Hout01+mltTL - 01. Freezing point depression Important...

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01. Freezing point depression Important concepts Phase equilibrium, thermodynamic conditions of phase equilibrium, phase equilibrium in multicomponent systems, ideal solutions, Raoult law, chemical potential, chemical potential as the function of composition, colligative properties, freezing point depression, boiling point elevation, osmotic pressure, cryoscopic constant. Objective In this cryoscopic experiment you will detect the difference of the freezing point of the pure solvent, water, and that of a dilute aqueous urea solution. Knowing the molecular mass of urea, and the molal freezing point depression of water (cryoscopic constant), you will be able to calculate the concentration of an unknown solution. If the cryoscopic constant for a particular solvent and the mole fraction of the solute are known, and if the solute molecules do no dissociate, the molar mass of the solute can be determined from the freezing point depression of the solution. Background Freezing point depression is a colligative property of solutions, that depends only on the solvent and the number of solute particles present regardless of their identity. When developing a quantitative expression for the freezing point depression, one usually makes two assumptions. Firstly, the solute is not volatile, and so it does not contribute to the vapour phase above the solution, and secondly, the solute does not dissolve in the solid phase. Freezing point depression is caused by the increase of entropy, which always takes place whenever a solution is formed from pure compounds (even in the case of ideal solutions). This increase of entropy lowers the chemical potential of the solvent (A) in the liquid phase: A A A x RT p T p T ln ) , ( ) , ( * + = μ , (1) where ) , ( p T A is the chemical potential of the solvent in the dilute solution, and ) , ( * p T A is the chemical potential of the pure solvent. The liquid solution and solid solvent form an equilibrium thermodynamic system. The condition of thermodynamic equilibrium can be expressed with the equality of the chemical potential of the solvent in solution and in the solid phase: ( 29 ( 29 p T x RT p T s A l A l A , ln , * ) ( ) ( * ) ( = + . (2) where T is the equilibrium temperature at a given pressure. If one compares equation (2) with a similar condition for the pure solvent ( 29 ( 29 p T p T sz A f A , , * * ) ( * * ) ( = , (3) the difference in the equilibrium temperatures, T T T = - * , the freezing point depression, can be expressed. 1
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The final expression for the freezing point depression can be given in terms of the molality of the solute, m B B f m m T T , = . (4) f m T , is the molal freezing point depression (cryoscopic constant) of the solvent. The value of f m T , is a property of the solvent only, and depends on the freezing point ( * T ), the molar mass ( A M ) and the molar enthalpy of melting ( H fus ) of the solvent. A
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Hout01+mltTL - 01. Freezing point depression Important...

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