NOTES
August, 1959
1325
causes a lower carbonyl intensity. When hydrogen is replaced by the CH3 ( A = 4.21) group, there is essentially no change. Finally, the splitting caused by rotational isomerism is not as large in the amides as it is in the closely relat8edesters. It is, in fact, too small to allow a satisfactory separation of the two peaks for the purpose of determining the area under each. It is clear, however, that the behavior of the amides is qualitatively quite similar to Results that of the esters : a bulky group cis to the carbonyl Table I shows the results of the intensity studies causes a lowering of the carbonyl band intensity, of nine amides, RCONH2; the group R is listed in and the lowering increases with the size of the the first column, the total integrated intensity A group. in the second, and the frequency vm of band maxiI t is surprising that the carbonyl band of acetammum in the third. I n some cases the band was ide is split into two well-defined maxima. Rotaclearly split, so that the presence of at least one tional isomerism of the sort which exists in, for exother maximum could be inferred. An (S) is ample, the monochloro derivative cannot be the placed alongside the frequency in these cases. The cause of this, for reasons of symmetry. The splitunits of intensity are 1 x lo4mole-’ liter cm.- 2, and ting has been ascribed by some investigators to inthe frequencies are given in cm.-l. termolecular hydrogen bonds formed on associaThe relative values of intensity are very prob- tion.6f7 However the ratio of the absorbancies for ably correct to within 0.1 intensity unit; the fre- the two band maxima mas measured, in the present quencies are considered correct to within 2 cm.-‘. study, for acetamide in chloroform solution in the Wing correctionss were not applied. For those concentration range 0.005-0.01-1, and was found to compounds with symmetric band shapes, these half- be essentially a constant. The ratio of absorbancy widths, in cm.-I, were observed: formamide, 15; of the band at 1678 cm.-l to that of the band at txifluoroacetamide, 25 ; benzamide, 21 ; trichloro- 1702 cm.-l is 1.80 f 0.04, with an apparently ranacetamide, 24. dom scatter of values. If an equilibrium between associated and non-associated molecules were reDiscussion A number of interesting points are illustrated by sponsible for the splitting, the relative sizes of the two bands should change with concentration.s Furthe data in Table I. thermore, the relative sizes of the two bands is not TABLE I that to be expected on the basis of equilibrium conINTEGRATED INTENSITIES A N D FREQUENCIES O F THE CAR- stants determined from distribution coefficients.6 B O N Y L BAND1.u SOME AMIDES, RCONHr, I N CHLOROFORMIt cannot be argued that the splitting is due to hyIntegrated drogen bonding of chloroform to the carbonyl, prointensity ducing a second carbonyl band, since the bands for A (mole-1 1. Croup R cm.-2 X 10-4) Y r n (crn.-l) formamide, benzamide, etc., are all symmetric and CHB 4.21 1678,1702 of reasonably narrow width. H 4.22 1709 It must be concluded that, as yet, no satisfactory CHBCHv 3.85 1687(S) explanation of the splitting of the carbonyl band in C,HF,OCH, 4.19 1691(S) this compound has been offered.
The procedure used in determining intensities is described elsewhere.3 The integration interval chosen was 100 cm.-’. Overlapping from adjacent bands was considered negligible, since the absorption fell to nearly zero at the edges of the integration interval. Solution concentrations were in the range 0.005-0.017 molar. At least three separate intensity determinations were made on each compound, and the results were averaged. Chloroform was used as solvent rather than carbon tetrachloride, because the compounds were not sufficiently soluble in the latter.
ClCHz CliCH
c13c C& CF,
3.05 3.76 3.37 4.06 4.04
1695 1716(S) 1732 1678 1750
First, for those compounds in which the group attached to the carbonyl is symmetric, the carbonyl band is also single and symmetric about the band maximum. I n all other cases, the band is clearly split or is irregular in shape, indicating the presence of rotational isomers.‘-3 Second, the intensity is considerably lower in those compounds where a bulky group is situated cis to the carbonyl, just as was found to be the case in estersa3 For example, the intensity for the trichloro compound is considerably lower t’han that for the trifluoro, apparently as a result of the larger van der Waals radius of chlorine as compared with fluorine. Also, it is to be noted that the intensity decrease which occurs when hydrogen, as the attached group ( A = 4.22), is replaced by CH3CH2 ( A = 3.85) may be attributed to the fact that the CH, group can occupy a position cis to the carbonyl, and in this position it (3) D. A. Ramsay, J. A m . Chem. Soc., 74, 7 2 (1952).
(13)M. Davies and H. E. Hallam, Trans. Faraday Soc., 47, 1170 (1951). (7) C. G. Cannon, Mzkrochim. Acta, 555 (1955). (8) Dairies’ and Hallam report the carbonyl absorption of acetamide in 0.04 and 0.2 molar solutions in CHCla; the relative intensities of the two bands do not appear from their figure to change b y very much in this concentration interval. The relative intensities are quite different, however, in 0 002 molar carbon tetrachloride as compared with dilute chloroform.
THE HEAT‘OF FORMATION OF ANHYDROUS LITHIUM PERCHLORATE BY MEYER M. MARKOWITZ, ROBERTF. HARRIS A N D HARVEY STEWART, JR. Foole Mineral Company, Research and Development Laboratories, Chemicals Division, Berwyn. Pennsuluania Received December 8 , 1968
In view of the various values reported for the heat of formation of anhydrous lithium perchlorate,’ it was felt that a redetermination of this quantity was warranted. (1) J. F. Suttle in “Comprehensive Inorganic Chemistry,” Vol. V I , D. Van Nostrand Co., Inc., Princeton, N. J., 1957, p. 108; “ D a t a Sheet on Anhydrous Lithium Perchlorate,” American Potash and Chemical Corp., N. Y.
NOTES
1320
Using a modified Parr model 1411 calorimeter with a cdorimeter thermometer capable of being read to O.O0lo, the heat of reaction a t 25' for LiOH (225 HzO) 3. HClO4 (225 HzO) + LiC104 (451 H20) HzO was determined to be -13.54 f 0.09 kcal./niolc, which R i consiHtent witJh the beat of iicutralization of a stroiig base and a st.rong acid. As a result, the molar heat of formation of lithium perchlorate (451 H20) a t 25' is calculated as - 97.95 kcal./mole.2 This latter value compares favorably wit)h the value a t infinite dilution a t 18" given by Bichowsky and Rossini3 if the inore recent value of the heat of formation of perchloric acid a t infinite dilution2is applied. Further calorimetric determinations made in this Laboratory have yielded the values of -G.25 f 0.03 kcal./mole and 7.91 f 0.03 kcal./mole for the heats of solution a t 25' of anhydrous lithium perchlorate (450 H20) and of lithium perchlorate trihydrate (450 HzO), respectively. Consequently, the enthalpy change a t 25" for t,he reaction LiC104(s) H20(1) -+ LiC104.3HzO(s) is -14.16 f 0.06 kc,zl./mole. These data are in good agreement with those reported by Smeets4 for experiments carried out a t 18'. Finally, the standard heat of formation of anhydrous Iithium perchlorate is -91.70 kcal./mole, quite in contrast to existent published values.'
+
+
(2) Complementary heat of formation data obtained from: F. D. Rossini, D. D. Wagman, W. H. Evans. S. Levine and J. Jaffe. "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1952. (3) T. R . Bichowsky and F. D. Rossini, "The Thermochemistry of the Cheniical Substances," Reinhold Publ. Corp., New York, N. Y., 1936, y. 132. (4) C. Srneeta, Noluurw. Tijdschrift, 16, 105 (1933); C. A., 27, 52673 (1983).
ON T H E DETERMINATION OF T H E SEDIMENTATION EQUILIBRIUM SECOND VIRIAL COEFFICIENT I N POLYMERIC SOLUTIONS
Vol. G3
perimentally as a function of the initial concentration COof the given solution. On the assumption that the partial specific volume of each polymeric solute is independent of its molecular weight and that the compressibility of tbe solution is negligible, the equations for the sedimentation equilibrium of the solutio11consisting of a solvent 1and n - 1 iieutral solutes 2, 3, . . , , n may be written in the form3,4
(i
= 3,
3, . . ., n ) ( I )
where
The concentration ci of solute i is expressed in grams per volume of solution, and the activity coefficient yi of solute i is defined in terms of the same concentration scale. The other symbols have the following significance: M i = molecular weight of solute i, p = density of the solution, a = partial specific volume of each solute, w = angular speed of the rotor, r = radial distance measured from the axis of the rotor, and a arid b = positions of the meniscus and cell bottom, respectively. In deriving equation 1 it was assumed that the solution is SO dilute that its density may be replaced by the density of the solvent. Because we are concerned with a system of neutral components, the logarithm of yi may be expanded about infinite dilution to give n 111 ui
=
Mi
BikCk
k=2
+
o(CjCh)
(i = 2, 3,
. . ., n)
It is important to note here that the coefficients B i k are independent of concentrations Ck ( k = 2,3, . . .,?a). They must be complicated functions of molecular weights M i and M k but are independent of the molecular weight distribution. By substituting the above expression for In yi into equation 1 we obtain
BY HIROSHI FUJITA~ Department of Chemistry, Universitu of Wisconsin, Madison, JFksconsin Received December 8, 1968
O(CiCjCk)
(i = 2, 3, . . ., n) (4)
This is the starting equation of the present analysis. There is some doubt whether the sedimentation Summation of equation 4 over all solute compoequilibrium experiment may be used to study sol- nents, integration of the resulting equation with reute-solvent thermodynamic interactions in poly- spect to [ over the range 0 < 4 < 1, and use of the meric solutiom2 With this note we seek to obtain relation more definite information with regard to the extent ci(E) dE = Ci0 (5) to which the experiment may be of significance with non-ideal solutions of polydisperse neutral molecules. yields Expressions are derived for the intercept and the limiting slope of a plot of l/(.Mw)apy us. CO as Co x CiOMi = C(0) - C(1) tends to zero, and it is shown that this intercept alk=2 lows evaluation of the weight-average molecular ci dE + higher terms (6) MiBik weight of the solute and the limiting slope can be i=2 B=2 correlated with the second virial coefficient obtained from light scattering measurements. Here (Mw)app Here Ciois the concentration of solute i in the original denotes the apparent molecular weight obtained ex- solution, and C ( 0 ) and C(1) are the total concentration of the solution a t the bottom and the meniscus (1) On leave from the Physiaal Chemistry Laboratory, Department
E
5
52
of Fisheries, University of Kyoto, Maizuru, Japan. (2) L. Mandelkern, L. C. Williams and S. Weissberg, THISJOURNAL, 61, 271 (1957).
%
(3) R. J. Goldberg, ibid., 67, 194 (1963). (4) J. W. Williams, K. E. Van Holde, R. L. Baldwin and H. Fujita, Chem. Reus., 58, 715 (1958).
*
