NOTES
818
TARLE I CRI'IYCAL
MICELLECONCENTRATIONS
Aniinc hyrlrorllloride
Teomp.,
CRIC, moles/l.
Decyl Dodecyl Tetradecyl hdecyl Ihdecyl I)odccyl
25.0 25.0 25.0
0.0540
C.
18.0 25.0 35.0
,0138 .0028 .0145 .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. (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
0.2
0.3
0.4
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 - 7 I L ) l - n - 1 Im --___ (1 - In')'-" - 1 lm' When n = 1, the equation can be derived i=-
(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 tJhe beginiiing 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
820
NOTES
Vol. 61
known from the preceding section of this paper, a simple division of k t m C o n - by the experimental - * will give the value of k. value of In order to check the correctness of the result and to obtain the best value of k, t, values obtained from a given run can be plotted against the values of t,kCon - obtained from Figs. 2 and 3. A good straight line should be obtained the slope of which is kCon In practice it seems that the k values obtained from the direct calculation are so consistent that the graph can be omitted. This method has been tested in several cases and has been found useful. 0.4
0.3
0.2
1It, kCo" - 1.
THE INTEGRATED INTENSITY OF THE INFRARED 0-H ABSORPTION I N PHENOLS
Fig. 2.--Orclcr of reaction us. kl,Co"-l.
BY THEODORE L. BROWN 2
A'oues Chemical Laboratory, Uniusrsilu o l IUinois, Urbana, Illinois
Rsceiued Januaru 14* 1067
ru
0 CI
g
o -1 0
1 .o
0.5
1.5
2.0
2.5
t m kCon-1.
Fig. 3.-Order
of reaction
V.Y.
klmCon-l.
values of kt,Con-l are only a function of n and m. If n is held constant, then it is a function of m only. From equation A, t,he equation is obtained ktmCon-1 =
1
[(l
- m)'-" - 11 = f(m),
For first-order reactions the following can he shown 1 Jn-, kt,Con-I = In (1-
-
= f(m)n-l
The values of ktmC0" - obtained are given in Table 11. From Table 11, Figs. 2 and 3 can be constructed. TABLEI1 VALUESOF kt,Co"-' Values of n
-1.0
-0.5 0.0 0.5 1 .o
1.5 2.0
2.5 3.0 4.0
kfl/sCo"-L kt*/iCo"-' kll/~Co"-' kll/,Co"-l
0.376 .431 .500 .586 ,693 ,828 1.000 1.219 1.500 2.333
0.445 .539 ,667 ,846 1.099
1.464 2.000 2.797 4.000 8.6G7
0.469 .583 ,750 1.OOO 1 .R87 2.000 3.000 4.667 7.500 21.000
0.278 ,304 ,333 ,368 ,406 ,449 .500 ,556 .625 ,792
k61/4Con-'
0.219 .234 .250 ,268 ,287 ,310 ,334 ,360 ,389 .457
From Figs. 2 and 3 the values of tmlcCon- where m equals l / 2 , l / a , l / l d l . 2/3, a//( and n equals any integral or even a fractional number between - 1 and 4, can be obtained. Since the value of n can be
Although frequency relationships in infrared vibrations have been studied t o a considerable extent, there has only recently arisen an interest in the absolute intensities of absorption. ?the variations in intensity of a vibrational band which is possessed in common by a series of related molecules can in many cases be correlated with structural variations in the series. For example, the intensity of the 0-H stretching band in aliphatic alcohols is determined by the inductive properties of the groups attached t o the hydroxyl;' for the C=N band in substituted benzonitriles it has been related to the Hammett u-constant of the substituent.2 I n the present note the intensities of the 0-H stretching band for some substituted phenols are examined to determine how this quantity is related to the nature of the substituent. Experimental Procedure.-The experimcntal procedure has been described elsewhere.'** Solution concentrations in the ran e 0.02-0.005 molar were employed. The Perkin-Elmer mock1 112 spectrometer, fitted with lithium fluoride prism, was frequency calibrated by use of water vapor absor tion. Materials.-Reagent grade carbon tetrachlori& was used as solvent. Mallinckrodt Analytical Reagent phenol from a newly opened bottle waa used without further purification. All of the other phenols were Eastman Kodak materials. Methoxy, t-butyl and 3,5-dimethylphenol were purified recrystalesation and vacuum sublimation; the other compounds were used without further treatment.
1;
Results The results of the intensity measurements are shown in Table I. The first column after the compound name lists the intensity, A ' , in units of 1 X 104 mole-' 1. The second column lists the half-intensity width, AvI/,, and the third lists the frequency of band maximum, vm, both in units of cm.-1. The intensities listed are not corrected for wing absorption4; the relative magnitudes are con(1) T. L. Brown and M. T. Rogers, J . A m . Cham. Soo., T O , 577 (1957). (2) H. W. Thompson and G. Steel, Trans. Faraday Soo., 69, 1451 (1956). (3) T. L. Brown,J. M. Sandri and H. Hart, THIEJOURNAI.,61, 698 (1057). (4) D. A. Ramaay, J . A m . Cham. Soc.. T4, 7 2 (1952).
