Dec., 1952
109.3
D-FRUCTOSW-WA TI311 P H A SI3 n 1 A GRAM
ture with the one me obtained for a 30.11% solution.
Mixtures cont,ainingsilver acetate logh'i log Ka = log K 1 = log K I =
TABLEIV DISSOCIATION CONSTANT, Kit OF SILVERACETATEAT 25' Solvent
This work
Davies and M o n k
Water 29.93% ethanol 20.1% ' acetone 30.1 1 % acetone
0.186 .0488 ,0775 .0436
0.235 .053 ,092 .053 (20.1 %?)
In view of the uncertainties in the calculated values of Ki, the agreement hetween the two sets of values is fairly satisfactory. I t is seen that the values obtained by Davies and Monk are from 10 to 20% higher than ours. Equilibrium Constants and Dielectric Constant. -The theory of BornI5 in its simplest form leads to the following relation between the equilibrium constant, K , of a reaction, and the dielectric constant D of the medium at 25" log K = constant
121.6 mi* - -D 2: __ ri
(7)
where vi is the coefficient of a substance in the chemical equation, taken as negative or positive according as the corresponding substance is on the left or the right hand side of the equation as it is usually written, zic is the electric charge on the molecule (or ion) and Ti is its radius. On plotting the logarithms of the various equilibrium constants, Ki,Kzand K,, against 1/D, it is found that the points lie pretty satisfactorily on straight lines that are given by the analytical expressions in the follo~vingsection. (15) hl. Born,
Z. Phusik, 1, 45
(1920).
1.448 - 171.1/0 3.25 307/D 0.652 - 264/0 (water-ethanol) 1.02 - 203/D (water-acctono)
(8 1 (9)
-
(IO) (11)
Mixtures containing silver chloroacetate log Ki = 0.791 log Kz 2.24 =i
- 113.6/D - 219/D
(12) (13)
If w e define a mean radius, ?, for thc two ions, Agf anrl It-, by means of the relation 2- = 1 1 P rig; + T A
~
(14)
we find on comparing equations 8, 10 and 11 with 7, for silver and acetate ions P = 1.43 A. from equation 8 = 0.93 A. from equation 10 = 0 , 8 3 A. from equation I 1
Similarly on comparing equations 12 and 7, we find, for silver and chloroacetate ions F. = 2.14 R. from equation (12)
From equations 7 , 9 and 13, we obtain 1 1 2 + -1 - rAsA1 rAa+ rA
= 2 . 5 2 ( A = acetate radical), = 1.80 ( 4 = chloroacetate radical).
Two remarks may be made about these calculated radii: First, they are of a reasonable order of magnitude. Second, the fact that the solubility product data give smaller values than are obtained from the dissociation constants is something that has been previously observed.'
D-FRUCTOSE-WATER PHASE DIAGRAM BY FRANK E. YOUNG,FRANCIS T. JONESAKD HAROLD J. LEWIS Western Regional Research Laboratory, Albany, California Received April 1.9, 1.966
The D-fructose-water system has been stydied between -30 and +40". Well defined crystalline phase: studied include anhydrous D-fructose, stable above +21.4 ; D-fructose hemihydrate, stable between +21.4 and +19.9 ; n-fructose dihydrate, stable below $19.9"; and ice. In addition, solubility data are given for a crystalline phase, found during this investigation, which appears to be a metastable form of o-fructose dihydrate. A D-fructose gel, also discovered during thiR investigation, is described and the approximate range of solution concentrations in which it can exist ha8 been determined between -20 and +lo".
Despite the widespread occurrence of D-fructose (levulose) in honey (in which it is the major constituent2) and in fruit and invert sugar, very little is known about phase relationships in the Dfructose-water system. Previous work on this system appears to be confined to approximate measurements of the solubility of anhydrous D-fructose at three temperatures* and to several measurements of the freezing points of dilute D-fructose (1) Bureau of Apricultrrral and Industrial Chemistry, Agricultural Reaearch Administration. U. S. Department of Agriculture. Presented a t American Chemical Society meeting, March 30-April 3, 1952, Milwaukee, Wisconsin. Article not cnpyrighted. (2) R. F. Jackson and C. G . Silsbee, Nail, Bur. Sfondards Technolo& Papers, 18, 295 (1924) (No.259). (3) R. F. Jackson, C. 0. Silsbee and M. J. Proffitt, Natl, Bur. Standardr Scimtifir Paprrr, SO, 587 (1926) (No.519)
solution^.^ No previous measurements of the solubility of D-fructose hemihydrate appear to have been made at any temperature, although it was first reported in 188Ek6 This paper reports measurements of the freezing points of D-fructose solutions and the solubilities of anhydrous D-f ructose, D-f ructose hemi hydrate and D-fructose dihydrate. The discovery of a gel which forms in concentrated D-fructose solutions at low temperatures is also reported. These measurements were made as part of the investigation being carried out at this Laboratory of phase equilibria (4) H. C. Jones and F. H. Getman, Am. Chsm. J . , 89, 308 (1904): E. H. Loomia, Z . phusik. Chcm., 87, 414 (1901): R. A. Abegg, ibid., 16, 222 (1894). (5) M. Hirnig and L. Jeaaer, Monatah., 0 , 663 (1888).
1094
FRANK 13.
Y O U N G , FR.4NCIs
T.JONESA N D HAROLD J. LEWIS
of basic importance in the freezing preservation of foods. The preparation and properties of D-fructose hemihydrate6 and D-fructose dihydrate' have recently been described. Experimental Solubilit,y measurements were made on solutions prrpared from distilled water and D-fructose (levulose) which contained less than 0.!5y0 ash, less than O . l y & moisture ctnd gave -92.15 . (Isbell and Pigmans gave -92.4" for pure D-fruct,ose under the same conditions.) The solubilities measured were not)changed by increasing the ratio of solid phase to solution, which indicates that any impurities present did not affect the results. After the discovcry of 11fructose dihydrate' most measurements were made on solutions of n-fructose dihydrate which had been purified by crystallization from aqueous solutions of anhydrous D-fructose. These measurements were in good agreement witah those made on solutions prepared from the anhydrous material. Solubilities of the crystalline phases (with a few exceptions discussed later) were measured refractometrically on solutions which had been allowed to come to equilipum in a constant-t,emperat,ure bat,h controlled to +0.03 Ample time was allowed for thermal mutarotation before the refractive index of a solut,ion was measured. Refractive indices were convert,ed t.o D-fructose concentrations by the table of .Jackson and ? r l a t h ~ w s . Solubilities ~ dehrmined with solutions which were init,ially oversaturated agreed within +0.1% with those found for initially undersaturated solutions. Bath temperatures were measured on thermometers which had been certified recently by the National Bureau of Standards. The results obtained by warming curves were found to be unreliable bccause of the slow approach to equilibrium encountered wit,h all of the solid phases in this systcm. The behavior of the gel made it necessary to determine its apparent solubility in a different way. This was done by tumbling a D-fructose solution containing a small lump of gel in a bath, the temperature of which was raised about each day until the highest temperature was found at which the gel was st'ill visible. The solution was analyzed refract oniet rically .
'FABLE
Ty"
Conon wt..
C.
(a)
1c.e
0.0 - 1 .:1 - 2.7 - 4.75 - 7.65 -12.3 - 1:).:
