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Chem Ch 25/#2 Today’s To Do List Binary Solid-Liquid Phase Diagrams Continued (not in text…) Colligative Properties

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Stable Compound Formation

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K/Na with incongruent MP & Unstable Compound Formation

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Colligative Properties l Depends upon only the number of (nonvolatile) solute particles l Independent of solute identity l From colligatus: “depending upon the collection” Vapor pressure lowering Boiling point elevation Freezing point depression Osmotic pressure

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Basis for Colligativity l Solvent chem potential (μ 1 ) is reduced when solute is added: μ * 1 μ * 1 + RT ln x 1 (“1” is solvent) Since x 1 < 1 ln x 1 < 0 Thus μ 1 (solution) < μ 1 (pure solvent)

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Chemical Potential

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Vapor Pressure lowering

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Freezing Point Depression: ΔT fus = K f m l Thermo Condition: At fp: solid solvent in equilib with solvent that’s in soln μ solid 1 (T fus ) = μ soln 1 (T fus ) μ solid 1 = μ * 1 + RT ln a 1 = μ liq 1 + RT ln a 1 l Rearranging: ln a 1 = (μ solid 1 - μ liq 1 )/RT

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l Take derivative: ( ln a 1 / T) P, x1 = [(μ solid 1 - μ liq 1 )/RT]/ T Recall Gibbs-Helmholtz equation: [ (μ/T)/ T] P, x1 = - H 1 /T 2 Substitute in above: ( ln a 1 / T) P, x1 = (H liq 1 – H sol 1 )/RT 2 = Δ fus H/RT 2

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( ln a 1 / T) P, x1 = Δ fus H/RT 2 l Integrate between T * fus and T fus : ln a 1 = ƒ (Δ fus H/RT 2 )d T l Since it’s a dilute solution: a 1 ~ x 1 = 1- x 2 ln (1 – x 2 ) ~ - x 2 l Substitute above: - x 2 = (Δ fus H/R)(1/T * fus – 1/T fus )

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- x 2 = (Δ fus H/R)(T fus - T * fus )/T * fus T fus l Solute lowers the freezing point: T fus < T * fus l Express in molality: x 2 = n 2 /(n 1 + n 2 ) = m/(1000/M 1 + m) But m << 1000/M 1 x 2 ~ M 1 m/1000 (substitute above for x 2 ) l Note: T * fus ~ T fus (T fus - T * fus )/T * fus T fus ~ (T fus - T * fus )/T* 2 fus = - Δ T/T* 2 fus

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Substitute! l Δ T fus = K f m Where K f = M 1 R(T * fus ) 2 /(1000Δ fus H) K f is function of solvent only l Similar expression obtained for bp elevation: Δ T vap = K b m Where K b = M 1 R(T * vap ) 2 /(1000Δ vap H) l Compare terms

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Example Comparison l Calc. fp and bp change of 25.0 mass % soln of ethylene glycol (M 1 = 62.1) in H 2 O. l m = n Gly /kg H 2 O = (250/62.1)/(750/10 3 ) = 5.37 l Δ T fus = K f m = (1.86)(5.37) = 10.0 O C l Δ T vap = K b m = (0.52)(5.37) = 2.8 O C

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Osmotic Pressure

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Example l Calc. Osmotic pressure of previous example at 298 K. l Π = c 2 RT c 2 = 4.0 R = L-atm/mol-K Π = c 2 RT = (4.0)(0.0821)(298) = 97 atm

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Debye-Hückel Model of Electrolyte Solutions l The Model: An electrically charged ion (q) immersed in a solvent of dielectric constant ε l Experimental Observations: All salt (electrolyte) solutions are nonideal even at low concentrations Equilibrium of any ionic solute is affected by conc. of all ions present.

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Next Time How to explain the experimental evidence: Debye-Huckel Model of electrolyte solutions

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