Freezing point/melting point depression

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prolixity29

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Can someone who understands the theory of this please explain it to me?

From what I have read, there are actually two different definitions of freezing point/melting point. One definition says that the freezing point is the temperature at which the vapor pressures of the solid and liquid phases are in equilibrium. Thus, if a non-volatile solute is added to a solution and the liquid vapor pressure lowers, the solid vapor pressure must lower by a correspondingly greater degree (i.e. lower temperature) in order to reach equilibrium with the liquid.

Then there is another intuitive definition that says that the freezing point is simply when the entropy of the system is lowered enough such that impurities can be excluded from the crystal structure. Or, from the melting point side of it, depression occurs when impurities disrupt the crystal lattice of the solid or weaken it such that less thermal energy is required to break the intermolecular forces.

My question is how to resolve these two ideas. My mind has an easier time understanding the second definition because its more intuitive, but I like the first definition better because it accords better with our understanding of how boiling point is affected by non-volatile solutes. Anyone know this stuff well?

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