Suggested Structures of Water in Inert Gas HydratesW. F. Claussen Citation: The Journal of Chemical Physics 19, 259 (1951); doi: 10.1063/1.1748187 View online: http://dx.doi.org/10.1063/1.1748187 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/19/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hydration structure of water confined between mica surfaces J. Chem. Phys. 124, 074711 (2006); 10.1063/1.2172589 Hydration of the tetramethylammonium ion: From water structure to the free energy of hydration AIP Conf. Proc. 492, 202 (1999); 10.1063/1.1301529 A Second Water Structure for Inert Gas Hydrates J. Chem. Phys. 19, 1425 (1951); 10.1063/1.1748079 On the Structure of Gas Hydrates J. Chem. Phys. 19, 1319 (1951); 10.1063/1.1748038 Erratum: Suggested Structures of Water in Inert Gas Hydrates J. Chem. Phys. 19, 662 (1951); 10.1063/1.1748327

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

132.248.9.8 On: Sat, 20 Dec 2014 18:44:40

LETTERS TO THE EDITOR 259

both pH and quantity of adsorbent are constant while the total quantity of M ion is varied, the ratio (y/1-y) would be constant. This is the region in which Henry's law applies.

Equation (1) does not represent the observed decreased ad­sorption of divalent cation with increased ammonium chloride concentration at constant pH. However, if it is postulated that the adsorbent has replacable anions the influence of ammonium chloride may be represented as

M+xHAd·S·Clw-+(x+w)OH-;:::::M(Ad·S·OHw-)x +wCl-+xH20. (4)

The equilibrium constant for Eq. (4) can be reduced, for constant pH, to

K,=-y- (Cl-)w 1-y (HAd.S.Cl w )x'

(5)

If the quantity of HAd· S· Cl w - is determined by the (Cl-) in solution a plot of log(y/1-y) vs log(Cl-) should give a straight line. This has been verified experimentally, and the results will be published.

It is a pleasure to express appreciation to Professor Edward Mack, Jr., for his interest in and support of this work. The grant­in-aid received from the Graduate School of The Ohio State Uni­versity is greatly appreciated by the authors.

Suggested Structures of Water in Inert Gas Hydrates

W. F. CLAUSSEN

Illinois State Water Survey. Urbana. Illinois September 26. 1950

GAS hydrates, such as methane hydrate, have been known for many years,' but even today their exact structure is not

known. The concept that these hydrates arise from the packing of the hydrating molecules into void spaces in an ice-like lattice has been generally considered. However, ordinary ice does not possess void spaces believed to be large enough to accommodate even the smaller of these hydrating molecules. M. v. Stackelberg2

has studied the structure of gas hydrates by means of x-rays, one conclusion of this work being that all crystals were in the cubic class. The structure proposed by v. Stackelberg is different from that proposed here, a criticism of the former being that some of the bond angles between water molecules appear to be around 60 degrees, much smaller than the tetrahedral angle, which is con­sidered to be a relatively strain free angle and which is present between water molecules in the ordinary ice lattice.

The study in this laboratory of possible ice-like hydrate struc­tures by means of molecular models two years ago revealed the

FIG.!' Pentagonal dodecahedron.

desirability of fitting a regular pentagonal dodecahedral water structure (Fig. 1) into some kind of a crystalline lattice because (1) this structure would give a large enough space for the smaller hydrating molecules, (2) the water molecules in this structure would be in about the same energy state as those of ordinary ice since the pentagonal angle (108°) is very close to the tetrahedral angle (lOnO), and (3) the number of water molecules belonging to a single hole would be 5, close to the hydrating number for the smaller inert gases. In the figure, each ball represents one water molecule, or each ball may represent an oxygen molecule with each stick being a hydrogen bond. It was apparent, after a little study,

FIG. 2. Pentagonal dodecahedral-diamond lattice.

that the regular pentagonal dodecahedron would not pack in any kind of a crystalline lattice.

A manner of packing these dodecahedra was recently dis­covered, which consisted of, first, slightly deforming the regular dodecahedron so that the angles around two opposite molecules were exactly tetrahedral, then superimposing these two tetrahedral points on pairs of carbon atoms in a diamond type lattice. The amazing result was the packing to form a cubic cell (Fig. 2). The longer sticks in this model pass through dodecahedra and are

FIG. 3. Diamond lattice.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

132.248.9.8 On: Sat, 20 Dec 2014 18:44:40

260 LETTERS TO THE EDITOR

FIG. 4. Hexakaidecahedroll.

attached at each end to tetrahedral water molecules; they do not represent bonds; however they are directly comparable to the bonds in the diamond lattice (Fig. 3).

Out of this diamond-pentagonal dodecahedral lattice has come a new hole or void, a hexakaidecahedron (16 hedron) containing 4 hexagonal and 12 pentagonal faces (Fig. 4). This structure contains a larger void space than the dodecahedron, thereby offering the possibility that large hydrating molecules can get into only the large holes while smaller molecules might get into all the holes. It is apparent that one might expect two hydrating numbers on the basis of this structure, in agreement with the known facts.

Some data on the unit cubic cell as shown in Fig. 2 are as follows:

Total number of balls (water molecules) in model 242 Number of molecules in unit cell 136 Number of pentagonal dodecahedra 12 Number of hexakaidecahedra 8 Hypothetical hydrating numbers

For large molecules 136/8 17 For small molecules 136/20 5i

Examples of the small and large molecule hydrates are as follows:

Small molecules

CH, 7.18 H,O' C2H 6 8.25 H 20 ' C2H 6 5.8 H 20 '

Large molecules

C3Hs 17.95 H 20 3 CH3I 17 H 20 2

C2H.CI 16 H 20 2

SO, 6.1 H 20' CJ, 5.9 H 20 2

Br, 7.9 H 20'

It is hoped that in a future publication the properties of this apparently new type of ~rystal may be more completely discussed, particularly as regards the density, the sizes of molecules which can go into the void spaces, and symmetry.

This work was made possible by grants from the U. S. Public Health Service and from the Office of Naval Research. The author is indebted to Drs. A. M. Buswell and W. H. Rodebush for their encouraging interest and their helpful comments in this develop­ment. Dr. Buswell aided considerably in the first application of the regular pentagonal dodecahedron to the structure of water molecules.

1 Summary by W. Schroeder. Die Beschichte der Gashydrate. Stuttgart (1926).

2 M. v. Stackelberg, Naturwiss. 36, 327, 359 (1949). • W. M. Deaton and E. M. Frost, Gas Hydrates and Their Relation to the

Operation of Natural Gas Pipe Lines, U. S. Bur. Mines Monograph 8, (1949), p. 27.

A Reply to Fu Regarding the New Method of Estimating the Surface Area of Powd.er

MASATAKA MIZUSHIMA

Physics Department, Facu1ty of Science, Tokyo University. Tokyo, Japan August 23, 1950

SOME remarks on my no tel regarding a method of estimation of the surface area of powder have been published by Fu.'

His letter is, unfortunately, full of elementary misunderstandings. Here I will show again that my method is correct.

(1) Fu says that my equation is obtained by equating the change of free energy of the adsorbate to the change of the available surface energy of the adsorbent. I cannot understand how my procedure can be so interpreted. I have equated two expressions for the free energy change during one thermodynamic process, which is a common procedure of thermodynamic theories. These expressions cannot be attributed to adsorbate or adsorbent, just as we cannot attribute a handclapping to a right or left hand. The equation of free energy change, t;,G=kT.lin In[Pa/p(v)]dv, in my process (4) may have confused him. This process may be divided into two parts; take a fraction of gas containing dv molecules, compress it to pressure P(v), and then condense it on the surface of the adsorbent. The free energy change in the former process is kT In[po/p(v)]dv, while that in the latter is zero, since we assumed the adsorption is reversible. Thus our equation ex­presses the change of the free energy of the system as a whole.

(2) My Eq. (4) is certainly not suitable, which is the only point which needs revision in my paper. It would be better to put USA-ULS=46.5 erg/cm' instead of (4). Bartell and Merrill3

measured this value by the contact angle of solid and two liquids, while the expression U LA cosO may be adopted for the case of contact angle of solid, liquid, and air system. But this is only a question of expression and has no effect on the confirmation of my theory.

(3) I compared the data of Carver on Pyrex glass' with that of Bartell and Merrill on silica.' Fu says that these two matters are quite different, but I wonder if they are so different that we cannot compare them at alL Even lead glass and silica are not so different in surface characteristics (contact angle) according to Bartell and Merrill's experiment itself.3

(4) Fu says that the change of surface free energy is not a(usL-uSA) but a(usL+uLA-USA), because a liquid surface has been created. As the reply to this remark I would say, "please take any textbook of college physics and learn the definition of inter­facial tension U SL".

(5) Fu says that Carver's data' is not reliable. Since I am a theoretical physicist, I cannot judge how reliable it is. But I think we may naturally put confidence in published papers, although there may be exceptional cases, as Fu's letter.

1 M. Mizushima, J. Chern. Phys. 17, 1357 (1949). 2 Ying Fu, J. Chern. Phys. 18, 899 (1950). 'Bartell and Merrill, J. Phys. Chern. 36,1178 (1932). • Carver, J. Am. Chern. Soc. 45, 63 (1932).

The Raman Spectrum of Allene-d4

R. C. LORD AND J. OCAMPO*

Spectroscopy Laboratory and Department of Chemistry, Massachusetts 1 nstitute of Technology, Cambridge, Massachusetts

December 18. 1950

I N our laboratory cyclopropane-d6 has recently been prepared for spectroscopic study by a series of synthesesl yielding,

successively, methyl acetylene-d., propylene-d6, allyl chloride-d., and 1-chloro-3-bromopropane-d6• It was noticed in the synthesis of methyl acetylene-d. that a small amount «5 percent) of allene-d, was formed as a by-product under certain conditions. We therefore prepared sufficient methyl acetylene-d, to enable the isolation of 2-3 cc of liquid allene-d •. The methyl acetylene-d, was removed from the allene-d. by means of ammoniacal silver solution.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

132.248.9.8 On: Sat, 20 Dec 2014 18:44:40