Freezing points of ideal binary liquid mixtures

1 Freezing points of ideal binary liquid mixtures 

Section 12.2.1 described the use of freezing-point measurements to determine the solvent chemical potential in a solution of arbitrary composition relative to the chemical potential of the pure solvent. The way in which freezing point varies with solution composition in the limit of infinite dilution was derived in Sec. 12.4.1. Now let us consider the freezing behavior over the entire composition range of an ideal liquid mixture. 

The general relation between temperature and the composition of a binary liquid mixture, when the mixture is in equilibrium with pure solid A, is given by Eq. 12.3.6  

We can replace T by Tf A to indicate this is the temperature at which the mixture freezes to form solid A. From the expression for the chemical potential of eomponent A in an ideal liquid mixture, /la = Ma + RT nxA, we have [d(fiA/T)/dxA]T,p = R/xa- With these substitutions, Eq. 12.5.1 becomes 

If we make the approximation that Asola is constant over the entire range of mixture composition, we can replace it by Afas,AH, the molar enthalpy of fusion of pure solid A at its melting point. This approximation allows us to separate the variables in Eq. 12.5.2 and integrate as follows from an arbitrary mixture composition at the freezing point to pure liquid A at its freezing point T.  

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