of Freezing Point Depressions Fernando Aguirre-Ode and Soledad Marliner Unlversldad Tecnlca Federlco Santa Maria, Valparaiso, Chile
Colligative properties are frequently used in a physical chemistry laboratory to determine molecular weights of solutes. If the molecular weight is not too great, the freezing point depression, 8, of the solvent is commonly used for the determination; measurements on only relatively dilute solutions are made in order to minimize the effects of the assumptions made in the derivation of the molecular weight equation,
Summary of the Results*
Solute +octane mwnane Mecane
cidecaline cyciohexane average
Molecular
Limltlng
weight
Slope
lo/moll
idRIdw3
114.23 128.28 142.29 128.25 84.16
0.1438 0.1332 0.1171 0.1152 0.1930
Heal of w109
fusion IJId
6.53 10.37 7.66 9.22 4.32
38.8 37.2 38.1 39.8 39.1 38.8
1.0
in which R is the molar gas constant, To is the melting point of the solvent, A is the heat of fusion per gram of solvent, and w is the weight of solute dissolved in 1000 g of solvent. We wish to raise two points: 1) The heat of
fusion of the solvent can be determined by means
of the same experiment as well, and 2) the ratio wlB becomes more and more uncertain as w approaches zero.
Thus we suggest using:
Since 8 = B(w)is a function that has to intersect the origin of the coordinate system, this form offers the advantage of minimizing the uncertainties in the lower concentration range. A mixture of cis- and trans-bicyclohexyl was being used in other work, and its heat of fusion was needed. When we could find only a very old value (1.74 kcallmol, i.e., 43.7 Jlg) in the available literature' and did not have other modern means for checking it, we decided to determine it by means of the freezing point lowering experiment. I t isconvenient to use solutes with which the solvent fonns nearly ideal solutions. We selected, because of their availability in our laboratory, three normal saturated alkanes, cyclohexane and cis-decaline, as the five solutes to be tried
' Mascarelli, L.; Vecchioni, L. Garr. Chim. Ital. 1912, 421, 106.
Gillespie. R. J.; Hughes, E. D.; Ingold, C. K. J. Chem. Soc. 1950,
2472.
1004
Journal of Chemical Education
with a mixture of cis- and trans-hicyclohexyl as the solvent. The exnerimental nrocedure was basicallv that -given hv ~ i l l e s p i eet aL2 Most svstems give nearlv linear 8-w results. Since the data are less accurate in the vicinity of w = 0 and solvent-solute interactions are more important in more concentrated solutions, the followingprocedure was adopted in order to define the best value of the limiting slope a. Data were fitted to equations of the form B = aw and 8= aw + Ow2 and the mean standard deviations ae for both fits were compared. The linear equation was preferred whenever elimination of successive data pointsfrom higher tolower valuesof w gave a mean standard deviation that was smaller or comparable to the one obtained by fitting the complete data set to the ouadratic eauation. ' Values o f 8 uncorrected for the supercooling effect' are used at first. Once the limiting slope is determined, il vnlues are corrected with the X thus obtained and the procedure can go on iteratively. In fact, only one or two iterations are needed. The table summarizes the selected slopes and the corresponding heats of fusion for hicyclohexyl determined by this method. The resultsare similar and the value 38.6 f 1.0 (Jlg) mav he assiened to the heat of fusion of hicvclohexvl. his re& shows the value of making freezing goint depression measurements in the physical chemistry laboratory not only for determining the molecular weight of the solute hut also for determining the heat of fusion of the solvent.
