OCt., 19%
THE:THERXILh L 4 L Y - S I SO F HETEROPOLY ACIDS
the first, step is 1-ertical. It is of int,erest to nobe that the stepn.ise adsorption of the third layer does not take place a t constant pressure. The position of t,he risers in the isotherin can lie calculat#etl t,heoretically iisiiig an c:qiia,tion de\*eloped hy Singleton and H a l ~ e y . ~They have modified Hill's equations1° for stepivise isotherms, and, with appropriate assumptions, obtained an equation giving the position of the riser of the nth step in terms of' p / p O I n ( p l p a ) , , = -E,/n3kt
+ ( l U / k l ) ( l - g)
(1)
E1 is an euergy of adsorptioii, t u the lateral interact'ion energy, and g a lattice comp:ttibility factor. Using data for lirypton adsorption on P-33 at 77"II., Siiigleton aiitl Halsey ca.lculated Ellkt and (w/lih) ( I - 9 ) to be 7.0 and O.OO, respectively. These numerical \ d u e s , corrected for the change in t>emperature,were used t,o apply their equation to tdie adsorpt'iou isotherm at 702°K. The partial prewire nt which t,lie first riser occurs \\.as c80rrectetlfor t,liermal traii,q)iration, using the equat'ioiill l'i/P% = (Tl/3'?)'/2
(2)
This equnt>ionis valid d i e r e the mean free path of t>hegas is very large compared t o {,he diameter of t'he tubing. Results of the cornpalison are shown i n Table I and it can lie seen that agreement is very good for all three steps. (9) J. H. Siiiglctuii aiul G . D. IInlsey, Can. J . Cirem, 33, 184 (1955). (10) T. L. IIiII. J . Chcm. Phus.. 15, 7137 (1047). (11) S.C. Lixng, Can. J. Ciiem., 33, 279 (1055).
OF
MOLYBDENUM AND T U N G S T E N TABLE I RISERS I N TERMS O F p/po
PO$I'TION L):? T H E
Step
Step
Step
x x
0.37 0.38
0.70 0.80
I
PIP0
{
C;tlcd. Esptl.
1069
1.9 2.2
I1
10-4 10-4
111
TABLE I1 IIEATS O F ADSORPTION ( C A I , . /MOLE)
C:iIctl. (isosteric) C:doriinetJric (Amberg, et 01
'
Step I
Step
I1
Step 111
4,300
2,iOO
2,G00
4,400
2,800
2,700
Lipproximate isosteric heats of adsorption were calculated f from isotherms a t 70 and 77"1hcstructures of the hydrated, 12heteropoly acids of niolybdeiiiim and tungsten had definitely 1)een estahlished, Scroggie arid Clark3 found tjlial samples of 12-silicotungstic acid, airdried, dried a t loo", mid dried a t 220" gave powder diffraction patterns having the same 'd-spacings. When dried a t looo, this substance contailis 8Hz0. Six molecules of water can be removed by fur(1) Abstracted in part frotii t h e doctornl dissertation presented to the Graduate College of t h e University of Illinois, 10>5. ( 2 ) %tor Chemical Worlrs Research Fellow in Cticinistry, University of Illiiwis, 1954-lnj5. (3) A. G. Scrognie a n d G. 1,.
