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Analysis of cryoscopy data
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Peter Wloch and E. A. Cherniak(1)
Brock University, St. Catharines, ON, L2S 3A1, Canada
Dependence of Solvent Activity on Freezing Point Depression
In cryoscopic studies on real solutions the dependence of the solvent activity (a sub 1 ) on the depression of the freezing point (Theta) is given by eq 1 (1):
(Equation 1 omitted)
where
(Equation 2 omitted)
and
(Equation 3 omitted)
Delta-H sub f is the molar enthalpy of fusion of the solvent, R is the molar gas constant, T sub f is the freezing point of the solvent, and
(Equation omitted)
where C sub p (1) and C sub p (s) are the molar constant-pressure heat capacities of liquid and solid solvent. f(Theta sup 3 ) is an (unknown) function of Theta sup 3 and
(Equation omitted)
In the derivation of eq 1 the temperature dependence of the enthalpy of fusion of the solvent has been taken into account.
The solvent activity (mol fraction scale) for a system consisting of W sub 1 gram of solvent (molar mass M sub 1 ) and W sub 2 gram of solute (molar mass M sub 2 ) is also given by eq 4.
(Equation 4 omitted)
where lambda sub 1 is the activity coefficient of the solvent. Equations 1 and 4 can be combined to give eq 5.
(Equation 5 omitted)
where C = lambda sub 1 - f(Theta sup 3 ), which is assumed to be constant.
Nonlinear (Quadratic) Regression Analyses
It 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 M sub 2 is treated as an adjustable parameter. The correct value chosen for M sub 2 is the one that yields...