Comrnunicatioiis to tire Editor
1841
consisting of the molar volumes and thermal expansibilities of the pure components. Accurate measurement of the solute parameters may be troublesome, but still more perplexing is quantitative application of dA W/dT values to problems of solution structure, especially I€ the pure solute i s not a liquid phase. I suggest a method for obviating some of these difficulties. The equation developed by Wada and Umedal expresses the shift in the temperature of maximum density, relative to that of water, as Figure 1. Diffuse reflectance spectra (solid line) of crystalline dlye-sucrose systems and the corresponding absorption spectra M, absorb(dotted line) in dilute aqueous solutions ( c a . ance on an arbitrary scale) at 25': M G , Malachite Green; CV, Crystal Violet; MtG, Methyl Green; AO, Acridine Orange; MtAO, 10-Methylacridiniurn Orange; MtAY, 10-Methylacridinium Yel. low. These dyes are in the chloride form. Spectra of the dyediiuent sample were recorded against the same nonabsorbing diluent on a Witachi EPS-ST spectrophotometer with an integrai sphere refiectance attachment. solid, which suggests that solvent water is involved in metachromasy. Detailed work will be published together with comparison of the L band of A 0 and CV with computed results.sgg The esr triplet excitation spectrum of A 0 was recently reported to show a maximum a t 570 nm but no absorption maximum.12 We believe the L band of solid A0 a t 550-570 nm in sucrose or Si02 corresponds to the missing maximum. This paper is Spectral Studies of Organic Dyes. I l l . For part I 1 of this series see ref 10. V. Zanker, Z. Phys. Chem., 199, 225 (1952). K. Yamaokaand R . A. Wesnik, J. Phys. Chem., 70,4051 (1966). K. Bergmann ana 6 . T.O'Konski, J. Phys. Cbem., 67, 2169 (1963). tvl, E. L.amm and D. M . Neville, Jr., J. Phys. Chem., 69, 3872 (1965). W . West and S.Pearce, J. Phys. Chem., 69, 1894 (1965) K. K. Rohatgi and G. S.Singhal, J. P h y s . Chem., 7 0 , 1695 (1966) E. Braswell, J. Phys. Chem., 72, 2477 (1968). v\! H. J Stork, G. J, M. Lippih, and M . Mandel, J. Pbys. Chem., 78, 1772 (1972). K. Yamaoka. J. Demoto, and M . Miura, J. Sci. Hiroshima Univ., in press. W. Wm. Wendlandt and ti. G. tiecht. "Reflectance Spectroscopy," Iivterscience, New Vork, N. Y . , 1966. p 55. H. Schmidt, Z. Phys. Chem. (Frankfurt am Main), 60, 44 (1972).
Faculty of S c i e n c e Hiroshima University
Hkoshima 730, J a p a n
Kiwamu Yamaoka* Yukio Matsuoka Masaji Miura
Received December 27, 1973
Partial Moial Expansibilities from the Temperature of ximum Density of Aqueous Solutions P u b k a t i o r i costs assisted by the National Science Foundat!on
Sir: Measurements of the effect of solutes upon the temperature of maximum density of aqueous solutions have been used for interpreting solvent structure in dilute solut n o n ~ . l -Although ~ the experimental technique is convenient, the results have been presented in terms of the excless volume of mixing, dA V l a T , and a set of parameters
Ad
-1/(1
- ~ ) 2 P V i * [ x a V-!, ~dAV'/dT]
(1)
where x is the mole fraction of solute, LY IS the thermal coefficient of expansion of pure solute, B is the coefficient in the parabolic relation to temperature of the molar volume of water in the vicinity of 3.98", VzOis the molar volume of pure solute a t O", and VI* is the molar volume of, water a t 3.98". Since one may express the molar volume of water at a particular temperature as V = (1 - x)Vl = (I .)VI xVz + A W , where # is the apparent molal volume of the solute, it follows that
+
+
JAV'/dT
x(d4/dT
- dVLldT)
(2)
Setting d Vz/a T = a VzO involves an assumption already included in (l),i e., that a is constant in the temperature range considered. Then, substituting (2) into (1)gives Note that a # p T is the apparent molal expansibility as defined by Gucker.5 The fact that A8 is a linear function of x over a wide concentration range of many electrolytes facilitates the determination of the limiting slope of AB us. x , the Despretz6 constant, which will be designated (AO/ x ) ~ , Furthermore, . as x approaches zero. then ( I - x ) approaches unity, and approaches avz*/aT, the partial molal expansibility at infinite dilution and 3.98". Then one may write
dV2*/JT =
- 2/3V1*tAd/x)~,
(4)
Equation 4 may be converted into an expression for the thermal coefficient of partial molal expansion of the solute a t infinite dilution and 3.98"
As an illustration of a possible application of eq 5, Despretz constants for a selection of 1:1 electrolytes were assembled from the literature, including some for which solvolysis is a dominant interaction between solute and solvent, some for which a quasi-clathrate o f the solvent may be a factor, but, without exception, ones for which electrostriction of solvent must be considered. A value of = 1.44 X 1 0 - 4 was computed from density tables,7 and values of were interpolated from tables of conventional partial molal volume of ions compiled by Mill-
vz*
era.* Detailed interpretation of trends in it* values (Table I) with relation to a specific model of solution structure is beyond the scope of this communication. Nevertheless, a few observations may be appropriate a t this point. The peaking of values with sodium chloride seems consistent with the concept that, among this set of electrolytes, this salt might be expected to come closest to affecting an uncomplicated electrostricturing of the solvent. Trends toward lower values correlate with lower charge densities The Journalof Physical Chemistry, Voi. 78, No. 10, 1974
Communicationsto the Editor
1042
TABLE I: Thermral Coefficients of Partial Molal Expansion at Infinite Dilution and 3.98" for Some 1:I Electrolytes in Aqueous Solutiona Chloride
Bromide
Iodide
5.02* 11.49* 6.61* 5.90b
3.75b
_ -x .I.
Lithium Sodium
5.94b 15.45b 7.71b
Potassium
Rubidium Cesium Ammonium Tetramethylammonium Tetraethylammoninm Tetra-n-propylammonium Tetra-n-butylammonium Tetra-n-amylammonium Botries in the table are a*. Reference 2. a
6.36h 5 . 24b 3 . 27b 1.35c 1.o o c
3.2Sd 1.42d l.Old
0 . 88c 0 . 96c
8.84b
5.9Sb 5.39*
1.16d 0.88*
1.06d
1.26< x
103, deg-1.
* Reference 7.
Reference 4.
of ions or with specific solvolysis. Among the quaternary ammonium salts, where quasi-clathrate solvent structure is a possibility, smaller and more uniform values are found, with amnionium halides intermediate between the alkali halides and the quaternary ammonium halides. 11lustrations of a reversal of the sign of & * can be found
The Journai of Physjsal Chemistry, Voi. 78, No. 10, 1974
with certain nonionic solutes such as low molecular weight alcohols.1,3 Temperature of maximum density measurements can provide, with relative ease and precision, the partial molal expansibility of solutes a t infinite dilution and 3.98" (the negative of the partial derivative of partial molal entropy with respect to pressure) and, therefore, may become more useful in the search for an understanding of the structure of aqueous solutions. References and Notes (1) G. Wada and S..Umeda, Buli. Chem. SOC.Jap.. 35, 646 (1962); 35, 1797 (1962). G. Wada and M. Miura, Bull. Chem. Soc. Jap.. 42,2498 (1969) F. Franks and 8.Watson, Tfans. Faraday Soc.. 63,329 (1967) A. J Darnell and J. Grayson, J. Phys. Chem.. 72, 3021 (1968). F. T. Gtrcker, Jr., J. Amer. Chem. Soc.. 56, 1017 (3934). (6) N . C . Despretz, Ann. Chem. Phys.. 70, 49 (1839). (7) E. W . Washburn, Ed,, "International Critical Tables," Vol. I l l , McGraw-Hill, New York, N . Y., 1933. (8) F. J. Millero, "Water and Aqueous Solutions: Structure, Thermodynamics, and Transport Processes," R. A. Horne, Ed., Wiley-lnterscience, New York. N . Y., 1972, Chapter 13, pp 532-534.
(2) (3) (4) (5)
D e p a r t m e n t of Chemistry The University of North Carolina at Charlotte Charlotte, N o r t h Carolina 28273 Received January 18, 1974
dames R. Kuppers
