On these bases, the excess function represents the deviation to that behavior and the ionic activity coefficient calculated from Debye-H~ickeltheory is the coefficient relative to the molarity scale (see, for instance, Hill, T. L., "An Introduction to Statistical Thermodynamics," Addison-Wesley, 1962, p. 321).
Extrapolation to WB = 0 gives MB = 152.2, compared with 153.8,3suggesting a significantly greater precision in the work of Bury and Jenkins than their interpretation had indicated.
' Schubert, F. E . , J. Chem. Educ., 56, 259 (1979).
Bury, C. R. and Jenkins, H. 0.. J. Chem. Soc., 688 (1934) IUPAC, Pure andAppl. Chem., 47, 75 (1975).
that once we have made this choice we must be coherent and respect all its consequences.
M. F. C. Ladd University of Surrey Guildford, Surrey GU2 5XH
J.-P. Morel
England
UniversitC de Clermant 2 Aubiere. France
To the Editor:
Depression of Freezing Point and Elevation of Boiling Point To the Editor:
Schnbertl has made useful observations on the removal of an assumption in deriving freezing-point depression and boiling-point elevation formulas. An even more direct and practical approach, which this author has used for several years, is possible. From Raoult's lzw, we have where the symbols have their usual meanings. This equation is easily converted to: AP We know also that AT
a
-
xs
(2)
Ap
(3)
so that we may immediately write AT = kzB
(4)
where k is a cryoscopic constant. Thus, MB = wg(k - A T ) / ~ A A T
(5)
with no mathematical approximations. Using the Clapeyron-Clansius equation, we can show that where Ti and AHj are the fusion temperature and enthalpy of fusion, respectively, of the solvent. I t follows that k = RTf21AHf
I t is possible to abbreviate derivations by referring to formulas or arguments previously developed. The presentation in the note employs this procedure. First, eqn. (3) is not obvious and deserves discussion; a graphical presentation like that of Gla~stone,~ or at least an argument involving limits and differentials would seem appropriate. I find it hard to accept the statement that equ. (3) involves "no mathematical approximations." Second, the form of the Clapeyron-Clausius equation used to arrive a t eqn. (6) involves, especially for the solid-liquid phase transition, several mathematical steps from its usual form. Also, the derivation of AT = K.m employing the chemical potential, to which my article referred, yields the expression for K as an integral part of its development rather than as an aside. The truncated logarithmic expansions approximating -1nxa which yield the simple formulas showing AT = M and AT XB in my article are different but ought to give similar extrapolation results since they do approach the same limit for dilute solutions. However, the error in assuming T = To, that is, that the solution and solvent have the same freezing point, moves in the opposite direction as that introduced by replacing -1nxa with x ~In. other words, x~ < - l n x ~and To > T. This is not the case in the simple molality formula and likely contributes to the improved limiting value obtained by the author of the note in employing mole fraction.' If one wishs to "push" the data further, -Inxa itself, rather than its approximations, should he used. For example, beginning with where
(7)
From eqn. (4), k may be defined as the temperature change (depression) per unit mole fraction of solute. In the case of benzene, k , from eqn. (71, is 64.9 K, instead of the more usual 5.07 K. This definition is of immediate practical use since the quantities of solvent and solute used in the experimental determination of freezing-point depression and boiling-point elevation elevation are prepared in terms of mass. Referring to the data of Bury and J e n k i n ~we , ~may tabulate the following data for carbon tetrachloride ( B )in 0.1280 mole of benzene ( A ) .
one arrives at
Ms
=
U)b
na(exp(-K1.AT) - 1) which yields better results than the formula suggested in the note. Both approaches are more appropriate to physical rather than college chemistry where the attractively simple AT = K.m is most efficacious.
'
Glasstone. S., "Physical Chemistry," 2nd Ed., 0. Van Nostrand Co., Inc., New York, 1946, p 645. Accordmg to this argument a boiling polnt extrapolation in molality ~ -InxA and T > TO. should have the edge since n d n > F. E. Schubert Suffolk County Community College Selden, NY 11784
88
Journal of Chemical Education
