Analysis of Cryoscopy Data Peter Wloch and E. A. ~ h e r n i a k ' Bock University, St. Catharines, ON, L2S 3A1, Canada Dependence of Solvent Activity on Freezing Point Depression
where yl is the activity coefficient of the solvent. Equations 1and 4 can be combined to give eq 5.
I n cryoscopic studies on real solutions the dependence of the solvent activity (al)on the depression of the freezing point (0) is given by eq 1( I ) : where C = In y, -j4OS), which is assumed to be constant where
Nonlinear (Quadratic) Regression Analyses
and
I t is now possible to perform nonlinear (quadratic) regression analyses on eq 5 using experimentally determined values of freezing point depressions for a set of solutions having different mole fractions of solute and in which Mz is treated a s a n adjustable parameter. The correct value chosen for M2 is the one that yields the value of A given by eq 6.
A& is the molar enthalpy of fusion of the solvent, R is the
molar gas constant, Tf is the freezing point of the solvent, and
where Cp(l)and Cp(s)are the molar constant-pressure heat capacities of liquid and solid solvent. fW3) is an (unknown) function of O3 and
I n the derivation of eq 1the temperature dependence of the enthalpy of fusion of the solvent has been taken into account. The solvent activity (mol fraction scale) for a system consistingof W, gram ofsolvent (molar massM,) and Wz gram of solute (molar mass Mz] is also given by eq 4. ~~~~~~~~
where Kfis the freezing point depression constant of the solvent, which is defined by eq 7 (2,3). R@M, Kr=1000 AHf
(7)
The freezing point depression constant for pyridine is 4.97 K kglmol (4). Those cryoscopic studies that consistently yield negative values for the constantA must be rejected. Experimental Caution:BDH Analar pyridine is toxic. The BDH Material Health and Safety Data Sheet states that "the vapor irritates the respiratory system and may cause headache, nausea, giddiness, and vomiting. The vapor and liquid irritate the eyes and may cause conjunctivitis. The liquid may irritate the skin causing dermatitis. Pyridine affectsthe central
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Volume 72 Number 1 January 1995
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compounds because minimum fragmentation occurs in these sources to yield intense molecular ion peaks (5). The two methods tested were thermistor and copperconstantan thermocouple cryoscopy. Sample solutions were prepared by adding appropriate weights of BDH Analar pyridine to a stock solution made by dissolving 0.33 g of the flame-retardant, which had been recrystallized twice from pyridiie, to 50 g of pyridine. Sample solution (7 mL) was introduced into a double-walled Pyrex vessel fitted with a motorized glass stirrer and a calibrated Sargent #S-81615 shielded thermistor probe. The cell was immersed in a n acetone cold bath, which was prepared by adding liquid nitrogen to acetone. I t provided temperatures in the range -84 "C to -76 "C. Thermistor Cryoscopy A Sargent #S-81601 thermistor bridge circuit was used to monitor temperatures during cooling. Its null detector was a Coleman-Hitachi 165 potentiometric recorder (5 mV FS), which had been initially nulled a t about - 4 2 "C, the freezing point of pure pyridine. Considerable supercooling was observed, and crystallization had to be induced by tapping the stirring rod lightly. Once a constant recorder reading was obtained the bridge circuit was nulled, and the freezing point of the soQuadratic Regression Coefficients (eq 5)
Thermistor Cryoscopic (I):
