons. nated by the surface tension of the liquid. These irregular channels will have an equally The considerations here discussed might well irregular cross section but the same principles simulate a “Jamin effect” in the penetration of will apply as with the circular cross sections soil or sand. (4) Compare the alternative presented by H. Engelhard and W. shown in Figs. l a and lb. A few of the pores may resemble Fig. l a in that they are of uniform cross Stiller in their Fig. 6 12.Elekfrochem., 40, 835 (1934)]. UNIV., CALIF. RECEIVED JANUARY 14, 1935 section and therefore will fill or empty a t a definite STANFORD relative humidity according as the pressure is increased or decreased. Others may be more like The Heat and Free Energy of Formation of Fig. l b in which the openings to the vapor phase Arsenic Trifluoride are of different dimensions and initial and comBY DONM. YOST AND JOHN E.SHERBORNE pleted filling correspond to different relative huThe heat of formation of liquid arsenic trimidities. In general, however, pores may be represented fluoride was obtained indirectly by determining diagrammatically as in Fig. 2, where the essential the heats of solution of the trifluoride, and of a feature is that larger cavities are accessible only mixture of arsenious oxide and sodium fluoride in through smaller channels or orifices. about 1 liter of 1 N sodium hydroxide solution. In pores of the type of Fig. 2, as the relative The reactions involved are humidity of a vapor is gradually increased, con- 2AsFs(l) GNaOH(1 N) = 6NaF (in 1 N NaOH) + A S 2 0 8 (in 1 N NaOH) 3Hz0(1) (1) densation of liquid will begin at the narrowest AsiOa(s) = 6NaF (in 1 N NaOH) cross section and will extend to wider cross sec- 6NaF(s) As208 (in 1 N NaOH) (2) tions only as the relative humidity is increased, until when the vapor is sufficiently nearly satuThe arsenic trifluoride was purified by fracrated the pore will be completely filled. Upon tional distillation and then condensed into thinsubsequent diminution of the relative humidity, walled evacuated bulbs. The bulbs, containing however, in general no evaporation will occur from a known weight of the material, were broken under this particular pore until the relative humidity has the sodium hydroxide solution in an adiabatic fallen to the value corresponding to the largest calorimeter. The same procedure was followed orifice or passage leading to the larger enclosed with the arsenious oxide-sodium fluoride mixcavities. Since chance determines the size of this tures. All thermal experiments with the arsenic
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