structcd hj. I\ hicli ,peed* of 180, 225, 300, 3G0, 450, 540, GOO. G75, and 720 R.P.X. were cleterminecl 11 itli i t r o l m - c q i c ohwvntion 011 the line frequency. One observer noted I\ lien the 1 ing cwrie-poiiding t o a certain y m d appeared to stand still and another oh-cr\-cr noted the time on :t i t o p \\ atch. The curve5 1,' 1 q . i u e r c plof t t d and thtl (wrrcctions n e r e obtained hy intrgrntion t)y mcm. of \\'etltllc'~ r d c . T l l t rorrcction- arc' h\te'tl in taljle 16. .ZPPCSDIX 111
Statistzcal ajialysis of the particlesize count Thc mcun- of tlic. mi( opic count and the hedimentation distribution (sector cells, I? S = 1.166) are 0.2393 micron and 0.2770 micron, respectively. The standard deviation of the microwopir count is 0.01004. From these data the probability of tlic separation of tlic tn-o distributions being attributable to sampling errors may he estimated hy thr methods of mathematical statistics (5). Thil- probnlility i i less than 1 t o 10,000. The proha1)le fluc~tuationsin each of particles lvere also estimated and are Iihtcd in t : i l ) l ~ 17 for the n r i o u - ( of particle sizes.
T H E SOLUBILITY O F n-DOTRIXCOSTANE (DICETYL) J II HILDL13Ii 2111) Ikpititiciit
of C'hciiiicti
i/,
A4 \VlCHTER'
\\I)
I ?iiicrsiii/ o f C a l i j o r n i a , R c r l t e l e y , Cnlzfornza
ICcceii ( d O r f o h e t
4 , 1948
The observations prebented in this paper were obtained many years ago but appeared SO surpribing at the time that they were withheld from publication, with the exception of the figures for the solubility in heptane (8) andstannic iodide ( 7 ) , pending verification of the data themselves and in the hope of a better explanation than n e were then able to offer. The data recently published by Ralston, Hoerr, and Crews (12), ho\\ever, include several of the solvents that we used and the two sets agree sufficiently well t o give us confidence that our entire set are free from any large error., so we now decide to publish them. Moreover, we are now in a better position t o analyze them than we were originally. ?IATERISLS
The dicetyl used has been described by Hildebrand and Wachter (11). It3 melting point was 70.2"C. The 2,2,4-trimethylpentane (or isooctane) was obtained from the Ethyl Gasoline Corporation. I t s preparation and properties have been described by Edgar (4). Our sample was tested and found free from butyl alcohol and unsaturated bodies. h l l of it boiled within 0.1"C. The carbon tetrachloride, benzene, n-heptane, carbon disulfide, and ether were purified I
I'rcscnt
i d 11 i-4
Shrll I>c\ clopmcnt C omp i i i v , I:mcrj 1 ille. C i l i f o i n i L i
by standard methods, and their boiling points remained constant within 0.1"C. Stannic chloride was fractionated till a sample was obtained with a constant boiling point. It was protected from hydrolysi5 nhen loading the solubility apparatus by handling in a "dry box." The stannic bromide 11as from the material that had been prepared by Hildebrand and Carter (9) for another inI-estigation. It melted at 33.1"C. The stannic iodide has been described by Dice and Hildebrand (3); it melted at ld3.6"C. PROCEDURE
The n ell-known "synthetic" method of Lilexejen-(1) was employed, the apparatus being greatlj- modified to secure greater accuracy and to assist in hastening the procedure. Essentially, the method consist5 in shaking a sealed tube containing knorm quantities of solvent and solute in a bath and noting the teniperature at which all of the solid phase disappears. This method has the advantage that an analysis of the saturated solution 13 not neceskary, a procedure n hich is rather uncertain in the case of most organic +ubbtanccs. (When 11e attempted to analyze an equilibrated solution by evaporating the solvent and weighing the heparated dicetyl we found it difficult to expel the last traces of the former.) I n addition, determinations may ieadily be carried out at temperatures above the boiling point of the solvent. Riilbs n i t h a capacity of 1-3 cc. ere uied; they vere first \\eighed, mclted dicetyl n as added from a pipet, they I\ ere re\\ eighed, solvent was added, and the bulbs nere sealed and reweighed. The filled bulb \vas heated until a11 of the licetyl had dissolved and \ \ a s then qiiickly ohilled uhile shaking, \o that the licetyl came out of solution as a very finely dirided precipitate. The bulb war hen placed in a small holder in the apparatus. -1motor irith a x ariable speed scntrol was used for rapidly shaking the bulb and stirring the bath of uater. The water bath \\as heated hy a vapor jacket from boiling chloroform, the tcni)erature of the vapor being controlled by regulating the pressure on the boiling hloroform by means of a vaouum pump and a series of mercury pressure-regusting bottles. The temperature of the nater bath could be hept a t any predeeimined temperature v ithin about 0.01"C. The point a t I\ hich thc la5t feu iinute crystals di-appeared could be determined n ith considerable esactnes5 hy areful observation through the magnifying lens in the eyepiece of the apparatus, specially since the bulb \\-as illuminated with a powerful light at iight angles t o he axis of observation. The temperature v a s slo~vly ed until only a very w crystals remained, nhen It v a s raised in steps of O.O5"C'., I\eeping i t a t each ew temperature for from 30 min. to an hour. The thermometers employed n-ere compared 11ith standards I\ hich had been lrtified by the Bureau of Standards and nhich nere uhed for htandardization urposes only. As a check on the technique, several holubility determinations of naphthalcne benzene and methyl alcohol n ere made and compared n i t h the results of Ward 4),who also used a synthetic method. The valuer obtained agreed nith his ithin 0.1"C.
888
J. 13. H I L D E B K L S D .'AD
.L. n'.lTCBER
The oh-enxtion, are recorded in table 1 and plotted, in part, in figure 1. The points for 2,2,4-t rimethylpentane have heen omitted to avoid overcrorr-ding. Our values for carbon tetrachloride agree rather ne11 with those by Ralston et al., but our points for ether are a little lower. Our points for heptane fall close t o thoqe of Seyer (13) for hesane, octane, and decane. Dotriacontane melts a t 70.2"C. hut it undergoes a transition, which appears not to be sharp, a t about G3.5"C. Garner, x i n Bibber, and Icing (5) determined the heats of transition and fusion for the neighboring paraffins lyith 22,2G,30 34, and 35 carbon atoms, from n-hich Tve have interpolated for Ca?H,jsthe values 10.4 kcal. and 17.6 kcnl., respectively. The dotted lines in figure 1 represent the ideal solubility of the a-form and 6-form, respwti.iielp, the latter having a
-
~
CS, _
'C.
17.4 20.6 25.9 31.7 45.9
2.03 4.li 10.5 23.9 103.5
'
Grams
___ '
~
'
'c.
26.6 44.3 4 .5 -I .S
'
0.46 1.57 3.92 4.33 6.12 8.51 20.1
'
21.3 22.6 24.3 25.6 27.1 27.5 35.0
~
1.55 4 Jj0 17.0
36.0 136.1
______
3i.5
SnCl,
42,s 44.7 50,6 53,0
~
,
30.1
37.8 4U.S
53.8
Grams --.~,
50.8 52.1 BEXZPSL ~ _ _ _ _ 50.0
24.6 30.3 37.3 41.6 51.6
n-C;Hie 1
'c.
Grams
___
CCI,
SnBrt
I
_ _______ _
1.31 4.02 9.12 38.3
"c.
Crams
___
2.04 I 28.4 4.11 2.44 ' 29.5 4.138 :3,15 34.2 8.68 3.h7 35.0 10.23 5.15 39.0 20.8 S.59 43.0 36.0 12.0 41.G 44.2 17.0 : (C:Hj)pO 31.9 . _~______, 37.0 io.5 32.5 4'44 87,6 38.3 12.0 45.G 41.0 4i.1 56.0
i-CrHa'
~
________
___ 1
,
I ~
I
- -'-
T.
1
21.7 1 29.6 32.2 , 32.6 33.3 3i.4 ' 39.0 40.S 40.9 ~
'
~
,
42.9 53.6
~
Grams
0.84 2.86 4.30 3.95 5.22 S.97 11.7 l5.S 16.9 23.8 108.0
liest of fuaion of 28.0 kcal. Ita melting point, if the transition could be avoided, would of course be below '70°C. Xow we see that although the solubilities in stannic bromide, with its high internal pressure, are considerably less than Raoult's law solubilities of the 0form, the points for the other solvents fall above that line. Bondi (2) has explained this situation as due t o the entropy of mixing molecular species of such different size, calculated by aid of the formula of Guggenheim (6), n-hich raises the Raoult's law solubility by an amount depending upon the ratio of molal volumes in each solution. Incidentally, Bondi did not allow for the transition point, so that his ideal line was too lox, making the discrepancies appear worse than they actually are. But it is not a t all certain that the entropy of solution is t o be calculated in this way for a t least some of these solutions. Hildebrand (8, 10) showed that if the molecules of two normal paraffins retain in the solution the parallel orien-
880
SOLVBILITT O F )L-DOTRI.ICOSTASE
tation they have in the solid, the entropy of mising is the Raoult’s law entropy, despite different molecular lengths. Further evidence may be been in t h e solubilities of dotriacontane in hexane and in dodecane reported by Seyer (13). Although the ratio of chain lengths is twice
-2
a 29
I 30
31
32
33
34
io4/ T Fit,. 1. Bulul)ilit> of )i-tiotriacoiitaiic
-
great iri the former, the tn-o sets of points differ by scarcely more tliari t h e nit of error; furthermore, they are hardly off fyom the ideal 3-line by more than ie uncertainty of the latter. The higher bolubilities in carbon disulfide, carbon tetrachloride, and, according the data of Ralston, cyclohexane, may be interpreted as due t o the volunietropy effect, for these solvents would presumably interfere more than the :?or-
nial paraffin solvents with ~i quabi-parallel order in dicetyl; hon-ever, there is mother pohiihle interpretation of the high solubilities, i.e., that the solid phase is the a-form. I t is easy to imagine that the solid. having been obtained in the method used by cryhtallizing out of the solution, could easily have sufficient uf the solvent entangled t o make it more difficult for the dicetyl chains t o coalesce to the non-rotating p-form. The don-nward shift in ciirbon disulfide points from near the a-line t o n r d s the @-linemay be evidence that the solid is finally altering in the direction of the &form. The fact that the tran4tion is not sharp a t 635°C. indicates that rotation does not suddenly set in for the full length of the molecules. The above facth h a w k e n nnalyzed in some detail because they furnihh an escellent esample of the variety of factors that may have to be considered hefore reaching conclusions and the err0r.s that can be made hy neglect of any one of them. We see in this ca>e the necehsity of considering (1) the actual nature of the solid phase; ( 2 ) the alteration of the ideal line caused by a transition; ( 3 ) the dependence of a non-ideal entropy upon the approximate arrangements of molecules of different size and shape; ( 4 ) the accuracy of the figure for the heat of fusion; (5) the possible curvature in the line for the Iiaoult’s law solubility due t o differences in heat capxities of solid and liquid; ( 6 ) the accuracy in the solubility data thembelves; ( 7 ) the solubility parameters; (5)the possible effect5 of non-additive solution volume-.
