COMMUNICATIONS TO THE EDITOR
Nov., 1963
quantum yields of ethylene compared to carbon dioxide may be due to polymerization of the ethylene subsequent to its formation, as well as to the creation of trace amounts of propylene. Primary process I is consistent, with the generally accepted primary photolysis of the aliphatic aldehydes into radical^.^ A variety of secondary reactions may follow I, among which the following seem pertinent.
0
/ ‘\
H2C---cH
CH3
-+
0 /’ \
+ HzC---CH-CHO
C H d O -t c H 3
+CH,
+
CH3c0
+ CO
(1)
+ co
(2)
0
/\
CHO -I- HzC--CR-CHO
-+
Hz
+
CH3CO
2503
than 4@cH,. To obtain B material balance, in some way carbon monoxide must become separated from substances which ultimately become condensate or polymer. The trace of propylene found may be accounted for by a reaction of CH3 with ethylene and the resulting propyl radical extracting a hydrogen atom in a manner analogous to reaction 2. The trace of formaldehyde, likewise, may have come from similar steps involving the formyl radical. The limited results given in Table I show that a t X 3130 A. substantial amounts of either 2,3-dimethylbutane or cyclohexene have little effect on @CO and @ p c ~ ~ . This indicates that the activation state leading to primary process I is of short duration and that the radicals formed in this and subsequent reactions are a t most only slightly trapped by cyclohexene. On the other hand, the drastic reductions of @conand @ca& brought about by the presence of these optically
*
+ c8
(3)
If reaction 3 is the principal consumer of formyl radicals, +” should be a measure of $1 and should be temperature independent. The results given in Fig. 1 bear out thira postulate and indicgte that about 10% of the absorbed enepgy at X 3130 A.initiates process I. From this 10% must come carbon monoxide quantum yields greater than one, indicating the involvement of cyclic reactions. Reactions 1 and 2 constitute one such chain. These reactions, however, are inadequate to explain all that takes place since they lead to @CO equal to 2@C&instead of the observed value of more (3) E. W. R. Steaoie, “Atomic and Free Radical Reactions,” 2nd Ed., Reinhold Publishing Corp., New York, N. Y., 1954, Chapter V.
transparent gases indicate that GDA in process I11 has a sufficiently long life so that it may undergo substantial collisional deactivation under the experimental conditions employed. Stabilization could be to either propiolactone or to the original glycidaldehyde. An exploratory experiment with pure GDA at wave length 2654 A. (run D, Table I) gave quantum yields of the major products consister$ with the mechanieims postulated herewith for X 3130 A. Additional explccration with mixtures of GDA and acetone in such proportion that the acetone absorbed about 90% of the radiant energy (runs E and F) gave surprisingly high quantum yields of carbon dioxide and ethylene. This suggests that acetone may photosensitize the deculmposition of glycidaldehyde in a manner analogous to primary process 111.
COMMUNICATIONS TO THE EDITOR A LEAST SQUARES SOLUTION FOR THE VAN LAAR CONSTANTS OF A BINARY MIXTURE
Sir: This note describes a statistical method for calculating the constants of a binary van Laar equation from equilibrium data a t constant temperature. When the total pressure is not given, it is necessary to use a tedious trial rmd error technique to solve for the constants. Furthermore, if more then two equilibrium compositions are known, then a series of different constants c m be calculated, which have to be averaged in some manner. The method outlined below overcomes both problems by eliminating trial and error procedures and using all available data to calculate the values of the constants which give the best fit to the data. The van Laar equation for a two-component system takes the form
and
where 7.4and YB are activity coefficients, X A and X B are mole fractions, and A and B are the unknown canstants which are to be determined. Equations l a aind l b can be combined with the equilibrium relationships
P A X A ~=AYAT and
(24
COMMUNICATIONS TO THE EDITOH.
2504
PBXBYB = YBT (2b) where PA and PB are the vapor pressures, to yield
A
where CXAB = in the form
(3)
(YAXB)/(YBXA). This result can be put
(4)
Equation 4 can be solved for A a,nd B using a least squares technique. This is done by assuming successive values for B / A and then solving for the associated least squares value of B in the regression equation
X
Bt (5) where S is the left-hand side of (4), and t is the factor in (4) which multiplies E. The regression results for B and the assumed values of B / A are Ohen plot,ted against. R2, the fraction of explained variance. Where this function is a maximum, the values of B and B I A are "best" in the least squares sense. Alternatively, t'he results can be plotted against the residual sum of squares which passes through a minimum where B and B / A are optimal. Consider the following example taken from Krelschmer, et u Z . , ~ for an ethyl alcohol-isooctane system at =
25". TABLE I (PA/PB = 1.14286) 1 2 3 4
5 6 7 8
XA
YA
aAB
XA/XB
0.0565 ,1182 ,1700 ,2748 ,3773 .5416 .7225 ,8511
0,4441 ,4762 ,4910 ,5073 ,5153 ,5285 .5501 ,5994
0,0749 ,1473 .2132 ,3688 .5699 1.0535 2.1356 3.8232
0.0598 ,1338 ,2048 ,3793 ,6051 1.1834 2.6101 5,7114
From plots of the data in Table 11,the optimum value of B / A was found to be 0.675 from which was found
1 2 3 4
5 6 7 8 9
B = 1.600 and B = 0.640. The above calculations mere carried out on an IBM 7090 regression program. PRODUCTS RESEARCH DIVISION LEOXMIR Esso RESEARCH ASD ENGINEERING COMPANY LINDEN,NEWJERSEY FRANK E. STEIDLER RECEIVED AUGUST12, 1963
THERMAL FORMATION OF FERRITES FROM AMORPHOUS PRECIPITATES
Sir: It is well known that spinel type ferrites are produced from mixtures of oxides, hydroxides, or salts of Fe3+ and a variety of bivalent metals in the desired proportions. The reaction may be carried out by heating the dry mixture for some hours a t a temperature around 1000". Alternatively, the desired metals may be coprecipitated as oxides, hydroxides, or carbonates which are then converted to a ferrite structure by heating. This conversion may be preceded by a drying operation or may be carried out by heating the precipitate in the reaction liquid. This last method is described in a paper by Sato, Sugihara, and Sait0.l The present communication is concerned with related work carried out in 1959 in the A.E.I. Research Laboratory, Harlow.2 A solution of metal sulfates in the ratios to yield Ki,$Zno$Fe2O4was allowed to react a t 60" with the stoichiometric equivalent of sodium carbonate solution containing a smaller proportion of sodium hydroxide (to ensure complete precipitation of the zinc and nickel). After reaction, a bulky flocculent precipitate was obtained; in numerous repetitions of the experiment the pH of the liquid after reaction mas 9.0 or slightly higher. Carbon dioxide was evolved on boiling, but it is not expected that this had a large effect on the pH. In this present work, spinel formation was judged by increase in density and development of ferrimagnetism; X-ray diffraction was not applied. It was found that heating in the reaction liquid for 30 min. a t 100' caused dehydration of the gelatinous precipitate ; this became darker in color, assumed a fine powdery texture, increased greatly in apparent density, and developed noticeable ferrimagnetism. Higher temperatures (using an autoclave) up to 210' increased the effect, so that after 30 min. at 210' the material began to resemble powder mechanically mixed and reacted TABLEI Temp. of
treatment, ' C .
TABLE I1 1,EAST S Q U d R E S S O L U T I O X FOR THE \'AS
LAARCONST.4NTS
B,
€314 assumed
calcd.
R=
0.2 .3 .4 .5 .6 .7 .8 .9 1.0
0.4030 ,4941 ,5787 ,6575 ,7315 ,8018 ,8689 .9336 ,9962
0.8759 ,9368 ,9687 .9847 ,9916 ,9928 ,9904 ,9857 ,9797
(1) C. E. Krelschmer, J. h-owakowska, and R. Kiebe, J. Am. Chem. Soc.9 70, 1786 (1948).
Vol. 67
Degree of magnetism, g. Heated Heated in after aashreaction ing and solution drying
Apparent density, g oc. Heated Heated after in washing reaction and solution drying
100 0 04 Xi1 3 17 120 0 11 Nl1 136 0 57 Xi1 150 2 34" Nil 3 82 210 3 41 Si1 4 18 400 0 05 500 1 56 600 1 90 900 2 68 a The corresponding value when this material 0.5 hr a t 150" in water m:ts 0 98.
-
2 92
__
3.18 3 40 4 35 4.52 5 05-5 10 was heated for
(1) C . Sato, M Sugihara, and NI. Saito, J. Chem. Soc Japan, I n d Chem. Sect., 68, 52 (1962). (2) F, G ,Stickland. British Patent 914,773 (1960).
