NOTES
Vol. 61
vinyl alcohol and are presumed to be oriented by the dipole field to form the polyiodine chains made UP of more than 15 atoms of iodine when the film is stretched. 2 3 Distancc on the film, cm. Fig. 2.-Meridional Rpoctrrim of the fourfold stretched polyvinyl alcohol-iodine film. 1
THE CRITICAL MICELLE CONCENTRATIONS OF DECYL-, DODECYL- AND TETRADECYLAMINE HYDROCHLORIDE BY HORSTW. HOYERA N D ANNGREENFIELD
burnin filmg did not occur in the case of the polyvinyl alcohol film, At 1 0 0 ~ oelongat,ion the preferred orientation indicated by arcing of the reflections from the crystallites of polyvinyl alcohol is conspicuous while the characteristic halo reflection caused by the polyiodine chains remains unchanged in one direction. These results would suggest that the molecular orientation does not occur but the hydrogen-bonded polyethylene sheets may be becoming parallel to the direction of elongation. Even a t 300% elongation the angle of dispersion of the crystallites round the stretched direction is estimated to be about 15". Configuration of Iodine Absorbed.-An important feature of the patterns obtained from the stretched polyvinyl alcohol-iodine film is the appearance of a new meridional reflection co responding to an identity period of 3.03 f 0.03 . which is spread out laterally with considerable intensity. It is to be noted that the extension of the reflection must arise from the polyiodine chain predominantly, whereas the arcing of the reflections arises from the crystallites of polyvinyl alcohol predominantly. The estensiveness of the former indicates that the intterplanar spacings extend from 3.03 to 2.85 A. while the identity period in the dircction of stretching remains constant. The photometric curve of the meridional spectrum of the fourfold &etched polyvinyl alcohol-iodine film is shown in Fig. 2. With the intrinsic broadening of this reflection, moreover, the approximate linear dimension of coherent region can be calculated from the Scherrer expressioni0 to be more than 45 f 10 A. The hydrogen bonds in the polyvinyl alcohol film are expected to form a dipole field which could permit the intrusion of iodine molecules and then the formation of the polyiodine chain with average length of about 15 atoms of iodine, Under parallel conditions the absorption band of 500 mp of iodine is shifted to 590 mp in soluble starch,li and to 610 mp in polyvinyl alcoholOi2The results of the present work are consistent with these implications and indicate that the length of the polyiodine chain occurring in the polyvinyl alcohol film is of the same order of magnitude as that in the soluble starch. Thus, we are presently inclined toward the view that the iodine molecules intrude into the amorphous regions between the crystallites of the poly-
Experimental The decyl-, dodecyl- and tetradecylamines used in these studies have already been described.9 Solutions were prepared by dilution of a standard sample with either distilled or conductivity water depending upon the precision required. Temperature was controlled to 3=0.01"in a water thermostat. The a.c. Wheatstone bridge, constructed from a Kohlrausch 450 cm. dido wire, ah oscilloscope null point detector, L & N standard resistances, a Wa ner earthing circuit and a 1000 cycle oscillator, was teste$ against BUreau of Standards resistors. Measurements were taken a t 25.0'' for solutions of decyl-, dodecyl- and tetradecylamine which had been neutralized by an equivalent amount of hydrochloric acid as determined by otentiometric titration, and a t 18.0 and 35.0' on simila! so7utions of dodecylamine. Cell constants were redetermined a t each temperature. The results are summarized in Table I. These results may be compared with those of Corrin and Harkins3 who used a dye adsorption method which gavf? a value of 0.0131 mole per liter for the CMC of dodecylamine hydrochloride a t 25 Klevens' reports values of 0.040 for the decylamine hydrochloride at 25O, 0.013 for the dodecylamine hydrochloride at 30' and 0.0031 for the tetradecylttmine salt at 40 No results are available for the
f9) W. T. Astbury, 8. Dickinson and K. Bailey, Biochem. J . , 89, 2351 (1935). (10) P. Soherrer, Gdllingar Nnchrirhlen., 9, 98 (1018). (11) R. R. Raldwin. R. 8. Bcnr w i l d R . E. Ituiidlr, J . Am. CAem. Sor., 68, 111 (1944). (12) Y . Hoshino. J . EI%clrochem.Soc. Japan, 18, G (1850).
(1) R. J. Williams, ,J, N. Phillips and K.J. Mysels, Trans. Faraday Soc., 61, 728 (1955). (2) €1. W. Hoycr and A. Greenfield, THISJOURNAL, 61, 735 (1957). (3) hf. L. Corrin and W . D. &&ins, J. Am. Chsm. SOC.,80, 883 (19.17). (4) 11. B. Klevona, ' ~ ( H I BJIJUIINAL, 68, 180 (IU.18).
A
Conlrzbution from Hunter College, New York 81, N . Y . Received November 17, 1068
As part of an investigation into the electrophoretic mobility of the micelles of some aliphatic amine hydrochlorides and the relationship of this property to micelle structure it was necessary to determine the concentration a t which the single molecules and/or ions associate into micelles. This concentration is generally called the critical micelle concentration, abbreviated CMC. We adopt the definition of Williams, Phillips and Mysels' for the CMC as the concentration of solute a t which the concentration of micelles would become zero if thejr concentration were to change a t the same rate as I t does a t a slightly higher concentration. Experimentally this means that we measure an additive property which varies linearly, or approximately linearly, with some function of the concentration of the micelles and which varies in a similar manner but with a different slope for the concentration of the unamociated solute molecules or ions. The method we chose as providing a convenient and precise means for determining the CMC is the conductivity method which depends upon the lower s ecific conductance of the micelles as compared to t e solute ions. For our systems, and over the concentration range studied, the specific conductance was found to vary in a linear manner with the molarity of the solution for both the associated and the simple ions.
R
.
.
NOTES
818
TARLE I CRI'IYCAL
Aniinc hyrlrorllloride
Decyl
Dodecyl Tetradecyl hdecyl Ihdecyl I)odccyl
MICELLECONCENTRATIONS Teomp.,
CRIC, moles/l.
25.0 25.0 25.0
0.0540
C.
18.0
,0138 .0028 .0145
25.0 35.0
.0138 .0133
(.c~rnricrr:ttrirc. v:tri:ttions of the CMC: of tJtc di1)Ii:it,ic :trnirio salts reported iipon in this paper although the work of Klevrnsd and of Wright, Abbott, Sivertz and Tartars shows t,hat there is a slight increase in tbe ChlC wit,h rising tJemperatures for some alkyl sulfate, sulfonatp and fatty acid salts. However, the effect of temperature u on tthe CMC of the alkyl sulfat,e is still in dispute sincc h o r k h n r t and Ubhelohde6 have reported rccently that the CMC of Rodiurn dodecyl sulfate i s a minimum a t 30". Our result8 indicate R dccrease of about 5.574 tor the CMC of dode2ylamine hydrochloride in the temperature range 18 to 35 .
Acknowledgment.-The authors gratefully acknowledge financial support furnished for this work by the National Science Foundation.
0.2
0.5 lm/lm
Fig. I.-Order
0.6
0.7
0.8
'.
of reaction vs. tm/l,,'.
If m' fract,ion of the react,ant Cois consumed, then by dividing two equat'ions of t'ype (A) (1 - 7IL)l-n --___ (1 - In')'-"
(5) K. A. Wright, A. D. Abhott. V. Siverta and H. V. Tnrtar, J . A m . Chem. S o c . , 6 1 , 549 (1939).
(6) R. D. Flockhart and A. R. Uhholohde, J. Cofl. Sci.. 8 , 428
0.4
0.3
-1 -1
Im
i=-
lm'
When n = 1, the equation can be derived
(1953).
A NEW METHOD OF DETERMINING T H E ORDER OF REACTION AND T H E REACTION CONSTANT FROM KINETICS DATA'
The values of t,,ltd obtained from equations I3 and C are given in 'rahle I.
B Y WEN-HSUAN CHANG
TABLE I VALUESOF t m / t , , , l
Contribution from Ihe Chemistry Depart,menL, NorLhu'estern University, Evanston, Illtnoia Received December 18, 1066
Value
of n
__
1112
1!/!
IS/,
la/#
4'/4
t'/S
I'/l
L'/P
tg/a
-1.0 0 84.1 0.800 0.584 0.741 0.626 A new method of determining the order of rem-0.5 800 .i3Y ,542 ,705 .564 tions and the reaction constants simpler than pre0.0 ,750 ,500 .GG7 .GG7 ,500 viously proposed2 is presented. This method per0.5 ,693 ,587 ,457 ,628 ,435 mits determination of reaction order and any 1 .o .G30 ,500 ,415 ,585 ,369 change of order in a chemical reaction without suc1.5 ,566 ,414 ,374 ,543 ,307 cessive approximation. The reaction constant of 2.0 ,500 ,333 ,334 ,500 ,250 any fractional order reactJion can be calculated by 2.5 ,433 ,261 ,295 ,456 ,199 this method as easily as for an integral order reac3.0 .3i5 ,200 ,269 ,417 ,156 tion. The new method proposed by Weight, et a1.,3 4.0 .260 ,111 . 196 .:I39 130 still involves a series of approximations. Method of Calculating the Order of a Reaction. Froin Table 1, Fig. 1 CRII lie coixdruckd. --If the rate expression of a chemical reaction is 111 orcler t o dktennine the order of reaction, one nth or pseudo nth order reaction, then plot's the values of the physical or chemical property measured against the time of measurement. From the smooth curve obtained the values of t, can be found easily by the following method. AsIf m fraction of the reactant Co is consumed, then sume Xo is t,he value of the physical or chemicnl by integration property at tJhebeginiiing of the reactiort; X, is the value of t,he same property a t the end of the reac.(1) T h e author wiahes t o express his sincere nratitudo to D r . Arthur A. Frost for his stimulating lectures which led t o the concept,ion of tion; A,,, is the value of the snnio propert,y at t m . this idea a n d his continued guidance in completion of this work, T h e Then author is also indebted to Abbott Lab., Reaearch Foundation Co. and ,
Vieking G o . for their financial assistance. (2) A . A. Frost and R. G. Pearson, "Kinetics and Mrrllanisin," J o h n Wiley and Sons, Inc.. New York, N. Y., 1063, pp. 1 4 , 23, 40, 41. K. J. Laidler, "Choinical Kinetics," MoGraw-Hill Book Co., Inc., New York, N. Y.,1950, p . 13. S. L. Vries and A. Wcissbcrgcr, "Investigation of Rate8 find hlechanism of Reactions," Intcrsricnco Puhlisliors. Inc.. New York. N. Y.,19.53, 111). 18C,-IOf,. (3) .I. 11. Wciglit, .1. t l . Ulnak and , I . Coiill, J . Clrcm. Educ., 3 3 , 542 ( I Q t t i ) . This appeared a f t h the prescnt paper was subiiiitt.ed.
xm
= m(h,
-
ho)
+ ho
After t, (where m equals 2/a, valucs are found, the values of tm/'tmt can he calculated. The latter values will give the order of reaction from Fig. 1. Method of Calculating the Rate Constant of a Chemical Reaction.-It can be sli~wiithat the
